order.upper_lower.basic ⟷ Mathlib.Order.UpperLower.Basic

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

@@ -4,8 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Sara Rousta
 -/
 import Data.SetLike.Basic
-import Data.Set.Intervals.OrdConnected
-import Data.Set.Intervals.OrderIso
+import Order.Interval.Set.OrdConnected
+import Order.Interval.Set.OrderIso
 import Tactic.ByContra
 
 #align_import order.upper_lower.basic from "leanprover-community/mathlib"@"c0c52abb75074ed8b73a948341f50521fbf43b4c"

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

@@ -145,13 +145,13 @@ theorem IsLowerSet.inter (hs : IsLowerSet s) (ht : IsLowerSet t) : IsLowerSet (s
 
 #print isUpperSet_iUnion /-
 theorem isUpperSet_iUnion {f : ι → Set α} (hf : ∀ i, IsUpperSet (f i)) : IsUpperSet (⋃ i, f i) :=
-  fun a b h => Exists₂.imp <| forall_range_iff.2 fun i => hf i h
+  fun a b h => Exists₂.imp <| forall_mem_range.2 fun i => hf i h
 #align is_upper_set_Union isUpperSet_iUnion
 -/
 
 #print isLowerSet_iUnion /-
 theorem isLowerSet_iUnion {f : ι → Set α} (hf : ∀ i, IsLowerSet (f i)) : IsLowerSet (⋃ i, f i) :=
-  fun a b h => Exists₂.imp <| forall_range_iff.2 fun i => hf i h
+  fun a b h => Exists₂.imp <| forall_mem_range.2 fun i => hf i h
 #align is_lower_set_Union isLowerSet_iUnion
 -/
 
@@ -185,13 +185,13 @@ theorem isLowerSet_sUnion {S : Set (Set α)} (hf : ∀ s ∈ S, IsLowerSet s) :
 
 #print isUpperSet_iInter /-
 theorem isUpperSet_iInter {f : ι → Set α} (hf : ∀ i, IsUpperSet (f i)) : IsUpperSet (⋂ i, f i) :=
-  fun a b h => forall₂_imp <| forall_range_iff.2 fun i => hf i h
+  fun a b h => forall₂_imp <| forall_mem_range.2 fun i => hf i h
 #align is_upper_set_Inter isUpperSet_iInter
 -/
 
 #print isLowerSet_iInter /-
 theorem isLowerSet_iInter {f : ι → Set α} (hf : ∀ i, IsLowerSet (f i)) : IsLowerSet (⋂ i, f i) :=
-  fun a b h => forall₂_imp <| forall_range_iff.2 fun i => hf i h
+  fun a b h => forall₂_imp <| forall_mem_range.2 fun i => hf i h
 #align is_lower_set_Inter isLowerSet_iInter
 -/
 
@@ -523,7 +523,7 @@ variable [LinearOrder α] {s t : Set α}
 theorem IsUpperSet.total (hs : IsUpperSet s) (ht : IsUpperSet t) : s ⊆ t ∨ t ⊆ s :=
   by
   by_contra! h
-  simp_rw [Set.not_subset] at h 
+  simp_rw [Set.not_subset] at h
   obtain ⟨⟨a, has, hat⟩, b, hbt, hbs⟩ := h
   obtain hab | hba := le_total a b
   · exact hbs (hs hab has)

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

@@ -1301,8 +1301,8 @@ noncomputable instance : CompleteLinearOrder (UpperSet α) :=
     decidableLe := Classical.decRel _
     DecidableEq := Classical.decRel _
     decidableLt := Classical.decRel _
-    max_def := by classical
-    min_def := by classical }
+    max_def := by classical exact sup_eq_maxDefault
+    min_def := by classical exact inf_eq_minDefault }
 
 noncomputable instance : CompleteLinearOrder (LowerSet α) :=
   { LowerSet.completeDistribLattice with
@@ -1310,8 +1310,8 @@ noncomputable instance : CompleteLinearOrder (LowerSet α) :=
     decidableLe := Classical.decRel _
     DecidableEq := Classical.decRel _
     decidableLt := Classical.decRel _
-    max_def := by classical
-    min_def := by classical }
+    max_def := by classical exact sup_eq_maxDefault
+    min_def := by classical exact inf_eq_minDefault }
 
 end LinearOrder
 

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

@@ -1301,8 +1301,8 @@ noncomputable instance : CompleteLinearOrder (UpperSet α) :=
     decidableLe := Classical.decRel _
     DecidableEq := Classical.decRel _
     decidableLt := Classical.decRel _
-    max_def := by classical exact sup_eq_maxDefault
-    min_def := by classical exact inf_eq_minDefault }
+    max_def := by classical
+    min_def := by classical }
 
 noncomputable instance : CompleteLinearOrder (LowerSet α) :=
   { LowerSet.completeDistribLattice with
@@ -1310,8 +1310,8 @@ noncomputable instance : CompleteLinearOrder (LowerSet α) :=
     decidableLe := Classical.decRel _
     DecidableEq := Classical.decRel _
     decidableLt := Classical.decRel _
-    max_def := by classical exact sup_eq_maxDefault
-    min_def := by classical exact inf_eq_minDefault }
+    max_def := by classical
+    min_def := by classical }
 
 end LinearOrder
 

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

@@ -1341,7 +1341,7 @@ def map (f : α ≃o β) : UpperSet α ≃o UpperSet β
 #print UpperSet.symm_map /-
 @[simp]
 theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
-  FunLike.ext _ _ fun s => ext <| Set.preimage_equiv_eq_image_symm _ _
+  DFunLike.ext _ _ fun s => ext <| Set.preimage_equiv_eq_image_symm _ _
 #align upper_set.symm_map UpperSet.symm_map
 -/
 
@@ -1393,7 +1393,7 @@ def map (f : α ≃o β) : LowerSet α ≃o LowerSet β
 #print LowerSet.symm_map /-
 @[simp]
 theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
-  FunLike.ext _ _ fun s => SetLike.coe_injective <| Set.preimage_equiv_eq_image_symm _ _
+  DFunLike.ext _ _ fun s => SetLike.coe_injective <| Set.preimage_equiv_eq_image_symm _ _
 #align lower_set.symm_map LowerSet.symm_map
 -/
 

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

@@ -522,7 +522,7 @@ variable [LinearOrder α] {s t : Set α}
 #print IsUpperSet.total /-
 theorem IsUpperSet.total (hs : IsUpperSet s) (ht : IsUpperSet t) : s ⊆ t ∨ t ⊆ s :=
   by
-  by_contra' h
+  by_contra! h
   simp_rw [Set.not_subset] at h 
   obtain ⟨⟨a, has, hat⟩, b, hbt, hbs⟩ := h
   obtain hab | hba := le_total a b

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

@@ -3,10 +3,10 @@ Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Sara Rousta
 -/
-import Mathbin.Data.SetLike.Basic
-import Mathbin.Data.Set.Intervals.OrdConnected
-import Mathbin.Data.Set.Intervals.OrderIso
-import Mathbin.Tactic.ByContra
+import Data.SetLike.Basic
+import Data.Set.Intervals.OrdConnected
+import Data.Set.Intervals.OrderIso
+import Tactic.ByContra
 
 #align_import order.upper_lower.basic from "leanprover-community/mathlib"@"c0c52abb75074ed8b73a948341f50521fbf43b4c"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/001ffdc42920050657fd45bd2b8bfbec8eaaeb29

@@ -519,6 +519,7 @@ section LinearOrder
 
 variable [LinearOrder α] {s t : Set α}
 
+#print IsUpperSet.total /-
 theorem IsUpperSet.total (hs : IsUpperSet s) (ht : IsUpperSet t) : s ⊆ t ∨ t ⊆ s :=
   by
   by_contra' h
@@ -528,10 +529,13 @@ theorem IsUpperSet.total (hs : IsUpperSet s) (ht : IsUpperSet t) : s ⊆ t ∨ t
   · exact hbs (hs hab has)
   · exact hat (ht hba hbt)
 #align is_upper_set.total IsUpperSet.total
+-/
 
+#print IsLowerSet.total /-
 theorem IsLowerSet.total (hs : IsLowerSet s) (ht : IsLowerSet t) : s ⊆ t ∨ t ⊆ s :=
   hs.toDual.Total ht.toDual
 #align is_lower_set.total IsLowerSet.total
+-/
 
 end LinearOrder
 
@@ -1279,13 +1283,17 @@ section LinearOrder
 
 variable [LinearOrder α]
 
+#print UpperSet.isTotal_le /-
 instance UpperSet.isTotal_le : IsTotal (UpperSet α) (· ≤ ·) :=
   ⟨fun s t => t.upper.Total s.upper⟩
 #align upper_set.is_total_le UpperSet.isTotal_le
+-/
 
+#print LowerSet.isTotal_le /-
 instance LowerSet.isTotal_le : IsTotal (LowerSet α) (· ≤ ·) :=
   ⟨fun s t => s.lower.Total t.lower⟩
 #align lower_set.is_total_le LowerSet.isTotal_le
+-/
 
 noncomputable instance : CompleteLinearOrder (UpperSet α) :=
   { UpperSet.completeDistribLattice with

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

@@ -251,16 +251,16 @@ theorem isUpperSet_preimage_toDual_iff {s : Set αᵒᵈ} : IsUpperSet (toDual 
 #align is_upper_set_preimage_to_dual_iff isUpperSet_preimage_toDual_iff
 -/
 
-alias isLowerSet_preimage_ofDual_iff ↔ _ IsUpperSet.toDual
+alias ⟨_, IsUpperSet.toDual⟩ := isLowerSet_preimage_ofDual_iff
 #align is_upper_set.to_dual IsUpperSet.toDual
 
-alias isUpperSet_preimage_ofDual_iff ↔ _ IsLowerSet.toDual
+alias ⟨_, IsLowerSet.toDual⟩ := isUpperSet_preimage_ofDual_iff
 #align is_lower_set.to_dual IsLowerSet.toDual
 
-alias isLowerSet_preimage_toDual_iff ↔ _ IsUpperSet.ofDual
+alias ⟨_, IsUpperSet.ofDual⟩ := isLowerSet_preimage_toDual_iff
 #align is_upper_set.of_dual IsUpperSet.ofDual
 
-alias isUpperSet_preimage_toDual_iff ↔ _ IsLowerSet.ofDual
+alias ⟨_, IsLowerSet.ofDual⟩ := isUpperSet_preimage_toDual_iff
 #align is_lower_set.of_dual IsLowerSet.ofDual
 
 end LE
@@ -301,10 +301,10 @@ theorem isLowerSet_iff_Iic_subset : IsLowerSet s ↔ ∀ ⦃a⦄, a ∈ s → Ii
 #align is_lower_set_iff_Iic_subset isLowerSet_iff_Iic_subset
 -/
 
-alias isUpperSet_iff_Ici_subset ↔ IsUpperSet.Ici_subset _
+alias ⟨IsUpperSet.Ici_subset, _⟩ := isUpperSet_iff_Ici_subset
 #align is_upper_set.Ici_subset IsUpperSet.Ici_subset
 
-alias isLowerSet_iff_Iic_subset ↔ IsLowerSet.Iic_subset _
+alias ⟨IsLowerSet.Iic_subset, _⟩ := isLowerSet_iff_Iic_subset
 #align is_lower_set.Iic_subset IsLowerSet.Iic_subset
 
 #print IsUpperSet.ordConnected /-
@@ -507,10 +507,10 @@ theorem isLowerSet_iff_Iio_subset : IsLowerSet s ↔ ∀ ⦃a⦄, a ∈ s → Ii
 #align is_lower_set_iff_Iio_subset isLowerSet_iff_Iio_subset
 -/
 
-alias isUpperSet_iff_Ioi_subset ↔ IsUpperSet.Ioi_subset _
+alias ⟨IsUpperSet.Ioi_subset, _⟩ := isUpperSet_iff_Ioi_subset
 #align is_upper_set.Ioi_subset IsUpperSet.Ioi_subset
 
-alias isLowerSet_iff_Iio_subset ↔ IsLowerSet.Iio_subset _
+alias ⟨IsLowerSet.Iio_subset, _⟩ := isLowerSet_iff_Iio_subset
 #align is_lower_set.Iio_subset IsLowerSet.Iio_subset
 
 end PartialOrder
@@ -2004,11 +2004,11 @@ theorem bddBelow_upperClosure : BddBelow (upperClosure s : Set α) ↔ BddBelow
 #align bdd_below_upper_closure bddBelow_upperClosure
 -/
 
-alias bddAbove_lowerClosure ↔ BddAbove.of_lowerClosure BddAbove.lowerClosure
+alias ⟨BddAbove.of_lowerClosure, BddAbove.lowerClosure⟩ := bddAbove_lowerClosure
 #align bdd_above.of_lower_closure BddAbove.of_lowerClosure
 #align bdd_above.lower_closure BddAbove.lowerClosure
 
-alias bddBelow_upperClosure ↔ BddBelow.of_upperClosure BddBelow.upperClosure
+alias ⟨BddBelow.of_upperClosure, BddBelow.upperClosure⟩ := bddBelow_upperClosure
 #align bdd_below.of_upper_closure BddBelow.of_upperClosure
 #align bdd_below.upper_closure BddBelow.upperClosure
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/c0c52abb75074ed8b73a948341f50521fbf43b4c

@@ -6,8 +6,9 @@ Authors: Yaël Dillies, Sara Rousta
 import Mathbin.Data.SetLike.Basic
 import Mathbin.Data.Set.Intervals.OrdConnected
 import Mathbin.Data.Set.Intervals.OrderIso
+import Mathbin.Tactic.ByContra
 
-#align_import order.upper_lower.basic from "leanprover-community/mathlib"@"e9ce88cd0d54891c714c604076084f763dd480ed"
+#align_import order.upper_lower.basic from "leanprover-community/mathlib"@"c0c52abb75074ed8b73a948341f50521fbf43b4c"
 
 /-!
 # Up-sets and down-sets
@@ -250,18 +251,18 @@ theorem isUpperSet_preimage_toDual_iff {s : Set αᵒᵈ} : IsUpperSet (toDual 
 #align is_upper_set_preimage_to_dual_iff isUpperSet_preimage_toDual_iff
 -/
 
-alias isLowerSet_preimage_ofDual_iff ↔ _ IsUpperSet.ofDual
-#align is_upper_set.of_dual IsUpperSet.ofDual
-
-alias isUpperSet_preimage_ofDual_iff ↔ _ IsLowerSet.ofDual
-#align is_lower_set.of_dual IsLowerSet.ofDual
-
-alias isLowerSet_preimage_toDual_iff ↔ _ IsUpperSet.toDual
+alias isLowerSet_preimage_ofDual_iff ↔ _ IsUpperSet.toDual
 #align is_upper_set.to_dual IsUpperSet.toDual
 
-alias isUpperSet_preimage_toDual_iff ↔ _ IsLowerSet.toDual
+alias isUpperSet_preimage_ofDual_iff ↔ _ IsLowerSet.toDual
 #align is_lower_set.to_dual IsLowerSet.toDual
 
+alias isLowerSet_preimage_toDual_iff ↔ _ IsUpperSet.ofDual
+#align is_upper_set.of_dual IsUpperSet.ofDual
+
+alias isUpperSet_preimage_toDual_iff ↔ _ IsLowerSet.ofDual
+#align is_lower_set.of_dual IsLowerSet.ofDual
+
 end LE
 
 section Preorder
@@ -514,6 +515,26 @@ alias isLowerSet_iff_Iio_subset ↔ IsLowerSet.Iio_subset _
 
 end PartialOrder
 
+section LinearOrder
+
+variable [LinearOrder α] {s t : Set α}
+
+theorem IsUpperSet.total (hs : IsUpperSet s) (ht : IsUpperSet t) : s ⊆ t ∨ t ⊆ s :=
+  by
+  by_contra' h
+  simp_rw [Set.not_subset] at h 
+  obtain ⟨⟨a, has, hat⟩, b, hbt, hbs⟩ := h
+  obtain hab | hba := le_total a b
+  · exact hbs (hs hab has)
+  · exact hat (ht hba hbt)
+#align is_upper_set.total IsUpperSet.total
+
+theorem IsLowerSet.total (hs : IsLowerSet s) (ht : IsLowerSet t) : s ⊆ t ∨ t ⊆ s :=
+  hs.toDual.Total ht.toDual
+#align is_lower_set.total IsLowerSet.total
+
+end LinearOrder
+
 /-! ### Bundled upper/lower sets -/
 
 
@@ -1254,6 +1275,38 @@ def upperSetIsoLowerSet : UpperSet α ≃o LowerSet α
 
 end LE
 
+section LinearOrder
+
+variable [LinearOrder α]
+
+instance UpperSet.isTotal_le : IsTotal (UpperSet α) (· ≤ ·) :=
+  ⟨fun s t => t.upper.Total s.upper⟩
+#align upper_set.is_total_le UpperSet.isTotal_le
+
+instance LowerSet.isTotal_le : IsTotal (LowerSet α) (· ≤ ·) :=
+  ⟨fun s t => s.lower.Total t.lower⟩
+#align lower_set.is_total_le LowerSet.isTotal_le
+
+noncomputable instance : CompleteLinearOrder (UpperSet α) :=
+  { UpperSet.completeDistribLattice with
+    le_total := IsTotal.total
+    decidableLe := Classical.decRel _
+    DecidableEq := Classical.decRel _
+    decidableLt := Classical.decRel _
+    max_def := by classical exact sup_eq_maxDefault
+    min_def := by classical exact inf_eq_minDefault }
+
+noncomputable instance : CompleteLinearOrder (LowerSet α) :=
+  { LowerSet.completeDistribLattice with
+    le_total := IsTotal.total
+    decidableLe := Classical.decRel _
+    DecidableEq := Classical.decRel _
+    decidableLt := Classical.decRel _
+    max_def := by classical exact sup_eq_maxDefault
+    min_def := by classical exact inf_eq_minDefault }
+
+end LinearOrder
+
 /-! #### Map -/
 
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Sara Rousta
-
-! This file was ported from Lean 3 source module order.upper_lower.basic
-! leanprover-community/mathlib commit e9ce88cd0d54891c714c604076084f763dd480ed
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.SetLike.Basic
 import Mathbin.Data.Set.Intervals.OrdConnected
 import Mathbin.Data.Set.Intervals.OrderIso
 
+#align_import order.upper_lower.basic from "leanprover-community/mathlib"@"e9ce88cd0d54891c714c604076084f763dd480ed"
+
 /-!
 # Up-sets and down-sets
 

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

@@ -97,57 +97,81 @@ theorem isLowerSet_univ : IsLowerSet (univ : Set α) := fun _ _ _ => id
 #align is_lower_set_univ isLowerSet_univ
 -/
 
+#print IsUpperSet.compl /-
 theorem IsUpperSet.compl (hs : IsUpperSet s) : IsLowerSet (sᶜ) := fun a b h hb ha => hb <| hs h ha
 #align is_upper_set.compl IsUpperSet.compl
+-/
 
+#print IsLowerSet.compl /-
 theorem IsLowerSet.compl (hs : IsLowerSet s) : IsUpperSet (sᶜ) := fun a b h hb ha => hb <| hs h ha
 #align is_lower_set.compl IsLowerSet.compl
+-/
 
+#print isUpperSet_compl /-
 @[simp]
 theorem isUpperSet_compl : IsUpperSet (sᶜ) ↔ IsLowerSet s :=
   ⟨fun h => by convert h.compl; rw [compl_compl], IsLowerSet.compl⟩
 #align is_upper_set_compl isUpperSet_compl
+-/
 
+#print isLowerSet_compl /-
 @[simp]
 theorem isLowerSet_compl : IsLowerSet (sᶜ) ↔ IsUpperSet s :=
   ⟨fun h => by convert h.compl; rw [compl_compl], IsUpperSet.compl⟩
 #align is_lower_set_compl isLowerSet_compl
+-/
 
+#print IsUpperSet.union /-
 theorem IsUpperSet.union (hs : IsUpperSet s) (ht : IsUpperSet t) : IsUpperSet (s ∪ t) :=
   fun a b h => Or.imp (hs h) (ht h)
 #align is_upper_set.union IsUpperSet.union
+-/
 
+#print IsLowerSet.union /-
 theorem IsLowerSet.union (hs : IsLowerSet s) (ht : IsLowerSet t) : IsLowerSet (s ∪ t) :=
   fun a b h => Or.imp (hs h) (ht h)
 #align is_lower_set.union IsLowerSet.union
+-/
 
+#print IsUpperSet.inter /-
 theorem IsUpperSet.inter (hs : IsUpperSet s) (ht : IsUpperSet t) : IsUpperSet (s ∩ t) :=
   fun a b h => And.imp (hs h) (ht h)
 #align is_upper_set.inter IsUpperSet.inter
+-/
 
+#print IsLowerSet.inter /-
 theorem IsLowerSet.inter (hs : IsLowerSet s) (ht : IsLowerSet t) : IsLowerSet (s ∩ t) :=
   fun a b h => And.imp (hs h) (ht h)
 #align is_lower_set.inter IsLowerSet.inter
+-/
 
+#print isUpperSet_iUnion /-
 theorem isUpperSet_iUnion {f : ι → Set α} (hf : ∀ i, IsUpperSet (f i)) : IsUpperSet (⋃ i, f i) :=
   fun a b h => Exists₂.imp <| forall_range_iff.2 fun i => hf i h
 #align is_upper_set_Union isUpperSet_iUnion
+-/
 
+#print isLowerSet_iUnion /-
 theorem isLowerSet_iUnion {f : ι → Set α} (hf : ∀ i, IsLowerSet (f i)) : IsLowerSet (⋃ i, f i) :=
   fun a b h => Exists₂.imp <| forall_range_iff.2 fun i => hf i h
 #align is_lower_set_Union isLowerSet_iUnion
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print isUpperSet_iUnion₂ /-
 theorem isUpperSet_iUnion₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsUpperSet (f i j)) :
     IsUpperSet (⋃ (i) (j), f i j) :=
   isUpperSet_iUnion fun i => isUpperSet_iUnion <| hf i
 #align is_upper_set_Union₂ isUpperSet_iUnion₂
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print isLowerSet_iUnion₂ /-
 theorem isLowerSet_iUnion₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsLowerSet (f i j)) :
     IsLowerSet (⋃ (i) (j), f i j) :=
   isLowerSet_iUnion fun i => isLowerSet_iUnion <| hf i
 #align is_lower_set_Union₂ isLowerSet_iUnion₂
+-/
 
 #print isUpperSet_sUnion /-
 theorem isUpperSet_sUnion {S : Set (Set α)} (hf : ∀ s ∈ S, IsUpperSet s) : IsUpperSet (⋃₀ S) :=
@@ -161,25 +185,33 @@ theorem isLowerSet_sUnion {S : Set (Set α)} (hf : ∀ s ∈ S, IsLowerSet s) :
 #align is_lower_set_sUnion isLowerSet_sUnion
 -/
 
+#print isUpperSet_iInter /-
 theorem isUpperSet_iInter {f : ι → Set α} (hf : ∀ i, IsUpperSet (f i)) : IsUpperSet (⋂ i, f i) :=
   fun a b h => forall₂_imp <| forall_range_iff.2 fun i => hf i h
 #align is_upper_set_Inter isUpperSet_iInter
+-/
 
+#print isLowerSet_iInter /-
 theorem isLowerSet_iInter {f : ι → Set α} (hf : ∀ i, IsLowerSet (f i)) : IsLowerSet (⋂ i, f i) :=
   fun a b h => forall₂_imp <| forall_range_iff.2 fun i => hf i h
 #align is_lower_set_Inter isLowerSet_iInter
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print isUpperSet_iInter₂ /-
 theorem isUpperSet_iInter₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsUpperSet (f i j)) :
     IsUpperSet (⋂ (i) (j), f i j) :=
   isUpperSet_iInter fun i => isUpperSet_iInter <| hf i
 #align is_upper_set_Inter₂ isUpperSet_iInter₂
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print isLowerSet_iInter₂ /-
 theorem isLowerSet_iInter₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsLowerSet (f i j)) :
     IsLowerSet (⋂ (i) (j), f i j) :=
   isLowerSet_iInter fun i => isLowerSet_iInter <| hf i
 #align is_lower_set_Inter₂ isLowerSet_iInter₂
+-/
 
 #print isUpperSet_sInter /-
 theorem isUpperSet_sInter {S : Set (Set α)} (hf : ∀ s ∈ S, IsUpperSet s) : IsUpperSet (⋂₀ S) :=
@@ -289,25 +321,33 @@ theorem IsLowerSet.ordConnected (h : IsLowerSet s) : s.OrdConnected :=
 #align is_lower_set.ord_connected IsLowerSet.ordConnected
 -/
 
+#print IsUpperSet.preimage /-
 theorem IsUpperSet.preimage (hs : IsUpperSet s) {f : β → α} (hf : Monotone f) :
     IsUpperSet (f ⁻¹' s : Set β) := fun x y hxy => hs <| hf hxy
 #align is_upper_set.preimage IsUpperSet.preimage
+-/
 
+#print IsLowerSet.preimage /-
 theorem IsLowerSet.preimage (hs : IsLowerSet s) {f : β → α} (hf : Monotone f) :
     IsLowerSet (f ⁻¹' s : Set β) := fun x y hxy => hs <| hf hxy
 #align is_lower_set.preimage IsLowerSet.preimage
+-/
 
+#print IsUpperSet.image /-
 theorem IsUpperSet.image (hs : IsUpperSet s) (f : α ≃o β) : IsUpperSet (f '' s : Set β) :=
   by
   change IsUpperSet ((f : α ≃ β) '' s); rw [Set.image_equiv_eq_preimage_symm]
   exact hs.preimage f.symm.monotone
 #align is_upper_set.image IsUpperSet.image
+-/
 
+#print IsLowerSet.image /-
 theorem IsLowerSet.image (hs : IsLowerSet s) (f : α ≃o β) : IsLowerSet (f '' s : Set β) :=
   by
   change IsLowerSet ((f : α ≃ β) '' s); rw [Set.image_equiv_eq_preimage_symm]
   exact hs.preimage f.symm.monotone
 #align is_lower_set.image IsLowerSet.image
+-/
 
 #print Set.monotone_mem /-
 @[simp]
@@ -341,17 +381,23 @@ section OrderTop
 
 variable [OrderTop α]
 
+#print IsLowerSet.top_mem /-
 theorem IsLowerSet.top_mem (hs : IsLowerSet s) : ⊤ ∈ s ↔ s = univ :=
   ⟨fun h => eq_univ_of_forall fun a => hs le_top h, fun h => h.symm ▸ mem_univ _⟩
 #align is_lower_set.top_mem IsLowerSet.top_mem
+-/
 
+#print IsUpperSet.top_mem /-
 theorem IsUpperSet.top_mem (hs : IsUpperSet s) : ⊤ ∈ s ↔ s.Nonempty :=
   ⟨fun h => ⟨_, h⟩, fun ⟨a, ha⟩ => hs le_top ha⟩
 #align is_upper_set.top_mem IsUpperSet.top_mem
+-/
 
+#print IsUpperSet.not_top_mem /-
 theorem IsUpperSet.not_top_mem (hs : IsUpperSet s) : ⊤ ∉ s ↔ s = ∅ :=
   hs.top_mem.Not.trans not_nonempty_iff_eq_empty
 #align is_upper_set.not_top_mem IsUpperSet.not_top_mem
+-/
 
 end OrderTop
 
@@ -359,17 +405,23 @@ section OrderBot
 
 variable [OrderBot α]
 
+#print IsUpperSet.bot_mem /-
 theorem IsUpperSet.bot_mem (hs : IsUpperSet s) : ⊥ ∈ s ↔ s = univ :=
   ⟨fun h => eq_univ_of_forall fun a => hs bot_le h, fun h => h.symm ▸ mem_univ _⟩
 #align is_upper_set.bot_mem IsUpperSet.bot_mem
+-/
 
+#print IsLowerSet.bot_mem /-
 theorem IsLowerSet.bot_mem (hs : IsLowerSet s) : ⊥ ∈ s ↔ s.Nonempty :=
   ⟨fun h => ⟨_, h⟩, fun ⟨a, ha⟩ => hs bot_le ha⟩
 #align is_lower_set.bot_mem IsLowerSet.bot_mem
+-/
 
+#print IsLowerSet.not_bot_mem /-
 theorem IsLowerSet.not_bot_mem (hs : IsLowerSet s) : ⊥ ∉ s ↔ s = ∅ :=
   hs.bot_mem.Not.trans not_nonempty_iff_eq_empty
 #align is_lower_set.not_bot_mem IsLowerSet.not_bot_mem
+-/
 
 end OrderBot
 
@@ -590,10 +642,12 @@ instance : CompleteDistribLattice (UpperSet α) :=
 instance : Inhabited (UpperSet α) :=
   ⟨⊥⟩
 
+#print UpperSet.coe_subset_coe /-
 @[simp, norm_cast]
 theorem coe_subset_coe : (s : Set α) ⊆ t ↔ t ≤ s :=
   Iff.rfl
 #align upper_set.coe_subset_coe UpperSet.coe_subset_coe
+-/
 
 #print UpperSet.coe_top /-
 @[simp, norm_cast]
@@ -621,47 +675,63 @@ theorem coe_eq_empty : (s : Set α) = ∅ ↔ s = ⊤ := by simp [SetLike.ext'_i
 #align upper_set.coe_eq_empty UpperSet.coe_eq_empty
 -/
 
+#print UpperSet.coe_sup /-
 @[simp, norm_cast]
 theorem coe_sup (s t : UpperSet α) : (↑(s ⊔ t) : Set α) = s ∩ t :=
   rfl
 #align upper_set.coe_sup UpperSet.coe_sup
+-/
 
+#print UpperSet.coe_inf /-
 @[simp, norm_cast]
 theorem coe_inf (s t : UpperSet α) : (↑(s ⊓ t) : Set α) = s ∪ t :=
   rfl
 #align upper_set.coe_inf UpperSet.coe_inf
+-/
 
+#print UpperSet.coe_sSup /-
 @[simp, norm_cast]
 theorem coe_sSup (S : Set (UpperSet α)) : (↑(sSup S) : Set α) = ⋂ s ∈ S, ↑s :=
   rfl
 #align upper_set.coe_Sup UpperSet.coe_sSup
+-/
 
+#print UpperSet.coe_sInf /-
 @[simp, norm_cast]
 theorem coe_sInf (S : Set (UpperSet α)) : (↑(sInf S) : Set α) = ⋃ s ∈ S, ↑s :=
   rfl
 #align upper_set.coe_Inf UpperSet.coe_sInf
+-/
 
+#print UpperSet.coe_iSup /-
 @[simp, norm_cast]
 theorem coe_iSup (f : ι → UpperSet α) : (↑(⨆ i, f i) : Set α) = ⋂ i, f i := by simp [iSup]
 #align upper_set.coe_supr UpperSet.coe_iSup
+-/
 
+#print UpperSet.coe_iInf /-
 @[simp, norm_cast]
 theorem coe_iInf (f : ι → UpperSet α) : (↑(⨅ i, f i) : Set α) = ⋃ i, f i := by simp [iInf]
 #align upper_set.coe_infi UpperSet.coe_iInf
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print UpperSet.coe_iSup₂ /-
 @[simp, norm_cast]
 theorem coe_iSup₂ (f : ∀ i, κ i → UpperSet α) : (↑(⨆ (i) (j), f i j) : Set α) = ⋂ (i) (j), f i j :=
   by simp_rw [coe_supr]
 #align upper_set.coe_supr₂ UpperSet.coe_iSup₂
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print UpperSet.coe_iInf₂ /-
 @[simp, norm_cast]
 theorem coe_iInf₂ (f : ∀ i, κ i → UpperSet α) : (↑(⨅ (i) (j), f i j) : Set α) = ⋃ (i) (j), f i j :=
   by simp_rw [coe_infi]
 #align upper_set.coe_infi₂ UpperSet.coe_iInf₂
+-/
 
 #print UpperSet.not_mem_top /-
 @[simp]
@@ -677,52 +747,70 @@ theorem mem_bot : a ∈ (⊥ : UpperSet α) :=
 #align upper_set.mem_bot UpperSet.mem_bot
 -/
 
+#print UpperSet.mem_sup_iff /-
 @[simp]
 theorem mem_sup_iff : a ∈ s ⊔ t ↔ a ∈ s ∧ a ∈ t :=
   Iff.rfl
 #align upper_set.mem_sup_iff UpperSet.mem_sup_iff
+-/
 
+#print UpperSet.mem_inf_iff /-
 @[simp]
 theorem mem_inf_iff : a ∈ s ⊓ t ↔ a ∈ s ∨ a ∈ t :=
   Iff.rfl
 #align upper_set.mem_inf_iff UpperSet.mem_inf_iff
+-/
 
+#print UpperSet.mem_sSup_iff /-
 @[simp]
 theorem mem_sSup_iff : a ∈ sSup S ↔ ∀ s ∈ S, a ∈ s :=
   mem_iInter₂
 #align upper_set.mem_Sup_iff UpperSet.mem_sSup_iff
+-/
 
+#print UpperSet.mem_sInf_iff /-
 @[simp]
 theorem mem_sInf_iff : a ∈ sInf S ↔ ∃ s ∈ S, a ∈ s :=
   mem_iUnion₂
 #align upper_set.mem_Inf_iff UpperSet.mem_sInf_iff
+-/
 
+#print UpperSet.mem_iSup_iff /-
 @[simp]
 theorem mem_iSup_iff {f : ι → UpperSet α} : (a ∈ ⨆ i, f i) ↔ ∀ i, a ∈ f i := by
   rw [← SetLike.mem_coe, coe_supr]; exact mem_Inter
 #align upper_set.mem_supr_iff UpperSet.mem_iSup_iff
+-/
 
+#print UpperSet.mem_iInf_iff /-
 @[simp]
 theorem mem_iInf_iff {f : ι → UpperSet α} : (a ∈ ⨅ i, f i) ↔ ∃ i, a ∈ f i := by
   rw [← SetLike.mem_coe, coe_infi]; exact mem_Union
 #align upper_set.mem_infi_iff UpperSet.mem_iInf_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print UpperSet.mem_iSup₂_iff /-
 @[simp]
 theorem mem_iSup₂_iff {f : ∀ i, κ i → UpperSet α} : (a ∈ ⨆ (i) (j), f i j) ↔ ∀ i j, a ∈ f i j := by
   simp_rw [mem_supr_iff]
 #align upper_set.mem_supr₂_iff UpperSet.mem_iSup₂_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print UpperSet.mem_iInf₂_iff /-
 @[simp]
 theorem mem_iInf₂_iff {f : ∀ i, κ i → UpperSet α} : (a ∈ ⨅ (i) (j), f i j) ↔ ∃ i j, a ∈ f i j := by
   simp_rw [mem_infi_iff]
 #align upper_set.mem_infi₂_iff UpperSet.mem_iInf₂_iff
+-/
 
+#print UpperSet.codisjoint_coe /-
 @[simp, norm_cast]
 theorem codisjoint_coe : Codisjoint (s : Set α) t ↔ Disjoint s t := by
   simp [disjoint_iff, codisjoint_iff, SetLike.ext'_iff]
 #align upper_set.codisjoint_coe UpperSet.codisjoint_coe
+-/
 
 end UpperSet
 
@@ -755,10 +843,12 @@ instance : CompleteDistribLattice (LowerSet α) :=
 instance : Inhabited (LowerSet α) :=
   ⟨⊥⟩
 
+#print LowerSet.coe_subset_coe /-
 @[simp, norm_cast]
 theorem coe_subset_coe : (s : Set α) ⊆ t ↔ s ≤ t :=
   Iff.rfl
 #align lower_set.coe_subset_coe LowerSet.coe_subset_coe
+-/
 
 #print LowerSet.coe_top /-
 @[simp, norm_cast]
@@ -786,49 +876,65 @@ theorem coe_eq_empty : (s : Set α) = ∅ ↔ s = ⊥ := by simp [SetLike.ext'_i
 #align lower_set.coe_eq_empty LowerSet.coe_eq_empty
 -/
 
+#print LowerSet.coe_sup /-
 @[simp, norm_cast]
 theorem coe_sup (s t : LowerSet α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
   rfl
 #align lower_set.coe_sup LowerSet.coe_sup
+-/
 
+#print LowerSet.coe_inf /-
 @[simp, norm_cast]
 theorem coe_inf (s t : LowerSet α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
   rfl
 #align lower_set.coe_inf LowerSet.coe_inf
+-/
 
+#print LowerSet.coe_sSup /-
 @[simp, norm_cast]
 theorem coe_sSup (S : Set (LowerSet α)) : (↑(sSup S) : Set α) = ⋃ s ∈ S, ↑s :=
   rfl
 #align lower_set.coe_Sup LowerSet.coe_sSup
+-/
 
+#print LowerSet.coe_sInf /-
 @[simp, norm_cast]
 theorem coe_sInf (S : Set (LowerSet α)) : (↑(sInf S) : Set α) = ⋂ s ∈ S, ↑s :=
   rfl
 #align lower_set.coe_Inf LowerSet.coe_sInf
+-/
 
+#print LowerSet.coe_iSup /-
 @[simp, norm_cast]
 theorem coe_iSup (f : ι → LowerSet α) : (↑(⨆ i, f i) : Set α) = ⋃ i, f i := by
   simp_rw [iSup, coe_Sup, mem_range, Union_exists, Union_Union_eq']
 #align lower_set.coe_supr LowerSet.coe_iSup
+-/
 
+#print LowerSet.coe_iInf /-
 @[simp, norm_cast]
 theorem coe_iInf (f : ι → LowerSet α) : (↑(⨅ i, f i) : Set α) = ⋂ i, f i := by
   simp_rw [iInf, coe_Inf, mem_range, Inter_exists, Inter_Inter_eq']
 #align lower_set.coe_infi LowerSet.coe_iInf
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print LowerSet.coe_iSup₂ /-
 @[simp, norm_cast]
 theorem coe_iSup₂ (f : ∀ i, κ i → LowerSet α) : (↑(⨆ (i) (j), f i j) : Set α) = ⋃ (i) (j), f i j :=
   by simp_rw [coe_supr]
 #align lower_set.coe_supr₂ LowerSet.coe_iSup₂
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print LowerSet.coe_iInf₂ /-
 @[simp, norm_cast]
 theorem coe_iInf₂ (f : ∀ i, κ i → LowerSet α) : (↑(⨅ (i) (j), f i j) : Set α) = ⋂ (i) (j), f i j :=
   by simp_rw [coe_infi]
 #align lower_set.coe_infi₂ LowerSet.coe_iInf₂
+-/
 
 #print LowerSet.mem_top /-
 @[simp]
@@ -844,52 +950,70 @@ theorem not_mem_bot : a ∉ (⊥ : LowerSet α) :=
 #align lower_set.not_mem_bot LowerSet.not_mem_bot
 -/
 
+#print LowerSet.mem_sup_iff /-
 @[simp]
 theorem mem_sup_iff : a ∈ s ⊔ t ↔ a ∈ s ∨ a ∈ t :=
   Iff.rfl
 #align lower_set.mem_sup_iff LowerSet.mem_sup_iff
+-/
 
+#print LowerSet.mem_inf_iff /-
 @[simp]
 theorem mem_inf_iff : a ∈ s ⊓ t ↔ a ∈ s ∧ a ∈ t :=
   Iff.rfl
 #align lower_set.mem_inf_iff LowerSet.mem_inf_iff
+-/
 
+#print LowerSet.mem_sSup_iff /-
 @[simp]
 theorem mem_sSup_iff : a ∈ sSup S ↔ ∃ s ∈ S, a ∈ s :=
   mem_iUnion₂
 #align lower_set.mem_Sup_iff LowerSet.mem_sSup_iff
+-/
 
+#print LowerSet.mem_sInf_iff /-
 @[simp]
 theorem mem_sInf_iff : a ∈ sInf S ↔ ∀ s ∈ S, a ∈ s :=
   mem_iInter₂
 #align lower_set.mem_Inf_iff LowerSet.mem_sInf_iff
+-/
 
+#print LowerSet.mem_iSup_iff /-
 @[simp]
 theorem mem_iSup_iff {f : ι → LowerSet α} : (a ∈ ⨆ i, f i) ↔ ∃ i, a ∈ f i := by
   rw [← SetLike.mem_coe, coe_supr]; exact mem_Union
 #align lower_set.mem_supr_iff LowerSet.mem_iSup_iff
+-/
 
+#print LowerSet.mem_iInf_iff /-
 @[simp]
 theorem mem_iInf_iff {f : ι → LowerSet α} : (a ∈ ⨅ i, f i) ↔ ∀ i, a ∈ f i := by
   rw [← SetLike.mem_coe, coe_infi]; exact mem_Inter
 #align lower_set.mem_infi_iff LowerSet.mem_iInf_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print LowerSet.mem_iSup₂_iff /-
 @[simp]
 theorem mem_iSup₂_iff {f : ∀ i, κ i → LowerSet α} : (a ∈ ⨆ (i) (j), f i j) ↔ ∃ i j, a ∈ f i j := by
   simp_rw [mem_supr_iff]
 #align lower_set.mem_supr₂_iff LowerSet.mem_iSup₂_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print LowerSet.mem_iInf₂_iff /-
 @[simp]
 theorem mem_iInf₂_iff {f : ∀ i, κ i → LowerSet α} : (a ∈ ⨅ (i) (j), f i j) ↔ ∀ i j, a ∈ f i j := by
   simp_rw [mem_infi_iff]
 #align lower_set.mem_infi₂_iff LowerSet.mem_iInf₂_iff
+-/
 
+#print LowerSet.disjoint_coe /-
 @[simp, norm_cast]
 theorem disjoint_coe : Disjoint (s : Set α) t ↔ Disjoint s t := by
   simp [disjoint_iff, SetLike.ext'_iff]
 #align lower_set.disjoint_coe LowerSet.disjoint_coe
+-/
 
 end LowerSet
 
@@ -914,10 +1038,12 @@ namespace UpperSet
 
 variable {s t : UpperSet α} {a : α}
 
+#print UpperSet.coe_compl /-
 @[simp]
 theorem coe_compl (s : UpperSet α) : (s.compl : Set α) = sᶜ :=
   rfl
 #align upper_set.coe_compl UpperSet.coe_compl
+-/
 
 #print UpperSet.mem_compl_iff /-
 @[simp]
@@ -933,20 +1059,26 @@ theorem compl_compl (s : UpperSet α) : s.compl.compl = s :=
 #align upper_set.compl_compl UpperSet.compl_compl
 -/
 
+#print UpperSet.compl_le_compl /-
 @[simp]
 theorem compl_le_compl : s.compl ≤ t.compl ↔ s ≤ t :=
   compl_subset_compl
 #align upper_set.compl_le_compl UpperSet.compl_le_compl
+-/
 
+#print UpperSet.compl_sup /-
 @[simp]
 protected theorem compl_sup (s t : UpperSet α) : (s ⊔ t).compl = s.compl ⊔ t.compl :=
   LowerSet.ext compl_inf
 #align upper_set.compl_sup UpperSet.compl_sup
+-/
 
+#print UpperSet.compl_inf /-
 @[simp]
 protected theorem compl_inf (s t : UpperSet α) : (s ⊓ t).compl = s.compl ⊓ t.compl :=
   LowerSet.ext compl_sup
 #align upper_set.compl_inf UpperSet.compl_inf
+-/
 
 #print UpperSet.compl_top /-
 @[simp]
@@ -962,39 +1094,51 @@ protected theorem compl_bot : (⊥ : UpperSet α).compl = ⊥ :=
 #align upper_set.compl_bot UpperSet.compl_bot
 -/
 
+#print UpperSet.compl_sSup /-
 @[simp]
 protected theorem compl_sSup (S : Set (UpperSet α)) : (sSup S).compl = ⨆ s ∈ S, UpperSet.compl s :=
   LowerSet.ext <| by simp only [coe_compl, coe_Sup, compl_Inter₂, LowerSet.coe_iSup₂]
 #align upper_set.compl_Sup UpperSet.compl_sSup
+-/
 
+#print UpperSet.compl_sInf /-
 @[simp]
 protected theorem compl_sInf (S : Set (UpperSet α)) : (sInf S).compl = ⨅ s ∈ S, UpperSet.compl s :=
   LowerSet.ext <| by simp only [coe_compl, coe_Inf, compl_Union₂, LowerSet.coe_iInf₂]
 #align upper_set.compl_Inf UpperSet.compl_sInf
+-/
 
+#print UpperSet.compl_iSup /-
 @[simp]
 protected theorem compl_iSup (f : ι → UpperSet α) : (⨆ i, f i).compl = ⨆ i, (f i).compl :=
   LowerSet.ext <| by simp only [coe_compl, coe_supr, compl_Inter, LowerSet.coe_iSup]
 #align upper_set.compl_supr UpperSet.compl_iSup
+-/
 
+#print UpperSet.compl_iInf /-
 @[simp]
 protected theorem compl_iInf (f : ι → UpperSet α) : (⨅ i, f i).compl = ⨅ i, (f i).compl :=
   LowerSet.ext <| by simp only [coe_compl, coe_infi, compl_Union, LowerSet.coe_iInf]
 #align upper_set.compl_infi UpperSet.compl_iInf
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print UpperSet.compl_iSup₂ /-
 @[simp]
 theorem compl_iSup₂ (f : ∀ i, κ i → UpperSet α) :
     (⨆ (i) (j), f i j).compl = ⨆ (i) (j), (f i j).compl := by simp_rw [UpperSet.compl_iSup]
 #align upper_set.compl_supr₂ UpperSet.compl_iSup₂
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print UpperSet.compl_iInf₂ /-
 @[simp]
 theorem compl_iInf₂ (f : ∀ i, κ i → UpperSet α) :
     (⨅ (i) (j), f i j).compl = ⨅ (i) (j), (f i j).compl := by simp_rw [UpperSet.compl_iInf]
 #align upper_set.compl_infi₂ UpperSet.compl_iInf₂
+-/
 
 end UpperSet
 
@@ -1002,10 +1146,12 @@ namespace LowerSet
 
 variable {s t : LowerSet α} {a : α}
 
+#print LowerSet.coe_compl /-
 @[simp]
 theorem coe_compl (s : LowerSet α) : (s.compl : Set α) = sᶜ :=
   rfl
 #align lower_set.coe_compl LowerSet.coe_compl
+-/
 
 #print LowerSet.mem_compl_iff /-
 @[simp]
@@ -1021,18 +1167,24 @@ theorem compl_compl (s : LowerSet α) : s.compl.compl = s :=
 #align lower_set.compl_compl LowerSet.compl_compl
 -/
 
+#print LowerSet.compl_le_compl /-
 @[simp]
 theorem compl_le_compl : s.compl ≤ t.compl ↔ s ≤ t :=
   compl_subset_compl
 #align lower_set.compl_le_compl LowerSet.compl_le_compl
+-/
 
+#print LowerSet.compl_sup /-
 protected theorem compl_sup (s t : LowerSet α) : (s ⊔ t).compl = s.compl ⊔ t.compl :=
   UpperSet.ext compl_sup
 #align lower_set.compl_sup LowerSet.compl_sup
+-/
 
+#print LowerSet.compl_inf /-
 protected theorem compl_inf (s t : LowerSet α) : (s ⊓ t).compl = s.compl ⊓ t.compl :=
   UpperSet.ext compl_inf
 #align lower_set.compl_inf LowerSet.compl_inf
+-/
 
 #print LowerSet.compl_top /-
 protected theorem compl_top : (⊤ : LowerSet α).compl = ⊤ :=
@@ -1058,30 +1210,39 @@ protected theorem compl_sInf (S : Set (LowerSet α)) : (sInf S).compl = ⨅ s 
 #align lower_set.compl_Inf LowerSet.compl_sInf
 -/
 
+#print LowerSet.compl_iSup /-
 protected theorem compl_iSup (f : ι → LowerSet α) : (⨆ i, f i).compl = ⨆ i, (f i).compl :=
   UpperSet.ext <| by simp only [coe_compl, coe_supr, compl_Union, UpperSet.coe_iSup]
 #align lower_set.compl_supr LowerSet.compl_iSup
+-/
 
+#print LowerSet.compl_iInf /-
 protected theorem compl_iInf (f : ι → LowerSet α) : (⨅ i, f i).compl = ⨅ i, (f i).compl :=
   UpperSet.ext <| by simp only [coe_compl, coe_infi, compl_Inter, UpperSet.coe_iInf]
 #align lower_set.compl_infi LowerSet.compl_iInf
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print LowerSet.compl_iSup₂ /-
 @[simp]
 theorem compl_iSup₂ (f : ∀ i, κ i → LowerSet α) :
     (⨆ (i) (j), f i j).compl = ⨆ (i) (j), (f i j).compl := by simp_rw [LowerSet.compl_iSup]
 #align lower_set.compl_supr₂ LowerSet.compl_iSup₂
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print LowerSet.compl_iInf₂ /-
 @[simp]
 theorem compl_iInf₂ (f : ∀ i, κ i → LowerSet α) :
     (⨅ (i) (j), f i j).compl = ⨅ (i) (j), (f i j).compl := by simp_rw [LowerSet.compl_iInf]
 #align lower_set.compl_infi₂ LowerSet.compl_iInf₂
+-/
 
 end LowerSet
 
+#print upperSetIsoLowerSet /-
 /-- Upper sets are order-isomorphic to lower sets under complementation. -/
 @[simps]
 def upperSetIsoLowerSet : UpperSet α ≃o LowerSet α
@@ -1092,6 +1253,7 @@ def upperSetIsoLowerSet : UpperSet α ≃o LowerSet α
   right_inv := LowerSet.compl_compl
   map_rel_iff' _ _ := UpperSet.compl_le_compl
 #align upper_set_iso_lower_set upperSetIsoLowerSet
+-/
 
 end LE
 
@@ -1106,6 +1268,7 @@ namespace UpperSet
 
 variable {f : α ≃o β} {s t : UpperSet α} {a : α} {b : β}
 
+#print UpperSet.map /-
 /-- An order isomorphism of preorders induces an order isomorphism of their upper sets. -/
 def map (f : α ≃o β) : UpperSet α ≃o UpperSet β
     where
@@ -1115,30 +1278,41 @@ def map (f : α ≃o β) : UpperSet α ≃o UpperSet β
   right_inv _ := ext <| f.image_preimage _
   map_rel_iff' s t := image_subset_image_iff f.Injective
 #align upper_set.map UpperSet.map
+-/
 
+#print UpperSet.symm_map /-
 @[simp]
 theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
   FunLike.ext _ _ fun s => ext <| Set.preimage_equiv_eq_image_symm _ _
 #align upper_set.symm_map UpperSet.symm_map
+-/
 
+#print UpperSet.mem_map /-
 @[simp]
 theorem mem_map : b ∈ map f s ↔ f.symm b ∈ s := by rw [← f.symm_symm, ← symm_map, f.symm_symm]; rfl
 #align upper_set.mem_map UpperSet.mem_map
+-/
 
+#print UpperSet.map_refl /-
 @[simp]
 theorem map_refl : map (OrderIso.refl α) = OrderIso.refl _ := by ext; simp
 #align upper_set.map_refl UpperSet.map_refl
+-/
 
+#print UpperSet.map_map /-
 @[simp]
 theorem map_map (g : β ≃o γ) (f : α ≃o β) : map g (map f s) = map (f.trans g) s := by ext; simp
 #align upper_set.map_map UpperSet.map_map
+-/
 
 variable (f s t)
 
+#print UpperSet.coe_map /-
 @[simp, norm_cast]
 theorem coe_map : (map f s : Set β) = f '' s :=
   rfl
 #align upper_set.coe_map UpperSet.coe_map
+-/
 
 end UpperSet
 
@@ -1146,6 +1320,7 @@ namespace LowerSet
 
 variable {f : α ≃o β} {s t : LowerSet α} {a : α} {b : β}
 
+#print LowerSet.map /-
 /-- An order isomorphism of preorders induces an order isomorphism of their lower sets. -/
 def map (f : α ≃o β) : LowerSet α ≃o LowerSet β
     where
@@ -1155,49 +1330,64 @@ def map (f : α ≃o β) : LowerSet α ≃o LowerSet β
   right_inv _ := SetLike.coe_injective <| f.image_preimage _
   map_rel_iff' s t := image_subset_image_iff f.Injective
 #align lower_set.map LowerSet.map
+-/
 
+#print LowerSet.symm_map /-
 @[simp]
 theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
   FunLike.ext _ _ fun s => SetLike.coe_injective <| Set.preimage_equiv_eq_image_symm _ _
 #align lower_set.symm_map LowerSet.symm_map
+-/
 
+#print LowerSet.mem_map /-
 @[simp]
 theorem mem_map {f : α ≃o β} {b : β} : b ∈ map f s ↔ f.symm b ∈ s := by
   rw [← f.symm_symm, ← symm_map, f.symm_symm]; rfl
 #align lower_set.mem_map LowerSet.mem_map
+-/
 
+#print LowerSet.map_refl /-
 @[simp]
 theorem map_refl : map (OrderIso.refl α) = OrderIso.refl _ := by ext; simp
 #align lower_set.map_refl LowerSet.map_refl
+-/
 
+#print LowerSet.map_map /-
 @[simp]
 theorem map_map (g : β ≃o γ) (f : α ≃o β) : map g (map f s) = map (f.trans g) s := by ext; simp
 #align lower_set.map_map LowerSet.map_map
+-/
 
 variable (f s t)
 
+#print LowerSet.coe_map /-
 @[simp, norm_cast]
 theorem coe_map : (map f s : Set β) = f '' s :=
   rfl
 #align lower_set.coe_map LowerSet.coe_map
+-/
 
 end LowerSet
 
 namespace UpperSet
 
+#print UpperSet.compl_map /-
 @[simp]
 theorem compl_map (f : α ≃o β) (s : UpperSet α) : (map f s).compl = LowerSet.map f s.compl :=
   SetLike.coe_injective (Set.image_compl_eq f.Bijective).symm
 #align upper_set.compl_map UpperSet.compl_map
+-/
 
 end UpperSet
 
 namespace LowerSet
 
+#print LowerSet.compl_map /-
 @[simp]
 theorem compl_map (f : α ≃o β) (s : LowerSet α) : (map f s).compl = UpperSet.map f s.compl :=
   SetLike.coe_injective (Set.image_compl_eq f.Bijective).symm
 #align lower_set.compl_map LowerSet.compl_map
+-/
 
 end LowerSet
 
@@ -1254,55 +1444,73 @@ theorem mem_Ioi_iff : b ∈ Ioi a ↔ a < b :=
 #align upper_set.mem_Ioi_iff UpperSet.mem_Ioi_iff
 -/
 
+#print UpperSet.map_Ici /-
 @[simp]
 theorem map_Ici (f : α ≃o β) (a : α) : map f (Ici a) = Ici (f a) := by ext; simp
 #align upper_set.map_Ici UpperSet.map_Ici
+-/
 
+#print UpperSet.map_Ioi /-
 @[simp]
 theorem map_Ioi (f : α ≃o β) (a : α) : map f (Ioi a) = Ioi (f a) := by ext; simp
 #align upper_set.map_Ioi UpperSet.map_Ioi
+-/
 
+#print UpperSet.Ici_le_Ioi /-
 theorem Ici_le_Ioi (a : α) : Ici a ≤ Ioi a :=
   Ioi_subset_Ici_self
 #align upper_set.Ici_le_Ioi UpperSet.Ici_le_Ioi
+-/
 
+#print UpperSet.Ioi_top /-
 @[simp]
 theorem Ioi_top [OrderTop α] : Ioi (⊤ : α) = ⊤ :=
   SetLike.coe_injective Ioi_top
 #align upper_set.Ioi_top UpperSet.Ioi_top
+-/
 
+#print UpperSet.Ici_bot /-
 @[simp]
 theorem Ici_bot [OrderBot α] : Ici (⊥ : α) = ⊥ :=
   SetLike.coe_injective Ici_bot
 #align upper_set.Ici_bot UpperSet.Ici_bot
+-/
 
 end Preorder
 
+#print UpperSet.Ici_sup /-
 @[simp]
 theorem Ici_sup [SemilatticeSup α] (a b : α) : Ici (a ⊔ b) = Ici a ⊔ Ici b :=
   ext Ici_inter_Ici.symm
 #align upper_set.Ici_sup UpperSet.Ici_sup
+-/
 
 section CompleteLattice
 
 variable [CompleteLattice α]
 
+#print UpperSet.Ici_sSup /-
 @[simp]
 theorem Ici_sSup (S : Set α) : Ici (sSup S) = ⨆ a ∈ S, Ici a :=
   SetLike.ext fun c => by simp only [mem_Ici_iff, mem_supr_iff, sSup_le_iff]
 #align upper_set.Ici_Sup UpperSet.Ici_sSup
+-/
 
+#print UpperSet.Ici_iSup /-
 @[simp]
 theorem Ici_iSup (f : ι → α) : Ici (⨆ i, f i) = ⨆ i, Ici (f i) :=
   SetLike.ext fun c => by simp only [mem_Ici_iff, mem_supr_iff, iSup_le_iff]
 #align upper_set.Ici_supr UpperSet.Ici_iSup
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print UpperSet.Ici_iSup₂ /-
 @[simp]
 theorem Ici_iSup₂ (f : ∀ i, κ i → α) : Ici (⨆ (i) (j), f i j) = ⨆ (i) (j), Ici (f i j) := by
   simp_rw [Ici_supr]
 #align upper_set.Ici_supr₂ UpperSet.Ici_iSup₂
+-/
 
 end CompleteLattice
 
@@ -1357,13 +1565,17 @@ theorem mem_Iio_iff : b ∈ Iio a ↔ b < a :=
 #align lower_set.mem_Iio_iff LowerSet.mem_Iio_iff
 -/
 
+#print LowerSet.map_Iic /-
 @[simp]
 theorem map_Iic (f : α ≃o β) (a : α) : map f (Iic a) = Iic (f a) := by ext; simp
 #align lower_set.map_Iic LowerSet.map_Iic
+-/
 
+#print LowerSet.map_Iio /-
 @[simp]
 theorem map_Iio (f : α ≃o β) (a : α) : map f (Iio a) = Iio (f a) := by ext; simp
 #align lower_set.map_Iio LowerSet.map_Iio
+-/
 
 #print LowerSet.Ioi_le_Ici /-
 theorem Ioi_le_Ici (a : α) : Ioi a ≤ Ici a :=
@@ -1371,43 +1583,55 @@ theorem Ioi_le_Ici (a : α) : Ioi a ≤ Ici a :=
 #align lower_set.Ioi_le_Ici LowerSet.Ioi_le_Ici
 -/
 
+#print LowerSet.Iic_top /-
 @[simp]
 theorem Iic_top [OrderTop α] : Iic (⊤ : α) = ⊤ :=
   SetLike.coe_injective Iic_top
 #align lower_set.Iic_top LowerSet.Iic_top
+-/
 
+#print LowerSet.Iio_bot /-
 @[simp]
 theorem Iio_bot [OrderBot α] : Iio (⊥ : α) = ⊥ :=
   SetLike.coe_injective Iio_bot
 #align lower_set.Iio_bot LowerSet.Iio_bot
+-/
 
 end Preorder
 
+#print LowerSet.Iic_inf /-
 @[simp]
 theorem Iic_inf [SemilatticeInf α] (a b : α) : Iic (a ⊓ b) = Iic a ⊓ Iic b :=
   SetLike.coe_injective Iic_inter_Iic.symm
 #align lower_set.Iic_inf LowerSet.Iic_inf
+-/
 
 section CompleteLattice
 
 variable [CompleteLattice α]
 
+#print LowerSet.Iic_sInf /-
 @[simp]
 theorem Iic_sInf (S : Set α) : Iic (sInf S) = ⨅ a ∈ S, Iic a :=
   SetLike.ext fun c => by simp only [mem_Iic_iff, mem_infi₂_iff, le_sInf_iff]
 #align lower_set.Iic_Inf LowerSet.Iic_sInf
+-/
 
+#print LowerSet.Iic_iInf /-
 @[simp]
 theorem Iic_iInf (f : ι → α) : Iic (⨅ i, f i) = ⨅ i, Iic (f i) :=
   SetLike.ext fun c => by simp only [mem_Iic_iff, mem_infi_iff, le_iInf_iff]
 #align lower_set.Iic_infi LowerSet.Iic_iInf
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print LowerSet.Iic_iInf₂ /-
 @[simp]
 theorem Iic_iInf₂ (f : ∀ i, κ i → α) : Iic (⨅ (i) (j), f i j) = ⨅ (i) (j), Iic (f i j) := by
   simp_rw [Iic_infi]
 #align lower_set.Iic_infi₂ LowerSet.Iic_iInf₂
+-/
 
 end CompleteLattice
 
@@ -1431,15 +1655,19 @@ def lowerClosure (s : Set α) : LowerSet α :=
 #align lower_closure lowerClosure
 -/
 
+#print mem_upperClosure /-
 @[simp]
 theorem mem_upperClosure : x ∈ upperClosure s ↔ ∃ a ∈ s, a ≤ x :=
   Iff.rfl
 #align mem_upper_closure mem_upperClosure
+-/
 
+#print mem_lowerClosure /-
 @[simp]
 theorem mem_lowerClosure : x ∈ lowerClosure s ↔ ∃ a ∈ s, x ≤ a :=
   Iff.rfl
 #align mem_lower_closure mem_lowerClosure
+-/
 
 #print coe_upperClosure /-
 -- We do not tag those two as `simp` to respect the abstraction.
@@ -1502,6 +1730,7 @@ protected theorem LowerSet.lowerClosure (s : LowerSet α) : lowerClosure (s : Se
 #align lower_set.lower_closure LowerSet.lowerClosure
 -/
 
+#print upperClosure_image /-
 @[simp]
 theorem upperClosure_image (f : α ≃o β) : upperClosure (f '' s) = UpperSet.map f (upperClosure s) :=
   by
@@ -1509,7 +1738,9 @@ theorem upperClosure_image (f : α ≃o β) : upperClosure (f '' s) = UpperSet.m
   ext
   simp [-UpperSet.symm_map, UpperSet.map, OrderIso.symm, ← f.le_symm_apply]
 #align upper_closure_image upperClosure_image
+-/
 
+#print lowerClosure_image /-
 @[simp]
 theorem lowerClosure_image (f : α ≃o β) : lowerClosure (f '' s) = LowerSet.map f (lowerClosure s) :=
   by
@@ -1517,10 +1748,13 @@ theorem lowerClosure_image (f : α ≃o β) : lowerClosure (f '' s) = LowerSet.m
   ext
   simp [-LowerSet.symm_map, LowerSet.map, OrderIso.symm, ← f.symm_apply_le]
 #align lower_closure_image lowerClosure_image
+-/
 
+#print UpperSet.iInf_Ici /-
 @[simp]
 theorem UpperSet.iInf_Ici (s : Set α) : (⨅ a ∈ s, UpperSet.Ici a) = upperClosure s := by ext; simp
 #align upper_set.infi_Ici UpperSet.iInf_Ici
+-/
 
 #print LowerSet.iSup_Iic /-
 @[simp]
@@ -1536,11 +1770,14 @@ theorem gc_upperClosure_coe :
 #align gc_upper_closure_coe gc_upperClosure_coe
 -/
 
+#print gc_lowerClosure_coe /-
 theorem gc_lowerClosure_coe : GaloisConnection (lowerClosure : Set α → LowerSet α) coe := fun s t =>
   ⟨fun h => subset_lowerClosure.trans <| LowerSet.coe_subset_coe.2 h, fun h =>
     lowerClosure_min h t.lower⟩
 #align gc_lower_closure_coe gc_lowerClosure_coe
+-/
 
+#print giUpperClosureCoe /-
 /-- `upper_closure` forms a reversed Galois insertion with the coercion from upper sets to sets. -/
 def giUpperClosureCoe :
     GaloisInsertion (toDual ∘ upperClosure : Set α → (UpperSet α)ᵒᵈ) (coe ∘ ofDual)
@@ -1550,7 +1787,9 @@ def giUpperClosureCoe :
   le_l_u _ := subset_upperClosure
   choice_eq s hs := ofDual.Injective <| SetLike.coe_injective <| subset_upperClosure.antisymm hs
 #align gi_upper_closure_coe giUpperClosureCoe
+-/
 
+#print giLowerClosureCoe /-
 /-- `lower_closure` forms a Galois insertion with the coercion from lower sets to sets. -/
 def giLowerClosureCoe : GaloisInsertion (lowerClosure : Set α → LowerSet α) coe
     where
@@ -1559,14 +1798,19 @@ def giLowerClosureCoe : GaloisInsertion (lowerClosure : Set α → LowerSet α)
   le_l_u _ := subset_lowerClosure
   choice_eq s hs := SetLike.coe_injective <| subset_lowerClosure.antisymm hs
 #align gi_lower_closure_coe giLowerClosureCoe
+-/
 
+#print upperClosure_anti /-
 theorem upperClosure_anti : Antitone (upperClosure : Set α → UpperSet α) :=
   gc_upperClosure_coe.monotone_l
 #align upper_closure_anti upperClosure_anti
+-/
 
+#print lowerClosure_mono /-
 theorem lowerClosure_mono : Monotone (lowerClosure : Set α → LowerSet α) :=
   gc_lowerClosure_coe.monotone_l
 #align lower_closure_mono lowerClosure_mono
+-/
 
 #print upperClosure_empty /-
 @[simp]
@@ -1622,30 +1866,40 @@ theorem lowerClosure_eq_bot_iff : lowerClosure s = ⊥ ↔ s = ∅ :=
 #align lower_closure_eq_bot_iff lowerClosure_eq_bot_iff
 -/
 
+#print upperClosure_union /-
 @[simp]
 theorem upperClosure_union (s t : Set α) : upperClosure (s ∪ t) = upperClosure s ⊓ upperClosure t :=
   by ext; simp [or_and_right, exists_or]
 #align upper_closure_union upperClosure_union
+-/
 
+#print lowerClosure_union /-
 @[simp]
 theorem lowerClosure_union (s t : Set α) : lowerClosure (s ∪ t) = lowerClosure s ⊔ lowerClosure t :=
   by ext; simp [or_and_right, exists_or]
 #align lower_closure_union lowerClosure_union
+-/
 
+#print upperClosure_iUnion /-
 @[simp]
 theorem upperClosure_iUnion (f : ι → Set α) : upperClosure (⋃ i, f i) = ⨅ i, upperClosure (f i) :=
   by ext; simp [← exists_and_right, @exists_comm α]
 #align upper_closure_Union upperClosure_iUnion
+-/
 
+#print lowerClosure_iUnion /-
 @[simp]
 theorem lowerClosure_iUnion (f : ι → Set α) : lowerClosure (⋃ i, f i) = ⨆ i, lowerClosure (f i) :=
   by ext; simp [← exists_and_right, @exists_comm α]
 #align lower_closure_Union lowerClosure_iUnion
+-/
 
+#print upperClosure_sUnion /-
 @[simp]
 theorem upperClosure_sUnion (S : Set (Set α)) : upperClosure (⋃₀ S) = ⨅ s ∈ S, upperClosure s := by
   simp_rw [sUnion_eq_bUnion, upperClosure_iUnion]
 #align upper_closure_sUnion upperClosure_sUnion
+-/
 
 #print lowerClosure_sUnion /-
 @[simp]
@@ -1654,12 +1908,15 @@ theorem lowerClosure_sUnion (S : Set (Set α)) : lowerClosure (⋃₀ S) = ⨆ s
 #align lower_closure_sUnion lowerClosure_sUnion
 -/
 
+#print Set.OrdConnected.upperClosure_inter_lowerClosure /-
 theorem Set.OrdConnected.upperClosure_inter_lowerClosure (h : s.OrdConnected) :
     ↑(upperClosure s) ∩ ↑(lowerClosure s) = s :=
   (subset_inter subset_upperClosure subset_lowerClosure).antisymm'
     fun a ⟨⟨b, hb, hba⟩, c, hc, hac⟩ => h.out hb hc ⟨hba, hac⟩
 #align set.ord_connected.upper_closure_inter_lower_closure Set.OrdConnected.upperClosure_inter_lowerClosure
+-/
 
+#print ordConnected_iff_upperClosure_inter_lowerClosure /-
 theorem ordConnected_iff_upperClosure_inter_lowerClosure :
     s.OrdConnected ↔ ↑(upperClosure s) ∩ ↑(lowerClosure s) = s :=
   by
@@ -1667,6 +1924,7 @@ theorem ordConnected_iff_upperClosure_inter_lowerClosure :
   rw [← h]
   exact (UpperSet.upper _).OrdConnected.inter (LowerSet.lower _).OrdConnected
 #align ord_connected_iff_upper_closure_inter_lower_closure ordConnected_iff_upperClosure_inter_lowerClosure
+-/
 
 #print upperBounds_lowerClosure /-
 @[simp]
@@ -1720,14 +1978,18 @@ section
 variable {s : Set α} {t : Set β} {x : α × β}
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print IsUpperSet.prod /-
 theorem IsUpperSet.prod (hs : IsUpperSet s) (ht : IsUpperSet t) : IsUpperSet (s ×ˢ t) :=
   fun a b h ha => ⟨hs h.1 ha.1, ht h.2 ha.2⟩
 #align is_upper_set.prod IsUpperSet.prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print IsLowerSet.prod /-
 theorem IsLowerSet.prod (hs : IsLowerSet s) (ht : IsLowerSet t) : IsLowerSet (s ×ˢ t) :=
   fun a b h ha => ⟨hs h.1 ha.1, ht h.2 ha.2⟩
 #align is_lower_set.prod IsLowerSet.prod
+-/
 
 end
 
@@ -1743,142 +2005,181 @@ def prod : UpperSet (α × β) :=
 #align upper_set.prod UpperSet.prod
 -/
 
--- mathport name: upper_set.prod
 infixr:82 " ×ˢ " => prod
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.coe_prod /-
 @[simp, norm_cast]
 theorem coe_prod : (↑(s ×ˢ t) : Set (α × β)) = s ×ˢ t :=
   rfl
 #align upper_set.coe_prod UpperSet.coe_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.mem_prod /-
 @[simp]
 theorem mem_prod {s : UpperSet α} {t : UpperSet β} : x ∈ s ×ˢ t ↔ x.1 ∈ s ∧ x.2 ∈ t :=
   Iff.rfl
 #align upper_set.mem_prod UpperSet.mem_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.Ici_prod /-
 theorem Ici_prod (x : α × β) : Ici x = Ici x.1 ×ˢ Ici x.2 :=
   rfl
 #align upper_set.Ici_prod UpperSet.Ici_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.Ici_prod_Ici /-
 @[simp]
 theorem Ici_prod_Ici (a : α) (b : β) : Ici a ×ˢ Ici b = Ici (a, b) :=
   rfl
 #align upper_set.Ici_prod_Ici UpperSet.Ici_prod_Ici
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.prod_top /-
 @[simp]
 theorem prod_top : s ×ˢ (⊤ : UpperSet β) = ⊤ :=
   ext prod_empty
 #align upper_set.prod_top UpperSet.prod_top
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.top_prod /-
 @[simp]
 theorem top_prod : (⊤ : UpperSet α) ×ˢ t = ⊤ :=
   ext empty_prod
 #align upper_set.top_prod UpperSet.top_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.bot_prod_bot /-
 @[simp]
 theorem bot_prod_bot : (⊥ : UpperSet α) ×ˢ (⊥ : UpperSet β) = ⊥ :=
   ext univ_prod_univ
 #align upper_set.bot_prod_bot UpperSet.bot_prod_bot
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.sup_prod /-
 @[simp]
 theorem sup_prod : (s₁ ⊔ s₂) ×ˢ t = s₁ ×ˢ t ⊔ s₂ ×ˢ t :=
   ext inter_prod
 #align upper_set.sup_prod UpperSet.sup_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.prod_sup /-
 @[simp]
 theorem prod_sup : s ×ˢ (t₁ ⊔ t₂) = s ×ˢ t₁ ⊔ s ×ˢ t₂ :=
   ext prod_inter
 #align upper_set.prod_sup UpperSet.prod_sup
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.inf_prod /-
 @[simp]
 theorem inf_prod : (s₁ ⊓ s₂) ×ˢ t = s₁ ×ˢ t ⊓ s₂ ×ˢ t :=
   ext union_prod
 #align upper_set.inf_prod UpperSet.inf_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.prod_inf /-
 @[simp]
 theorem prod_inf : s ×ˢ (t₁ ⊓ t₂) = s ×ˢ t₁ ⊓ s ×ˢ t₂ :=
   ext prod_union
 #align upper_set.prod_inf UpperSet.prod_inf
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.prod_sup_prod /-
 theorem prod_sup_prod : s₁ ×ˢ t₁ ⊔ s₂ ×ˢ t₂ = (s₁ ⊔ s₂) ×ˢ (t₁ ⊔ t₂) :=
   ext prod_inter_prod
 #align upper_set.prod_sup_prod UpperSet.prod_sup_prod
+-/
 
 variable {s s₁ s₂ t t₁ t₂}
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.prod_mono /-
 theorem prod_mono : s₁ ≤ s₂ → t₁ ≤ t₂ → s₁ ×ˢ t₁ ≤ s₂ ×ˢ t₂ :=
   prod_mono
 #align upper_set.prod_mono UpperSet.prod_mono
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.prod_mono_left /-
 theorem prod_mono_left : s₁ ≤ s₂ → s₁ ×ˢ t ≤ s₂ ×ˢ t :=
   prod_mono_left
 #align upper_set.prod_mono_left UpperSet.prod_mono_left
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.prod_mono_right /-
 theorem prod_mono_right : t₁ ≤ t₂ → s ×ˢ t₁ ≤ s ×ˢ t₂ :=
   prod_mono_right
 #align upper_set.prod_mono_right UpperSet.prod_mono_right
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.prod_self_le_prod_self /-
 @[simp]
 theorem prod_self_le_prod_self : s₁ ×ˢ s₁ ≤ s₂ ×ˢ s₂ ↔ s₁ ≤ s₂ :=
   prod_self_subset_prod_self
 #align upper_set.prod_self_le_prod_self UpperSet.prod_self_le_prod_self
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.prod_self_lt_prod_self /-
 @[simp]
 theorem prod_self_lt_prod_self : s₁ ×ˢ s₁ < s₂ ×ˢ s₂ ↔ s₁ < s₂ :=
   prod_self_ssubset_prod_self
 #align upper_set.prod_self_lt_prod_self UpperSet.prod_self_lt_prod_self
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.prod_le_prod_iff /-
 theorem prod_le_prod_iff : s₁ ×ˢ t₁ ≤ s₂ ×ˢ t₂ ↔ s₁ ≤ s₂ ∧ t₁ ≤ t₂ ∨ s₂ = ⊤ ∨ t₂ = ⊤ :=
   prod_subset_prod_iff.trans <| by simp
 #align upper_set.prod_le_prod_iff UpperSet.prod_le_prod_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.prod_eq_top /-
 @[simp]
 theorem prod_eq_top : s ×ˢ t = ⊤ ↔ s = ⊤ ∨ t = ⊤ := by simp_rw [SetLike.ext'_iff];
   exact prod_eq_empty_iff
 #align upper_set.prod_eq_top UpperSet.prod_eq_top
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.codisjoint_prod /-
 @[simp]
 theorem codisjoint_prod : Codisjoint (s₁ ×ˢ t₁) (s₂ ×ˢ t₂) ↔ Codisjoint s₁ s₂ ∨ Codisjoint t₁ t₂ :=
   by simp_rw [codisjoint_iff, prod_sup_prod, prod_eq_top]
 #align upper_set.codisjoint_prod UpperSet.codisjoint_prod
+-/
 
 end UpperSet
 
@@ -1894,160 +2195,203 @@ def prod : LowerSet (α × β) :=
 #align lower_set.prod LowerSet.prod
 -/
 
--- mathport name: lower_set.prod
 infixr:82 " ×ˢ " => LowerSet.prod
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.coe_prod /-
 @[simp, norm_cast]
 theorem coe_prod : (↑(s ×ˢ t) : Set (α × β)) = s ×ˢ t :=
   rfl
 #align lower_set.coe_prod LowerSet.coe_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.mem_prod /-
 @[simp]
 theorem mem_prod {s : LowerSet α} {t : LowerSet β} : x ∈ s ×ˢ t ↔ x.1 ∈ s ∧ x.2 ∈ t :=
   Iff.rfl
 #align lower_set.mem_prod LowerSet.mem_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.Iic_prod /-
 theorem Iic_prod (x : α × β) : Iic x = Iic x.1 ×ˢ Iic x.2 :=
   rfl
 #align lower_set.Iic_prod LowerSet.Iic_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.Ici_prod_Ici /-
 @[simp]
 theorem Ici_prod_Ici (a : α) (b : β) : Iic a ×ˢ Iic b = Iic (a, b) :=
   rfl
 #align lower_set.Ici_prod_Ici LowerSet.Ici_prod_Ici
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.prod_bot /-
 @[simp]
 theorem prod_bot : s ×ˢ (⊥ : LowerSet β) = ⊥ :=
   ext prod_empty
 #align lower_set.prod_bot LowerSet.prod_bot
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.bot_prod /-
 @[simp]
 theorem bot_prod : (⊥ : LowerSet α) ×ˢ t = ⊥ :=
   ext empty_prod
 #align lower_set.bot_prod LowerSet.bot_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.top_prod_top /-
 @[simp]
 theorem top_prod_top : (⊤ : LowerSet α) ×ˢ (⊤ : LowerSet β) = ⊤ :=
   ext univ_prod_univ
 #align lower_set.top_prod_top LowerSet.top_prod_top
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.inf_prod /-
 @[simp]
 theorem inf_prod : (s₁ ⊓ s₂) ×ˢ t = s₁ ×ˢ t ⊓ s₂ ×ˢ t :=
   ext inter_prod
 #align lower_set.inf_prod LowerSet.inf_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.prod_inf /-
 @[simp]
 theorem prod_inf : s ×ˢ (t₁ ⊓ t₂) = s ×ˢ t₁ ⊓ s ×ˢ t₂ :=
   ext prod_inter
 #align lower_set.prod_inf LowerSet.prod_inf
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.sup_prod /-
 @[simp]
 theorem sup_prod : (s₁ ⊔ s₂) ×ˢ t = s₁ ×ˢ t ⊔ s₂ ×ˢ t :=
   ext union_prod
 #align lower_set.sup_prod LowerSet.sup_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.prod_sup /-
 @[simp]
 theorem prod_sup : s ×ˢ (t₁ ⊔ t₂) = s ×ˢ t₁ ⊔ s ×ˢ t₂ :=
   ext prod_union
 #align lower_set.prod_sup LowerSet.prod_sup
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.prod_inf_prod /-
 theorem prod_inf_prod : s₁ ×ˢ t₁ ⊓ s₂ ×ˢ t₂ = (s₁ ⊓ s₂) ×ˢ (t₁ ⊓ t₂) :=
   ext prod_inter_prod
 #align lower_set.prod_inf_prod LowerSet.prod_inf_prod
+-/
 
 variable {s s₁ s₂ t t₁ t₂}
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.prod_mono /-
 theorem prod_mono : s₁ ≤ s₂ → t₁ ≤ t₂ → s₁ ×ˢ t₁ ≤ s₂ ×ˢ t₂ :=
   prod_mono
 #align lower_set.prod_mono LowerSet.prod_mono
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.prod_mono_left /-
 theorem prod_mono_left : s₁ ≤ s₂ → s₁ ×ˢ t ≤ s₂ ×ˢ t :=
   prod_mono_left
 #align lower_set.prod_mono_left LowerSet.prod_mono_left
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.prod_mono_right /-
 theorem prod_mono_right : t₁ ≤ t₂ → s ×ˢ t₁ ≤ s ×ˢ t₂ :=
   prod_mono_right
 #align lower_set.prod_mono_right LowerSet.prod_mono_right
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.prod_self_le_prod_self /-
 @[simp]
 theorem prod_self_le_prod_self : s₁ ×ˢ s₁ ≤ s₂ ×ˢ s₂ ↔ s₁ ≤ s₂ :=
   prod_self_subset_prod_self
 #align lower_set.prod_self_le_prod_self LowerSet.prod_self_le_prod_self
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.prod_self_lt_prod_self /-
 @[simp]
 theorem prod_self_lt_prod_self : s₁ ×ˢ s₁ < s₂ ×ˢ s₂ ↔ s₁ < s₂ :=
   prod_self_ssubset_prod_self
 #align lower_set.prod_self_lt_prod_self LowerSet.prod_self_lt_prod_self
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.prod_le_prod_iff /-
 theorem prod_le_prod_iff : s₁ ×ˢ t₁ ≤ s₂ ×ˢ t₂ ↔ s₁ ≤ s₂ ∧ t₁ ≤ t₂ ∨ s₁ = ⊥ ∨ t₁ = ⊥ :=
   prod_subset_prod_iff.trans <| by simp
 #align lower_set.prod_le_prod_iff LowerSet.prod_le_prod_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.prod_eq_bot /-
 @[simp]
 theorem prod_eq_bot : s ×ˢ t = ⊥ ↔ s = ⊥ ∨ t = ⊥ := by simp_rw [SetLike.ext'_iff];
   exact prod_eq_empty_iff
 #align lower_set.prod_eq_bot LowerSet.prod_eq_bot
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.disjoint_prod /-
 @[simp]
 theorem disjoint_prod : Disjoint (s₁ ×ˢ t₁) (s₂ ×ˢ t₂) ↔ Disjoint s₁ s₂ ∨ Disjoint t₁ t₂ := by
   simp_rw [disjoint_iff, prod_inf_prod, prod_eq_bot]
 #align lower_set.disjoint_prod LowerSet.disjoint_prod
+-/
 
 end LowerSet
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print upperClosure_prod /-
 @[simp]
 theorem upperClosure_prod (s : Set α) (t : Set β) :
     upperClosure (s ×ˢ t) = upperClosure s ×ˢ upperClosure t := by ext;
   simp [Prod.le_def, and_and_and_comm _ (_ ∈ t)]
 #align upper_closure_prod upperClosure_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print lowerClosure_prod /-
 @[simp]
 theorem lowerClosure_prod (s : Set α) (t : Set β) :
     lowerClosure (s ×ˢ t) = lowerClosure s ×ˢ lowerClosure t := by ext;
   simp [Prod.le_def, and_and_and_comm _ (_ ∈ t)]
 #align lower_closure_prod lowerClosure_prod
+-/
 
 end Preorder
 

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

@@ -325,14 +325,14 @@ theorem Set.antitone_mem : Antitone (· ∈ s) ↔ IsLowerSet s :=
 
 #print isUpperSet_setOf /-
 @[simp]
-theorem isUpperSet_setOf : IsUpperSet { a | p a } ↔ Monotone p :=
+theorem isUpperSet_setOf : IsUpperSet {a | p a} ↔ Monotone p :=
   Iff.rfl
 #align is_upper_set_set_of isUpperSet_setOf
 -/
 
 #print isLowerSet_setOf /-
 @[simp]
-theorem isLowerSet_setOf : IsLowerSet { a | p a } ↔ Antitone p :=
+theorem isLowerSet_setOf : IsLowerSet {a | p a} ↔ Antitone p :=
   forall_swap
 #align is_lower_set_set_of isLowerSet_setOf
 -/
@@ -1420,14 +1420,14 @@ variable [Preorder α] [Preorder β] {s t : Set α} {x : α}
 #print upperClosure /-
 /-- The greatest upper set containing a given set. -/
 def upperClosure (s : Set α) : UpperSet α :=
-  ⟨{ x | ∃ a ∈ s, a ≤ x }, fun x y h => Exists₂.imp fun a _ => h.trans'⟩
+  ⟨{x | ∃ a ∈ s, a ≤ x}, fun x y h => Exists₂.imp fun a _ => h.trans'⟩
 #align upper_closure upperClosure
 -/
 
 #print lowerClosure /-
 /-- The least lower set containing a given set. -/
 def lowerClosure (s : Set α) : LowerSet α :=
-  ⟨{ x | ∃ a ∈ s, x ≤ a }, fun x y h => Exists₂.imp fun a _ => h.trans⟩
+  ⟨{x | ∃ a ∈ s, x ≤ a}, fun x y h => Exists₂.imp fun a _ => h.trans⟩
 #align lower_closure lowerClosure
 -/
 

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

@@ -239,25 +239,37 @@ section Preorder
 
 variable [Preorder α] [Preorder β] {s : Set α} {p : α → Prop} (a : α)
 
+#print isUpperSet_Ici /-
 theorem isUpperSet_Ici : IsUpperSet (Ici a) := fun _ _ => ge_trans
 #align is_upper_set_Ici isUpperSet_Ici
+-/
 
+#print isLowerSet_Iic /-
 theorem isLowerSet_Iic : IsLowerSet (Iic a) := fun _ _ => le_trans
 #align is_lower_set_Iic isLowerSet_Iic
+-/
 
+#print isUpperSet_Ioi /-
 theorem isUpperSet_Ioi : IsUpperSet (Ioi a) := fun _ _ => flip lt_of_lt_of_le
 #align is_upper_set_Ioi isUpperSet_Ioi
+-/
 
+#print isLowerSet_Iio /-
 theorem isLowerSet_Iio : IsLowerSet (Iio a) := fun _ _ => lt_of_le_of_lt
 #align is_lower_set_Iio isLowerSet_Iio
+-/
 
+#print isUpperSet_iff_Ici_subset /-
 theorem isUpperSet_iff_Ici_subset : IsUpperSet s ↔ ∀ ⦃a⦄, a ∈ s → Ici a ⊆ s := by
   simp [IsUpperSet, subset_def, @forall_swap (_ ∈ s)]
 #align is_upper_set_iff_Ici_subset isUpperSet_iff_Ici_subset
+-/
 
+#print isLowerSet_iff_Iic_subset /-
 theorem isLowerSet_iff_Iic_subset : IsLowerSet s ↔ ∀ ⦃a⦄, a ∈ s → Iic a ⊆ s := by
   simp [IsLowerSet, subset_def, @forall_swap (_ ∈ s)]
 #align is_lower_set_iff_Iic_subset isLowerSet_iff_Iic_subset
+-/
 
 alias isUpperSet_iff_Ici_subset ↔ IsUpperSet.Ici_subset _
 #align is_upper_set.Ici_subset IsUpperSet.Ici_subset
@@ -265,13 +277,17 @@ alias isUpperSet_iff_Ici_subset ↔ IsUpperSet.Ici_subset _
 alias isLowerSet_iff_Iic_subset ↔ IsLowerSet.Iic_subset _
 #align is_lower_set.Iic_subset IsLowerSet.Iic_subset
 
+#print IsUpperSet.ordConnected /-
 theorem IsUpperSet.ordConnected (h : IsUpperSet s) : s.OrdConnected :=
   ⟨fun a ha b _ => Icc_subset_Ici_self.trans <| h.Ici_subset ha⟩
 #align is_upper_set.ord_connected IsUpperSet.ordConnected
+-/
 
+#print IsLowerSet.ordConnected /-
 theorem IsLowerSet.ordConnected (h : IsLowerSet s) : s.OrdConnected :=
   ⟨fun a _ b hb => Icc_subset_Iic_self.trans <| h.Iic_subset hb⟩
 #align is_lower_set.ord_connected IsLowerSet.ordConnected
+-/
 
 theorem IsUpperSet.preimage (hs : IsUpperSet s) {f : β → α} (hf : Monotone f) :
     IsUpperSet (f ⁻¹' s : Set β) := fun x y hxy => hs <| hf hxy
@@ -293,25 +309,33 @@ theorem IsLowerSet.image (hs : IsLowerSet s) (f : α ≃o β) : IsLowerSet (f ''
   exact hs.preimage f.symm.monotone
 #align is_lower_set.image IsLowerSet.image
 
+#print Set.monotone_mem /-
 @[simp]
 theorem Set.monotone_mem : Monotone (· ∈ s) ↔ IsUpperSet s :=
   Iff.rfl
 #align set.monotone_mem Set.monotone_mem
+-/
 
+#print Set.antitone_mem /-
 @[simp]
 theorem Set.antitone_mem : Antitone (· ∈ s) ↔ IsLowerSet s :=
   forall_swap
 #align set.antitone_mem Set.antitone_mem
+-/
 
+#print isUpperSet_setOf /-
 @[simp]
 theorem isUpperSet_setOf : IsUpperSet { a | p a } ↔ Monotone p :=
   Iff.rfl
 #align is_upper_set_set_of isUpperSet_setOf
+-/
 
+#print isLowerSet_setOf /-
 @[simp]
 theorem isLowerSet_setOf : IsLowerSet { a | p a } ↔ Antitone p :=
   forall_swap
 #align is_lower_set_set_of isLowerSet_setOf
+-/
 
 section OrderTop
 
@@ -353,20 +377,26 @@ section NoMaxOrder
 
 variable [NoMaxOrder α] (a)
 
+#print IsUpperSet.not_bddAbove /-
 theorem IsUpperSet.not_bddAbove (hs : IsUpperSet s) : s.Nonempty → ¬BddAbove s :=
   by
   rintro ⟨a, ha⟩ ⟨b, hb⟩
   obtain ⟨c, hc⟩ := exists_gt b
   exact hc.not_le (hb <| hs ((hb ha).trans hc.le) ha)
 #align is_upper_set.not_bdd_above IsUpperSet.not_bddAbove
+-/
 
+#print not_bddAbove_Ici /-
 theorem not_bddAbove_Ici : ¬BddAbove (Ici a) :=
   (isUpperSet_Ici _).not_bddAbove nonempty_Ici
 #align not_bdd_above_Ici not_bddAbove_Ici
+-/
 
+#print not_bddAbove_Ioi /-
 theorem not_bddAbove_Ioi : ¬BddAbove (Ioi a) :=
   (isUpperSet_Ioi _).not_bddAbove nonempty_Ioi
 #align not_bdd_above_Ioi not_bddAbove_Ioi
+-/
 
 end NoMaxOrder
 
@@ -374,20 +404,26 @@ section NoMinOrder
 
 variable [NoMinOrder α] (a)
 
+#print IsLowerSet.not_bddBelow /-
 theorem IsLowerSet.not_bddBelow (hs : IsLowerSet s) : s.Nonempty → ¬BddBelow s :=
   by
   rintro ⟨a, ha⟩ ⟨b, hb⟩
   obtain ⟨c, hc⟩ := exists_lt b
   exact hc.not_le (hb <| hs (hc.le.trans <| hb ha) ha)
 #align is_lower_set.not_bdd_below IsLowerSet.not_bddBelow
+-/
 
+#print not_bddBelow_Iic /-
 theorem not_bddBelow_Iic : ¬BddBelow (Iic a) :=
   (isLowerSet_Iic _).not_bddBelow nonempty_Iic
 #align not_bdd_below_Iic not_bddBelow_Iic
+-/
 
+#print not_bddBelow_Iio /-
 theorem not_bddBelow_Iio : ¬BddBelow (Iio a) :=
   (isLowerSet_Iio _).not_bddBelow nonempty_Iio
 #align not_bdd_below_Iio not_bddBelow_Iio
+-/
 
 end NoMinOrder
 
@@ -397,21 +433,29 @@ section PartialOrder
 
 variable [PartialOrder α] {s : Set α}
 
+#print isUpperSet_iff_forall_lt /-
 theorem isUpperSet_iff_forall_lt : IsUpperSet s ↔ ∀ ⦃a b : α⦄, a < b → a ∈ s → b ∈ s :=
   forall_congr' fun a => by simp [le_iff_eq_or_lt, or_imp, forall_and]
 #align is_upper_set_iff_forall_lt isUpperSet_iff_forall_lt
+-/
 
+#print isLowerSet_iff_forall_lt /-
 theorem isLowerSet_iff_forall_lt : IsLowerSet s ↔ ∀ ⦃a b : α⦄, b < a → a ∈ s → b ∈ s :=
   forall_congr' fun a => by simp [le_iff_eq_or_lt, or_imp, forall_and]
 #align is_lower_set_iff_forall_lt isLowerSet_iff_forall_lt
+-/
 
+#print isUpperSet_iff_Ioi_subset /-
 theorem isUpperSet_iff_Ioi_subset : IsUpperSet s ↔ ∀ ⦃a⦄, a ∈ s → Ioi a ⊆ s := by
   simp [isUpperSet_iff_forall_lt, subset_def, @forall_swap (_ ∈ s)]
 #align is_upper_set_iff_Ioi_subset isUpperSet_iff_Ioi_subset
+-/
 
+#print isLowerSet_iff_Iio_subset /-
 theorem isLowerSet_iff_Iio_subset : IsLowerSet s ↔ ∀ ⦃a⦄, a ∈ s → Iio a ⊆ s := by
   simp [isLowerSet_iff_forall_lt, subset_def, @forall_swap (_ ∈ s)]
 #align is_lower_set_iff_Iio_subset isLowerSet_iff_Iio_subset
+-/
 
 alias isUpperSet_iff_Ioi_subset ↔ IsUpperSet.Ioi_subset _
 #align is_upper_set.Ioi_subset IsUpperSet.Ioi_subset
@@ -1168,15 +1212,19 @@ section Preorder
 
 variable [Preorder α] [Preorder β] {s : UpperSet α} {a b : α}
 
+#print UpperSet.Ici /-
 /-- The smallest upper set containing a given element. -/
 def Ici (a : α) : UpperSet α :=
   ⟨Ici a, isUpperSet_Ici a⟩
 #align upper_set.Ici UpperSet.Ici
+-/
 
+#print UpperSet.Ioi /-
 /-- The smallest upper set containing a given element. -/
 def Ioi (a : α) : UpperSet α :=
   ⟨Ioi a, isUpperSet_Ioi a⟩
 #align upper_set.Ioi UpperSet.Ioi
+-/
 
 #print UpperSet.coe_Ici /-
 @[simp]
@@ -1192,15 +1240,19 @@ theorem coe_Ioi (a : α) : ↑(Ioi a) = Set.Ioi a :=
 #align upper_set.coe_Ioi UpperSet.coe_Ioi
 -/
 
+#print UpperSet.mem_Ici_iff /-
 @[simp]
 theorem mem_Ici_iff : b ∈ Ici a ↔ a ≤ b :=
   Iff.rfl
 #align upper_set.mem_Ici_iff UpperSet.mem_Ici_iff
+-/
 
+#print UpperSet.mem_Ioi_iff /-
 @[simp]
 theorem mem_Ioi_iff : b ∈ Ioi a ↔ a < b :=
   Iff.rfl
 #align upper_set.mem_Ioi_iff UpperSet.mem_Ioi_iff
+-/
 
 @[simp]
 theorem map_Ici (f : α ≃o β) (a : α) : map f (Ici a) = Ici (f a) := by ext; simp
@@ -1262,16 +1314,20 @@ section Preorder
 
 variable [Preorder α] [Preorder β] {s : LowerSet α} {a b : α}
 
+#print LowerSet.Iic /-
 /-- Principal lower set. `set.Iic` as a lower set. The smallest lower set containing a given
 element. -/
 def Iic (a : α) : LowerSet α :=
   ⟨Iic a, isLowerSet_Iic a⟩
 #align lower_set.Iic LowerSet.Iic
+-/
 
+#print LowerSet.Iio /-
 /-- Strict principal lower set. `set.Iio` as a lower set. -/
 def Iio (a : α) : LowerSet α :=
   ⟨Iio a, isLowerSet_Iio a⟩
 #align lower_set.Iio LowerSet.Iio
+-/
 
 #print LowerSet.coe_Iic /-
 @[simp]
@@ -1287,15 +1343,19 @@ theorem coe_Iio (a : α) : ↑(Iio a) = Set.Iio a :=
 #align lower_set.coe_Iio LowerSet.coe_Iio
 -/
 
+#print LowerSet.mem_Iic_iff /-
 @[simp]
 theorem mem_Iic_iff : b ∈ Iic a ↔ b ≤ a :=
   Iff.rfl
 #align lower_set.mem_Iic_iff LowerSet.mem_Iic_iff
+-/
 
+#print LowerSet.mem_Iio_iff /-
 @[simp]
 theorem mem_Iio_iff : b ∈ Iio a ↔ b < a :=
   Iff.rfl
 #align lower_set.mem_Iio_iff LowerSet.mem_Iio_iff
+-/
 
 @[simp]
 theorem map_Iic (f : α ≃o β) (a : α) : map f (Iic a) = Iic (f a) := by ext; simp
@@ -1357,15 +1417,19 @@ section closure
 
 variable [Preorder α] [Preorder β] {s t : Set α} {x : α}
 
+#print upperClosure /-
 /-- The greatest upper set containing a given set. -/
 def upperClosure (s : Set α) : UpperSet α :=
   ⟨{ x | ∃ a ∈ s, a ≤ x }, fun x y h => Exists₂.imp fun a _ => h.trans'⟩
 #align upper_closure upperClosure
+-/
 
+#print lowerClosure /-
 /-- The least lower set containing a given set. -/
 def lowerClosure (s : Set α) : LowerSet α :=
   ⟨{ x | ∃ a ∈ s, x ≤ a }, fun x y h => Exists₂.imp fun a _ => h.trans⟩
 #align lower_closure lowerClosure
+-/
 
 @[simp]
 theorem mem_upperClosure : x ∈ upperClosure s ↔ ∃ a ∈ s, a ≤ x :=
@@ -1400,31 +1464,43 @@ theorem subset_lowerClosure : s ⊆ lowerClosure s := fun x hx => ⟨x, hx, le_r
 #align subset_lower_closure subset_lowerClosure
 -/
 
+#print upperClosure_min /-
 theorem upperClosure_min (h : s ⊆ t) (ht : IsUpperSet t) : ↑(upperClosure s) ⊆ t :=
   fun a ⟨b, hb, hba⟩ => ht hba <| h hb
 #align upper_closure_min upperClosure_min
+-/
 
+#print lowerClosure_min /-
 theorem lowerClosure_min (h : s ⊆ t) (ht : IsLowerSet t) : ↑(lowerClosure s) ⊆ t :=
   fun a ⟨b, hb, hab⟩ => ht hab <| h hb
 #align lower_closure_min lowerClosure_min
+-/
 
+#print IsUpperSet.upperClosure /-
 protected theorem IsUpperSet.upperClosure (hs : IsUpperSet s) : ↑(upperClosure s) = s :=
   (upperClosure_min Subset.rfl hs).antisymm subset_upperClosure
 #align is_upper_set.upper_closure IsUpperSet.upperClosure
+-/
 
+#print IsLowerSet.lowerClosure /-
 protected theorem IsLowerSet.lowerClosure (hs : IsLowerSet s) : ↑(lowerClosure s) = s :=
   (lowerClosure_min Subset.rfl hs).antisymm subset_lowerClosure
 #align is_lower_set.lower_closure IsLowerSet.lowerClosure
+-/
 
+#print UpperSet.upperClosure /-
 @[simp]
 protected theorem UpperSet.upperClosure (s : UpperSet α) : upperClosure (s : Set α) = s :=
   SetLike.coe_injective s.2.upperClosure
 #align upper_set.upper_closure UpperSet.upperClosure
+-/
 
+#print LowerSet.lowerClosure /-
 @[simp]
 protected theorem LowerSet.lowerClosure (s : LowerSet α) : lowerClosure (s : Set α) = s :=
   SetLike.coe_injective s.2.lowerClosure
 #align lower_set.lower_closure LowerSet.lowerClosure
+-/
 
 @[simp]
 theorem upperClosure_image (f : α ≃o β) : upperClosure (f '' s) = UpperSet.map f (upperClosure s) :=
@@ -1446,9 +1522,11 @@ theorem lowerClosure_image (f : α ≃o β) : lowerClosure (f '' s) = LowerSet.m
 theorem UpperSet.iInf_Ici (s : Set α) : (⨅ a ∈ s, UpperSet.Ici a) = upperClosure s := by ext; simp
 #align upper_set.infi_Ici UpperSet.iInf_Ici
 
+#print LowerSet.iSup_Iic /-
 @[simp]
 theorem LowerSet.iSup_Iic (s : Set α) : (⨆ a ∈ s, LowerSet.Iic a) = lowerClosure s := by ext; simp
 #align lower_set.supr_Iic LowerSet.iSup_Iic
+-/
 
 #print gc_upperClosure_coe /-
 theorem gc_upperClosure_coe :
@@ -1490,43 +1568,59 @@ theorem lowerClosure_mono : Monotone (lowerClosure : Set α → LowerSet α) :=
   gc_lowerClosure_coe.monotone_l
 #align lower_closure_mono lowerClosure_mono
 
+#print upperClosure_empty /-
 @[simp]
 theorem upperClosure_empty : upperClosure (∅ : Set α) = ⊤ := by ext; simp
 #align upper_closure_empty upperClosure_empty
+-/
 
+#print lowerClosure_empty /-
 @[simp]
 theorem lowerClosure_empty : lowerClosure (∅ : Set α) = ⊥ := by ext; simp
 #align lower_closure_empty lowerClosure_empty
+-/
 
+#print upperClosure_singleton /-
 @[simp]
 theorem upperClosure_singleton (a : α) : upperClosure ({a} : Set α) = UpperSet.Ici a := by ext; simp
 #align upper_closure_singleton upperClosure_singleton
+-/
 
+#print lowerClosure_singleton /-
 @[simp]
 theorem lowerClosure_singleton (a : α) : lowerClosure ({a} : Set α) = LowerSet.Iic a := by ext; simp
 #align lower_closure_singleton lowerClosure_singleton
+-/
 
+#print upperClosure_univ /-
 @[simp]
 theorem upperClosure_univ : upperClosure (univ : Set α) = ⊥ :=
   le_bot_iff.1 subset_upperClosure
 #align upper_closure_univ upperClosure_univ
+-/
 
+#print lowerClosure_univ /-
 @[simp]
 theorem lowerClosure_univ : lowerClosure (univ : Set α) = ⊤ :=
   top_le_iff.1 subset_lowerClosure
 #align lower_closure_univ lowerClosure_univ
+-/
 
+#print upperClosure_eq_top_iff /-
 @[simp]
 theorem upperClosure_eq_top_iff : upperClosure s = ⊤ ↔ s = ∅ :=
   ⟨fun h => subset_empty_iff.1 <| subset_upperClosure.trans (congr_arg coe h).Subset, by rintro rfl;
     exact upperClosure_empty⟩
 #align upper_closure_eq_top_iff upperClosure_eq_top_iff
+-/
 
+#print lowerClosure_eq_bot_iff /-
 @[simp]
 theorem lowerClosure_eq_bot_iff : lowerClosure s = ⊥ ↔ s = ∅ :=
   ⟨fun h => subset_empty_iff.1 <| subset_lowerClosure.trans (congr_arg coe h).Subset, by rintro rfl;
     exact lowerClosure_empty⟩
 #align lower_closure_eq_bot_iff lowerClosure_eq_bot_iff
+-/
 
 @[simp]
 theorem upperClosure_union (s t : Set α) : upperClosure (s ∪ t) = upperClosure s ⊓ upperClosure t :=
@@ -1553,10 +1647,12 @@ theorem upperClosure_sUnion (S : Set (Set α)) : upperClosure (⋃₀ S) = ⨅ s
   simp_rw [sUnion_eq_bUnion, upperClosure_iUnion]
 #align upper_closure_sUnion upperClosure_sUnion
 
+#print lowerClosure_sUnion /-
 @[simp]
 theorem lowerClosure_sUnion (S : Set (Set α)) : lowerClosure (⋃₀ S) = ⨆ s ∈ S, lowerClosure s := by
   simp_rw [sUnion_eq_bUnion, lowerClosure_iUnion]
 #align lower_closure_sUnion lowerClosure_sUnion
+-/
 
 theorem Set.OrdConnected.upperClosure_inter_lowerClosure (h : s.OrdConnected) :
     ↑(upperClosure s) ∩ ↑(lowerClosure s) = s :=
@@ -1640,10 +1736,12 @@ namespace UpperSet
 variable (s s₁ s₂ : UpperSet α) (t t₁ t₂ : UpperSet β) {x : α × β}
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print UpperSet.prod /-
 /-- The product of two upper sets as an upper set. -/
 def prod : UpperSet (α × β) :=
   ⟨s ×ˢ t, s.2.Prod t.2⟩
 #align upper_set.prod UpperSet.prod
+-/
 
 -- mathport name: upper_set.prod
 infixr:82 " ×ˢ " => prod
@@ -1789,10 +1887,12 @@ namespace LowerSet
 variable (s s₁ s₂ : LowerSet α) (t t₁ t₂ : LowerSet β) {x : α × β}
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSet.prod /-
 /-- The product of two lower sets as a lower set. -/
 def prod : LowerSet (α × β) :=
   ⟨s ×ˢ t, s.2.Prod t.2⟩
 #align lower_set.prod LowerSet.prod
+-/
 
 -- mathport name: lower_set.prod
 infixr:82 " ×ˢ " => LowerSet.prod

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

@@ -97,124 +97,52 @@ theorem isLowerSet_univ : IsLowerSet (univ : Set α) := fun _ _ _ => id
 #align is_lower_set_univ isLowerSet_univ
 -/
 
-/- warning: is_upper_set.compl -> IsUpperSet.compl is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : Set.{u1} α}, (IsUpperSet.{u1} α _inst_1 s) -> (IsLowerSet.{u1} α _inst_1 (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : Set.{u1} α}, (IsUpperSet.{u1} α _inst_1 s) -> (IsLowerSet.{u1} α _inst_1 (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) s))
-Case conversion may be inaccurate. Consider using '#align is_upper_set.compl IsUpperSet.complₓ'. -/
 theorem IsUpperSet.compl (hs : IsUpperSet s) : IsLowerSet (sᶜ) := fun a b h hb ha => hb <| hs h ha
 #align is_upper_set.compl IsUpperSet.compl
 
-/- warning: is_lower_set.compl -> IsLowerSet.compl is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : Set.{u1} α}, (IsLowerSet.{u1} α _inst_1 s) -> (IsUpperSet.{u1} α _inst_1 (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : Set.{u1} α}, (IsLowerSet.{u1} α _inst_1 s) -> (IsUpperSet.{u1} α _inst_1 (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) s))
-Case conversion may be inaccurate. Consider using '#align is_lower_set.compl IsLowerSet.complₓ'. -/
 theorem IsLowerSet.compl (hs : IsLowerSet s) : IsUpperSet (sᶜ) := fun a b h hb ha => hb <| hs h ha
 #align is_lower_set.compl IsLowerSet.compl
 
-/- warning: is_upper_set_compl -> isUpperSet_compl is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : Set.{u1} α}, Iff (IsUpperSet.{u1} α _inst_1 (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s)) (IsLowerSet.{u1} α _inst_1 s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : Set.{u1} α}, Iff (IsUpperSet.{u1} α _inst_1 (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) s)) (IsLowerSet.{u1} α _inst_1 s)
-Case conversion may be inaccurate. Consider using '#align is_upper_set_compl isUpperSet_complₓ'. -/
 @[simp]
 theorem isUpperSet_compl : IsUpperSet (sᶜ) ↔ IsLowerSet s :=
   ⟨fun h => by convert h.compl; rw [compl_compl], IsLowerSet.compl⟩
 #align is_upper_set_compl isUpperSet_compl
 
-/- warning: is_lower_set_compl -> isLowerSet_compl is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : Set.{u1} α}, Iff (IsLowerSet.{u1} α _inst_1 (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s)) (IsUpperSet.{u1} α _inst_1 s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : Set.{u1} α}, Iff (IsLowerSet.{u1} α _inst_1 (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) s)) (IsUpperSet.{u1} α _inst_1 s)
-Case conversion may be inaccurate. Consider using '#align is_lower_set_compl isLowerSet_complₓ'. -/
 @[simp]
 theorem isLowerSet_compl : IsLowerSet (sᶜ) ↔ IsUpperSet s :=
   ⟨fun h => by convert h.compl; rw [compl_compl], IsUpperSet.compl⟩
 #align is_lower_set_compl isLowerSet_compl
 
-/- warning: is_upper_set.union -> IsUpperSet.union is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (IsUpperSet.{u1} α _inst_1 s) -> (IsUpperSet.{u1} α _inst_1 t) -> (IsUpperSet.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (IsUpperSet.{u1} α _inst_1 s) -> (IsUpperSet.{u1} α _inst_1 t) -> (IsUpperSet.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t))
-Case conversion may be inaccurate. Consider using '#align is_upper_set.union IsUpperSet.unionₓ'. -/
 theorem IsUpperSet.union (hs : IsUpperSet s) (ht : IsUpperSet t) : IsUpperSet (s ∪ t) :=
   fun a b h => Or.imp (hs h) (ht h)
 #align is_upper_set.union IsUpperSet.union
 
-/- warning: is_lower_set.union -> IsLowerSet.union is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (IsLowerSet.{u1} α _inst_1 s) -> (IsLowerSet.{u1} α _inst_1 t) -> (IsLowerSet.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (IsLowerSet.{u1} α _inst_1 s) -> (IsLowerSet.{u1} α _inst_1 t) -> (IsLowerSet.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t))
-Case conversion may be inaccurate. Consider using '#align is_lower_set.union IsLowerSet.unionₓ'. -/
 theorem IsLowerSet.union (hs : IsLowerSet s) (ht : IsLowerSet t) : IsLowerSet (s ∪ t) :=
   fun a b h => Or.imp (hs h) (ht h)
 #align is_lower_set.union IsLowerSet.union
 
-/- warning: is_upper_set.inter -> IsUpperSet.inter is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (IsUpperSet.{u1} α _inst_1 s) -> (IsUpperSet.{u1} α _inst_1 t) -> (IsUpperSet.{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 : LE.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (IsUpperSet.{u1} α _inst_1 s) -> (IsUpperSet.{u1} α _inst_1 t) -> (IsUpperSet.{u1} α _inst_1 (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t))
-Case conversion may be inaccurate. Consider using '#align is_upper_set.inter IsUpperSet.interₓ'. -/
 theorem IsUpperSet.inter (hs : IsUpperSet s) (ht : IsUpperSet t) : IsUpperSet (s ∩ t) :=
   fun a b h => And.imp (hs h) (ht h)
 #align is_upper_set.inter IsUpperSet.inter
 
-/- warning: is_lower_set.inter -> IsLowerSet.inter is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (IsLowerSet.{u1} α _inst_1 s) -> (IsLowerSet.{u1} α _inst_1 t) -> (IsLowerSet.{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 : LE.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (IsLowerSet.{u1} α _inst_1 s) -> (IsLowerSet.{u1} α _inst_1 t) -> (IsLowerSet.{u1} α _inst_1 (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t))
-Case conversion may be inaccurate. Consider using '#align is_lower_set.inter IsLowerSet.interₓ'. -/
 theorem IsLowerSet.inter (hs : IsLowerSet s) (ht : IsLowerSet t) : IsLowerSet (s ∩ t) :=
   fun a b h => And.imp (hs h) (ht h)
 #align is_lower_set.inter IsLowerSet.inter
 
-/- warning: is_upper_set_Union -> isUpperSet_iUnion is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {f : ι -> (Set.{u1} α)}, (forall (i : ι), IsUpperSet.{u1} α _inst_1 (f i)) -> (IsUpperSet.{u1} α _inst_1 (Set.iUnion.{u1, u2} α ι (fun (i : ι) => f i)))
-but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {f : ι -> (Set.{u2} α)}, (forall (i : ι), IsUpperSet.{u2} α _inst_1 (f i)) -> (IsUpperSet.{u2} α _inst_1 (Set.iUnion.{u2, u1} α ι (fun (i : ι) => f i)))
-Case conversion may be inaccurate. Consider using '#align is_upper_set_Union isUpperSet_iUnionₓ'. -/
 theorem isUpperSet_iUnion {f : ι → Set α} (hf : ∀ i, IsUpperSet (f i)) : IsUpperSet (⋃ i, f i) :=
   fun a b h => Exists₂.imp <| forall_range_iff.2 fun i => hf i h
 #align is_upper_set_Union isUpperSet_iUnion
 
-/- warning: is_lower_set_Union -> isLowerSet_iUnion is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {f : ι -> (Set.{u1} α)}, (forall (i : ι), IsLowerSet.{u1} α _inst_1 (f i)) -> (IsLowerSet.{u1} α _inst_1 (Set.iUnion.{u1, u2} α ι (fun (i : ι) => f i)))
-but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {f : ι -> (Set.{u2} α)}, (forall (i : ι), IsLowerSet.{u2} α _inst_1 (f i)) -> (IsLowerSet.{u2} α _inst_1 (Set.iUnion.{u2, u1} α ι (fun (i : ι) => f i)))
-Case conversion may be inaccurate. Consider using '#align is_lower_set_Union isLowerSet_iUnionₓ'. -/
 theorem isLowerSet_iUnion {f : ι → Set α} (hf : ∀ i, IsLowerSet (f i)) : IsLowerSet (⋃ i, f i) :=
   fun a b h => Exists₂.imp <| forall_range_iff.2 fun i => hf i h
 #align is_lower_set_Union isLowerSet_iUnion
 
-/- warning: is_upper_set_Union₂ -> isUpperSet_iUnion₂ is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {f : forall (i : ι), (κ i) -> (Set.{u1} α)}, (forall (i : ι) (j : κ i), IsUpperSet.{u1} α _inst_1 (f i j)) -> (IsUpperSet.{u1} α _inst_1 (Set.iUnion.{u1, u2} α ι (fun (i : ι) => Set.iUnion.{u1, u3} α (κ i) (fun (j : κ i) => f i j))))
-but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {f : forall (i : ι), (κ i) -> (Set.{u3} α)}, (forall (i : ι) (j : κ i), IsUpperSet.{u3} α _inst_1 (f i j)) -> (IsUpperSet.{u3} α _inst_1 (Set.iUnion.{u3, u2} α ι (fun (i : ι) => Set.iUnion.{u3, u1} α (κ i) (fun (j : κ i) => f i j))))
-Case conversion may be inaccurate. Consider using '#align is_upper_set_Union₂ isUpperSet_iUnion₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem isUpperSet_iUnion₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsUpperSet (f i j)) :
     IsUpperSet (⋃ (i) (j), f i j) :=
   isUpperSet_iUnion fun i => isUpperSet_iUnion <| hf i
 #align is_upper_set_Union₂ isUpperSet_iUnion₂
 
-/- warning: is_lower_set_Union₂ -> isLowerSet_iUnion₂ is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {f : forall (i : ι), (κ i) -> (Set.{u1} α)}, (forall (i : ι) (j : κ i), IsLowerSet.{u1} α _inst_1 (f i j)) -> (IsLowerSet.{u1} α _inst_1 (Set.iUnion.{u1, u2} α ι (fun (i : ι) => Set.iUnion.{u1, u3} α (κ i) (fun (j : κ i) => f i j))))
-but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {f : forall (i : ι), (κ i) -> (Set.{u3} α)}, (forall (i : ι) (j : κ i), IsLowerSet.{u3} α _inst_1 (f i j)) -> (IsLowerSet.{u3} α _inst_1 (Set.iUnion.{u3, u2} α ι (fun (i : ι) => Set.iUnion.{u3, u1} α (κ i) (fun (j : κ i) => f i j))))
-Case conversion may be inaccurate. Consider using '#align is_lower_set_Union₂ isLowerSet_iUnion₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem isLowerSet_iUnion₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsLowerSet (f i j)) :
     IsLowerSet (⋃ (i) (j), f i j) :=
@@ -233,44 +161,20 @@ theorem isLowerSet_sUnion {S : Set (Set α)} (hf : ∀ s ∈ S, IsLowerSet s) :
 #align is_lower_set_sUnion isLowerSet_sUnion
 -/
 
-/- warning: is_upper_set_Inter -> isUpperSet_iInter is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {f : ι -> (Set.{u1} α)}, (forall (i : ι), IsUpperSet.{u1} α _inst_1 (f i)) -> (IsUpperSet.{u1} α _inst_1 (Set.iInter.{u1, u2} α ι (fun (i : ι) => f i)))
-but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {f : ι -> (Set.{u2} α)}, (forall (i : ι), IsUpperSet.{u2} α _inst_1 (f i)) -> (IsUpperSet.{u2} α _inst_1 (Set.iInter.{u2, u1} α ι (fun (i : ι) => f i)))
-Case conversion may be inaccurate. Consider using '#align is_upper_set_Inter isUpperSet_iInterₓ'. -/
 theorem isUpperSet_iInter {f : ι → Set α} (hf : ∀ i, IsUpperSet (f i)) : IsUpperSet (⋂ i, f i) :=
   fun a b h => forall₂_imp <| forall_range_iff.2 fun i => hf i h
 #align is_upper_set_Inter isUpperSet_iInter
 
-/- warning: is_lower_set_Inter -> isLowerSet_iInter is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {f : ι -> (Set.{u1} α)}, (forall (i : ι), IsLowerSet.{u1} α _inst_1 (f i)) -> (IsLowerSet.{u1} α _inst_1 (Set.iInter.{u1, u2} α ι (fun (i : ι) => f i)))
-but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {f : ι -> (Set.{u2} α)}, (forall (i : ι), IsLowerSet.{u2} α _inst_1 (f i)) -> (IsLowerSet.{u2} α _inst_1 (Set.iInter.{u2, u1} α ι (fun (i : ι) => f i)))
-Case conversion may be inaccurate. Consider using '#align is_lower_set_Inter isLowerSet_iInterₓ'. -/
 theorem isLowerSet_iInter {f : ι → Set α} (hf : ∀ i, IsLowerSet (f i)) : IsLowerSet (⋂ i, f i) :=
   fun a b h => forall₂_imp <| forall_range_iff.2 fun i => hf i h
 #align is_lower_set_Inter isLowerSet_iInter
 
-/- warning: is_upper_set_Inter₂ -> isUpperSet_iInter₂ is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {f : forall (i : ι), (κ i) -> (Set.{u1} α)}, (forall (i : ι) (j : κ i), IsUpperSet.{u1} α _inst_1 (f i j)) -> (IsUpperSet.{u1} α _inst_1 (Set.iInter.{u1, u2} α ι (fun (i : ι) => Set.iInter.{u1, u3} α (κ i) (fun (j : κ i) => f i j))))
-but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {f : forall (i : ι), (κ i) -> (Set.{u3} α)}, (forall (i : ι) (j : κ i), IsUpperSet.{u3} α _inst_1 (f i j)) -> (IsUpperSet.{u3} α _inst_1 (Set.iInter.{u3, u2} α ι (fun (i : ι) => Set.iInter.{u3, u1} α (κ i) (fun (j : κ i) => f i j))))
-Case conversion may be inaccurate. Consider using '#align is_upper_set_Inter₂ isUpperSet_iInter₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem isUpperSet_iInter₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsUpperSet (f i j)) :
     IsUpperSet (⋂ (i) (j), f i j) :=
   isUpperSet_iInter fun i => isUpperSet_iInter <| hf i
 #align is_upper_set_Inter₂ isUpperSet_iInter₂
 
-/- warning: is_lower_set_Inter₂ -> isLowerSet_iInter₂ is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {f : forall (i : ι), (κ i) -> (Set.{u1} α)}, (forall (i : ι) (j : κ i), IsLowerSet.{u1} α _inst_1 (f i j)) -> (IsLowerSet.{u1} α _inst_1 (Set.iInter.{u1, u2} α ι (fun (i : ι) => Set.iInter.{u1, u3} α (κ i) (fun (j : κ i) => f i j))))
-but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {f : forall (i : ι), (κ i) -> (Set.{u3} α)}, (forall (i : ι) (j : κ i), IsLowerSet.{u3} α _inst_1 (f i j)) -> (IsLowerSet.{u3} α _inst_1 (Set.iInter.{u3, u2} α ι (fun (i : ι) => Set.iInter.{u3, u1} α (κ i) (fun (j : κ i) => f i j))))
-Case conversion may be inaccurate. Consider using '#align is_lower_set_Inter₂ isLowerSet_iInter₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem isLowerSet_iInter₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsLowerSet (f i j)) :
     IsLowerSet (⋂ (i) (j), f i j) :=
@@ -335,183 +239,75 @@ section Preorder
 
 variable [Preorder α] [Preorder β] {s : Set α} {p : α → Prop} (a : α)
 
-/- warning: is_upper_set_Ici -> isUpperSet_Ici is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_upper_set_Ici isUpperSet_Iciₓ'. -/
 theorem isUpperSet_Ici : IsUpperSet (Ici a) := fun _ _ => ge_trans
 #align is_upper_set_Ici isUpperSet_Ici
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_lower_set_Iic isLowerSet_Iicₓ'. -/
 theorem isLowerSet_Iic : IsLowerSet (Iic a) := fun _ _ => le_trans
 #align is_lower_set_Iic isLowerSet_Iic
 
-/- warning: is_upper_set_Ioi -> isUpperSet_Ioi 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_upper_set_Ioi isUpperSet_Ioiₓ'. -/
 theorem isUpperSet_Ioi : IsUpperSet (Ioi a) := fun _ _ => flip lt_of_lt_of_le
 #align is_upper_set_Ioi isUpperSet_Ioi
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_lower_set_Iio isLowerSet_Iioₓ'. -/
 theorem isLowerSet_Iio : IsLowerSet (Iio a) := fun _ _ => lt_of_le_of_lt
 #align is_lower_set_Iio isLowerSet_Iio
 
-/- warning: is_upper_set_iff_Ici_subset -> isUpperSet_iff_Ici_subset 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_upper_set_iff_Ici_subset isUpperSet_iff_Ici_subsetₓ'. -/
 theorem isUpperSet_iff_Ici_subset : IsUpperSet s ↔ ∀ ⦃a⦄, a ∈ s → Ici a ⊆ s := by
   simp [IsUpperSet, subset_def, @forall_swap (_ ∈ s)]
 #align is_upper_set_iff_Ici_subset isUpperSet_iff_Ici_subset
 
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-Case conversion may be inaccurate. Consider using '#align is_lower_set_iff_Iic_subset isLowerSet_iff_Iic_subsetₓ'. -/
 theorem isLowerSet_iff_Iic_subset : IsLowerSet s ↔ ∀ ⦃a⦄, a ∈ s → Iic a ⊆ s := by
   simp [IsLowerSet, subset_def, @forall_swap (_ ∈ s)]
 #align is_lower_set_iff_Iic_subset isLowerSet_iff_Iic_subset
 
-/- warning: is_upper_set.Ici_subset -> IsUpperSet.Ici_subset is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_upper_set.Ici_subset IsUpperSet.Ici_subsetₓ'. -/
 alias isUpperSet_iff_Ici_subset ↔ IsUpperSet.Ici_subset _
 #align is_upper_set.Ici_subset IsUpperSet.Ici_subset
 
-/- warning: is_lower_set.Iic_subset -> IsLowerSet.Iic_subset is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_lower_set.Iic_subset IsLowerSet.Iic_subsetₓ'. -/
 alias isLowerSet_iff_Iic_subset ↔ IsLowerSet.Iic_subset _
 #align is_lower_set.Iic_subset IsLowerSet.Iic_subset
 
-/- warning: is_upper_set.ord_connected -> IsUpperSet.ordConnected is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (Set.OrdConnected.{u1} α _inst_1 s)
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-Case conversion may be inaccurate. Consider using '#align is_upper_set.ord_connected IsUpperSet.ordConnectedₓ'. -/
 theorem IsUpperSet.ordConnected (h : IsUpperSet s) : s.OrdConnected :=
   ⟨fun a ha b _ => Icc_subset_Ici_self.trans <| h.Ici_subset ha⟩
 #align is_upper_set.ord_connected IsUpperSet.ordConnected
 
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-Case conversion may be inaccurate. Consider using '#align is_lower_set.ord_connected IsLowerSet.ordConnectedₓ'. -/
 theorem IsLowerSet.ordConnected (h : IsLowerSet s) : s.OrdConnected :=
   ⟨fun a _ b hb => Icc_subset_Iic_self.trans <| h.Iic_subset hb⟩
 #align is_lower_set.ord_connected IsLowerSet.ordConnected
 
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-Case conversion may be inaccurate. Consider using '#align is_upper_set.preimage IsUpperSet.preimageₓ'. -/
 theorem IsUpperSet.preimage (hs : IsUpperSet s) {f : β → α} (hf : Monotone f) :
     IsUpperSet (f ⁻¹' s : Set β) := fun x y hxy => hs <| hf hxy
 #align is_upper_set.preimage IsUpperSet.preimage
 
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align is_lower_set.preimage IsLowerSet.preimageₓ'. -/
 theorem IsLowerSet.preimage (hs : IsLowerSet s) {f : β → α} (hf : Monotone f) :
     IsLowerSet (f ⁻¹' s : Set β) := fun x y hxy => hs <| hf hxy
 #align is_lower_set.preimage IsLowerSet.preimage
 
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 theorem IsUpperSet.image (hs : IsUpperSet s) (f : α ≃o β) : IsUpperSet (f '' s : Set β) :=
   by
   change IsUpperSet ((f : α ≃ β) '' s); rw [Set.image_equiv_eq_preimage_symm]
   exact hs.preimage f.symm.monotone
 #align is_upper_set.image IsUpperSet.image
 
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 theorem IsLowerSet.image (hs : IsLowerSet s) (f : α ≃o β) : IsLowerSet (f '' s : Set β) :=
   by
   change IsLowerSet ((f : α ≃ β) '' s); rw [Set.image_equiv_eq_preimage_symm]
   exact hs.preimage f.symm.monotone
 #align is_lower_set.image IsLowerSet.image
 
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 @[simp]
 theorem Set.monotone_mem : Monotone (· ∈ s) ↔ IsUpperSet s :=
   Iff.rfl
 #align set.monotone_mem Set.monotone_mem
 
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 @[simp]
 theorem Set.antitone_mem : Antitone (· ∈ s) ↔ IsLowerSet s :=
   forall_swap
 #align set.antitone_mem Set.antitone_mem
 
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 @[simp]
 theorem isUpperSet_setOf : IsUpperSet { a | p a } ↔ Monotone p :=
   Iff.rfl
 #align is_upper_set_set_of isUpperSet_setOf
 
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 @[simp]
 theorem isLowerSet_setOf : IsLowerSet { a | p a } ↔ Antitone p :=
   forall_swap
@@ -521,32 +317,14 @@ section OrderTop
 
 variable [OrderTop α]
 
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 theorem IsLowerSet.top_mem (hs : IsLowerSet s) : ⊤ ∈ s ↔ s = univ :=
   ⟨fun h => eq_univ_of_forall fun a => hs le_top h, fun h => h.symm ▸ mem_univ _⟩
 #align is_lower_set.top_mem IsLowerSet.top_mem
 
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 theorem IsUpperSet.top_mem (hs : IsUpperSet s) : ⊤ ∈ s ↔ s.Nonempty :=
   ⟨fun h => ⟨_, h⟩, fun ⟨a, ha⟩ => hs le_top ha⟩
 #align is_upper_set.top_mem IsUpperSet.top_mem
 
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 theorem IsUpperSet.not_top_mem (hs : IsUpperSet s) : ⊤ ∉ s ↔ s = ∅ :=
   hs.top_mem.Not.trans not_nonempty_iff_eq_empty
 #align is_upper_set.not_top_mem IsUpperSet.not_top_mem
@@ -557,32 +335,14 @@ section OrderBot
 
 variable [OrderBot α]
 
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-Case conversion may be inaccurate. Consider using '#align is_upper_set.bot_mem IsUpperSet.bot_memₓ'. -/
 theorem IsUpperSet.bot_mem (hs : IsUpperSet s) : ⊥ ∈ s ↔ s = univ :=
   ⟨fun h => eq_univ_of_forall fun a => hs bot_le h, fun h => h.symm ▸ mem_univ _⟩
 #align is_upper_set.bot_mem IsUpperSet.bot_mem
 
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 theorem IsLowerSet.bot_mem (hs : IsLowerSet s) : ⊥ ∈ s ↔ s.Nonempty :=
   ⟨fun h => ⟨_, h⟩, fun ⟨a, ha⟩ => hs bot_le ha⟩
 #align is_lower_set.bot_mem IsLowerSet.bot_mem
 
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 theorem IsLowerSet.not_bot_mem (hs : IsLowerSet s) : ⊥ ∉ s ↔ s = ∅ :=
   hs.bot_mem.Not.trans not_nonempty_iff_eq_empty
 #align is_lower_set.not_bot_mem IsLowerSet.not_bot_mem
@@ -593,12 +353,6 @@ section NoMaxOrder
 
 variable [NoMaxOrder α] (a)
 
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-Case conversion may be inaccurate. Consider using '#align is_upper_set.not_bdd_above IsUpperSet.not_bddAboveₓ'. -/
 theorem IsUpperSet.not_bddAbove (hs : IsUpperSet s) : s.Nonempty → ¬BddAbove s :=
   by
   rintro ⟨a, ha⟩ ⟨b, hb⟩
@@ -606,22 +360,10 @@ theorem IsUpperSet.not_bddAbove (hs : IsUpperSet s) : s.Nonempty → ¬BddAbove
   exact hc.not_le (hb <| hs ((hb ha).trans hc.le) ha)
 #align is_upper_set.not_bdd_above IsUpperSet.not_bddAbove
 
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-Case conversion may be inaccurate. Consider using '#align not_bdd_above_Ici not_bddAbove_Iciₓ'. -/
 theorem not_bddAbove_Ici : ¬BddAbove (Ici a) :=
   (isUpperSet_Ici _).not_bddAbove nonempty_Ici
 #align not_bdd_above_Ici not_bddAbove_Ici
 
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-Case conversion may be inaccurate. Consider using '#align not_bdd_above_Ioi not_bddAbove_Ioiₓ'. -/
 theorem not_bddAbove_Ioi : ¬BddAbove (Ioi a) :=
   (isUpperSet_Ioi _).not_bddAbove nonempty_Ioi
 #align not_bdd_above_Ioi not_bddAbove_Ioi
@@ -632,12 +374,6 @@ section NoMinOrder
 
 variable [NoMinOrder α] (a)
 
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-Case conversion may be inaccurate. Consider using '#align is_lower_set.not_bdd_below IsLowerSet.not_bddBelowₓ'. -/
 theorem IsLowerSet.not_bddBelow (hs : IsLowerSet s) : s.Nonempty → ¬BddBelow s :=
   by
   rintro ⟨a, ha⟩ ⟨b, hb⟩
@@ -645,22 +381,10 @@ theorem IsLowerSet.not_bddBelow (hs : IsLowerSet s) : s.Nonempty → ¬BddBelow
   exact hc.not_le (hb <| hs (hc.le.trans <| hb ha) ha)
 #align is_lower_set.not_bdd_below IsLowerSet.not_bddBelow
 
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-Case conversion may be inaccurate. Consider using '#align not_bdd_below_Iic not_bddBelow_Iicₓ'. -/
 theorem not_bddBelow_Iic : ¬BddBelow (Iic a) :=
   (isLowerSet_Iic _).not_bddBelow nonempty_Iic
 #align not_bdd_below_Iic not_bddBelow_Iic
 
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 theorem not_bddBelow_Iio : ¬BddBelow (Iio a) :=
   (isLowerSet_Iio _).not_bddBelow nonempty_Iio
 #align not_bdd_below_Iio not_bddBelow_Iio
@@ -673,61 +397,25 @@ section PartialOrder
 
 variable [PartialOrder α] {s : Set α}
 
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-Case conversion may be inaccurate. Consider using '#align is_upper_set_iff_forall_lt isUpperSet_iff_forall_ltₓ'. -/
 theorem isUpperSet_iff_forall_lt : IsUpperSet s ↔ ∀ ⦃a b : α⦄, a < b → a ∈ s → b ∈ s :=
   forall_congr' fun a => by simp [le_iff_eq_or_lt, or_imp, forall_and]
 #align is_upper_set_iff_forall_lt isUpperSet_iff_forall_lt
 
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 theorem isLowerSet_iff_forall_lt : IsLowerSet s ↔ ∀ ⦃a b : α⦄, b < a → a ∈ s → b ∈ s :=
   forall_congr' fun a => by simp [le_iff_eq_or_lt, or_imp, forall_and]
 #align is_lower_set_iff_forall_lt isLowerSet_iff_forall_lt
 
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 theorem isUpperSet_iff_Ioi_subset : IsUpperSet s ↔ ∀ ⦃a⦄, a ∈ s → Ioi a ⊆ s := by
   simp [isUpperSet_iff_forall_lt, subset_def, @forall_swap (_ ∈ s)]
 #align is_upper_set_iff_Ioi_subset isUpperSet_iff_Ioi_subset
 
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 theorem isLowerSet_iff_Iio_subset : IsLowerSet s ↔ ∀ ⦃a⦄, a ∈ s → Iio a ⊆ s := by
   simp [isLowerSet_iff_forall_lt, subset_def, @forall_swap (_ ∈ s)]
 #align is_lower_set_iff_Iio_subset isLowerSet_iff_Iio_subset
 
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 alias isUpperSet_iff_Ioi_subset ↔ IsUpperSet.Ioi_subset _
 #align is_upper_set.Ioi_subset IsUpperSet.Ioi_subset
 
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 alias isLowerSet_iff_Iio_subset ↔ IsLowerSet.Iio_subset _
 #align is_lower_set.Iio_subset IsLowerSet.Iio_subset
 
@@ -858,12 +546,6 @@ instance : CompleteDistribLattice (UpperSet α) :=
 instance : Inhabited (UpperSet α) :=
   ⟨⊥⟩
 
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 @[simp, norm_cast]
 theorem coe_subset_coe : (s : Set α) ⊆ t ↔ t ≤ s :=
   Iff.rfl
@@ -895,76 +577,34 @@ theorem coe_eq_empty : (s : Set α) = ∅ ↔ s = ⊤ := by simp [SetLike.ext'_i
 #align upper_set.coe_eq_empty UpperSet.coe_eq_empty
 -/
 
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 @[simp, norm_cast]
 theorem coe_sup (s t : UpperSet α) : (↑(s ⊔ t) : Set α) = s ∩ t :=
   rfl
 #align upper_set.coe_sup UpperSet.coe_sup
 
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 @[simp, norm_cast]
 theorem coe_inf (s t : UpperSet α) : (↑(s ⊓ t) : Set α) = s ∪ t :=
   rfl
 #align upper_set.coe_inf UpperSet.coe_inf
 
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 @[simp, norm_cast]
 theorem coe_sSup (S : Set (UpperSet α)) : (↑(sSup S) : Set α) = ⋂ s ∈ S, ↑s :=
   rfl
 #align upper_set.coe_Sup UpperSet.coe_sSup
 
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 @[simp, norm_cast]
 theorem coe_sInf (S : Set (UpperSet α)) : (↑(sInf S) : Set α) = ⋃ s ∈ S, ↑s :=
   rfl
 #align upper_set.coe_Inf UpperSet.coe_sInf
 
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 @[simp, norm_cast]
 theorem coe_iSup (f : ι → UpperSet α) : (↑(⨆ i, f i) : Set α) = ⋂ i, f i := by simp [iSup]
 #align upper_set.coe_supr UpperSet.coe_iSup
 
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 @[simp, norm_cast]
 theorem coe_iInf (f : ι → UpperSet α) : (↑(⨅ i, f i) : Set α) = ⋃ i, f i := by simp [iInf]
 #align upper_set.coe_infi UpperSet.coe_iInf
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp, norm_cast]
@@ -972,12 +612,6 @@ theorem coe_iSup₂ (f : ∀ i, κ i → UpperSet α) : (↑(⨆ (i) (j), f i j)
   by simp_rw [coe_supr]
 #align upper_set.coe_supr₂ UpperSet.coe_iSup₂
 
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-Case conversion may be inaccurate. Consider using '#align upper_set.coe_infi₂ UpperSet.coe_iInf₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp, norm_cast]
@@ -999,102 +633,48 @@ theorem mem_bot : a ∈ (⊥ : UpperSet α) :=
 #align upper_set.mem_bot UpperSet.mem_bot
 -/
 
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-Case conversion may be inaccurate. Consider using '#align upper_set.mem_sup_iff UpperSet.mem_sup_iffₓ'. -/
 @[simp]
 theorem mem_sup_iff : a ∈ s ⊔ t ↔ a ∈ s ∧ a ∈ t :=
   Iff.rfl
 #align upper_set.mem_sup_iff UpperSet.mem_sup_iff
 
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-Case conversion may be inaccurate. Consider using '#align upper_set.mem_inf_iff UpperSet.mem_inf_iffₓ'. -/
 @[simp]
 theorem mem_inf_iff : a ∈ s ⊓ t ↔ a ∈ s ∨ a ∈ t :=
   Iff.rfl
 #align upper_set.mem_inf_iff UpperSet.mem_inf_iff
 
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 @[simp]
 theorem mem_sSup_iff : a ∈ sSup S ↔ ∀ s ∈ S, a ∈ s :=
   mem_iInter₂
 #align upper_set.mem_Sup_iff UpperSet.mem_sSup_iff
 
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-Case conversion may be inaccurate. Consider using '#align upper_set.mem_Inf_iff UpperSet.mem_sInf_iffₓ'. -/
 @[simp]
 theorem mem_sInf_iff : a ∈ sInf S ↔ ∃ s ∈ S, a ∈ s :=
   mem_iUnion₂
 #align upper_set.mem_Inf_iff UpperSet.mem_sInf_iff
 
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 @[simp]
 theorem mem_iSup_iff {f : ι → UpperSet α} : (a ∈ ⨆ i, f i) ↔ ∀ i, a ∈ f i := by
   rw [← SetLike.mem_coe, coe_supr]; exact mem_Inter
 #align upper_set.mem_supr_iff UpperSet.mem_iSup_iff
 
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 @[simp]
 theorem mem_iInf_iff {f : ι → UpperSet α} : (a ∈ ⨅ i, f i) ↔ ∃ i, a ∈ f i := by
   rw [← SetLike.mem_coe, coe_infi]; exact mem_Union
 #align upper_set.mem_infi_iff UpperSet.mem_iInf_iff
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
 theorem mem_iSup₂_iff {f : ∀ i, κ i → UpperSet α} : (a ∈ ⨆ (i) (j), f i j) ↔ ∀ i j, a ∈ f i j := by
   simp_rw [mem_supr_iff]
 #align upper_set.mem_supr₂_iff UpperSet.mem_iSup₂_iff
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
 theorem mem_iInf₂_iff {f : ∀ i, κ i → UpperSet α} : (a ∈ ⨅ (i) (j), f i j) ↔ ∃ i j, a ∈ f i j := by
   simp_rw [mem_infi_iff]
 #align upper_set.mem_infi₂_iff UpperSet.mem_iInf₂_iff
 
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 @[simp, norm_cast]
 theorem codisjoint_coe : Codisjoint (s : Set α) t ↔ Disjoint s t := by
   simp [disjoint_iff, codisjoint_iff, SetLike.ext'_iff]
@@ -1131,12 +711,6 @@ instance : CompleteDistribLattice (LowerSet α) :=
 instance : Inhabited (LowerSet α) :=
   ⟨⊥⟩
 
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 @[simp, norm_cast]
 theorem coe_subset_coe : (s : Set α) ⊆ t ↔ s ≤ t :=
   Iff.rfl
@@ -1168,78 +742,36 @@ theorem coe_eq_empty : (s : Set α) = ∅ ↔ s = ⊥ := by simp [SetLike.ext'_i
 #align lower_set.coe_eq_empty LowerSet.coe_eq_empty
 -/
 
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 @[simp, norm_cast]
 theorem coe_sup (s t : LowerSet α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
   rfl
 #align lower_set.coe_sup LowerSet.coe_sup
 
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 @[simp, norm_cast]
 theorem coe_inf (s t : LowerSet α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
   rfl
 #align lower_set.coe_inf LowerSet.coe_inf
 
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 @[simp, norm_cast]
 theorem coe_sSup (S : Set (LowerSet α)) : (↑(sSup S) : Set α) = ⋃ s ∈ S, ↑s :=
   rfl
 #align lower_set.coe_Sup LowerSet.coe_sSup
 
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 @[simp, norm_cast]
 theorem coe_sInf (S : Set (LowerSet α)) : (↑(sInf S) : Set α) = ⋂ s ∈ S, ↑s :=
   rfl
 #align lower_set.coe_Inf LowerSet.coe_sInf
 
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 @[simp, norm_cast]
 theorem coe_iSup (f : ι → LowerSet α) : (↑(⨆ i, f i) : Set α) = ⋃ i, f i := by
   simp_rw [iSup, coe_Sup, mem_range, Union_exists, Union_Union_eq']
 #align lower_set.coe_supr LowerSet.coe_iSup
 
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 @[simp, norm_cast]
 theorem coe_iInf (f : ι → LowerSet α) : (↑(⨅ i, f i) : Set α) = ⋂ i, f i := by
   simp_rw [iInf, coe_Inf, mem_range, Inter_exists, Inter_Inter_eq']
 #align lower_set.coe_infi LowerSet.coe_iInf
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp, norm_cast]
@@ -1247,12 +779,6 @@ theorem coe_iSup₂ (f : ∀ i, κ i → LowerSet α) : (↑(⨆ (i) (j), f i j)
   by simp_rw [coe_supr]
 #align lower_set.coe_supr₂ LowerSet.coe_iSup₂
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp, norm_cast]
@@ -1274,102 +800,48 @@ theorem not_mem_bot : a ∉ (⊥ : LowerSet α) :=
 #align lower_set.not_mem_bot LowerSet.not_mem_bot
 -/
 
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 @[simp]
 theorem mem_sup_iff : a ∈ s ⊔ t ↔ a ∈ s ∨ a ∈ t :=
   Iff.rfl
 #align lower_set.mem_sup_iff LowerSet.mem_sup_iff
 
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 @[simp]
 theorem mem_inf_iff : a ∈ s ⊓ t ↔ a ∈ s ∧ a ∈ t :=
   Iff.rfl
 #align lower_set.mem_inf_iff LowerSet.mem_inf_iff
 
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 @[simp]
 theorem mem_sSup_iff : a ∈ sSup S ↔ ∃ s ∈ S, a ∈ s :=
   mem_iUnion₂
 #align lower_set.mem_Sup_iff LowerSet.mem_sSup_iff
 
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 @[simp]
 theorem mem_sInf_iff : a ∈ sInf S ↔ ∀ s ∈ S, a ∈ s :=
   mem_iInter₂
 #align lower_set.mem_Inf_iff LowerSet.mem_sInf_iff
 
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 @[simp]
 theorem mem_iSup_iff {f : ι → LowerSet α} : (a ∈ ⨆ i, f i) ↔ ∃ i, a ∈ f i := by
   rw [← SetLike.mem_coe, coe_supr]; exact mem_Union
 #align lower_set.mem_supr_iff LowerSet.mem_iSup_iff
 
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 @[simp]
 theorem mem_iInf_iff {f : ι → LowerSet α} : (a ∈ ⨅ i, f i) ↔ ∀ i, a ∈ f i := by
   rw [← SetLike.mem_coe, coe_infi]; exact mem_Inter
 #align lower_set.mem_infi_iff LowerSet.mem_iInf_iff
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
 theorem mem_iSup₂_iff {f : ∀ i, κ i → LowerSet α} : (a ∈ ⨆ (i) (j), f i j) ↔ ∃ i j, a ∈ f i j := by
   simp_rw [mem_supr_iff]
 #align lower_set.mem_supr₂_iff LowerSet.mem_iSup₂_iff
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
 theorem mem_iInf₂_iff {f : ∀ i, κ i → LowerSet α} : (a ∈ ⨅ (i) (j), f i j) ↔ ∀ i j, a ∈ f i j := by
   simp_rw [mem_infi_iff]
 #align lower_set.mem_infi₂_iff LowerSet.mem_iInf₂_iff
 
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 @[simp, norm_cast]
 theorem disjoint_coe : Disjoint (s : Set α) t ↔ Disjoint s t := by
   simp [disjoint_iff, SetLike.ext'_iff]
@@ -1398,12 +870,6 @@ namespace UpperSet
 
 variable {s t : UpperSet α} {a : α}
 
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 @[simp]
 theorem coe_compl (s : UpperSet α) : (s.compl : Set α) = sᶜ :=
   rfl
@@ -1423,34 +889,16 @@ theorem compl_compl (s : UpperSet α) : s.compl.compl = s :=
 #align upper_set.compl_compl UpperSet.compl_compl
 -/
 
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 @[simp]
 theorem compl_le_compl : s.compl ≤ t.compl ↔ s ≤ t :=
   compl_subset_compl
 #align upper_set.compl_le_compl UpperSet.compl_le_compl
 
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 @[simp]
 protected theorem compl_sup (s t : UpperSet α) : (s ⊔ t).compl = s.compl ⊔ t.compl :=
   LowerSet.ext compl_inf
 #align upper_set.compl_sup UpperSet.compl_sup
 
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 @[simp]
 protected theorem compl_inf (s t : UpperSet α) : (s ⊓ t).compl = s.compl ⊓ t.compl :=
   LowerSet.ext compl_sup
@@ -1470,56 +918,26 @@ protected theorem compl_bot : (⊥ : UpperSet α).compl = ⊥ :=
 #align upper_set.compl_bot UpperSet.compl_bot
 -/
 
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 @[simp]
 protected theorem compl_sSup (S : Set (UpperSet α)) : (sSup S).compl = ⨆ s ∈ S, UpperSet.compl s :=
   LowerSet.ext <| by simp only [coe_compl, coe_Sup, compl_Inter₂, LowerSet.coe_iSup₂]
 #align upper_set.compl_Sup UpperSet.compl_sSup
 
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 @[simp]
 protected theorem compl_sInf (S : Set (UpperSet α)) : (sInf S).compl = ⨅ s ∈ S, UpperSet.compl s :=
   LowerSet.ext <| by simp only [coe_compl, coe_Inf, compl_Union₂, LowerSet.coe_iInf₂]
 #align upper_set.compl_Inf UpperSet.compl_sInf
 
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 @[simp]
 protected theorem compl_iSup (f : ι → UpperSet α) : (⨆ i, f i).compl = ⨆ i, (f i).compl :=
   LowerSet.ext <| by simp only [coe_compl, coe_supr, compl_Inter, LowerSet.coe_iSup]
 #align upper_set.compl_supr UpperSet.compl_iSup
 
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 @[simp]
 protected theorem compl_iInf (f : ι → UpperSet α) : (⨅ i, f i).compl = ⨅ i, (f i).compl :=
   LowerSet.ext <| by simp only [coe_compl, coe_infi, compl_Union, LowerSet.coe_iInf]
 #align upper_set.compl_infi UpperSet.compl_iInf
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
@@ -1527,12 +945,6 @@ theorem compl_iSup₂ (f : ∀ i, κ i → UpperSet α) :
     (⨆ (i) (j), f i j).compl = ⨆ (i) (j), (f i j).compl := by simp_rw [UpperSet.compl_iSup]
 #align upper_set.compl_supr₂ UpperSet.compl_iSup₂
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
@@ -1546,12 +958,6 @@ namespace LowerSet
 
 variable {s t : LowerSet α} {a : α}
 
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 @[simp]
 theorem coe_compl (s : LowerSet α) : (s.compl : Set α) = sᶜ :=
   rfl
@@ -1571,33 +977,15 @@ theorem compl_compl (s : LowerSet α) : s.compl.compl = s :=
 #align lower_set.compl_compl LowerSet.compl_compl
 -/
 
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 @[simp]
 theorem compl_le_compl : s.compl ≤ t.compl ↔ s ≤ t :=
   compl_subset_compl
 #align lower_set.compl_le_compl LowerSet.compl_le_compl
 
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 protected theorem compl_sup (s t : LowerSet α) : (s ⊔ t).compl = s.compl ⊔ t.compl :=
   UpperSet.ext compl_sup
 #align lower_set.compl_sup LowerSet.compl_sup
 
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 protected theorem compl_inf (s t : LowerSet α) : (s ⊓ t).compl = s.compl ⊓ t.compl :=
   UpperSet.ext compl_inf
 #align lower_set.compl_inf LowerSet.compl_inf
@@ -1626,32 +1014,14 @@ protected theorem compl_sInf (S : Set (LowerSet α)) : (sInf S).compl = ⨅ s 
 #align lower_set.compl_Inf LowerSet.compl_sInf
 -/
 
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 protected theorem compl_iSup (f : ι → LowerSet α) : (⨆ i, f i).compl = ⨆ i, (f i).compl :=
   UpperSet.ext <| by simp only [coe_compl, coe_supr, compl_Union, UpperSet.coe_iSup]
 #align lower_set.compl_supr LowerSet.compl_iSup
 
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 protected theorem compl_iInf (f : ι → LowerSet α) : (⨅ i, f i).compl = ⨅ i, (f i).compl :=
   UpperSet.ext <| by simp only [coe_compl, coe_infi, compl_Inter, UpperSet.coe_iInf]
 #align lower_set.compl_infi LowerSet.compl_iInf
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
@@ -1659,12 +1029,6 @@ theorem compl_iSup₂ (f : ∀ i, κ i → LowerSet α) :
     (⨆ (i) (j), f i j).compl = ⨆ (i) (j), (f i j).compl := by simp_rw [LowerSet.compl_iSup]
 #align lower_set.compl_supr₂ LowerSet.compl_iSup₂
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
@@ -1674,12 +1038,6 @@ theorem compl_iInf₂ (f : ∀ i, κ i → LowerSet α) :
 
 end LowerSet
 
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 /-- Upper sets are order-isomorphic to lower sets under complementation. -/
 @[simps]
 def upperSetIsoLowerSet : UpperSet α ≃o LowerSet α
@@ -1704,12 +1062,6 @@ namespace UpperSet
 
 variable {f : α ≃o β} {s t : UpperSet α} {a : α} {b : β}
 
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 /-- An order isomorphism of preorders induces an order isomorphism of their upper sets. -/
 def map (f : α ≃o β) : UpperSet α ≃o UpperSet β
     where
@@ -1720,46 +1072,25 @@ def map (f : α ≃o β) : UpperSet α ≃o UpperSet β
   map_rel_iff' s t := image_subset_image_iff f.Injective
 #align upper_set.map UpperSet.map
 
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 @[simp]
 theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
   FunLike.ext _ _ fun s => ext <| Set.preimage_equiv_eq_image_symm _ _
 #align upper_set.symm_map UpperSet.symm_map
 
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 @[simp]
 theorem mem_map : b ∈ map f s ↔ f.symm b ∈ s := by rw [← f.symm_symm, ← symm_map, f.symm_symm]; rfl
 #align upper_set.mem_map UpperSet.mem_map
 
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 @[simp]
 theorem map_refl : map (OrderIso.refl α) = OrderIso.refl _ := by ext; simp
 #align upper_set.map_refl UpperSet.map_refl
 
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 @[simp]
 theorem map_map (g : β ≃o γ) (f : α ≃o β) : map g (map f s) = map (f.trans g) s := by ext; simp
 #align upper_set.map_map UpperSet.map_map
 
 variable (f s t)
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align upper_set.coe_map UpperSet.coe_mapₓ'. -/
 @[simp, norm_cast]
 theorem coe_map : (map f s : Set β) = f '' s :=
   rfl
@@ -1771,12 +1102,6 @@ namespace LowerSet
 
 variable {f : α ≃o β} {s t : LowerSet α} {a : α} {b : β}
 
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 /-- An order isomorphism of preorders induces an order isomorphism of their lower sets. -/
 def map (f : α ≃o β) : LowerSet α ≃o LowerSet β
     where
@@ -1787,47 +1112,26 @@ def map (f : α ≃o β) : LowerSet α ≃o LowerSet β
   map_rel_iff' s t := image_subset_image_iff f.Injective
 #align lower_set.map LowerSet.map
 
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 @[simp]
 theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
   FunLike.ext _ _ fun s => SetLike.coe_injective <| Set.preimage_equiv_eq_image_symm _ _
 #align lower_set.symm_map LowerSet.symm_map
 
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 @[simp]
 theorem mem_map {f : α ≃o β} {b : β} : b ∈ map f s ↔ f.symm b ∈ s := by
   rw [← f.symm_symm, ← symm_map, f.symm_symm]; rfl
 #align lower_set.mem_map LowerSet.mem_map
 
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 @[simp]
 theorem map_refl : map (OrderIso.refl α) = OrderIso.refl _ := by ext; simp
 #align lower_set.map_refl LowerSet.map_refl
 
-/- warning: lower_set.map_map -> LowerSet.map_map is a dubious translation:
-<too large>
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 @[simp]
 theorem map_map (g : β ≃o γ) (f : α ≃o β) : map g (map f s) = map (f.trans g) s := by ext; simp
 #align lower_set.map_map LowerSet.map_map
 
 variable (f s t)
 
-/- warning: lower_set.coe_map -> LowerSet.coe_map is a dubious translation:
-<too large>
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 @[simp, norm_cast]
 theorem coe_map : (map f s : Set β) = f '' s :=
   rfl
@@ -1837,9 +1141,6 @@ end LowerSet
 
 namespace UpperSet
 
-/- warning: upper_set.compl_map -> UpperSet.compl_map is a dubious translation:
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 @[simp]
 theorem compl_map (f : α ≃o β) (s : UpperSet α) : (map f s).compl = LowerSet.map f s.compl :=
   SetLike.coe_injective (Set.image_compl_eq f.Bijective).symm
@@ -1849,9 +1150,6 @@ end UpperSet
 
 namespace LowerSet
 
-/- warning: lower_set.compl_map -> LowerSet.compl_map is a dubious translation:
-<too large>
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 @[simp]
 theorem compl_map (f : α ≃o β) (s : LowerSet α) : (map f s).compl = UpperSet.map f s.compl :=
   SetLike.coe_injective (Set.image_compl_eq f.Bijective).symm
@@ -1870,23 +1168,11 @@ section Preorder
 
 variable [Preorder α] [Preorder β] {s : UpperSet α} {a b : α}
 
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 /-- The smallest upper set containing a given element. -/
 def Ici (a : α) : UpperSet α :=
   ⟨Ici a, isUpperSet_Ici a⟩
 #align upper_set.Ici UpperSet.Ici
 
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 /-- The smallest upper set containing a given element. -/
 def Ioi (a : α) : UpperSet α :=
   ⟨Ioi a, isUpperSet_Ioi a⟩
@@ -1906,69 +1192,33 @@ theorem coe_Ioi (a : α) : ↑(Ioi a) = Set.Ioi a :=
 #align upper_set.coe_Ioi UpperSet.coe_Ioi
 -/
 
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 @[simp]
 theorem mem_Ici_iff : b ∈ Ici a ↔ a ≤ b :=
   Iff.rfl
 #align upper_set.mem_Ici_iff UpperSet.mem_Ici_iff
 
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 @[simp]
 theorem mem_Ioi_iff : b ∈ Ioi a ↔ a < b :=
   Iff.rfl
 #align upper_set.mem_Ioi_iff UpperSet.mem_Ioi_iff
 
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 @[simp]
 theorem map_Ici (f : α ≃o β) (a : α) : map f (Ici a) = Ici (f a) := by ext; simp
 #align upper_set.map_Ici UpperSet.map_Ici
 
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 @[simp]
 theorem map_Ioi (f : α ≃o β) (a : α) : map f (Ioi a) = Ioi (f a) := by ext; simp
 #align upper_set.map_Ioi UpperSet.map_Ioi
 
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 theorem Ici_le_Ioi (a : α) : Ici a ≤ Ioi a :=
   Ioi_subset_Ici_self
 #align upper_set.Ici_le_Ioi UpperSet.Ici_le_Ioi
 
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 @[simp]
 theorem Ioi_top [OrderTop α] : Ioi (⊤ : α) = ⊤ :=
   SetLike.coe_injective Ioi_top
 #align upper_set.Ioi_top UpperSet.Ioi_top
 
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 @[simp]
 theorem Ici_bot [OrderBot α] : Ici (⊥ : α) = ⊥ :=
   SetLike.coe_injective Ici_bot
@@ -1976,12 +1226,6 @@ theorem Ici_bot [OrderBot α] : Ici (⊥ : α) = ⊥ :=
 
 end Preorder
 
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 @[simp]
 theorem Ici_sup [SemilatticeSup α] (a b : α) : Ici (a ⊔ b) = Ici a ⊔ Ici b :=
   ext Ici_inter_Ici.symm
@@ -1991,34 +1235,16 @@ section CompleteLattice
 
 variable [CompleteLattice α]
 
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 @[simp]
 theorem Ici_sSup (S : Set α) : Ici (sSup S) = ⨆ a ∈ S, Ici a :=
   SetLike.ext fun c => by simp only [mem_Ici_iff, mem_supr_iff, sSup_le_iff]
 #align upper_set.Ici_Sup UpperSet.Ici_sSup
 
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 @[simp]
 theorem Ici_iSup (f : ι → α) : Ici (⨆ i, f i) = ⨆ i, Ici (f i) :=
   SetLike.ext fun c => by simp only [mem_Ici_iff, mem_supr_iff, iSup_le_iff]
 #align upper_set.Ici_supr UpperSet.Ici_iSup
 
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-Case conversion may be inaccurate. Consider using '#align upper_set.Ici_supr₂ UpperSet.Ici_iSup₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
@@ -2036,24 +1262,12 @@ section Preorder
 
 variable [Preorder α] [Preorder β] {s : LowerSet α} {a b : α}
 
-/- warning: lower_set.Iic -> LowerSet.Iic is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align lower_set.Iic LowerSet.Iicₓ'. -/
 /-- Principal lower set. `set.Iic` as a lower set. The smallest lower set containing a given
 element. -/
 def Iic (a : α) : LowerSet α :=
   ⟨Iic a, isLowerSet_Iic a⟩
 #align lower_set.Iic LowerSet.Iic
 
-/- warning: lower_set.Iio -> LowerSet.Iio is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align lower_set.Iio LowerSet.Iioₓ'. -/
 /-- Strict principal lower set. `set.Iio` as a lower set. -/
 def Iio (a : α) : LowerSet α :=
   ⟨Iio a, isLowerSet_Iio a⟩
@@ -2073,38 +1287,20 @@ theorem coe_Iio (a : α) : ↑(Iio a) = Set.Iio a :=
 #align lower_set.coe_Iio LowerSet.coe_Iio
 -/
 
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-Case conversion may be inaccurate. Consider using '#align lower_set.mem_Iic_iff LowerSet.mem_Iic_iffₓ'. -/
 @[simp]
 theorem mem_Iic_iff : b ∈ Iic a ↔ b ≤ a :=
   Iff.rfl
 #align lower_set.mem_Iic_iff LowerSet.mem_Iic_iff
 
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-Case conversion may be inaccurate. Consider using '#align lower_set.mem_Iio_iff LowerSet.mem_Iio_iffₓ'. -/
 @[simp]
 theorem mem_Iio_iff : b ∈ Iio a ↔ b < a :=
   Iff.rfl
 #align lower_set.mem_Iio_iff LowerSet.mem_Iio_iff
 
-/- warning: lower_set.map_Iic -> LowerSet.map_Iic is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lower_set.map_Iic LowerSet.map_Iicₓ'. -/
 @[simp]
 theorem map_Iic (f : α ≃o β) (a : α) : map f (Iic a) = Iic (f a) := by ext; simp
 #align lower_set.map_Iic LowerSet.map_Iic
 
-/- warning: lower_set.map_Iio -> LowerSet.map_Iio is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lower_set.map_Iio LowerSet.map_Iioₓ'. -/
 @[simp]
 theorem map_Iio (f : α ≃o β) (a : α) : map f (Iio a) = Iio (f a) := by ext; simp
 #align lower_set.map_Iio LowerSet.map_Iio
@@ -2115,23 +1311,11 @@ theorem Ioi_le_Ici (a : α) : Ioi a ≤ Ici a :=
 #align lower_set.Ioi_le_Ici LowerSet.Ioi_le_Ici
 -/
 
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-Case conversion may be inaccurate. Consider using '#align lower_set.Iic_top LowerSet.Iic_topₓ'. -/
 @[simp]
 theorem Iic_top [OrderTop α] : Iic (⊤ : α) = ⊤ :=
   SetLike.coe_injective Iic_top
 #align lower_set.Iic_top LowerSet.Iic_top
 
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-Case conversion may be inaccurate. Consider using '#align lower_set.Iio_bot LowerSet.Iio_botₓ'. -/
 @[simp]
 theorem Iio_bot [OrderBot α] : Iio (⊥ : α) = ⊥ :=
   SetLike.coe_injective Iio_bot
@@ -2139,12 +1323,6 @@ theorem Iio_bot [OrderBot α] : Iio (⊥ : α) = ⊥ :=
 
 end Preorder
 
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-Case conversion may be inaccurate. Consider using '#align lower_set.Iic_inf LowerSet.Iic_infₓ'. -/
 @[simp]
 theorem Iic_inf [SemilatticeInf α] (a b : α) : Iic (a ⊓ b) = Iic a ⊓ Iic b :=
   SetLike.coe_injective Iic_inter_Iic.symm
@@ -2154,34 +1332,16 @@ section CompleteLattice
 
 variable [CompleteLattice α]
 
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-Case conversion may be inaccurate. Consider using '#align lower_set.Iic_Inf LowerSet.Iic_sInfₓ'. -/
 @[simp]
 theorem Iic_sInf (S : Set α) : Iic (sInf S) = ⨅ a ∈ S, Iic a :=
   SetLike.ext fun c => by simp only [mem_Iic_iff, mem_infi₂_iff, le_sInf_iff]
 #align lower_set.Iic_Inf LowerSet.Iic_sInf
 
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 @[simp]
 theorem Iic_iInf (f : ι → α) : Iic (⨅ i, f i) = ⨅ i, Iic (f i) :=
   SetLike.ext fun c => by simp only [mem_Iic_iff, mem_infi_iff, le_iInf_iff]
 #align lower_set.Iic_infi LowerSet.Iic_iInf
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
@@ -2197,45 +1357,21 @@ section closure
 
 variable [Preorder α] [Preorder β] {s t : Set α} {x : α}
 
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-Case conversion may be inaccurate. Consider using '#align upper_closure upperClosureₓ'. -/
 /-- The greatest upper set containing a given set. -/
 def upperClosure (s : Set α) : UpperSet α :=
   ⟨{ x | ∃ a ∈ s, a ≤ x }, fun x y h => Exists₂.imp fun a _ => h.trans'⟩
 #align upper_closure upperClosure
 
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-Case conversion may be inaccurate. Consider using '#align lower_closure lowerClosureₓ'. -/
 /-- The least lower set containing a given set. -/
 def lowerClosure (s : Set α) : LowerSet α :=
   ⟨{ x | ∃ a ∈ s, x ≤ a }, fun x y h => Exists₂.imp fun a _ => h.trans⟩
 #align lower_closure lowerClosure
 
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 @[simp]
 theorem mem_upperClosure : x ∈ upperClosure s ↔ ∃ a ∈ s, a ≤ x :=
   Iff.rfl
 #align mem_upper_closure mem_upperClosure
 
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 @[simp]
 theorem mem_lowerClosure : x ∈ lowerClosure s ↔ ∃ a ∈ s, x ≤ a :=
   Iff.rfl
@@ -2264,71 +1400,32 @@ theorem subset_lowerClosure : s ⊆ lowerClosure s := fun x hx => ⟨x, hx, le_r
 #align subset_lower_closure subset_lowerClosure
 -/
 
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 theorem upperClosure_min (h : s ⊆ t) (ht : IsUpperSet t) : ↑(upperClosure s) ⊆ t :=
   fun a ⟨b, hb, hba⟩ => ht hba <| h hb
 #align upper_closure_min upperClosure_min
 
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 theorem lowerClosure_min (h : s ⊆ t) (ht : IsLowerSet t) : ↑(lowerClosure s) ⊆ t :=
   fun a ⟨b, hb, hab⟩ => ht hab <| h hb
 #align lower_closure_min lowerClosure_min
 
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 protected theorem IsUpperSet.upperClosure (hs : IsUpperSet s) : ↑(upperClosure s) = s :=
   (upperClosure_min Subset.rfl hs).antisymm subset_upperClosure
 #align is_upper_set.upper_closure IsUpperSet.upperClosure
 
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 protected theorem IsLowerSet.lowerClosure (hs : IsLowerSet s) : ↑(lowerClosure s) = s :=
   (lowerClosure_min Subset.rfl hs).antisymm subset_lowerClosure
 #align is_lower_set.lower_closure IsLowerSet.lowerClosure
 
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 @[simp]
 protected theorem UpperSet.upperClosure (s : UpperSet α) : upperClosure (s : Set α) = s :=
   SetLike.coe_injective s.2.upperClosure
 #align upper_set.upper_closure UpperSet.upperClosure
 
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 @[simp]
 protected theorem LowerSet.lowerClosure (s : LowerSet α) : lowerClosure (s : Set α) = s :=
   SetLike.coe_injective s.2.lowerClosure
 #align lower_set.lower_closure LowerSet.lowerClosure
 
-/- warning: upper_closure_image -> upperClosure_image is a dubious translation:
-<too large>
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 @[simp]
 theorem upperClosure_image (f : α ≃o β) : upperClosure (f '' s) = UpperSet.map f (upperClosure s) :=
   by
@@ -2337,9 +1434,6 @@ theorem upperClosure_image (f : α ≃o β) : upperClosure (f '' s) = UpperSet.m
   simp [-UpperSet.symm_map, UpperSet.map, OrderIso.symm, ← f.le_symm_apply]
 #align upper_closure_image upperClosure_image
 
-/- warning: lower_closure_image -> lowerClosure_image is a dubious translation:
-<too large>
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 @[simp]
 theorem lowerClosure_image (f : α ≃o β) : lowerClosure (f '' s) = LowerSet.map f (lowerClosure s) :=
   by
@@ -2348,22 +1442,10 @@ theorem lowerClosure_image (f : α ≃o β) : lowerClosure (f '' s) = LowerSet.m
   simp [-LowerSet.symm_map, LowerSet.map, OrderIso.symm, ← f.symm_apply_le]
 #align lower_closure_image lowerClosure_image
 
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 @[simp]
 theorem UpperSet.iInf_Ici (s : Set α) : (⨅ a ∈ s, UpperSet.Ici a) = upperClosure s := by ext; simp
 #align upper_set.infi_Ici UpperSet.iInf_Ici
 
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 @[simp]
 theorem LowerSet.iSup_Iic (s : Set α) : (⨆ a ∈ s, LowerSet.Iic a) = lowerClosure s := by ext; simp
 #align lower_set.supr_Iic LowerSet.iSup_Iic
@@ -2376,23 +1458,11 @@ theorem gc_upperClosure_coe :
 #align gc_upper_closure_coe gc_upperClosure_coe
 -/
 
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 theorem gc_lowerClosure_coe : GaloisConnection (lowerClosure : Set α → LowerSet α) coe := fun s t =>
   ⟨fun h => subset_lowerClosure.trans <| LowerSet.coe_subset_coe.2 h, fun h =>
     lowerClosure_min h t.lower⟩
 #align gc_lower_closure_coe gc_lowerClosure_coe
 
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 /-- `upper_closure` forms a reversed Galois insertion with the coercion from upper sets to sets. -/
 def giUpperClosureCoe :
     GaloisInsertion (toDual ∘ upperClosure : Set α → (UpperSet α)ᵒᵈ) (coe ∘ ofDual)
@@ -2403,12 +1473,6 @@ def giUpperClosureCoe :
   choice_eq s hs := ofDual.Injective <| SetLike.coe_injective <| subset_upperClosure.antisymm hs
 #align gi_upper_closure_coe giUpperClosureCoe
 
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 /-- `lower_closure` forms a Galois insertion with the coercion from lower sets to sets. -/
 def giLowerClosureCoe : GaloisInsertion (lowerClosure : Set α → LowerSet α) coe
     where
@@ -2418,196 +1482,88 @@ def giLowerClosureCoe : GaloisInsertion (lowerClosure : Set α → LowerSet α)
   choice_eq s hs := SetLike.coe_injective <| subset_lowerClosure.antisymm hs
 #align gi_lower_closure_coe giLowerClosureCoe
 
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 theorem upperClosure_anti : Antitone (upperClosure : Set α → UpperSet α) :=
   gc_upperClosure_coe.monotone_l
 #align upper_closure_anti upperClosure_anti
 
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 theorem lowerClosure_mono : Monotone (lowerClosure : Set α → LowerSet α) :=
   gc_lowerClosure_coe.monotone_l
 #align lower_closure_mono lowerClosure_mono
 
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 @[simp]
 theorem upperClosure_empty : upperClosure (∅ : Set α) = ⊤ := by ext; simp
 #align upper_closure_empty upperClosure_empty
 
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 @[simp]
 theorem lowerClosure_empty : lowerClosure (∅ : Set α) = ⊥ := by ext; simp
 #align lower_closure_empty lowerClosure_empty
 
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-Case conversion may be inaccurate. Consider using '#align upper_closure_singleton upperClosure_singletonₓ'. -/
 @[simp]
 theorem upperClosure_singleton (a : α) : upperClosure ({a} : Set α) = UpperSet.Ici a := by ext; simp
 #align upper_closure_singleton upperClosure_singleton
 
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 @[simp]
 theorem lowerClosure_singleton (a : α) : lowerClosure ({a} : Set α) = LowerSet.Iic a := by ext; simp
 #align lower_closure_singleton lowerClosure_singleton
 
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 @[simp]
 theorem upperClosure_univ : upperClosure (univ : Set α) = ⊥ :=
   le_bot_iff.1 subset_upperClosure
 #align upper_closure_univ upperClosure_univ
 
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 @[simp]
 theorem lowerClosure_univ : lowerClosure (univ : Set α) = ⊤ :=
   top_le_iff.1 subset_lowerClosure
 #align lower_closure_univ lowerClosure_univ
 
-/- warning: upper_closure_eq_top_iff -> upperClosure_eq_top_iff is a dubious translation:
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 @[simp]
 theorem upperClosure_eq_top_iff : upperClosure s = ⊤ ↔ s = ∅ :=
   ⟨fun h => subset_empty_iff.1 <| subset_upperClosure.trans (congr_arg coe h).Subset, by rintro rfl;
     exact upperClosure_empty⟩
 #align upper_closure_eq_top_iff upperClosure_eq_top_iff
 
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 @[simp]
 theorem lowerClosure_eq_bot_iff : lowerClosure s = ⊥ ↔ s = ∅ :=
   ⟨fun h => subset_empty_iff.1 <| subset_lowerClosure.trans (congr_arg coe h).Subset, by rintro rfl;
     exact lowerClosure_empty⟩
 #align lower_closure_eq_bot_iff lowerClosure_eq_bot_iff
 
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 @[simp]
 theorem upperClosure_union (s t : Set α) : upperClosure (s ∪ t) = upperClosure s ⊓ upperClosure t :=
   by ext; simp [or_and_right, exists_or]
 #align upper_closure_union upperClosure_union
 
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 @[simp]
 theorem lowerClosure_union (s t : Set α) : lowerClosure (s ∪ t) = lowerClosure s ⊔ lowerClosure t :=
   by ext; simp [or_and_right, exists_or]
 #align lower_closure_union lowerClosure_union
 
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 @[simp]
 theorem upperClosure_iUnion (f : ι → Set α) : upperClosure (⋃ i, f i) = ⨅ i, upperClosure (f i) :=
   by ext; simp [← exists_and_right, @exists_comm α]
 #align upper_closure_Union upperClosure_iUnion
 
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 @[simp]
 theorem lowerClosure_iUnion (f : ι → Set α) : lowerClosure (⋃ i, f i) = ⨆ i, lowerClosure (f i) :=
   by ext; simp [← exists_and_right, @exists_comm α]
 #align lower_closure_Union lowerClosure_iUnion
 
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 @[simp]
 theorem upperClosure_sUnion (S : Set (Set α)) : upperClosure (⋃₀ S) = ⨅ s ∈ S, upperClosure s := by
   simp_rw [sUnion_eq_bUnion, upperClosure_iUnion]
 #align upper_closure_sUnion upperClosure_sUnion
 
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 @[simp]
 theorem lowerClosure_sUnion (S : Set (Set α)) : lowerClosure (⋃₀ S) = ⨆ s ∈ S, lowerClosure s := by
   simp_rw [sUnion_eq_bUnion, lowerClosure_iUnion]
 #align lower_closure_sUnion lowerClosure_sUnion
 
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 theorem Set.OrdConnected.upperClosure_inter_lowerClosure (h : s.OrdConnected) :
     ↑(upperClosure s) ∩ ↑(lowerClosure s) = s :=
   (subset_inter subset_upperClosure subset_lowerClosure).antisymm'
     fun a ⟨⟨b, hb, hba⟩, c, hc, hac⟩ => h.out hb hc ⟨hba, hac⟩
 #align set.ord_connected.upper_closure_inter_lower_closure Set.OrdConnected.upperClosure_inter_lowerClosure
 
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 theorem ordConnected_iff_upperClosure_inter_lowerClosure :
     s.OrdConnected ↔ ↑(upperClosure s) ∩ ↑(lowerClosure s) = s :=
   by
@@ -2667,23 +1623,11 @@ section
 
 variable {s : Set α} {t : Set β} {x : α × β}
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem IsUpperSet.prod (hs : IsUpperSet s) (ht : IsUpperSet t) : IsUpperSet (s ×ˢ t) :=
   fun a b h ha => ⟨hs h.1 ha.1, ht h.2 ha.2⟩
 #align is_upper_set.prod IsUpperSet.prod
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem IsLowerSet.prod (hs : IsLowerSet s) (ht : IsLowerSet t) : IsLowerSet (s ×ˢ t) :=
   fun a b h ha => ⟨hs h.1 ha.1, ht h.2 ha.2⟩
@@ -2695,12 +1639,6 @@ namespace UpperSet
 
 variable (s s₁ s₂ : UpperSet α) (t t₁ t₂ : UpperSet β) {x : α × β}
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The product of two upper sets as an upper set. -/
 def prod : UpperSet (α × β) :=
@@ -2710,12 +1648,6 @@ def prod : UpperSet (α × β) :=
 -- mathport name: upper_set.prod
 infixr:82 " ×ˢ " => prod
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp, norm_cast]
@@ -2723,83 +1655,41 @@ theorem coe_prod : (↑(s ×ˢ t) : Set (α × β)) = s ×ˢ t :=
   rfl
 #align upper_set.coe_prod UpperSet.coe_prod
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
 theorem mem_prod {s : UpperSet α} {t : UpperSet β} : x ∈ s ×ˢ t ↔ x.1 ∈ s ∧ x.2 ∈ t :=
   Iff.rfl
 #align upper_set.mem_prod UpperSet.mem_prod
 
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 theorem Ici_prod (x : α × β) : Ici x = Ici x.1 ×ˢ Ici x.2 :=
   rfl
 #align upper_set.Ici_prod UpperSet.Ici_prod
 
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 @[simp]
 theorem Ici_prod_Ici (a : α) (b : β) : Ici a ×ˢ Ici b = Ici (a, b) :=
   rfl
 #align upper_set.Ici_prod_Ici UpperSet.Ici_prod_Ici
 
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 @[simp]
 theorem prod_top : s ×ˢ (⊤ : UpperSet β) = ⊤ :=
   ext prod_empty
 #align upper_set.prod_top UpperSet.prod_top
 
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 @[simp]
 theorem top_prod : (⊤ : UpperSet α) ×ˢ t = ⊤ :=
   ext empty_prod
 #align upper_set.top_prod UpperSet.top_prod
 
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 @[simp]
 theorem bot_prod_bot : (⊥ : UpperSet α) ×ˢ (⊥ : UpperSet β) = ⊥ :=
   ext univ_prod_univ
 #align upper_set.bot_prod_bot UpperSet.bot_prod_bot
 
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@@ -2808,12 +1698,6 @@ theorem sup_prod : (s₁ ⊔ s₂) ×ˢ t = s₁ ×ˢ t ⊔ s₂ ×ˢ t :=
   ext inter_prod
 #align upper_set.sup_prod UpperSet.sup_prod
 
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@@ -2822,12 +1706,6 @@ theorem prod_sup : s ×ˢ (t₁ ⊔ t₂) = s ×ˢ t₁ ⊔ s ×ˢ t₂ :=
   ext prod_inter
 #align upper_set.prod_sup UpperSet.prod_sup
 
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@@ -2836,12 +1714,6 @@ theorem inf_prod : (s₁ ⊓ s₂) ×ˢ t = s₁ ×ˢ t ⊓ s₂ ×ˢ t :=
   ext union_prod
 #align upper_set.inf_prod UpperSet.inf_prod
 
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@@ -2850,12 +1722,6 @@ theorem prod_inf : s ×ˢ (t₁ ⊓ t₂) = s ×ˢ t₁ ⊓ s ×ˢ t₂ :=
   ext prod_union
 #align upper_set.prod_inf UpperSet.prod_inf
 
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@@ -2865,48 +1731,24 @@ theorem prod_sup_prod : s₁ ×ˢ t₁ ⊔ s₂ ×ˢ t₂ = (s₁ ⊔ s₂) ×ˢ
 
 variable {s s₁ s₂ t t₁ t₂}
 
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 theorem prod_mono : s₁ ≤ s₂ → t₁ ≤ t₂ → s₁ ×ˢ t₁ ≤ s₂ ×ˢ t₂ :=
   prod_mono
 #align upper_set.prod_mono UpperSet.prod_mono
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem prod_mono_left : s₁ ≤ s₂ → s₁ ×ˢ t ≤ s₂ ×ˢ t :=
   prod_mono_left
 #align upper_set.prod_mono_left UpperSet.prod_mono_left
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem prod_mono_right : t₁ ≤ t₂ → s ×ˢ t₁ ≤ s ×ˢ t₂ :=
   prod_mono_right
 #align upper_set.prod_mono_right UpperSet.prod_mono_right
 
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-Case conversion may be inaccurate. Consider using '#align upper_set.prod_self_le_prod_self UpperSet.prod_self_le_prod_selfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
@@ -2914,12 +1756,6 @@ theorem prod_self_le_prod_self : s₁ ×ˢ s₁ ≤ s₂ ×ˢ s₂ ↔ s₁ ≤
   prod_self_subset_prod_self
 #align upper_set.prod_self_le_prod_self UpperSet.prod_self_le_prod_self
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
@@ -2927,33 +1763,18 @@ theorem prod_self_lt_prod_self : s₁ ×ˢ s₁ < s₂ ×ˢ s₂ ↔ s₁ < s₂
   prod_self_ssubset_prod_self
 #align upper_set.prod_self_lt_prod_self UpperSet.prod_self_lt_prod_self
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem prod_le_prod_iff : s₁ ×ˢ t₁ ≤ s₂ ×ˢ t₂ ↔ s₁ ≤ s₂ ∧ t₁ ≤ t₂ ∨ s₂ = ⊤ ∨ t₂ = ⊤ :=
   prod_subset_prod_iff.trans <| by simp
 #align upper_set.prod_le_prod_iff UpperSet.prod_le_prod_iff
 
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 @[simp]
 theorem prod_eq_top : s ×ˢ t = ⊤ ↔ s = ⊤ ∨ t = ⊤ := by simp_rw [SetLike.ext'_iff];
   exact prod_eq_empty_iff
 #align upper_set.prod_eq_top UpperSet.prod_eq_top
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
@@ -2967,12 +1788,6 @@ namespace LowerSet
 
 variable (s s₁ s₂ : LowerSet α) (t t₁ t₂ : LowerSet β) {x : α × β}
 
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 /-- The product of two lower sets as a lower set. -/
 def prod : LowerSet (α × β) :=
@@ -2982,12 +1797,6 @@ def prod : LowerSet (α × β) :=
 -- mathport name: lower_set.prod
 infixr:82 " ×ˢ " => LowerSet.prod
 
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 @[simp, norm_cast]
@@ -2995,83 +1804,41 @@ theorem coe_prod : (↑(s ×ˢ t) : Set (α × β)) = s ×ˢ t :=
   rfl
 #align lower_set.coe_prod LowerSet.coe_prod
 
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 @[simp]
 theorem mem_prod {s : LowerSet α} {t : LowerSet β} : x ∈ s ×ˢ t ↔ x.1 ∈ s ∧ x.2 ∈ t :=
   Iff.rfl
 #align lower_set.mem_prod LowerSet.mem_prod
 
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 theorem Iic_prod (x : α × β) : Iic x = Iic x.1 ×ˢ Iic x.2 :=
   rfl
 #align lower_set.Iic_prod LowerSet.Iic_prod
 
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 @[simp]
 theorem Ici_prod_Ici (a : α) (b : β) : Iic a ×ˢ Iic b = Iic (a, b) :=
   rfl
 #align lower_set.Ici_prod_Ici LowerSet.Ici_prod_Ici
 
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 @[simp]
 theorem prod_bot : s ×ˢ (⊥ : LowerSet β) = ⊥ :=
   ext prod_empty
 #align lower_set.prod_bot LowerSet.prod_bot
 
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 @[simp]
 theorem bot_prod : (⊥ : LowerSet α) ×ˢ t = ⊥ :=
   ext empty_prod
 #align lower_set.bot_prod LowerSet.bot_prod
 
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 @[simp]
 theorem top_prod_top : (⊤ : LowerSet α) ×ˢ (⊤ : LowerSet β) = ⊤ :=
   ext univ_prod_univ
 #align lower_set.top_prod_top LowerSet.top_prod_top
 
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@@ -3080,12 +1847,6 @@ theorem inf_prod : (s₁ ⊓ s₂) ×ˢ t = s₁ ×ˢ t ⊓ s₂ ×ˢ t :=
   ext inter_prod
 #align lower_set.inf_prod LowerSet.inf_prod
 
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@@ -3094,12 +1855,6 @@ theorem prod_inf : s ×ˢ (t₁ ⊓ t₂) = s ×ˢ t₁ ⊓ s ×ˢ t₂ :=
   ext prod_inter
 #align lower_set.prod_inf LowerSet.prod_inf
 
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@@ -3108,12 +1863,6 @@ theorem sup_prod : (s₁ ⊔ s₂) ×ˢ t = s₁ ×ˢ t ⊔ s₂ ×ˢ t :=
   ext union_prod
 #align lower_set.sup_prod LowerSet.sup_prod
 
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@@ -3122,12 +1871,6 @@ theorem prod_sup : s ×ˢ (t₁ ⊔ t₂) = s ×ˢ t₁ ⊔ s ×ˢ t₂ :=
   ext prod_union
 #align lower_set.prod_sup LowerSet.prod_sup
 
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@@ -3137,48 +1880,24 @@ theorem prod_inf_prod : s₁ ×ˢ t₁ ⊓ s₂ ×ˢ t₂ = (s₁ ⊓ s₂) ×ˢ
 
 variable {s s₁ s₂ t t₁ t₂}
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem prod_mono : s₁ ≤ s₂ → t₁ ≤ t₂ → s₁ ×ˢ t₁ ≤ s₂ ×ˢ t₂ :=
   prod_mono
 #align lower_set.prod_mono LowerSet.prod_mono
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem prod_mono_left : s₁ ≤ s₂ → s₁ ×ˢ t ≤ s₂ ×ˢ t :=
   prod_mono_left
 #align lower_set.prod_mono_left LowerSet.prod_mono_left
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem prod_mono_right : t₁ ≤ t₂ → s ×ˢ t₁ ≤ s ×ˢ t₂ :=
   prod_mono_right
 #align lower_set.prod_mono_right LowerSet.prod_mono_right
 
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-Case conversion may be inaccurate. Consider using '#align lower_set.prod_self_le_prod_self LowerSet.prod_self_le_prod_selfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
@@ -3186,12 +1905,6 @@ theorem prod_self_le_prod_self : s₁ ×ˢ s₁ ≤ s₂ ×ˢ s₂ ↔ s₁ ≤
   prod_self_subset_prod_self
 #align lower_set.prod_self_le_prod_self LowerSet.prod_self_le_prod_self
 
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-Case conversion may be inaccurate. Consider using '#align lower_set.prod_self_lt_prod_self LowerSet.prod_self_lt_prod_selfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
@@ -3199,33 +1912,18 @@ theorem prod_self_lt_prod_self : s₁ ×ˢ s₁ < s₂ ×ˢ s₂ ↔ s₁ < s₂
   prod_self_ssubset_prod_self
 #align lower_set.prod_self_lt_prod_self LowerSet.prod_self_lt_prod_self
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem prod_le_prod_iff : s₁ ×ˢ t₁ ≤ s₂ ×ˢ t₂ ↔ s₁ ≤ s₂ ∧ t₁ ≤ t₂ ∨ s₁ = ⊥ ∨ t₁ = ⊥ :=
   prod_subset_prod_iff.trans <| by simp
 #align lower_set.prod_le_prod_iff LowerSet.prod_le_prod_iff
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
 theorem prod_eq_bot : s ×ˢ t = ⊥ ↔ s = ⊥ ∨ t = ⊥ := by simp_rw [SetLike.ext'_iff];
   exact prod_eq_empty_iff
 #align lower_set.prod_eq_bot LowerSet.prod_eq_bot
 
-/- warning: lower_set.disjoint_prod -> LowerSet.disjoint_prod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align lower_set.disjoint_prod LowerSet.disjoint_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
@@ -3235,12 +1933,6 @@ theorem disjoint_prod : Disjoint (s₁ ×ˢ t₁) (s₂ ×ˢ t₂) ↔ Disjoint
 
 end LowerSet
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
@@ -3249,12 +1941,6 @@ theorem upperClosure_prod (s : Set α) (t : Set β) :
   simp [Prod.le_def, and_and_and_comm _ (_ ∈ t)]
 #align upper_closure_prod upperClosure_prod
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]

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

@@ -123,9 +123,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align is_upper_set_compl isUpperSet_complₓ'. -/
 @[simp]
 theorem isUpperSet_compl : IsUpperSet (sᶜ) ↔ IsLowerSet s :=
-  ⟨fun h => by
-    convert h.compl
-    rw [compl_compl], IsLowerSet.compl⟩
+  ⟨fun h => by convert h.compl; rw [compl_compl], IsLowerSet.compl⟩
 #align is_upper_set_compl isUpperSet_compl
 
 /- warning: is_lower_set_compl -> isLowerSet_compl is a dubious translation:
@@ -136,9 +134,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align is_lower_set_compl isLowerSet_complₓ'. -/
 @[simp]
 theorem isLowerSet_compl : IsLowerSet (sᶜ) ↔ IsUpperSet s :=
-  ⟨fun h => by
-    convert h.compl
-    rw [compl_compl], IsUpperSet.compl⟩
+  ⟨fun h => by convert h.compl; rw [compl_compl], IsUpperSet.compl⟩
 #align is_lower_set_compl isLowerSet_compl
 
 /- warning: is_upper_set.union -> IsUpperSet.union is a dubious translation:
@@ -461,8 +457,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align is_upper_set.image IsUpperSet.imageₓ'. -/
 theorem IsUpperSet.image (hs : IsUpperSet s) (f : α ≃o β) : IsUpperSet (f '' s : Set β) :=
   by
-  change IsUpperSet ((f : α ≃ β) '' s)
-  rw [Set.image_equiv_eq_preimage_symm]
+  change IsUpperSet ((f : α ≃ β) '' s); rw [Set.image_equiv_eq_preimage_symm]
   exact hs.preimage f.symm.monotone
 #align is_upper_set.image IsUpperSet.image
 
@@ -474,8 +469,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align is_lower_set.image IsLowerSet.imageₓ'. -/
 theorem IsLowerSet.image (hs : IsLowerSet s) (f : α ≃o β) : IsLowerSet (f '' s : Set β) :=
   by
-  change IsLowerSet ((f : α ≃ β) '' s)
-  rw [Set.image_equiv_eq_preimage_symm]
+  change IsLowerSet ((f : α ≃ β) '' s); rw [Set.image_equiv_eq_preimage_symm]
   exact hs.preimage f.symm.monotone
 #align is_lower_set.image IsLowerSet.image
 
@@ -766,10 +760,7 @@ namespace UpperSet
 
 instance : SetLike (UpperSet α) α where
   coe := UpperSet.carrier
-  coe_injective' s t h := by
-    cases s
-    cases t
-    congr
+  coe_injective' s t h := by cases s; cases t; congr
 
 #print UpperSet.ext /-
 @[ext]
@@ -804,10 +795,7 @@ namespace LowerSet
 
 instance : SetLike (LowerSet α) α where
   coe := LowerSet.carrier
-  coe_injective' s t h := by
-    cases s
-    cases t
-    congr
+  coe_injective' s t h := by cases s; cases t; congr
 
 #print LowerSet.ext /-
 @[ext]
@@ -1062,10 +1050,8 @@ but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {a : α} {f : ι -> (UpperSet.{u2} α _inst_1)}, Iff (Membership.mem.{u2, u2} α (UpperSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1)) a (iSup.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instSupSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (forall (i : ι), Membership.mem.{u2, u2} α (UpperSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1)) a (f i))
 Case conversion may be inaccurate. Consider using '#align upper_set.mem_supr_iff UpperSet.mem_iSup_iffₓ'. -/
 @[simp]
-theorem mem_iSup_iff {f : ι → UpperSet α} : (a ∈ ⨆ i, f i) ↔ ∀ i, a ∈ f i :=
-  by
-  rw [← SetLike.mem_coe, coe_supr]
-  exact mem_Inter
+theorem mem_iSup_iff {f : ι → UpperSet α} : (a ∈ ⨆ i, f i) ↔ ∀ i, a ∈ f i := by
+  rw [← SetLike.mem_coe, coe_supr]; exact mem_Inter
 #align upper_set.mem_supr_iff UpperSet.mem_iSup_iff
 
 /- warning: upper_set.mem_infi_iff -> UpperSet.mem_iInf_iff is a dubious translation:
@@ -1075,10 +1061,8 @@ but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {a : α} {f : ι -> (UpperSet.{u2} α _inst_1)}, Iff (Membership.mem.{u2, u2} α (UpperSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1)) a (iInf.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instInfSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (Exists.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} α (UpperSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1)) a (f i)))
 Case conversion may be inaccurate. Consider using '#align upper_set.mem_infi_iff UpperSet.mem_iInf_iffₓ'. -/
 @[simp]
-theorem mem_iInf_iff {f : ι → UpperSet α} : (a ∈ ⨅ i, f i) ↔ ∃ i, a ∈ f i :=
-  by
-  rw [← SetLike.mem_coe, coe_infi]
-  exact mem_Union
+theorem mem_iInf_iff {f : ι → UpperSet α} : (a ∈ ⨅ i, f i) ↔ ∃ i, a ∈ f i := by
+  rw [← SetLike.mem_coe, coe_infi]; exact mem_Union
 #align upper_set.mem_infi_iff UpperSet.mem_iInf_iff
 
 /- warning: upper_set.mem_supr₂_iff -> UpperSet.mem_iSup₂_iff is a dubious translation:
@@ -1341,10 +1325,8 @@ but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {a : α} {f : ι -> (LowerSet.{u2} α _inst_1)}, Iff (Membership.mem.{u2, u2} α (LowerSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1)) a (iSup.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instSupSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (Exists.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} α (LowerSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1)) a (f i)))
 Case conversion may be inaccurate. Consider using '#align lower_set.mem_supr_iff LowerSet.mem_iSup_iffₓ'. -/
 @[simp]
-theorem mem_iSup_iff {f : ι → LowerSet α} : (a ∈ ⨆ i, f i) ↔ ∃ i, a ∈ f i :=
-  by
-  rw [← SetLike.mem_coe, coe_supr]
-  exact mem_Union
+theorem mem_iSup_iff {f : ι → LowerSet α} : (a ∈ ⨆ i, f i) ↔ ∃ i, a ∈ f i := by
+  rw [← SetLike.mem_coe, coe_supr]; exact mem_Union
 #align lower_set.mem_supr_iff LowerSet.mem_iSup_iff
 
 /- warning: lower_set.mem_infi_iff -> LowerSet.mem_iInf_iff is a dubious translation:
@@ -1354,10 +1336,8 @@ but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {a : α} {f : ι -> (LowerSet.{u2} α _inst_1)}, Iff (Membership.mem.{u2, u2} α (LowerSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1)) a (iInf.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instInfSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (forall (i : ι), Membership.mem.{u2, u2} α (LowerSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1)) a (f i))
 Case conversion may be inaccurate. Consider using '#align lower_set.mem_infi_iff LowerSet.mem_iInf_iffₓ'. -/
 @[simp]
-theorem mem_iInf_iff {f : ι → LowerSet α} : (a ∈ ⨅ i, f i) ↔ ∀ i, a ∈ f i :=
-  by
-  rw [← SetLike.mem_coe, coe_infi]
-  exact mem_Inter
+theorem mem_iInf_iff {f : ι → LowerSet α} : (a ∈ ⨅ i, f i) ↔ ∀ i, a ∈ f i := by
+  rw [← SetLike.mem_coe, coe_infi]; exact mem_Inter
 #align lower_set.mem_infi_iff LowerSet.mem_iInf_iff
 
 /- warning: lower_set.mem_supr₂_iff -> LowerSet.mem_iSup₂_iff is a dubious translation:
@@ -1755,10 +1735,7 @@ theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
 <too large>
 Case conversion may be inaccurate. Consider using '#align upper_set.mem_map UpperSet.mem_mapₓ'. -/
 @[simp]
-theorem mem_map : b ∈ map f s ↔ f.symm b ∈ s :=
-  by
-  rw [← f.symm_symm, ← symm_map, f.symm_symm]
-  rfl
+theorem mem_map : b ∈ map f s ↔ f.symm b ∈ s := by rw [← f.symm_symm, ← symm_map, f.symm_symm]; rfl
 #align upper_set.mem_map UpperSet.mem_map
 
 /- warning: upper_set.map_refl -> UpperSet.map_refl is a dubious translation:
@@ -1768,20 +1745,14 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Eq.{succ u1} (OrderIso.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (UpperSet.map.{u1, u1} α α _inst_1 _inst_1 (OrderIso.refl.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderIso.refl.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align upper_set.map_refl UpperSet.map_reflₓ'. -/
 @[simp]
-theorem map_refl : map (OrderIso.refl α) = OrderIso.refl _ :=
-  by
-  ext
-  simp
+theorem map_refl : map (OrderIso.refl α) = OrderIso.refl _ := by ext; simp
 #align upper_set.map_refl UpperSet.map_refl
 
 /- warning: upper_set.map_map -> UpperSet.map_map is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align upper_set.map_map UpperSet.map_mapₓ'. -/
 @[simp]
-theorem map_map (g : β ≃o γ) (f : α ≃o β) : map g (map f s) = map (f.trans g) s :=
-  by
-  ext
-  simp
+theorem map_map (g : β ≃o γ) (f : α ≃o β) : map g (map f s) = map (f.trans g) s := by ext; simp
 #align upper_set.map_map UpperSet.map_map
 
 variable (f s t)
@@ -1831,10 +1802,8 @@ theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
 <too large>
 Case conversion may be inaccurate. Consider using '#align lower_set.mem_map LowerSet.mem_mapₓ'. -/
 @[simp]
-theorem mem_map {f : α ≃o β} {b : β} : b ∈ map f s ↔ f.symm b ∈ s :=
-  by
-  rw [← f.symm_symm, ← symm_map, f.symm_symm]
-  rfl
+theorem mem_map {f : α ≃o β} {b : β} : b ∈ map f s ↔ f.symm b ∈ s := by
+  rw [← f.symm_symm, ← symm_map, f.symm_symm]; rfl
 #align lower_set.mem_map LowerSet.mem_map
 
 /- warning: lower_set.map_refl -> LowerSet.map_refl is a dubious translation:
@@ -1844,20 +1813,14 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Eq.{succ u1} (OrderIso.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LowerSet.map.{u1, u1} α α _inst_1 _inst_1 (OrderIso.refl.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderIso.refl.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align lower_set.map_refl LowerSet.map_reflₓ'. -/
 @[simp]
-theorem map_refl : map (OrderIso.refl α) = OrderIso.refl _ :=
-  by
-  ext
-  simp
+theorem map_refl : map (OrderIso.refl α) = OrderIso.refl _ := by ext; simp
 #align lower_set.map_refl LowerSet.map_refl
 
 /- warning: lower_set.map_map -> LowerSet.map_map is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align lower_set.map_map LowerSet.map_mapₓ'. -/
 @[simp]
-theorem map_map (g : β ≃o γ) (f : α ≃o β) : map g (map f s) = map (f.trans g) s :=
-  by
-  ext
-  simp
+theorem map_map (g : β ≃o γ) (f : α ≃o β) : map g (map f s) = map (f.trans g) s := by ext; simp
 #align lower_set.map_map LowerSet.map_map
 
 variable (f s t)
@@ -1969,20 +1932,14 @@ theorem mem_Ioi_iff : b ∈ Ioi a ↔ a < b :=
 <too large>
 Case conversion may be inaccurate. Consider using '#align upper_set.map_Ici UpperSet.map_Iciₓ'. -/
 @[simp]
-theorem map_Ici (f : α ≃o β) (a : α) : map f (Ici a) = Ici (f a) :=
-  by
-  ext
-  simp
+theorem map_Ici (f : α ≃o β) (a : α) : map f (Ici a) = Ici (f a) := by ext; simp
 #align upper_set.map_Ici UpperSet.map_Ici
 
 /- warning: upper_set.map_Ioi -> UpperSet.map_Ioi is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align upper_set.map_Ioi UpperSet.map_Ioiₓ'. -/
 @[simp]
-theorem map_Ioi (f : α ≃o β) (a : α) : map f (Ioi a) = Ioi (f a) :=
-  by
-  ext
-  simp
+theorem map_Ioi (f : α ≃o β) (a : α) : map f (Ioi a) = Ioi (f a) := by ext; simp
 #align upper_set.map_Ioi UpperSet.map_Ioi
 
 /- warning: upper_set.Ici_le_Ioi -> UpperSet.Ici_le_Ioi is a dubious translation:
@@ -2142,20 +2099,14 @@ theorem mem_Iio_iff : b ∈ Iio a ↔ b < a :=
 <too large>
 Case conversion may be inaccurate. Consider using '#align lower_set.map_Iic LowerSet.map_Iicₓ'. -/
 @[simp]
-theorem map_Iic (f : α ≃o β) (a : α) : map f (Iic a) = Iic (f a) :=
-  by
-  ext
-  simp
+theorem map_Iic (f : α ≃o β) (a : α) : map f (Iic a) = Iic (f a) := by ext; simp
 #align lower_set.map_Iic LowerSet.map_Iic
 
 /- warning: lower_set.map_Iio -> LowerSet.map_Iio is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align lower_set.map_Iio LowerSet.map_Iioₓ'. -/
 @[simp]
-theorem map_Iio (f : α ≃o β) (a : α) : map f (Iio a) = Iio (f a) :=
-  by
-  ext
-  simp
+theorem map_Iio (f : α ≃o β) (a : α) : map f (Iio a) = Iio (f a) := by ext; simp
 #align lower_set.map_Iio LowerSet.map_Iio
 
 #print LowerSet.Ioi_le_Ici /-
@@ -2293,19 +2244,13 @@ theorem mem_lowerClosure : x ∈ lowerClosure s ↔ ∃ a ∈ s, x ≤ a :=
 #print coe_upperClosure /-
 -- We do not tag those two as `simp` to respect the abstraction.
 @[norm_cast]
-theorem coe_upperClosure (s : Set α) : ↑(upperClosure s) = ⋃ a ∈ s, Ici a :=
-  by
-  ext
-  simp
+theorem coe_upperClosure (s : Set α) : ↑(upperClosure s) = ⋃ a ∈ s, Ici a := by ext; simp
 #align coe_upper_closure coe_upperClosure
 -/
 
 #print coe_lowerClosure /-
 @[norm_cast]
-theorem coe_lowerClosure (s : Set α) : ↑(lowerClosure s) = ⋃ a ∈ s, Iic a :=
-  by
-  ext
-  simp
+theorem coe_lowerClosure (s : Set α) : ↑(lowerClosure s) = ⋃ a ∈ s, Iic a := by ext; simp
 #align coe_lower_closure coe_lowerClosure
 -/
 
@@ -2410,10 +2355,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (iInf.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instInfSetUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (fun (a : α) => iInf.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instInfSetUpperSet.{u1} α (Preorder.toLE.{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) => UpperSet.Ici.{u1} α _inst_1 a))) (upperClosure.{u1} α _inst_1 s)
 Case conversion may be inaccurate. Consider using '#align upper_set.infi_Ici UpperSet.iInf_Iciₓ'. -/
 @[simp]
-theorem UpperSet.iInf_Ici (s : Set α) : (⨅ a ∈ s, UpperSet.Ici a) = upperClosure s :=
-  by
-  ext
-  simp
+theorem UpperSet.iInf_Ici (s : Set α) : (⨅ a ∈ s, UpperSet.Ici a) = upperClosure s := by ext; simp
 #align upper_set.infi_Ici UpperSet.iInf_Ici
 
 /- warning: lower_set.supr_Iic -> LowerSet.iSup_Iic is a dubious translation:
@@ -2423,10 +2365,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (iSup.{u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instSupSetLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (fun (a : α) => iSup.{u1, 0} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instSupSetLowerSet.{u1} α (Preorder.toLE.{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) => LowerSet.Iic.{u1} α _inst_1 a))) (lowerClosure.{u1} α _inst_1 s)
 Case conversion may be inaccurate. Consider using '#align lower_set.supr_Iic LowerSet.iSup_Iicₓ'. -/
 @[simp]
-theorem LowerSet.iSup_Iic (s : Set α) : (⨆ a ∈ s, LowerSet.Iic a) = lowerClosure s :=
-  by
-  ext
-  simp
+theorem LowerSet.iSup_Iic (s : Set α) : (⨆ a ∈ s, LowerSet.Iic a) = lowerClosure s := by ext; simp
 #align lower_set.supr_Iic LowerSet.iSup_Iic
 
 #print gc_upperClosure_coe /-
@@ -2506,10 +2445,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (Top.top.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instTopUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))
 Case conversion may be inaccurate. Consider using '#align upper_closure_empty upperClosure_emptyₓ'. -/
 @[simp]
-theorem upperClosure_empty : upperClosure (∅ : Set α) = ⊤ :=
-  by
-  ext
-  simp
+theorem upperClosure_empty : upperClosure (∅ : Set α) = ⊤ := by ext; simp
 #align upper_closure_empty upperClosure_empty
 
 /- warning: lower_closure_empty -> lowerClosure_empty is a dubious translation:
@@ -2519,10 +2455,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (Bot.bot.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instBotLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))
 Case conversion may be inaccurate. Consider using '#align lower_closure_empty lowerClosure_emptyₓ'. -/
 @[simp]
-theorem lowerClosure_empty : lowerClosure (∅ : Set α) = ⊥ :=
-  by
-  ext
-  simp
+theorem lowerClosure_empty : lowerClosure (∅ : Set α) = ⊥ := by ext; simp
 #align lower_closure_empty lowerClosure_empty
 
 /- warning: upper_closure_singleton -> upperClosure_singleton is a dubious translation:
@@ -2532,10 +2465,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)) (UpperSet.Ici.{u1} α _inst_1 a)
 Case conversion may be inaccurate. Consider using '#align upper_closure_singleton upperClosure_singletonₓ'. -/
 @[simp]
-theorem upperClosure_singleton (a : α) : upperClosure ({a} : Set α) = UpperSet.Ici a :=
-  by
-  ext
-  simp
+theorem upperClosure_singleton (a : α) : upperClosure ({a} : Set α) = UpperSet.Ici a := by ext; simp
 #align upper_closure_singleton upperClosure_singleton
 
 /- warning: lower_closure_singleton -> lowerClosure_singleton is a dubious translation:
@@ -2545,10 +2475,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)) (LowerSet.Iic.{u1} α _inst_1 a)
 Case conversion may be inaccurate. Consider using '#align lower_closure_singleton lowerClosure_singletonₓ'. -/
 @[simp]
-theorem lowerClosure_singleton (a : α) : lowerClosure ({a} : Set α) = LowerSet.Iic a :=
-  by
-  ext
-  simp
+theorem lowerClosure_singleton (a : α) : lowerClosure ({a} : Set α) = LowerSet.Iic a := by ext; simp
 #align lower_closure_singleton lowerClosure_singleton
 
 /- warning: upper_closure_univ -> upperClosure_univ is a dubious translation:
@@ -2581,9 +2508,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align upper_closure_eq_top_iff upperClosure_eq_top_iffₓ'. -/
 @[simp]
 theorem upperClosure_eq_top_iff : upperClosure s = ⊤ ↔ s = ∅ :=
-  ⟨fun h => subset_empty_iff.1 <| subset_upperClosure.trans (congr_arg coe h).Subset,
-    by
-    rintro rfl
+  ⟨fun h => subset_empty_iff.1 <| subset_upperClosure.trans (congr_arg coe h).Subset, by rintro rfl;
     exact upperClosure_empty⟩
 #align upper_closure_eq_top_iff upperClosure_eq_top_iff
 
@@ -2595,9 +2520,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align lower_closure_eq_bot_iff lowerClosure_eq_bot_iffₓ'. -/
 @[simp]
 theorem lowerClosure_eq_bot_iff : lowerClosure s = ⊥ ↔ s = ∅ :=
-  ⟨fun h => subset_empty_iff.1 <| subset_lowerClosure.trans (congr_arg coe h).Subset,
-    by
-    rintro rfl
+  ⟨fun h => subset_empty_iff.1 <| subset_lowerClosure.trans (congr_arg coe h).Subset, by rintro rfl;
     exact lowerClosure_empty⟩
 #align lower_closure_eq_bot_iff lowerClosure_eq_bot_iff
 
@@ -2609,9 +2532,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align upper_closure_union upperClosure_unionₓ'. -/
 @[simp]
 theorem upperClosure_union (s t : Set α) : upperClosure (s ∪ t) = upperClosure s ⊓ upperClosure t :=
-  by
-  ext
-  simp [or_and_right, exists_or]
+  by ext; simp [or_and_right, exists_or]
 #align upper_closure_union upperClosure_union
 
 /- warning: lower_closure_union -> lowerClosure_union is a dubious translation:
@@ -2622,9 +2543,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align lower_closure_union lowerClosure_unionₓ'. -/
 @[simp]
 theorem lowerClosure_union (s t : Set α) : lowerClosure (s ∪ t) = lowerClosure s ⊔ lowerClosure t :=
-  by
-  ext
-  simp [or_and_right, exists_or]
+  by ext; simp [or_and_right, exists_or]
 #align lower_closure_union lowerClosure_union
 
 /- warning: upper_closure_Union -> upperClosure_iUnion is a dubious translation:
@@ -2635,9 +2554,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align upper_closure_Union upperClosure_iUnionₓ'. -/
 @[simp]
 theorem upperClosure_iUnion (f : ι → Set α) : upperClosure (⋃ i, f i) = ⨅ i, upperClosure (f i) :=
-  by
-  ext
-  simp [← exists_and_right, @exists_comm α]
+  by ext; simp [← exists_and_right, @exists_comm α]
 #align upper_closure_Union upperClosure_iUnion
 
 /- warning: lower_closure_Union -> lowerClosure_iUnion is a dubious translation:
@@ -2648,9 +2565,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align lower_closure_Union lowerClosure_iUnionₓ'. -/
 @[simp]
 theorem lowerClosure_iUnion (f : ι → Set α) : lowerClosure (⋃ i, f i) = ⨆ i, lowerClosure (f i) :=
-  by
-  ext
-  simp [← exists_and_right, @exists_comm α]
+  by ext; simp [← exists_and_right, @exists_comm α]
 #align lower_closure_Union lowerClosure_iUnion
 
 /- warning: upper_closure_sUnion -> upperClosure_sUnion is a dubious translation:
@@ -3032,9 +2947,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align upper_set.prod_eq_top UpperSet.prod_eq_topₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
-theorem prod_eq_top : s ×ˢ t = ⊤ ↔ s = ⊤ ∨ t = ⊤ :=
-  by
-  simp_rw [SetLike.ext'_iff]
+theorem prod_eq_top : s ×ˢ t = ⊤ ↔ s = ⊤ ∨ t = ⊤ := by simp_rw [SetLike.ext'_iff];
   exact prod_eq_empty_iff
 #align upper_set.prod_eq_top UpperSet.prod_eq_top
 
@@ -3306,9 +3219,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align lower_set.prod_eq_bot LowerSet.prod_eq_botₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
-theorem prod_eq_bot : s ×ˢ t = ⊥ ↔ s = ⊥ ∨ t = ⊥ :=
-  by
-  simp_rw [SetLike.ext'_iff]
+theorem prod_eq_bot : s ×ˢ t = ⊥ ↔ s = ⊥ ∨ t = ⊥ := by simp_rw [SetLike.ext'_iff];
   exact prod_eq_empty_iff
 #align lower_set.prod_eq_bot LowerSet.prod_eq_bot
 
@@ -3334,9 +3245,7 @@ Case conversion may be inaccurate. Consider using '#align upper_closure_prod upp
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
 theorem upperClosure_prod (s : Set α) (t : Set β) :
-    upperClosure (s ×ˢ t) = upperClosure s ×ˢ upperClosure t :=
-  by
-  ext
+    upperClosure (s ×ˢ t) = upperClosure s ×ˢ upperClosure t := by ext;
   simp [Prod.le_def, and_and_and_comm _ (_ ∈ t)]
 #align upper_closure_prod upperClosure_prod
 
@@ -3350,9 +3259,7 @@ Case conversion may be inaccurate. Consider using '#align lower_closure_prod low
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[simp]
 theorem lowerClosure_prod (s : Set α) (t : Set β) :
-    lowerClosure (s ×ˢ t) = lowerClosure s ×ˢ lowerClosure t :=
-  by
-  ext
+    lowerClosure (s ×ˢ t) = lowerClosure s ×ˢ lowerClosure t := by ext;
   simp [Prod.le_def, and_and_and_comm _ (_ ∈ t)]
 #align lower_closure_prod lowerClosure_prod
 

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

@@ -1752,10 +1752,7 @@ theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
 #align upper_set.symm_map UpperSet.symm_map
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align upper_set.mem_map UpperSet.mem_mapₓ'. -/
 @[simp]
 theorem mem_map : b ∈ map f s ↔ f.symm b ∈ s :=
@@ -1778,10 +1775,7 @@ theorem map_refl : map (OrderIso.refl α) = OrderIso.refl _ :=
 #align upper_set.map_refl UpperSet.map_refl
 
 /- warning: upper_set.map_map -> UpperSet.map_map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align upper_set.map_map UpperSet.map_mapₓ'. -/
 @[simp]
 theorem map_map (g : β ≃o γ) (f : α ≃o β) : map g (map f s) = map (f.trans g) s :=
@@ -1793,10 +1787,7 @@ theorem map_map (g : β ≃o γ) (f : α ≃o β) : map g (map f s) = map (f.tra
 variable (f s t)
 
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 Case conversion may be inaccurate. Consider using '#align upper_set.coe_map UpperSet.coe_mapₓ'. -/
 @[simp, norm_cast]
 theorem coe_map : (map f s : Set β) = f '' s :=
@@ -1837,10 +1828,7 @@ theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
 #align lower_set.symm_map LowerSet.symm_map
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lower_set.mem_map LowerSet.mem_mapₓ'. -/
 @[simp]
 theorem mem_map {f : α ≃o β} {b : β} : b ∈ map f s ↔ f.symm b ∈ s :=
@@ -1863,10 +1851,7 @@ theorem map_refl : map (OrderIso.refl α) = OrderIso.refl _ :=
 #align lower_set.map_refl LowerSet.map_refl
 
 /- warning: lower_set.map_map -> LowerSet.map_map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lower_set.map_map LowerSet.map_mapₓ'. -/
 @[simp]
 theorem map_map (g : β ≃o γ) (f : α ≃o β) : map g (map f s) = map (f.trans g) s :=
@@ -1878,10 +1863,7 @@ theorem map_map (g : β ≃o γ) (f : α ≃o β) : map g (map f s) = map (f.tra
 variable (f s t)
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lower_set.coe_map LowerSet.coe_mapₓ'. -/
 @[simp, norm_cast]
 theorem coe_map : (map f s : Set β) = f '' s :=
@@ -1893,10 +1875,7 @@ end LowerSet
 namespace UpperSet
 
 /- warning: upper_set.compl_map -> UpperSet.compl_map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align upper_set.compl_map UpperSet.compl_mapₓ'. -/
 @[simp]
 theorem compl_map (f : α ≃o β) (s : UpperSet α) : (map f s).compl = LowerSet.map f s.compl :=
@@ -1908,10 +1887,7 @@ end UpperSet
 namespace LowerSet
 
 /- warning: lower_set.compl_map -> LowerSet.compl_map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lower_set.compl_map LowerSet.compl_mapₓ'. -/
 @[simp]
 theorem compl_map (f : α ≃o β) (s : LowerSet α) : (map f s).compl = UpperSet.map f s.compl :=
@@ -1990,10 +1966,7 @@ theorem mem_Ioi_iff : b ∈ Ioi a ↔ a < b :=
 #align upper_set.mem_Ioi_iff UpperSet.mem_Ioi_iff
 
 /- warning: upper_set.map_Ici -> UpperSet.map_Ici is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align upper_set.map_Ici UpperSet.map_Iciₓ'. -/
 @[simp]
 theorem map_Ici (f : α ≃o β) (a : α) : map f (Ici a) = Ici (f a) :=
@@ -2003,10 +1976,7 @@ theorem map_Ici (f : α ≃o β) (a : α) : map f (Ici a) = Ici (f a) :=
 #align upper_set.map_Ici UpperSet.map_Ici
 
 /- warning: upper_set.map_Ioi -> UpperSet.map_Ioi is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align upper_set.map_Ioi UpperSet.map_Ioiₓ'. -/
 @[simp]
 theorem map_Ioi (f : α ≃o β) (a : α) : map f (Ioi a) = Ioi (f a) :=
@@ -2169,10 +2139,7 @@ theorem mem_Iio_iff : b ∈ Iio a ↔ b < a :=
 #align lower_set.mem_Iio_iff LowerSet.mem_Iio_iff
 
 /- warning: lower_set.map_Iic -> LowerSet.map_Iic is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lower_set.map_Iic LowerSet.map_Iicₓ'. -/
 @[simp]
 theorem map_Iic (f : α ≃o β) (a : α) : map f (Iic a) = Iic (f a) :=
@@ -2182,10 +2149,7 @@ theorem map_Iic (f : α ≃o β) (a : α) : map f (Iic a) = Iic (f a) :=
 #align lower_set.map_Iic LowerSet.map_Iic
 
 /- warning: lower_set.map_Iio -> LowerSet.map_Iio is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lower_set.map_Iio LowerSet.map_Iioₓ'. -/
 @[simp]
 theorem map_Iio (f : α ≃o β) (a : α) : map f (Iio a) = Iio (f a) :=
@@ -2418,10 +2382,7 @@ protected theorem LowerSet.lowerClosure (s : LowerSet α) : lowerClosure (s : Se
 #align lower_set.lower_closure LowerSet.lowerClosure
 
 /- warning: upper_closure_image -> upperClosure_image is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align upper_closure_image upperClosure_imageₓ'. -/
 @[simp]
 theorem upperClosure_image (f : α ≃o β) : upperClosure (f '' s) = UpperSet.map f (upperClosure s) :=
@@ -2432,10 +2393,7 @@ theorem upperClosure_image (f : α ≃o β) : upperClosure (f '' s) = UpperSet.m
 #align upper_closure_image upperClosure_image
 
 /- warning: lower_closure_image -> lowerClosure_image is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align lower_closure_image lowerClosure_imageₓ'. -/
 @[simp]
 theorem lowerClosure_image (f : α ≃o β) : lowerClosure (f '' s) = LowerSet.map f (lowerClosure s) :=
@@ -3081,10 +3039,7 @@ theorem prod_eq_top : s ×ˢ t = ⊤ ↔ s = ⊤ ∨ t = ⊤ :=
 #align upper_set.prod_eq_top UpperSet.prod_eq_top
 
 /- warning: upper_set.codisjoint_prod -> UpperSet.codisjoint_prod is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align upper_set.codisjoint_prod UpperSet.codisjoint_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -3358,10 +3313,7 @@ theorem prod_eq_bot : s ×ˢ t = ⊥ ↔ s = ⊥ ∨ t = ⊥ :=
 #align lower_set.prod_eq_bot LowerSet.prod_eq_bot
 
 /- warning: lower_set.disjoint_prod -> LowerSet.disjoint_prod is a dubious translation:
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(Preorder.toHasLe.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (Or (Disjoint.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))) (BoundedOrder.toOrderBot.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (CompleteLattice.toBoundedOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))) s₁ s₂) (Disjoint.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))) (BoundedOrder.toOrderBot.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))) (CompleteLattice.toBoundedOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))) t₁ t₂))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t₁ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)} {t₂ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, Iff (Disjoint.{max u2 u1} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.instCompleteDistribLatticeLowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))) (BoundedOrder.toOrderBot.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Preorder.toLE.{max u2 u1} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u2 u1} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.instCompleteDistribLatticeLowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))))) (CompleteLattice.toBoundedOrder.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.instCompleteDistribLatticeLowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (Or (Disjoint.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))) (BoundedOrder.toOrderBot.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (CompleteLattice.toBoundedOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))) s₁ s₂) (Disjoint.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))) (BoundedOrder.toOrderBot.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) (CompleteLattice.toBoundedOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))) t₁ t₂))
+<too large>
 Case conversion may be inaccurate. Consider using '#align lower_set.disjoint_prod LowerSet.disjoint_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/

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

@@ -457,7 +457,7 @@ theorem IsLowerSet.preimage (hs : IsLowerSet s) {f : β → α} (hf : Monotone f
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α}, (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (forall (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)), IsUpperSet.{u2} β (Preorder.toHasLe.{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 _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) f) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α}, (IsUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1) s) -> (forall (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), IsUpperSet.{u1} β (Preorder.toLE.{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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) s))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α}, (IsUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1) s) -> (forall (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), IsUpperSet.{u1} β (Preorder.toLE.{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 _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 _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 _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 _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 _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 _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 _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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f) s))
 Case conversion may be inaccurate. Consider using '#align is_upper_set.image IsUpperSet.imageₓ'. -/
 theorem IsUpperSet.image (hs : IsUpperSet s) (f : α ≃o β) : IsUpperSet (f '' s : Set β) :=
   by
@@ -470,7 +470,7 @@ theorem IsUpperSet.image (hs : IsUpperSet s) (f : α ≃o β) : IsUpperSet (f ''
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α}, (IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (forall (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)), IsLowerSet.{u2} β (Preorder.toHasLe.{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 _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) f) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α}, (IsLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1) s) -> (forall (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), IsLowerSet.{u1} β (Preorder.toLE.{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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) s))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α}, (IsLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1) s) -> (forall (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), IsLowerSet.{u1} β (Preorder.toLE.{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 _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 _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 _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 _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 _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 _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 _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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f) s))
 Case conversion may be inaccurate. Consider using '#align is_lower_set.image IsLowerSet.imageₓ'. -/
 theorem IsLowerSet.image (hs : IsLowerSet s) (f : α ≃o β) : IsLowerSet (f '' s : Set β) :=
   by
@@ -1755,7 +1755,7 @@ theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)} {s : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {b : β}, Iff (Membership.Mem.{u2, u2} β (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (SetLike.hasMem.{u2, u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) β (UpperSet.setLike.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) b (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) => (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (Membership.Mem.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderIso.{u2, u1} β α (Preorder.toHasLe.{u2} β _inst_2) (Preorder.toHasLe.{u1} α _inst_1)) (fun (_x : RelIso.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) => β -> α) (RelIso.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (OrderIso.symm.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2) f) b) s)
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)} {s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {b : β}, Iff (Membership.mem.{u2, u2} β (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (SetLike.instMembership.{u2, u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (UpperSet.instSetLikeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) b (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (Membership.mem.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) 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x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (OrderIso.symm.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2) f) b) s)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)} {s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {b : β}, Iff (Membership.mem.{u2, u2} β (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (SetLike.instMembership.{u2, u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (UpperSet.instSetLikeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) b (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} 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 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} 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 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} 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 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} 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 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (Membership.mem.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β (fun (_x : β) => α) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (OrderIso.symm.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2) f) b) s)
 Case conversion may be inaccurate. Consider using '#align upper_set.mem_map UpperSet.mem_mapₓ'. -/
 @[simp]
 theorem mem_map : b ∈ map f s ↔ f.symm b ∈ s :=
@@ -1781,7 +1781,7 @@ theorem map_refl : map (OrderIso.refl α) = OrderIso.refl _ :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : Preorder.{u3} γ] {s : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} (g : OrderIso.{u2, u3} β γ (Preorder.toHasLe.{u2} β _inst_2) (Preorder.toHasLe.{u3} γ _inst_3)) (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (OrderIso.{u2, u3} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))) (Preorder.toHasLe.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (PartialOrder.toPreorder.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (UpperSet.completeDistribLattice.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3))))))))) (fun (_x : RelIso.{u2, u3} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))))) (LE.le.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (Preorder.toHasLe.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (PartialOrder.toPreorder.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (UpperSet.completeDistribLattice.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)))))))))) => (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) -> (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3))) (RelIso.hasCoeToFun.{u2, u3} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))))) (LE.le.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (Preorder.toHasLe.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (PartialOrder.toPreorder.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u3} (UpperSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (UpperSet.completeDistribLattice.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)))))))))) (UpperSet.map.{u2, u3} 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 but is expected to have type
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(Preorder.toLE.{u2} γ _inst_3)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u1, u2} α γ _inst_1 _inst_3 (OrderIso.trans.{u1, u3, u2} α β γ (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) f g)) s)
+  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u3} β] [_inst_3 : Preorder.{u2} γ] {s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} (g : OrderIso.{u3, u2} β γ (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3)) (f : OrderIso.{u1, u3} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2)), Eq.{succ u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) => LE.le.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (Preorder.toLE.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (PartialOrder.toPreorder.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (Order.Coframe.toCompleteLattice.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteDistribLattice.toCoframe.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} γ 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(UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (Preorder.toLE.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (PartialOrder.toPreorder.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (Order.Coframe.toCompleteLattice.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteDistribLattice.toCoframe.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) => LE.le.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (Preorder.toLE.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (PartialOrder.toPreorder.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (Order.Coframe.toCompleteLattice.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteDistribLattice.toCoframe.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u3, u2} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) => LE.le.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (Preorder.toLE.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (PartialOrder.toPreorder.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (Order.Coframe.toCompleteLattice.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteDistribLattice.toCoframe.{u3} (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (UpperSet.map.{u3, u2} β γ _inst_2 _inst_3 g) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RelIso.{u1, u3} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} 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 : UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) => LE.le.{u3} (UpperSet.{u3} β 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u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} 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 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α 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(CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} 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 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} 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 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (UpperSet.map.{u1, u2} α γ _inst_1 _inst_3 (OrderIso.trans.{u1, u3, u2} α β γ (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) f g)) s)
 Case conversion may be inaccurate. Consider using '#align upper_set.map_map UpperSet.map_mapₓ'. -/
 @[simp]
 theorem map_map (g : β ≃o γ) (f : α ≃o β) : map g (map f s) = map (f.trans g) s :=
@@ -1796,7 +1796,7 @@ variable (f s t)
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (s : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)), Eq.{succ u2} (Set.{u2} β) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Set.{u2} β) (SetLike.Set.hasCoeT.{u2, u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) β (UpperSet.setLike.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) => (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (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 _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))) s))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)), Eq.{succ u2} (Set.{u2} β) (SetLike.coe.{u2, u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (UpperSet.instSetLikeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (Set.image.{u1, u2} α β (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) (SetLike.coe.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)), Eq.{succ u2} (Set.{u2} β) (SetLike.coe.{u2, u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (UpperSet.instSetLikeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} 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 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} 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 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} 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 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} 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 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (Set.image.{u1, u2} α β (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u1} α (Preorder.toLE.{u1} 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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u1} α (Preorder.toLE.{u1} 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 _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.{u1} α (Preorder.toLE.{u1} 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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u1} α (Preorder.toLE.{u1} 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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f) (SetLike.coe.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) s))
 Case conversion may be inaccurate. Consider using '#align upper_set.coe_map UpperSet.coe_mapₓ'. -/
 @[simp, norm_cast]
 theorem coe_map : (map f s : Set β) = f '' s :=
@@ -1840,7 +1840,7 @@ theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)} {b : β}, Iff (Membership.Mem.{u2, u2} β (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (SetLike.hasMem.{u2, u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) β (LowerSet.setLike.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) b (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α 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(LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} 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 but is expected to have type
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+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)} {b : β}, Iff (Membership.mem.{u1, u1} β (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) β (LowerSet.instSetLikeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) s)) (Membership.mem.{u2, u2} α (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (SetLike.instMembership.{u2, u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) α (LowerSet.instSetLikeLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β (fun (_x : β) => α) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (OrderIso.symm.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) f) b) s)
 Case conversion may be inaccurate. Consider using '#align lower_set.mem_map LowerSet.mem_mapₓ'. -/
 @[simp]
 theorem mem_map {f : α ≃o β} {b : β} : b ∈ map f s ↔ f.symm b ∈ s :=
@@ -1866,7 +1866,7 @@ theorem map_refl : map (OrderIso.refl α) = OrderIso.refl _ :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] [_inst_3 : Preorder.{u3} γ] {s : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} (g : OrderIso.{u2, u3} β γ (Preorder.toHasLe.{u2} β _inst_2) (Preorder.toHasLe.{u3} γ _inst_3)) (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ u3} (LowerSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (OrderIso.{u2, u3} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))) (Preorder.toHasLe.{u3} (LowerSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (PartialOrder.toPreorder.{u3} (LowerSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u3} (LowerSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (LowerSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u3} (LowerSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u3} (LowerSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (LowerSet.completeDistribLattice.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3))))))))) (fun (_x : RelIso.{u2, u3} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))))) (LE.le.{u3} (LowerSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (Preorder.toHasLe.{u3} (LowerSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (PartialOrder.toPreorder.{u3} (LowerSet.{u3} γ (Preorder.toHasLe.{u3} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u3} (LowerSet.{u3} γ (Preorder.toHasLe.{u3} γ 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 but is expected to have type
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x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u1, u2} α γ _inst_1 _inst_3 (OrderIso.trans.{u1, u3, u2} α β γ (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) f g)) s)
+  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u3} β] [_inst_3 : Preorder.{u2} γ] {s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} (g : OrderIso.{u3, u2} β γ (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3)) (f : OrderIso.{u1, u3} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2)), Eq.{succ u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) => LE.le.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (Preorder.toLE.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (PartialOrder.toPreorder.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (Order.Coframe.toCompleteLattice.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteDistribLattice.toCoframe.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (fun (_x : LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) => LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) => LE.le.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (Preorder.toLE.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (PartialOrder.toPreorder.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (Order.Coframe.toCompleteLattice.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteDistribLattice.toCoframe.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) => LE.le.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (Preorder.toLE.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (PartialOrder.toPreorder.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (Order.Coframe.toCompleteLattice.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (CompleteDistribLattice.toCoframe.{u3} (LowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u3} β (Preorder.toLE.{u3} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ 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(Preorder.toLE.{u2} γ _inst_3)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} 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 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (LowerSet.map.{u1, u2} α γ _inst_1 _inst_3 (OrderIso.trans.{u1, u3, u2} α β γ (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) f g)) s)
 Case conversion may be inaccurate. Consider using '#align lower_set.map_map LowerSet.map_mapₓ'. -/
 @[simp]
 theorem map_map (g : β ≃o γ) (f : α ≃o β) : map g (map f s) = map (f.trans g) s :=
@@ -1881,7 +1881,7 @@ variable (f s t)
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (s : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)), Eq.{succ u2} (Set.{u2} β) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Set.{u2} β) (SetLike.Set.hasCoeT.{u2, u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) β (LowerSet.setLike.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) => (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (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 _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))) s))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)), Eq.{succ u2} (Set.{u2} β) (SetLike.coe.{u2, u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (LowerSet.instSetLikeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} 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_inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β 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_inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (Set.image.{u1, u2} α β (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) (SetLike.coe.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.instSetLikeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)), Eq.{succ u2} (Set.{u2} β) (SetLike.coe.{u2, u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (LowerSet.instSetLikeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} 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 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} 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 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} 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 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} 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 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (Set.image.{u1, u2} α β (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u1} α (Preorder.toLE.{u1} 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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u1} α (Preorder.toLE.{u1} 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 _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.{u1} α (Preorder.toLE.{u1} 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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u1} α (Preorder.toLE.{u1} 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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f) (SetLike.coe.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.instSetLikeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) s))
 Case conversion may be inaccurate. Consider using '#align lower_set.coe_map LowerSet.coe_mapₓ'. -/
 @[simp, norm_cast]
 theorem coe_map : (map f s : Set β) = f '' s :=
@@ -1896,7 +1896,7 @@ namespace UpperSet
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (s : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)), Eq.{succ u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.compl.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) => (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) => (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) (UpperSet.compl.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (s : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.compl.{u1} β (Preorder.toLE.{u1} β _inst_2) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) 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(Preorder.toLE.{u2} α _inst_1) s))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (s : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.compl.{u1} β (Preorder.toLE.{u1} β _inst_2) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) (UpperSet.compl.{u2} α (Preorder.toLE.{u2} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align upper_set.compl_map UpperSet.compl_mapₓ'. -/
 @[simp]
 theorem compl_map (f : α ≃o β) (s : UpperSet α) : (map f s).compl = LowerSet.map f s.compl :=
@@ -1911,7 +1911,7 @@ namespace LowerSet
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (s : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)), Eq.{succ u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.compl.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) => (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) => (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) (LowerSet.compl.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (s : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.compl.{u1} β (Preorder.toLE.{u1} β _inst_2) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} 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α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun 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(Preorder.toLE.{u2} α _inst_1) s))
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_inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β 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(PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β 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(Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun 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(Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f) (LowerSet.compl.{u2} α (Preorder.toLE.{u2} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align lower_set.compl_map LowerSet.compl_mapₓ'. -/
 @[simp]
 theorem compl_map (f : α ≃o β) (s : LowerSet α) : (map f s).compl = UpperSet.map f s.compl :=
@@ -1993,7 +1993,7 @@ theorem mem_Ioi_iff : b ∈ Ioi a ↔ a < b :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (a : α), Eq.{succ u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) => (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) (UpperSet.Ici.{u1} α _inst_1 a)) (UpperSet.Ici.{u2} β _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) f a))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f) (UpperSet.Ici.{u2} α _inst_1 a)) (UpperSet.Ici.{u1} β _inst_2 (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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f) (UpperSet.Ici.{u2} α _inst_1 a)) (UpperSet.Ici.{u1} β _inst_2 (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 _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 _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 _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 _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 _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 _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 _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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f a))
 Case conversion may be inaccurate. Consider using '#align upper_set.map_Ici UpperSet.map_Iciₓ'. -/
 @[simp]
 theorem map_Ici (f : α ≃o β) (a : α) : map f (Ici a) = Ici (f a) :=
@@ -2006,7 +2006,7 @@ theorem map_Ici (f : α ≃o β) (a : α) : map f (Ici a) = Ici (f a) :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (a : α), Eq.{succ u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) => (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) (UpperSet.Ioi.{u1} α _inst_1 a)) (UpperSet.Ioi.{u2} β _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) f a))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f) (UpperSet.Ioi.{u2} α _inst_1 a)) (UpperSet.Ioi.{u1} β _inst_2 (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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f) (UpperSet.Ioi.{u2} α _inst_1 a)) (UpperSet.Ioi.{u1} β _inst_2 (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 _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 _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 _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 _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 _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 _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 _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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f a))
 Case conversion may be inaccurate. Consider using '#align upper_set.map_Ioi UpperSet.map_Ioiₓ'. -/
 @[simp]
 theorem map_Ioi (f : α ≃o β) (a : α) : map f (Ioi a) = Ioi (f a) :=
@@ -2172,7 +2172,7 @@ theorem mem_Iio_iff : b ∈ Iio a ↔ b < a :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (a : α), Eq.{succ u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) => (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) (LowerSet.Iic.{u1} α _inst_1 a)) (LowerSet.Iic.{u2} β _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) f a))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) (LowerSet.Iic.{u2} α _inst_1 a)) (LowerSet.Iic.{u1} β _inst_2 (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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) (LowerSet.Iic.{u2} α _inst_1 a)) (LowerSet.Iic.{u1} β _inst_2 (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 _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 _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 _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 _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 _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 _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 _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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f a))
 Case conversion may be inaccurate. Consider using '#align lower_set.map_Iic LowerSet.map_Iicₓ'. -/
 @[simp]
 theorem map_Iic (f : α ≃o β) (a : α) : map f (Iic a) = Iic (f a) :=
@@ -2185,7 +2185,7 @@ theorem map_Iic (f : α ≃o β) (a : α) : map f (Iic a) = Iic (f a) :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (a : α), Eq.{succ u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) => (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) (LowerSet.Iio.{u1} α _inst_1 a)) (LowerSet.Iio.{u2} β _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) f a))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) (LowerSet.Iio.{u2} α _inst_1 a)) (LowerSet.Iio.{u1} β _inst_2 (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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) (LowerSet.Iio.{u2} α _inst_1 a)) (LowerSet.Iio.{u1} β _inst_2 (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 _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 _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 _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 _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 _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 _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 _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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f a))
 Case conversion may be inaccurate. Consider using '#align lower_set.map_Iio LowerSet.map_Iioₓ'. -/
 @[simp]
 theorem map_Iio (f : α ≃o β) (a : α) : map f (Iio a) = Iio (f a) :=
@@ -2421,7 +2421,7 @@ protected theorem LowerSet.lowerClosure (s : LowerSet α) : lowerClosure (s : Se
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (upperClosure.{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 _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) f) s)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) => (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) (upperClosure.{u1} α _inst_1 s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (upperClosure.{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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f) (upperClosure.{u2} α _inst_1 s))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (upperClosure.{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 _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 _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 _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 _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 _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 _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 _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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f) (upperClosure.{u2} α _inst_1 s))
 Case conversion may be inaccurate. Consider using '#align upper_closure_image upperClosure_imageₓ'. -/
 @[simp]
 theorem upperClosure_image (f : α ≃o β) : upperClosure (f '' s) = UpperSet.map f (upperClosure s) :=
@@ -2435,7 +2435,7 @@ theorem upperClosure_image (f : α ≃o β) : upperClosure (f '' s) = UpperSet.m
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (lowerClosure.{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 _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) f) s)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α 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_inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) => (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) (lowerClosure.{u1} α _inst_1 s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), Eq.{succ u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (lowerClosure.{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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) 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(PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) (lowerClosure.{u2} α _inst_1 s))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), Eq.{succ u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (lowerClosure.{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 _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 _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 _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 _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 _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 _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 _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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) (lowerClosure.{u2} α _inst_1 s))
 Case conversion may be inaccurate. Consider using '#align lower_closure_image lowerClosure_imageₓ'. -/
 @[simp]
 theorem lowerClosure_image (f : α ≃o β) : lowerClosure (f '' s) = LowerSet.map f (lowerClosure s) :=
@@ -2494,7 +2494,7 @@ theorem gc_lowerClosure_coe : GaloisConnection (lowerClosure : Set α → LowerS
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], GaloisInsertion.{u1, u1} (Set.{u1} α) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (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))))))) (OrderDual.preorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Function.comp.{succ u1, succ u1, succ u1} (Set.{u1} α) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))) (fun (_x : Equiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))) => (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))) (Equiv.hasCoeToFun.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))) (OrderDual.toDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))) (upperClosure.{u1} α _inst_1)) (Function.comp.{succ u1, succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) => (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) -> (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (OrderDual.ofDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], GaloisInsertion.{u1, u1} (Set.{u1} α) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (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))))))) (OrderDual.preorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Function.comp.{succ u1, succ u1, succ u1} (Set.{u1} α) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (OrderDual.toDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (upperClosure.{u1} α _inst_1)) (Function.comp.{succ u1, succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (fun (_x : OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) => UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderDual.ofDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], GaloisInsertion.{u1, u1} (Set.{u1} α) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (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))))))) (OrderDual.preorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Function.comp.{succ u1, succ u1, succ u1} (Set.{u1} α) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (OrderDual.toDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (upperClosure.{u1} α _inst_1)) (Function.comp.{succ u1, succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (fun (_x : OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) => UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderDual.ofDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align gi_upper_closure_coe giUpperClosureCoeₓ'. -/
 /-- `upper_closure` forms a reversed Galois insertion with the coercion from upper sets to sets. -/
 def giUpperClosureCoe :

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

@@ -339,59 +339,103 @@ section Preorder
 
 variable [Preorder α] [Preorder β] {s : Set α} {p : α → Prop} (a : α)
 
-#print isUpperSet_Ici /-
+/- warning: is_upper_set_Ici -> isUpperSet_Ici is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (Set.Ici.{u1} α _inst_1 a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) (Set.Ici.{u1} α _inst_1 a)
+Case conversion may be inaccurate. Consider using '#align is_upper_set_Ici isUpperSet_Iciₓ'. -/
 theorem isUpperSet_Ici : IsUpperSet (Ici a) := fun _ _ => ge_trans
 #align is_upper_set_Ici isUpperSet_Ici
--/
 
-#print isLowerSet_Iic /-
+/- warning: is_lower_set_Iic -> isLowerSet_Iic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (Set.Iic.{u1} α _inst_1 a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) (Set.Iic.{u1} α _inst_1 a)
+Case conversion may be inaccurate. Consider using '#align is_lower_set_Iic isLowerSet_Iicₓ'. -/
 theorem isLowerSet_Iic : IsLowerSet (Iic a) := fun _ _ => le_trans
 #align is_lower_set_Iic isLowerSet_Iic
--/
 
-#print isUpperSet_Ioi /-
+/- warning: is_upper_set_Ioi -> isUpperSet_Ioi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (Set.Ioi.{u1} α _inst_1 a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) (Set.Ioi.{u1} α _inst_1 a)
+Case conversion may be inaccurate. Consider using '#align is_upper_set_Ioi isUpperSet_Ioiₓ'. -/
 theorem isUpperSet_Ioi : IsUpperSet (Ioi a) := fun _ _ => flip lt_of_lt_of_le
 #align is_upper_set_Ioi isUpperSet_Ioi
--/
 
-#print isLowerSet_Iio /-
+/- warning: is_lower_set_Iio -> isLowerSet_Iio is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (Set.Iio.{u1} α _inst_1 a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) (Set.Iio.{u1} α _inst_1 a)
+Case conversion may be inaccurate. Consider using '#align is_lower_set_Iio isLowerSet_Iioₓ'. -/
 theorem isLowerSet_Iio : IsLowerSet (Iio a) := fun _ _ => lt_of_le_of_lt
 #align is_lower_set_Iio isLowerSet_Iio
--/
 
-#print isUpperSet_iff_Ici_subset /-
+/- warning: is_upper_set_iff_Ici_subset -> isUpperSet_iff_Ici_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, Iff (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) (forall {{a : α}}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ici.{u1} α _inst_1 a) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, Iff (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) (forall {{a : α}}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ici.{u1} α _inst_1 a) s))
+Case conversion may be inaccurate. Consider using '#align is_upper_set_iff_Ici_subset isUpperSet_iff_Ici_subsetₓ'. -/
 theorem isUpperSet_iff_Ici_subset : IsUpperSet s ↔ ∀ ⦃a⦄, a ∈ s → Ici a ⊆ s := by
   simp [IsUpperSet, subset_def, @forall_swap (_ ∈ s)]
 #align is_upper_set_iff_Ici_subset isUpperSet_iff_Ici_subset
--/
 
-#print isLowerSet_iff_Iic_subset /-
+/- warning: is_lower_set_iff_Iic_subset -> isLowerSet_iff_Iic_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, Iff (IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) (forall {{a : α}}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Iic.{u1} α _inst_1 a) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, Iff (IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) (forall {{a : α}}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Iic.{u1} α _inst_1 a) s))
+Case conversion may be inaccurate. Consider using '#align is_lower_set_iff_Iic_subset isLowerSet_iff_Iic_subsetₓ'. -/
 theorem isLowerSet_iff_Iic_subset : IsLowerSet s ↔ ∀ ⦃a⦄, a ∈ s → Iic a ⊆ s := by
   simp [IsLowerSet, subset_def, @forall_swap (_ ∈ s)]
 #align is_lower_set_iff_Iic_subset isLowerSet_iff_Iic_subset
--/
 
+/- warning: is_upper_set.Ici_subset -> IsUpperSet.Ici_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (forall {{a : α}}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ici.{u1} α _inst_1 a) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (forall {{a : α}}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ici.{u1} α _inst_1 a) s))
+Case conversion may be inaccurate. Consider using '#align is_upper_set.Ici_subset IsUpperSet.Ici_subsetₓ'. -/
 alias isUpperSet_iff_Ici_subset ↔ IsUpperSet.Ici_subset _
 #align is_upper_set.Ici_subset IsUpperSet.Ici_subset
 
+/- warning: is_lower_set.Iic_subset -> IsLowerSet.Iic_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, (IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (forall {{a : α}}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Iic.{u1} α _inst_1 a) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, (IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (forall {{a : α}}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Iic.{u1} α _inst_1 a) s))
+Case conversion may be inaccurate. Consider using '#align is_lower_set.Iic_subset IsLowerSet.Iic_subsetₓ'. -/
 alias isLowerSet_iff_Iic_subset ↔ IsLowerSet.Iic_subset _
 #align is_lower_set.Iic_subset IsLowerSet.Iic_subset
 
-#print IsUpperSet.ordConnected /-
+/- warning: is_upper_set.ord_connected -> IsUpperSet.ordConnected is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (Set.OrdConnected.{u1} α _inst_1 s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Set.OrdConnected.{u1} α _inst_1 s)
+Case conversion may be inaccurate. Consider using '#align is_upper_set.ord_connected IsUpperSet.ordConnectedₓ'. -/
 theorem IsUpperSet.ordConnected (h : IsUpperSet s) : s.OrdConnected :=
   ⟨fun a ha b _ => Icc_subset_Ici_self.trans <| h.Ici_subset ha⟩
 #align is_upper_set.ord_connected IsUpperSet.ordConnected
--/
 
-#print IsLowerSet.ordConnected /-
+/- warning: is_lower_set.ord_connected -> IsLowerSet.ordConnected is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, (IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (Set.OrdConnected.{u1} α _inst_1 s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, (IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Set.OrdConnected.{u1} α _inst_1 s)
+Case conversion may be inaccurate. Consider using '#align is_lower_set.ord_connected IsLowerSet.ordConnectedₓ'. -/
 theorem IsLowerSet.ordConnected (h : IsLowerSet s) : s.OrdConnected :=
   ⟨fun a _ b hb => Icc_subset_Iic_self.trans <| h.Iic_subset hb⟩
 #align is_lower_set.ord_connected IsLowerSet.ordConnected
--/
 
 /- warning: is_upper_set.preimage -> IsUpperSet.preimage is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α}, (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (forall {f : β -> α}, (Monotone.{u2, u1} β α _inst_2 _inst_1 f) -> (IsUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2) (Set.preimage.{u2, u1} β α f s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α}, (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (forall {f : β -> α}, (Monotone.{u2, u1} β α _inst_2 _inst_1 f) -> (IsUpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (Set.preimage.{u2, u1} β α f s)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α}, (IsUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1) s) -> (forall {f : β -> α}, (Monotone.{u1, u2} β α _inst_2 _inst_1 f) -> (IsUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2) (Set.preimage.{u1, u2} β α f s)))
 Case conversion may be inaccurate. Consider using '#align is_upper_set.preimage IsUpperSet.preimageₓ'. -/
@@ -401,7 +445,7 @@ theorem IsUpperSet.preimage (hs : IsUpperSet s) {f : β → α} (hf : Monotone f
 
 /- warning: is_lower_set.preimage -> IsLowerSet.preimage is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α}, (IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (forall {f : β -> α}, (Monotone.{u2, u1} β α _inst_2 _inst_1 f) -> (IsLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2) (Set.preimage.{u2, u1} β α f s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α}, (IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (forall {f : β -> α}, (Monotone.{u2, u1} β α _inst_2 _inst_1 f) -> (IsLowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (Set.preimage.{u2, u1} β α f s)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α}, (IsLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1) s) -> (forall {f : β -> α}, (Monotone.{u1, u2} β α _inst_2 _inst_1 f) -> (IsLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2) (Set.preimage.{u1, u2} β α f s)))
 Case conversion may be inaccurate. Consider using '#align is_lower_set.preimage IsLowerSet.preimageₓ'. -/
@@ -411,7 +455,7 @@ theorem IsLowerSet.preimage (hs : IsLowerSet s) {f : β → α} (hf : Monotone f
 
 /- warning: is_upper_set.image -> IsUpperSet.image is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α}, (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (forall (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)), IsUpperSet.{u2} β (Preorder.toLE.{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 _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) f) s))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α}, (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (forall (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)), IsUpperSet.{u2} β (Preorder.toHasLe.{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 _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) f) s))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α}, (IsUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1) s) -> (forall (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), IsUpperSet.{u1} β (Preorder.toLE.{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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) s))
 Case conversion may be inaccurate. Consider using '#align is_upper_set.image IsUpperSet.imageₓ'. -/
@@ -424,7 +468,7 @@ theorem IsUpperSet.image (hs : IsUpperSet s) (f : α ≃o β) : IsUpperSet (f ''
 
 /- warning: is_lower_set.image -> IsLowerSet.image is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α}, (IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (forall (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)), IsLowerSet.{u2} β (Preorder.toLE.{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 _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) f) s))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α}, (IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (forall (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)), IsLowerSet.{u2} β (Preorder.toHasLe.{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 _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) f) s))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α}, (IsLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1) s) -> (forall (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), IsLowerSet.{u1} β (Preorder.toLE.{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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) s))
 Case conversion may be inaccurate. Consider using '#align is_lower_set.image IsLowerSet.imageₓ'. -/
@@ -435,33 +479,49 @@ theorem IsLowerSet.image (hs : IsLowerSet s) (f : α ≃o β) : IsLowerSet (f ''
   exact hs.preimage f.symm.monotone
 #align is_lower_set.image IsLowerSet.image
 
-#print Set.monotone_mem /-
+/- warning: set.monotone_mem -> Set.monotone_mem is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, Iff (Monotone.{u1, 0} α Prop _inst_1 (PartialOrder.toPreorder.{0} Prop Prop.partialOrder) (fun (_x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) _x s)) (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, Iff (Monotone.{u1, 0} α Prop _inst_1 (PartialOrder.toPreorder.{0} Prop Prop.partialOrder) (fun (_x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) _x s)) (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s)
+Case conversion may be inaccurate. Consider using '#align set.monotone_mem Set.monotone_memₓ'. -/
 @[simp]
 theorem Set.monotone_mem : Monotone (· ∈ s) ↔ IsUpperSet s :=
   Iff.rfl
 #align set.monotone_mem Set.monotone_mem
--/
 
-#print Set.antitone_mem /-
+/- warning: set.antitone_mem -> Set.antitone_mem is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, Iff (Antitone.{u1, 0} α Prop _inst_1 (PartialOrder.toPreorder.{0} Prop Prop.partialOrder) (fun (_x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) _x s)) (IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, Iff (Antitone.{u1, 0} α Prop _inst_1 (PartialOrder.toPreorder.{0} Prop Prop.partialOrder) (fun (_x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) _x s)) (IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s)
+Case conversion may be inaccurate. Consider using '#align set.antitone_mem Set.antitone_memₓ'. -/
 @[simp]
 theorem Set.antitone_mem : Antitone (· ∈ s) ↔ IsLowerSet s :=
   forall_swap
 #align set.antitone_mem Set.antitone_mem
--/
 
-#print isUpperSet_setOf /-
+/- warning: is_upper_set_set_of -> isUpperSet_setOf is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {p : α -> Prop}, Iff (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => p a))) (Monotone.{u1, 0} α Prop _inst_1 (PartialOrder.toPreorder.{0} Prop Prop.partialOrder) p)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {p : α -> Prop}, Iff (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => p a))) (Monotone.{u1, 0} α Prop _inst_1 (PartialOrder.toPreorder.{0} Prop Prop.partialOrder) p)
+Case conversion may be inaccurate. Consider using '#align is_upper_set_set_of isUpperSet_setOfₓ'. -/
 @[simp]
 theorem isUpperSet_setOf : IsUpperSet { a | p a } ↔ Monotone p :=
   Iff.rfl
 #align is_upper_set_set_of isUpperSet_setOf
--/
 
-#print isLowerSet_setOf /-
+/- warning: is_lower_set_set_of -> isLowerSet_setOf is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {p : α -> Prop}, Iff (IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => p a))) (Antitone.{u1, 0} α Prop _inst_1 (PartialOrder.toPreorder.{0} Prop Prop.partialOrder) p)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {p : α -> Prop}, Iff (IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) (setOf.{u1} α (fun (a : α) => p a))) (Antitone.{u1, 0} α Prop _inst_1 (PartialOrder.toPreorder.{0} Prop Prop.partialOrder) p)
+Case conversion may be inaccurate. Consider using '#align is_lower_set_set_of isLowerSet_setOfₓ'. -/
 @[simp]
 theorem isLowerSet_setOf : IsLowerSet { a | p a } ↔ Antitone p :=
   forall_swap
 #align is_lower_set_set_of isLowerSet_setOf
--/
 
 section OrderTop
 
@@ -469,7 +529,7 @@ variable [OrderTop α]
 
 /- warning: is_lower_set.top_mem -> IsLowerSet.top_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)], (IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3)) s) (Eq.{succ u1} (Set.{u1} α) s (Set.univ.{u1} α)))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)], (IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_3)) s) (Eq.{succ u1} (Set.{u1} α) s (Set.univ.{u1} α)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)], (IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3)) s) (Eq.{succ u1} (Set.{u1} α) s (Set.univ.{u1} α)))
 Case conversion may be inaccurate. Consider using '#align is_lower_set.top_mem IsLowerSet.top_memₓ'. -/
@@ -479,7 +539,7 @@ theorem IsLowerSet.top_mem (hs : IsLowerSet s) : ⊤ ∈ s ↔ s = univ :=
 
 /- warning: is_upper_set.top_mem -> IsUpperSet.top_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)], (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3)) s) (Set.Nonempty.{u1} α s))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)], (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_3)) s) (Set.Nonempty.{u1} α s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)], (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3)) s) (Set.Nonempty.{u1} α s))
 Case conversion may be inaccurate. Consider using '#align is_upper_set.top_mem IsUpperSet.top_memₓ'. -/
@@ -489,7 +549,7 @@ theorem IsUpperSet.top_mem (hs : IsUpperSet s) : ⊤ ∈ s ↔ s.Nonempty :=
 
 /- warning: is_upper_set.not_top_mem -> IsUpperSet.not_top_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)], (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Iff (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3)) s)) (Eq.{succ u1} (Set.{u1} α) s (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)], (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (Iff (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_3)) s)) (Eq.{succ u1} (Set.{u1} α) s (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)], (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Iff (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3)) s)) (Eq.{succ u1} (Set.{u1} α) s (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))))
 Case conversion may be inaccurate. Consider using '#align is_upper_set.not_top_mem IsUpperSet.not_top_memₓ'. -/
@@ -505,7 +565,7 @@ variable [OrderBot α]
 
 /- warning: is_upper_set.bot_mem -> IsUpperSet.bot_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)], (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3)) s) (Eq.{succ u1} (Set.{u1} α) s (Set.univ.{u1} α)))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)], (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_3)) s) (Eq.{succ u1} (Set.{u1} α) s (Set.univ.{u1} α)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)], (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3)) s) (Eq.{succ u1} (Set.{u1} α) s (Set.univ.{u1} α)))
 Case conversion may be inaccurate. Consider using '#align is_upper_set.bot_mem IsUpperSet.bot_memₓ'. -/
@@ -515,7 +575,7 @@ theorem IsUpperSet.bot_mem (hs : IsUpperSet s) : ⊥ ∈ s ↔ s = univ :=
 
 /- warning: is_lower_set.bot_mem -> IsLowerSet.bot_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)], (IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3)) s) (Set.Nonempty.{u1} α s))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)], (IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_3)) s) (Set.Nonempty.{u1} α s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)], (IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3)) s) (Set.Nonempty.{u1} α s))
 Case conversion may be inaccurate. Consider using '#align is_lower_set.bot_mem IsLowerSet.bot_memₓ'. -/
@@ -525,7 +585,7 @@ theorem IsLowerSet.bot_mem (hs : IsLowerSet s) : ⊥ ∈ s ↔ s.Nonempty :=
 
 /- warning: is_lower_set.not_bot_mem -> IsLowerSet.not_bot_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)], (IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Iff (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3)) s)) (Eq.{succ u1} (Set.{u1} α) s (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)], (IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (Iff (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_3)) s)) (Eq.{succ u1} (Set.{u1} α) s (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)], (IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Iff (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3)) s)) (Eq.{succ u1} (Set.{u1} α) s (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))))
 Case conversion may be inaccurate. Consider using '#align is_lower_set.not_bot_mem IsLowerSet.not_bot_memₓ'. -/
@@ -539,26 +599,38 @@ section NoMaxOrder
 
 variable [NoMaxOrder α] (a)
 
-#print IsUpperSet.not_bddAbove /-
+/- warning: is_upper_set.not_bdd_above -> IsUpperSet.not_bddAbove is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α _inst_1)], (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (Set.Nonempty.{u1} α s) -> (Not (BddAbove.{u1} α _inst_1 s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α _inst_1)], (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Set.Nonempty.{u1} α s) -> (Not (BddAbove.{u1} α _inst_1 s))
+Case conversion may be inaccurate. Consider using '#align is_upper_set.not_bdd_above IsUpperSet.not_bddAboveₓ'. -/
 theorem IsUpperSet.not_bddAbove (hs : IsUpperSet s) : s.Nonempty → ¬BddAbove s :=
   by
   rintro ⟨a, ha⟩ ⟨b, hb⟩
   obtain ⟨c, hc⟩ := exists_gt b
   exact hc.not_le (hb <| hs ((hb ha).trans hc.le) ha)
 #align is_upper_set.not_bdd_above IsUpperSet.not_bddAbove
--/
 
-#print not_bddAbove_Ici /-
+/- warning: not_bdd_above_Ici -> not_bddAbove_Ici is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α) [_inst_3 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α _inst_1)], Not (BddAbove.{u1} α _inst_1 (Set.Ici.{u1} α _inst_1 a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α) [_inst_3 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α _inst_1)], Not (BddAbove.{u1} α _inst_1 (Set.Ici.{u1} α _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align not_bdd_above_Ici not_bddAbove_Iciₓ'. -/
 theorem not_bddAbove_Ici : ¬BddAbove (Ici a) :=
   (isUpperSet_Ici _).not_bddAbove nonempty_Ici
 #align not_bdd_above_Ici not_bddAbove_Ici
--/
 
-#print not_bddAbove_Ioi /-
+/- warning: not_bdd_above_Ioi -> not_bddAbove_Ioi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α) [_inst_3 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α _inst_1)], Not (BddAbove.{u1} α _inst_1 (Set.Ioi.{u1} α _inst_1 a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α) [_inst_3 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α _inst_1)], Not (BddAbove.{u1} α _inst_1 (Set.Ioi.{u1} α _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align not_bdd_above_Ioi not_bddAbove_Ioiₓ'. -/
 theorem not_bddAbove_Ioi : ¬BddAbove (Ioi a) :=
   (isUpperSet_Ioi _).not_bddAbove nonempty_Ioi
 #align not_bdd_above_Ioi not_bddAbove_Ioi
--/
 
 end NoMaxOrder
 
@@ -566,26 +638,38 @@ section NoMinOrder
 
 variable [NoMinOrder α] (a)
 
-#print IsLowerSet.not_bddBelow /-
+/- warning: is_lower_set.not_bdd_below -> IsLowerSet.not_bddBelow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α _inst_1)], (IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (Set.Nonempty.{u1} α s) -> (Not (BddBelow.{u1} α _inst_1 s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} [_inst_3 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α _inst_1)], (IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Set.Nonempty.{u1} α s) -> (Not (BddBelow.{u1} α _inst_1 s))
+Case conversion may be inaccurate. Consider using '#align is_lower_set.not_bdd_below IsLowerSet.not_bddBelowₓ'. -/
 theorem IsLowerSet.not_bddBelow (hs : IsLowerSet s) : s.Nonempty → ¬BddBelow s :=
   by
   rintro ⟨a, ha⟩ ⟨b, hb⟩
   obtain ⟨c, hc⟩ := exists_lt b
   exact hc.not_le (hb <| hs (hc.le.trans <| hb ha) ha)
 #align is_lower_set.not_bdd_below IsLowerSet.not_bddBelow
--/
 
-#print not_bddBelow_Iic /-
+/- warning: not_bdd_below_Iic -> not_bddBelow_Iic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α) [_inst_3 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α _inst_1)], Not (BddBelow.{u1} α _inst_1 (Set.Iic.{u1} α _inst_1 a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α) [_inst_3 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α _inst_1)], Not (BddBelow.{u1} α _inst_1 (Set.Iic.{u1} α _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align not_bdd_below_Iic not_bddBelow_Iicₓ'. -/
 theorem not_bddBelow_Iic : ¬BddBelow (Iic a) :=
   (isLowerSet_Iic _).not_bddBelow nonempty_Iic
 #align not_bdd_below_Iic not_bddBelow_Iic
--/
 
-#print not_bddBelow_Iio /-
+/- warning: not_bdd_below_Iio -> not_bddBelow_Iio is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α) [_inst_3 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α _inst_1)], Not (BddBelow.{u1} α _inst_1 (Set.Iio.{u1} α _inst_1 a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α) [_inst_3 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α _inst_1)], Not (BddBelow.{u1} α _inst_1 (Set.Iio.{u1} α _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align not_bdd_below_Iio not_bddBelow_Iioₓ'. -/
 theorem not_bddBelow_Iio : ¬BddBelow (Iio a) :=
   (isLowerSet_Iio _).not_bddBelow nonempty_Iio
 #align not_bdd_below_Iio not_bddBelow_Iio
--/
 
 end NoMinOrder
 
@@ -595,33 +679,61 @@ section PartialOrder
 
 variable [PartialOrder α] {s : Set α}
 
-#print isUpperSet_iff_forall_lt /-
+/- warning: is_upper_set_iff_forall_lt -> isUpperSet_iff_forall_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {s : Set.{u1} α}, Iff (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) s) (forall {{a : α}} {{b : α}}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a b) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {s : Set.{u1} α}, Iff (IsUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) s) (forall {{a : α}} {{b : α}}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) a b) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s))
+Case conversion may be inaccurate. Consider using '#align is_upper_set_iff_forall_lt isUpperSet_iff_forall_ltₓ'. -/
 theorem isUpperSet_iff_forall_lt : IsUpperSet s ↔ ∀ ⦃a b : α⦄, a < b → a ∈ s → b ∈ s :=
   forall_congr' fun a => by simp [le_iff_eq_or_lt, or_imp, forall_and]
 #align is_upper_set_iff_forall_lt isUpperSet_iff_forall_lt
--/
 
-#print isLowerSet_iff_forall_lt /-
+/- warning: is_lower_set_iff_forall_lt -> isLowerSet_iff_forall_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {s : Set.{u1} α}, Iff (IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) s) (forall {{a : α}} {{b : α}}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) b a) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {s : Set.{u1} α}, Iff (IsLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) s) (forall {{a : α}} {{b : α}}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) b a) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s))
+Case conversion may be inaccurate. Consider using '#align is_lower_set_iff_forall_lt isLowerSet_iff_forall_ltₓ'. -/
 theorem isLowerSet_iff_forall_lt : IsLowerSet s ↔ ∀ ⦃a b : α⦄, b < a → a ∈ s → b ∈ s :=
   forall_congr' fun a => by simp [le_iff_eq_or_lt, or_imp, forall_and]
 #align is_lower_set_iff_forall_lt isLowerSet_iff_forall_lt
--/
 
-#print isUpperSet_iff_Ioi_subset /-
+/- warning: is_upper_set_iff_Ioi_subset -> isUpperSet_iff_Ioi_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {s : Set.{u1} α}, Iff (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) s) (forall {{a : α}}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {s : Set.{u1} α}, Iff (IsUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) s) (forall {{a : α}}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) s))
+Case conversion may be inaccurate. Consider using '#align is_upper_set_iff_Ioi_subset isUpperSet_iff_Ioi_subsetₓ'. -/
 theorem isUpperSet_iff_Ioi_subset : IsUpperSet s ↔ ∀ ⦃a⦄, a ∈ s → Ioi a ⊆ s := by
   simp [isUpperSet_iff_forall_lt, subset_def, @forall_swap (_ ∈ s)]
 #align is_upper_set_iff_Ioi_subset isUpperSet_iff_Ioi_subset
--/
 
-#print isLowerSet_iff_Iio_subset /-
+/- warning: is_lower_set_iff_Iio_subset -> isLowerSet_iff_Iio_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {s : Set.{u1} α}, Iff (IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) s) (forall {{a : α}}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {s : Set.{u1} α}, Iff (IsLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) s) (forall {{a : α}}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) s))
+Case conversion may be inaccurate. Consider using '#align is_lower_set_iff_Iio_subset isLowerSet_iff_Iio_subsetₓ'. -/
 theorem isLowerSet_iff_Iio_subset : IsLowerSet s ↔ ∀ ⦃a⦄, a ∈ s → Iio a ⊆ s := by
   simp [isLowerSet_iff_forall_lt, subset_def, @forall_swap (_ ∈ s)]
 #align is_lower_set_iff_Iio_subset isLowerSet_iff_Iio_subset
--/
 
+/- warning: is_upper_set.Ioi_subset -> IsUpperSet.Ioi_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {s : Set.{u1} α}, (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) s) -> (forall {{a : α}}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {s : Set.{u1} α}, (IsUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) s) -> (forall {{a : α}}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) s))
+Case conversion may be inaccurate. Consider using '#align is_upper_set.Ioi_subset IsUpperSet.Ioi_subsetₓ'. -/
 alias isUpperSet_iff_Ioi_subset ↔ IsUpperSet.Ioi_subset _
 #align is_upper_set.Ioi_subset IsUpperSet.Ioi_subset
 
+/- warning: is_lower_set.Iio_subset -> IsLowerSet.Iio_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {s : Set.{u1} α}, (IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) s) -> (forall {{a : α}}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PartialOrder.{u1} α] {s : Set.{u1} α}, (IsLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1)) s) -> (forall {{a : α}}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α _inst_1) a) s))
+Case conversion may be inaccurate. Consider using '#align is_lower_set.Iio_subset IsLowerSet.Iio_subsetₓ'. -/
 alias isLowerSet_iff_Iio_subset ↔ IsLowerSet.Iio_subset _
 #align is_lower_set.Iio_subset IsLowerSet.Iio_subset
 
@@ -760,7 +872,7 @@ instance : Inhabited (UpperSet α) :=
 
 /- warning: upper_set.coe_subset_coe -> UpperSet.coe_subset_coe is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1}, Iff (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) t)) (LE.le.{u1} (UpperSet.{u1} α _inst_1) (Preorder.toLE.{u1} (UpperSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.completeDistribLattice.{u1} α _inst_1))))))) t s)
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1}, Iff (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) t)) (LE.le.{u1} (UpperSet.{u1} α _inst_1) (Preorder.toHasLe.{u1} (UpperSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.completeDistribLattice.{u1} α _inst_1))))))) t s)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1}, Iff (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) t)) (LE.le.{u1} (UpperSet.{u1} α _inst_1) (Preorder.toLE.{u1} (UpperSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α _inst_1))))))) t s)
 Case conversion may be inaccurate. Consider using '#align upper_set.coe_subset_coe UpperSet.coe_subset_coeₓ'. -/
@@ -995,7 +1107,7 @@ theorem mem_iInf₂_iff {f : ∀ i, κ i → UpperSet α} : (a ∈ ⨅ (i) (j),
 
 /- warning: upper_set.codisjoint_coe -> UpperSet.codisjoint_coe is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1}, Iff (Codisjoint.{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)))))) (Set.orderTop.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) t)) (Disjoint.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.completeDistribLattice.{u1} α _inst_1))))) (BoundedOrder.toOrderBot.{u1} (UpperSet.{u1} α _inst_1) (Preorder.toLE.{u1} (UpperSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.completeDistribLattice.{u1} α _inst_1))))))) (CompleteLattice.toBoundedOrder.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.completeDistribLattice.{u1} α _inst_1))))) s t)
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1}, Iff (Codisjoint.{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)))))) (Set.orderTop.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) t)) (Disjoint.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.completeDistribLattice.{u1} α _inst_1))))) (BoundedOrder.toOrderBot.{u1} (UpperSet.{u1} α _inst_1) (Preorder.toHasLe.{u1} (UpperSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.completeDistribLattice.{u1} α _inst_1))))))) (CompleteLattice.toBoundedOrder.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.completeDistribLattice.{u1} α _inst_1))))) s t)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1}, Iff (Codisjoint.{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)))))) (Set.instOrderTopSetInstLESet.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) t)) (Disjoint.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α _inst_1))))) (BoundedOrder.toOrderBot.{u1} (UpperSet.{u1} α _inst_1) (Preorder.toLE.{u1} (UpperSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α _inst_1))))))) (CompleteLattice.toBoundedOrder.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α _inst_1))))) s t)
 Case conversion may be inaccurate. Consider using '#align upper_set.codisjoint_coe UpperSet.codisjoint_coeₓ'. -/
@@ -1037,7 +1149,7 @@ instance : Inhabited (LowerSet α) :=
 
 /- warning: lower_set.coe_subset_coe -> LowerSet.coe_subset_coe is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1}, Iff (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) t)) (LE.le.{u1} (LowerSet.{u1} α _inst_1) (Preorder.toLE.{u1} (LowerSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.completeDistribLattice.{u1} α _inst_1))))))) s t)
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1}, Iff (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) t)) (LE.le.{u1} (LowerSet.{u1} α _inst_1) (Preorder.toHasLe.{u1} (LowerSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.completeDistribLattice.{u1} α _inst_1))))))) s t)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1}, Iff (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) t)) (LE.le.{u1} (LowerSet.{u1} α _inst_1) (Preorder.toLE.{u1} (LowerSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α _inst_1))))))) s t)
 Case conversion may be inaccurate. Consider using '#align lower_set.coe_subset_coe LowerSet.coe_subset_coeₓ'. -/
@@ -1274,7 +1386,7 @@ theorem mem_iInf₂_iff {f : ∀ i, κ i → LowerSet α} : (a ∈ ⨅ (i) (j),
 
 /- warning: lower_set.disjoint_coe -> LowerSet.disjoint_coe is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1}, Iff (Disjoint.{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)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) t)) (Disjoint.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.completeDistribLattice.{u1} α _inst_1))))) (BoundedOrder.toOrderBot.{u1} (LowerSet.{u1} α _inst_1) (Preorder.toLE.{u1} (LowerSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.completeDistribLattice.{u1} α _inst_1))))))) (CompleteLattice.toBoundedOrder.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.completeDistribLattice.{u1} α _inst_1))))) s t)
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1}, Iff (Disjoint.{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)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) t)) (Disjoint.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.completeDistribLattice.{u1} α _inst_1))))) (BoundedOrder.toOrderBot.{u1} (LowerSet.{u1} α _inst_1) (Preorder.toHasLe.{u1} (LowerSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.completeDistribLattice.{u1} α _inst_1))))))) (CompleteLattice.toBoundedOrder.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.completeDistribLattice.{u1} α _inst_1))))) s t)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1}, Iff (Disjoint.{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)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (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)))))))) (CompleteLattice.toBoundedOrder.{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)))))) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) t)) (Disjoint.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α _inst_1))))) (BoundedOrder.toOrderBot.{u1} (LowerSet.{u1} α _inst_1) (Preorder.toLE.{u1} (LowerSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α _inst_1))))))) (CompleteLattice.toBoundedOrder.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α _inst_1))))) s t)
 Case conversion may be inaccurate. Consider using '#align lower_set.disjoint_coe LowerSet.disjoint_coeₓ'. -/
@@ -1333,7 +1445,7 @@ theorem compl_compl (s : UpperSet α) : s.compl.compl = s :=
 
 /- warning: upper_set.compl_le_compl -> UpperSet.compl_le_compl is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1}, Iff (LE.le.{u1} (LowerSet.{u1} α _inst_1) (Preorder.toLE.{u1} (LowerSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.completeDistribLattice.{u1} α _inst_1))))))) (UpperSet.compl.{u1} α _inst_1 s) (UpperSet.compl.{u1} α _inst_1 t)) (LE.le.{u1} (UpperSet.{u1} α _inst_1) (Preorder.toLE.{u1} (UpperSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.completeDistribLattice.{u1} α _inst_1))))))) s t)
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1}, Iff (LE.le.{u1} (LowerSet.{u1} α _inst_1) (Preorder.toHasLe.{u1} (LowerSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.completeDistribLattice.{u1} α _inst_1))))))) (UpperSet.compl.{u1} α _inst_1 s) (UpperSet.compl.{u1} α _inst_1 t)) (LE.le.{u1} (UpperSet.{u1} α _inst_1) (Preorder.toHasLe.{u1} (UpperSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.completeDistribLattice.{u1} α _inst_1))))))) s t)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1}, Iff (LE.le.{u1} (LowerSet.{u1} α _inst_1) (Preorder.toLE.{u1} (LowerSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α _inst_1))))))) (UpperSet.compl.{u1} α _inst_1 s) (UpperSet.compl.{u1} α _inst_1 t)) (LE.le.{u1} (UpperSet.{u1} α _inst_1) (Preorder.toLE.{u1} (UpperSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α _inst_1))))))) s t)
 Case conversion may be inaccurate. Consider using '#align upper_set.compl_le_compl UpperSet.compl_le_complₓ'. -/
@@ -1481,7 +1593,7 @@ theorem compl_compl (s : LowerSet α) : s.compl.compl = s :=
 
 /- warning: lower_set.compl_le_compl -> LowerSet.compl_le_compl is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1}, Iff (LE.le.{u1} (UpperSet.{u1} α _inst_1) (Preorder.toLE.{u1} (UpperSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.completeDistribLattice.{u1} α _inst_1))))))) (LowerSet.compl.{u1} α _inst_1 s) (LowerSet.compl.{u1} α _inst_1 t)) (LE.le.{u1} (LowerSet.{u1} α _inst_1) (Preorder.toLE.{u1} (LowerSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.completeDistribLattice.{u1} α _inst_1))))))) s t)
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1}, Iff (LE.le.{u1} (UpperSet.{u1} α _inst_1) (Preorder.toHasLe.{u1} (UpperSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.completeDistribLattice.{u1} α _inst_1))))))) (LowerSet.compl.{u1} α _inst_1 s) (LowerSet.compl.{u1} α _inst_1 t)) (LE.le.{u1} (LowerSet.{u1} α _inst_1) (Preorder.toHasLe.{u1} (LowerSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.completeDistribLattice.{u1} α _inst_1))))))) s t)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1}, Iff (LE.le.{u1} (UpperSet.{u1} α _inst_1) (Preorder.toLE.{u1} (UpperSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α _inst_1))))))) (LowerSet.compl.{u1} α _inst_1 s) (LowerSet.compl.{u1} α _inst_1 t)) (LE.le.{u1} (LowerSet.{u1} α _inst_1) (Preorder.toLE.{u1} (LowerSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α _inst_1))))))) s t)
 Case conversion may be inaccurate. Consider using '#align lower_set.compl_le_compl LowerSet.compl_le_complₓ'. -/
@@ -1584,7 +1696,7 @@ end LowerSet
 
 /- warning: upper_set_iso_lower_set -> upperSetIsoLowerSet is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α], OrderIso.{u1, u1} (UpperSet.{u1} α _inst_1) (LowerSet.{u1} α _inst_1) (Preorder.toLE.{u1} (UpperSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.completeDistribLattice.{u1} α _inst_1))))))) (Preorder.toLE.{u1} (LowerSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.completeDistribLattice.{u1} α _inst_1)))))))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α], OrderIso.{u1, u1} (UpperSet.{u1} α _inst_1) (LowerSet.{u1} α _inst_1) (Preorder.toHasLe.{u1} (UpperSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.completeDistribLattice.{u1} α _inst_1))))))) (Preorder.toHasLe.{u1} (LowerSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.completeDistribLattice.{u1} α _inst_1)))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LE.{u1} α], OrderIso.{u1, u1} (UpperSet.{u1} α _inst_1) (LowerSet.{u1} α _inst_1) (Preorder.toLE.{u1} (UpperSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α _inst_1))))))) (Preorder.toLE.{u1} (LowerSet.{u1} α _inst_1) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α _inst_1) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α _inst_1) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α _inst_1) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α _inst_1) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align upper_set_iso_lower_set upperSetIsoLowerSetₓ'. -/
@@ -1614,7 +1726,7 @@ variable {f : α ≃o β} {s t : UpperSet α} {a : α} {b : β}
 
 /- warning: upper_set.map -> UpperSet.map is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β], (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) -> (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β], (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) -> (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β], (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) -> (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))
 Case conversion may be inaccurate. Consider using '#align upper_set.map UpperSet.mapₓ'. -/
@@ -1630,7 +1742,7 @@ def map (f : α ≃o β) : UpperSet α ≃o UpperSet β
 
 /- warning: upper_set.symm_map -> UpperSet.symm_map is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)), Eq.{max (succ u2) (succ u1)} (OrderIso.{u2, u1} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (OrderIso.symm.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f)) (UpperSet.map.{u2, u1} β α _inst_2 _inst_1 (OrderIso.symm.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2) f))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)), Eq.{max (succ u2) (succ u1)} (OrderIso.{u2, u1} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (OrderIso.symm.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f)) (UpperSet.map.{u2, u1} β α _inst_2 _inst_1 (OrderIso.symm.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2) f))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (OrderIso.{u1, u2} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1))))))))) (OrderIso.symm.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)))))))) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f)) (UpperSet.map.{u1, u2} β α _inst_2 _inst_1 (OrderIso.symm.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) f))
 Case conversion may be inaccurate. Consider using '#align upper_set.symm_map UpperSet.symm_mapₓ'. -/
@@ -1641,7 +1753,7 @@ theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
 
 /- warning: upper_set.mem_map -> UpperSet.mem_map is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (OrderIso.symm.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2) f) b) s)
 Case conversion may be inaccurate. Consider using '#align upper_set.mem_map UpperSet.mem_mapₓ'. -/
@@ -1654,7 +1766,7 @@ theorem mem_map : b ∈ map f s ↔ f.symm b ∈ s :=
 
 /- warning: upper_set.map_refl -> UpperSet.map_refl is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Eq.{succ u1} (OrderIso.{u1, u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (UpperSet.map.{u1, u1} α α _inst_1 _inst_1 (OrderIso.refl.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (OrderIso.refl.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Eq.{succ u1} (OrderIso.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (UpperSet.map.{u1, u1} α α _inst_1 _inst_1 (OrderIso.refl.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderIso.refl.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align upper_set.map_refl UpperSet.map_reflₓ'. -/
@@ -1667,7 +1779,7 @@ theorem map_refl : map (OrderIso.refl α) = OrderIso.refl _ :=
 
 /- warning: upper_set.map_map -> UpperSet.map_map is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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(Preorder.toLE.{u2} γ _inst_3)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u1, u2} α γ _inst_1 _inst_3 (OrderIso.trans.{u1, u3, u2} α β γ (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) f g)) s)
 Case conversion may be inaccurate. Consider using '#align upper_set.map_map UpperSet.map_mapₓ'. -/
@@ -1682,7 +1794,7 @@ variable (f s t)
 
 /- warning: upper_set.coe_map -> UpperSet.coe_map is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)), Eq.{succ u2} (Set.{u2} β) (SetLike.coe.{u2, u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (UpperSet.instSetLikeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (Set.image.{u1, u2} α β (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) (SetLike.coe.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) s))
 Case conversion may be inaccurate. Consider using '#align upper_set.coe_map UpperSet.coe_mapₓ'. -/
@@ -1699,7 +1811,7 @@ variable {f : α ≃o β} {s t : LowerSet α} {a : α} {b : β}
 
 /- warning: lower_set.map -> LowerSet.map is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β], (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) -> (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β], (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) -> (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β], (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) -> (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))
 Case conversion may be inaccurate. Consider using '#align lower_set.map LowerSet.mapₓ'. -/
@@ -1715,7 +1827,7 @@ def map (f : α ≃o β) : LowerSet α ≃o LowerSet β
 
 /- warning: lower_set.symm_map -> LowerSet.symm_map is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)), Eq.{max (succ u2) (succ u1)} (OrderIso.{u2, u1} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (OrderIso.symm.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f)) (LowerSet.map.{u2, u1} β α _inst_2 _inst_1 (OrderIso.symm.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2) f))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (OrderIso.{u1, u2} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1))))))))) (OrderIso.symm.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)))))))) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f)) (LowerSet.map.{u1, u2} β α _inst_2 _inst_1 (OrderIso.symm.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) f))
 Case conversion may be inaccurate. Consider using '#align lower_set.symm_map LowerSet.symm_mapₓ'. -/
@@ -1726,7 +1838,7 @@ theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
 
 /- warning: lower_set.mem_map -> LowerSet.mem_map is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (OrderIso.symm.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) f) b) s)
 Case conversion may be inaccurate. Consider using '#align lower_set.mem_map LowerSet.mem_mapₓ'. -/
@@ -1739,7 +1851,7 @@ theorem mem_map {f : α ≃o β} {b : β} : b ∈ map f s ↔ f.symm b ∈ s :=
 
 /- warning: lower_set.map_refl -> LowerSet.map_refl is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Eq.{succ u1} (OrderIso.{u1, u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LowerSet.map.{u1, u1} α α _inst_1 _inst_1 (OrderIso.refl.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (OrderIso.refl.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Eq.{succ u1} (OrderIso.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LowerSet.map.{u1, u1} α α _inst_1 _inst_1 (OrderIso.refl.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderIso.refl.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align lower_set.map_refl LowerSet.map_reflₓ'. -/
@@ -1752,7 +1864,7 @@ theorem map_refl : map (OrderIso.refl α) = OrderIso.refl _ :=
 
 /- warning: lower_set.map_map -> LowerSet.map_map is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align lower_set.map_map LowerSet.map_mapₓ'. -/
@@ -1767,7 +1879,7 @@ variable (f s t)
 
 /- warning: lower_set.coe_map -> LowerSet.coe_map is a dubious translation:
 lean 3 declaration is
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u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))) s))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)), Eq.{succ u2} (Set.{u2} β) (SetLike.coe.{u2, u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (LowerSet.instSetLikeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) 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(Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β 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_inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (Set.image.{u1, u2} α β (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) (SetLike.coe.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.instSetLikeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) s))
 Case conversion may be inaccurate. Consider using '#align lower_set.coe_map LowerSet.coe_mapₓ'. -/
@@ -1782,7 +1894,7 @@ namespace UpperSet
 
 /- warning: upper_set.compl_map -> UpperSet.compl_map is a dubious translation:
 lean 3 declaration is
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u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) (UpperSet.compl.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (s : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.compl.{u1} β (Preorder.toLE.{u1} β _inst_2) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α 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(Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) 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(Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) (UpperSet.compl.{u2} α (Preorder.toLE.{u2} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align upper_set.compl_map UpperSet.compl_mapₓ'. -/
@@ -1797,7 +1909,7 @@ namespace LowerSet
 
 /- warning: lower_set.compl_map -> LowerSet.compl_map is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (s : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.compl.{u1} β (Preorder.toLE.{u1} β _inst_2) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α 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(x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β 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(x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f) (LowerSet.compl.{u2} α (Preorder.toLE.{u2} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align lower_set.compl_map LowerSet.compl_mapₓ'. -/
@@ -1819,19 +1931,27 @@ section Preorder
 
 variable [Preorder α] [Preorder β] {s : UpperSet α} {a b : α}
 
-#print UpperSet.Ici /-
+/- warning: upper_set.Ici -> UpperSet.Ici is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], α -> (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], α -> (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align upper_set.Ici UpperSet.Iciₓ'. -/
 /-- The smallest upper set containing a given element. -/
 def Ici (a : α) : UpperSet α :=
   ⟨Ici a, isUpperSet_Ici a⟩
 #align upper_set.Ici UpperSet.Ici
--/
 
-#print UpperSet.Ioi /-
+/- warning: upper_set.Ioi -> UpperSet.Ioi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], α -> (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], α -> (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align upper_set.Ioi UpperSet.Ioiₓ'. -/
 /-- The smallest upper set containing a given element. -/
 def Ioi (a : α) : UpperSet α :=
   ⟨Ioi a, isUpperSet_Ioi a⟩
 #align upper_set.Ioi UpperSet.Ioi
--/
 
 #print UpperSet.coe_Ici /-
 @[simp]
@@ -1847,23 +1967,31 @@ theorem coe_Ioi (a : α) : ↑(Ioi a) = Set.Ioi a :=
 #align upper_set.coe_Ioi UpperSet.coe_Ioi
 -/
 
-#print UpperSet.mem_Ici_iff /-
+/- warning: upper_set.mem_Ici_iff -> UpperSet.mem_Ici_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α} {b : α}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) b (UpperSet.Ici.{u1} α _inst_1 a)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) a b)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α} {b : α}, Iff (Membership.mem.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) b (UpperSet.Ici.{u1} α _inst_1 a)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) a b)
+Case conversion may be inaccurate. Consider using '#align upper_set.mem_Ici_iff UpperSet.mem_Ici_iffₓ'. -/
 @[simp]
 theorem mem_Ici_iff : b ∈ Ici a ↔ a ≤ b :=
   Iff.rfl
 #align upper_set.mem_Ici_iff UpperSet.mem_Ici_iff
--/
 
-#print UpperSet.mem_Ioi_iff /-
+/- warning: upper_set.mem_Ioi_iff -> UpperSet.mem_Ioi_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α} {b : α}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) b (UpperSet.Ioi.{u1} α _inst_1 a)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_1) a b)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α} {b : α}, Iff (Membership.mem.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) b (UpperSet.Ioi.{u1} α _inst_1 a)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) a b)
+Case conversion may be inaccurate. Consider using '#align upper_set.mem_Ioi_iff UpperSet.mem_Ioi_iffₓ'. -/
 @[simp]
 theorem mem_Ioi_iff : b ∈ Ioi a ↔ a < b :=
   Iff.rfl
 #align upper_set.mem_Ioi_iff UpperSet.mem_Ioi_iff
--/
 
 /- warning: upper_set.map_Ici -> UpperSet.map_Ici is a dubious translation:
 lean 3 declaration is
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(Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) => (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) (UpperSet.Ici.{u1} α _inst_1 a)) (UpperSet.Ici.{u2} β _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β 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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (a : α), Eq.{succ u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β 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 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α 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 Case conversion may be inaccurate. Consider using '#align upper_set.map_Ici UpperSet.map_Iciₓ'. -/
@@ -1876,7 +2004,7 @@ theorem map_Ici (f : α ≃o β) (a : α) : map f (Ici a) = Ici (f a) :=
 
 /- warning: upper_set.map_Ioi -> UpperSet.map_Ioi is a dubious translation:
 lean 3 declaration is
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β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) f a))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α 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(UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f) (UpperSet.Ioi.{u2} α _inst_1 a)) (UpperSet.Ioi.{u1} β _inst_2 (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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a))
 Case conversion may be inaccurate. Consider using '#align upper_set.map_Ioi UpperSet.map_Ioiₓ'. -/
@@ -1889,7 +2017,7 @@ theorem map_Ioi (f : α ≃o β) (a : α) : map f (Ioi a) = Ioi (f a) :=
 
 /- warning: upper_set.Ici_le_Ioi -> UpperSet.Ici_le_Ioi is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (UpperSet.Ici.{u1} α _inst_1 a) (UpperSet.Ioi.{u1} α _inst_1 a)
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (UpperSet.Ici.{u1} α _inst_1 a) (UpperSet.Ioi.{u1} α _inst_1 a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (UpperSet.Ici.{u1} α _inst_1 a) (UpperSet.Ioi.{u1} α _inst_1 a)
 Case conversion may be inaccurate. Consider using '#align upper_set.Ici_le_Ioi UpperSet.Ici_le_Ioiₓ'. -/
@@ -1899,7 +2027,7 @@ theorem Ici_le_Ioi (a : α) : Ici a ≤ Ioi a :=
 
 /- warning: upper_set.Ioi_top -> UpperSet.Ioi_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)], Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.Ioi.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3))) (Top.top.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasTop.{u1} α (Preorder.toLE.{u1} α _inst_1)))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)], Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.Ioi.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_3))) (Top.top.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)], Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.Ioi.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3))) (Top.top.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instTopUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))
 Case conversion may be inaccurate. Consider using '#align upper_set.Ioi_top UpperSet.Ioi_topₓ'. -/
@@ -1910,7 +2038,7 @@ theorem Ioi_top [OrderTop α] : Ioi (⊤ : α) = ⊤ :=
 
 /- warning: upper_set.Ici_bot -> UpperSet.Ici_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)], Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.Ici.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3))) (Bot.bot.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasBot.{u1} α (Preorder.toLE.{u1} α _inst_1)))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)], Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.Ici.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_3))) (Bot.bot.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)], Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.Ici.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3))) (Bot.bot.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instBotUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))
 Case conversion may be inaccurate. Consider using '#align upper_set.Ici_bot UpperSet.Ici_botₓ'. -/
@@ -1923,7 +2051,7 @@ end Preorder
 
 /- warning: upper_set.Ici_sup -> UpperSet.Ici_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α] (a : α) (b : α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) a b)) (Sup.sup.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) a) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) b))
+  forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α] (a : α) (b : α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) a b)) (Sup.sup.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) a) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) b))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α] (a : α) (b : α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α _inst_1) a b)) (Sup.sup.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.instSupUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) a) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) b))
 Case conversion may be inaccurate. Consider using '#align upper_set.Ici_sup UpperSet.Ici_supₓ'. -/
@@ -1938,7 +2066,7 @@ variable [CompleteLattice α]
 
 /- warning: upper_set.Ici_Sup -> UpperSet.Ici_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (S : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) S)) (iSup.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) α (fun (a : α) => iSup.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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) => UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) a)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (S : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) S)) (iSup.{u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) α (fun (a : α) => iSup.{u1, 0} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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) => UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (S : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) S)) (iSup.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.instSupSetUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) α (fun (a : α) => iSup.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.instSupSetUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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) => UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) a)))
 Case conversion may be inaccurate. Consider using '#align upper_set.Ici_Sup UpperSet.Ici_sSupₓ'. -/
@@ -1949,7 +2077,7 @@ theorem Ici_sSup (S : Set α) : Ici (sSup S) = ⨆ a ∈ S, Ici a :=
 
 /- warning: upper_set.Ici_supr -> UpperSet.Ici_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i))) (iSup.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) ι (fun (i : ι) => UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i))) (iSup.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) ι (fun (i : ι) => UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (f i)))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α), Eq.{succ u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) (UpperSet.Ici.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) (UpperSet.instSupSetUpperSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) ι (fun (i : ι) => UpperSet.Ici.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (f i)))
 Case conversion may be inaccurate. Consider using '#align upper_set.Ici_supr UpperSet.Ici_iSupₓ'. -/
@@ -1960,7 +2088,7 @@ theorem Ici_iSup (f : ι → α) : Ici (⨆ i, f i) = ⨆ i, Ici (f i) :=
 
 /- warning: upper_set.Ici_supr₂ -> UpperSet.Ici_iSup₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] (f : forall (i : ι), (κ i) -> α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ i) (fun (j : κ i) => f i j)))) (iSup.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) ι (fun (i : ι) => iSup.{u1, u3} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (κ i) (fun (j : κ i) => UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] (f : forall (i : ι), (κ i) -> α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ i) (fun (j : κ i) => f i j)))) (iSup.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) ι (fun (i : ι) => iSup.{u1, u3} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (κ i) (fun (j : κ i) => UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (f i j))))
 but is expected to have type
   forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] (f : forall (i : ι), (κ i) -> α), Eq.{succ u3} (UpperSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (UpperSet.Ici.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (iSup.{u3, u2} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => iSup.{u3, u1} α (CompleteLattice.toSupSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (iSup.{u3, u2} (UpperSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (UpperSet.instSupSetUpperSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) ι (fun (i : ι) => iSup.{u3, u1} (UpperSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (UpperSet.instSupSetUpperSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (κ i) (fun (j : κ i) => UpperSet.Ici.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (f i j))))
 Case conversion may be inaccurate. Consider using '#align upper_set.Ici_supr₂ UpperSet.Ici_iSup₂ₓ'. -/
@@ -1981,20 +2109,28 @@ section Preorder
 
 variable [Preorder α] [Preorder β] {s : LowerSet α} {a b : α}
 
-#print LowerSet.Iic /-
+/- warning: lower_set.Iic -> LowerSet.Iic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], α -> (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], α -> (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align lower_set.Iic LowerSet.Iicₓ'. -/
 /-- Principal lower set. `set.Iic` as a lower set. The smallest lower set containing a given
 element. -/
 def Iic (a : α) : LowerSet α :=
   ⟨Iic a, isLowerSet_Iic a⟩
 #align lower_set.Iic LowerSet.Iic
--/
 
-#print LowerSet.Iio /-
+/- warning: lower_set.Iio -> LowerSet.Iio is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], α -> (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], α -> (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align lower_set.Iio LowerSet.Iioₓ'. -/
 /-- Strict principal lower set. `set.Iio` as a lower set. -/
 def Iio (a : α) : LowerSet α :=
   ⟨Iio a, isLowerSet_Iio a⟩
 #align lower_set.Iio LowerSet.Iio
--/
 
 #print LowerSet.coe_Iic /-
 @[simp]
@@ -2010,23 +2146,31 @@ theorem coe_Iio (a : α) : ↑(Iio a) = Set.Iio a :=
 #align lower_set.coe_Iio LowerSet.coe_Iio
 -/
 
-#print LowerSet.mem_Iic_iff /-
+/- warning: lower_set.mem_Iic_iff -> LowerSet.mem_Iic_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α} {b : α}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) b (LowerSet.Iic.{u1} α _inst_1 a)) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) b a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α} {b : α}, Iff (Membership.mem.{u1, u1} α (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.instSetLikeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) b (LowerSet.Iic.{u1} α _inst_1 a)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) b a)
+Case conversion may be inaccurate. Consider using '#align lower_set.mem_Iic_iff LowerSet.mem_Iic_iffₓ'. -/
 @[simp]
 theorem mem_Iic_iff : b ∈ Iic a ↔ b ≤ a :=
   Iff.rfl
 #align lower_set.mem_Iic_iff LowerSet.mem_Iic_iff
--/
 
-#print LowerSet.mem_Iio_iff /-
+/- warning: lower_set.mem_Iio_iff -> LowerSet.mem_Iio_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α} {b : α}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) b (LowerSet.Iio.{u1} α _inst_1 a)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_1) b a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {a : α} {b : α}, Iff (Membership.mem.{u1, u1} α (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.instSetLikeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) b (LowerSet.Iio.{u1} α _inst_1 a)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) b a)
+Case conversion may be inaccurate. Consider using '#align lower_set.mem_Iio_iff LowerSet.mem_Iio_iffₓ'. -/
 @[simp]
 theorem mem_Iio_iff : b ∈ Iio a ↔ b < a :=
   Iff.rfl
 #align lower_set.mem_Iio_iff LowerSet.mem_Iio_iff
--/
 
 /- warning: lower_set.map_Iic -> LowerSet.map_Iic is a dubious translation:
 lean 3 declaration is
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β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) f a))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α 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(LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) 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(PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) (LowerSet.Iic.{u2} α _inst_1 a)) (LowerSet.Iic.{u1} β _inst_2 (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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a))
 Case conversion may be inaccurate. Consider using '#align lower_set.map_Iic LowerSet.map_Iicₓ'. -/
@@ -2039,7 +2183,7 @@ theorem map_Iic (f : α ≃o β) (a : α) : map f (Iic a) = Iic (f a) :=
 
 /- warning: lower_set.map_Iio -> LowerSet.map_Iio is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (a : α), Eq.{succ u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) 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 but is expected to have type
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(CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) (LowerSet.Iio.{u2} α _inst_1 a)) (LowerSet.Iio.{u1} β _inst_2 (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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a))
 Case conversion may be inaccurate. Consider using '#align lower_set.map_Iio LowerSet.map_Iioₓ'. -/
@@ -2058,7 +2202,7 @@ theorem Ioi_le_Ici (a : α) : Ioi a ≤ Ici a :=
 
 /- warning: lower_set.Iic_top -> LowerSet.Iic_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)], Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.Iic.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3))) (Top.top.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasTop.{u1} α (Preorder.toLE.{u1} α _inst_1)))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)], Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.Iic.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_3))) (Top.top.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_1)], Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.Iic.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3))) (Top.top.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instTopLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))
 Case conversion may be inaccurate. Consider using '#align lower_set.Iic_top LowerSet.Iic_topₓ'. -/
@@ -2069,7 +2213,7 @@ theorem Iic_top [OrderTop α] : Iic (⊤ : α) = ⊤ :=
 
 /- warning: lower_set.Iio_bot -> LowerSet.Iio_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)], Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.Iio.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3))) (Bot.bot.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasBot.{u1} α (Preorder.toLE.{u1} α _inst_1)))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)], Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.Iio.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1) _inst_3))) (Bot.bot.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_1)], Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.Iio.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_1) _inst_3))) (Bot.bot.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instBotLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))
 Case conversion may be inaccurate. Consider using '#align lower_set.Iio_bot LowerSet.Iio_botₓ'. -/
@@ -2082,7 +2226,7 @@ end Preorder
 
 /- warning: lower_set.Iic_inf -> LowerSet.Iic_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] (a : α) (b : α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) a b)) (Inf.inf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) a) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) b))
+  forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] (a : α) (b : α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) a b)) (Inf.inf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) a) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) b))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] (a : α) (b : α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) (Inf.inf.{u1} α (SemilatticeInf.toInf.{u1} α _inst_1) a b)) (Inf.inf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.instInfLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) a) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) b))
 Case conversion may be inaccurate. Consider using '#align lower_set.Iic_inf LowerSet.Iic_infₓ'. -/
@@ -2097,7 +2241,7 @@ variable [CompleteLattice α]
 
 /- warning: lower_set.Iic_Inf -> LowerSet.Iic_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (S : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) S)) (iInf.{u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) α (fun (a : α) => iInf.{u1, 0} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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) => LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) a)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (S : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) S)) (iInf.{u1, succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) α (fun (a : α) => iInf.{u1, 0} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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) => LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (S : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) S)) (iInf.{u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.instInfSetLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) α (fun (a : α) => iInf.{u1, 0} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.instInfSetLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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) => LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) a)))
 Case conversion may be inaccurate. Consider using '#align lower_set.Iic_Inf LowerSet.Iic_sInfₓ'. -/
@@ -2108,7 +2252,7 @@ theorem Iic_sInf (S : Set α) : Iic (sInf S) = ⨅ a ∈ S, Iic a :=
 
 /- warning: lower_set.Iic_infi -> LowerSet.Iic_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => f i))) (iInf.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) ι (fun (i : ι) => LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => f i))) (iInf.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) ι (fun (i : ι) => LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (f i)))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α), Eq.{succ u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) (LowerSet.Iic.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) (LowerSet.instInfSetLowerSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) ι (fun (i : ι) => LowerSet.Iic.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (f i)))
 Case conversion may be inaccurate. Consider using '#align lower_set.Iic_infi LowerSet.Iic_iInfₓ'. -/
@@ -2119,7 +2263,7 @@ theorem Iic_iInf (f : ι → α) : Iic (⨅ i, f i) = ⨅ i, Iic (f i) :=
 
 /- warning: lower_set.Iic_infi₂ -> LowerSet.Iic_iInf₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] (f : forall (i : ι), (κ i) -> α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ i) (fun (j : κ i) => f i j)))) (iInf.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) ι (fun (i : ι) => iInf.{u1, u3} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (κ i) (fun (j : κ i) => LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] (f : forall (i : ι), (κ i) -> α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ i) (fun (j : κ i) => f i j)))) (iInf.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) ι (fun (i : ι) => iInf.{u1, u3} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (κ i) (fun (j : κ i) => LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (f i j))))
 but is expected to have type
   forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] (f : forall (i : ι), (κ i) -> α), Eq.{succ u3} (LowerSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (LowerSet.Iic.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (iInf.{u3, u2} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => iInf.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (iInf.{u3, u2} (LowerSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (LowerSet.instInfSetLowerSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) ι (fun (i : ι) => iInf.{u3, u1} (LowerSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (LowerSet.instInfSetLowerSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (κ i) (fun (j : κ i) => LowerSet.Iic.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (f i j))))
 Case conversion may be inaccurate. Consider using '#align lower_set.Iic_infi₂ LowerSet.Iic_iInf₂ₓ'. -/
@@ -2138,23 +2282,31 @@ section closure
 
 variable [Preorder α] [Preorder β] {s t : Set α} {x : α}
 
-#print upperClosure /-
+/- warning: upper_closure -> upperClosure is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], (Set.{u1} α) -> (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], (Set.{u1} α) -> (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align upper_closure upperClosureₓ'. -/
 /-- The greatest upper set containing a given set. -/
 def upperClosure (s : Set α) : UpperSet α :=
   ⟨{ x | ∃ a ∈ s, a ≤ x }, fun x y h => Exists₂.imp fun a _ => h.trans'⟩
 #align upper_closure upperClosure
--/
 
-#print lowerClosure /-
+/- warning: lower_closure -> lowerClosure is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], (Set.{u1} α) -> (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], (Set.{u1} α) -> (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align lower_closure lowerClosureₓ'. -/
 /-- The least lower set containing a given set. -/
 def lowerClosure (s : Set α) : LowerSet α :=
   ⟨{ x | ∃ a ∈ s, x ≤ a }, fun x y h => Exists₂.imp fun a _ => h.trans⟩
 #align lower_closure lowerClosure
--/
 
 /- warning: mem_upper_closure -> mem_upperClosure is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} {x : α}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1))) x (upperClosure.{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) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) a x)))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} {x : α}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) x (upperClosure.{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) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) a x)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} {x : α}, Iff (Membership.mem.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) x (upperClosure.{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) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) a x)))
 Case conversion may be inaccurate. Consider using '#align mem_upper_closure mem_upperClosureₓ'. -/
@@ -2165,7 +2317,7 @@ theorem mem_upperClosure : x ∈ upperClosure s ↔ ∃ a ∈ s, a ≤ x :=
 
 /- warning: mem_lower_closure -> mem_lowerClosure is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} {x : α}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1))) x (lowerClosure.{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) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x a)))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} {x : α}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) x (lowerClosure.{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) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_1) x a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} {x : α}, Iff (Membership.mem.{u1, u1} α (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.instSetLikeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) x (lowerClosure.{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) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x a)))
 Case conversion may be inaccurate. Consider using '#align mem_lower_closure mem_lowerClosureₓ'. -/
@@ -2203,47 +2355,71 @@ theorem subset_lowerClosure : s ⊆ lowerClosure s := fun x hx => ⟨x, hx, le_r
 #align subset_lower_closure subset_lowerClosure
 -/
 
-#print upperClosure_min /-
+/- warning: upper_closure_min -> upperClosure_min is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 s)) t)
+Case conversion may be inaccurate. Consider using '#align upper_closure_min upperClosure_minₓ'. -/
 theorem upperClosure_min (h : s ⊆ t) (ht : IsUpperSet t) : ↑(upperClosure s) ⊆ t :=
   fun a ⟨b, hb, hba⟩ => ht hba <| h hb
 #align upper_closure_min upperClosure_min
--/
 
-#print lowerClosure_min /-
+/- warning: lower_closure_min -> lowerClosure_min is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align lower_closure_min lowerClosure_minₓ'. -/
 theorem lowerClosure_min (h : s ⊆ t) (ht : IsLowerSet t) : ↑(lowerClosure s) ⊆ t :=
   fun a ⟨b, hb, hab⟩ => ht hab <| h hb
 #align lower_closure_min lowerClosure_min
--/
 
-#print IsUpperSet.upperClosure /-
+/- warning: is_upper_set.upper_closure -> IsUpperSet.upperClosure is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))) (upperClosure.{u1} α _inst_1 s)) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 s)) s)
+Case conversion may be inaccurate. Consider using '#align is_upper_set.upper_closure IsUpperSet.upperClosureₓ'. -/
 protected theorem IsUpperSet.upperClosure (hs : IsUpperSet s) : ↑(upperClosure s) = s :=
   (upperClosure_min Subset.rfl hs).antisymm subset_upperClosure
 #align is_upper_set.upper_closure IsUpperSet.upperClosure
--/
 
-#print IsLowerSet.lowerClosure /-
+/- warning: is_lower_set.lower_closure -> IsLowerSet.lowerClosure 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_lower_set.lower_closure IsLowerSet.lowerClosureₓ'. -/
 protected theorem IsLowerSet.lowerClosure (hs : IsLowerSet s) : ↑(lowerClosure s) = s :=
   (lowerClosure_min Subset.rfl hs).antisymm subset_lowerClosure
 #align is_lower_set.lower_closure IsLowerSet.lowerClosure
--/
 
-#print UpperSet.upperClosure /-
+/- warning: upper_set.upper_closure -> UpperSet.upperClosure is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align upper_set.upper_closure UpperSet.upperClosureₓ'. -/
 @[simp]
 protected theorem UpperSet.upperClosure (s : UpperSet α) : upperClosure (s : Set α) = s :=
   SetLike.coe_injective s.2.upperClosure
 #align upper_set.upper_closure UpperSet.upperClosure
--/
 
-#print LowerSet.lowerClosure /-
+/- warning: lower_set.lower_closure -> LowerSet.lowerClosure is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align lower_set.lower_closure LowerSet.lowerClosureₓ'. -/
 @[simp]
 protected theorem LowerSet.lowerClosure (s : LowerSet α) : lowerClosure (s : Set α) = s :=
   SetLike.coe_injective s.2.lowerClosure
 #align lower_set.lower_closure LowerSet.lowerClosure
--/
 
 /- warning: upper_closure_image -> upperClosure_image is a dubious translation:
 lean 3 declaration is
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_inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) => (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α 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(UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) (upperClosure.{u1} α _inst_1 s))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (upperClosure.{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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β 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_inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) 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(PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f) (upperClosure.{u2} α _inst_1 s))
 Case conversion may be inaccurate. Consider using '#align upper_closure_image upperClosure_imageₓ'. -/
@@ -2257,7 +2433,7 @@ theorem upperClosure_image (f : α ≃o β) : upperClosure (f '' s) = UpperSet.m
 
 /- warning: lower_closure_image -> lowerClosure_image is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), Eq.{succ u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (lowerClosure.{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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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) 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(Preorder.toLE.{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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) (lowerClosure.{u2} α _inst_1 s))
 Case conversion may be inaccurate. Consider using '#align lower_closure_image lowerClosure_imageₓ'. -/
@@ -2271,7 +2447,7 @@ theorem lowerClosure_image (f : α ≃o β) : lowerClosure (f '' s) = LowerSet.m
 
 /- warning: upper_set.infi_Ici -> UpperSet.iInf_Ici is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (iInf.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (fun (a : α) => iInf.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{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) => UpperSet.Ici.{u1} α _inst_1 a))) (upperClosure.{u1} α _inst_1 s)
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (iInf.{u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (fun (a : α) => iInf.{u1, 0} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toHasLe.{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) => UpperSet.Ici.{u1} α _inst_1 a))) (upperClosure.{u1} α _inst_1 s)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (iInf.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instInfSetUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (fun (a : α) => iInf.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instInfSetUpperSet.{u1} α (Preorder.toLE.{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) => UpperSet.Ici.{u1} α _inst_1 a))) (upperClosure.{u1} α _inst_1 s)
 Case conversion may be inaccurate. Consider using '#align upper_set.infi_Ici UpperSet.iInf_Iciₓ'. -/
@@ -2282,14 +2458,18 @@ theorem UpperSet.iInf_Ici (s : Set α) : (⨅ a ∈ s, UpperSet.Ici a) = upperCl
   simp
 #align upper_set.infi_Ici UpperSet.iInf_Ici
 
-#print LowerSet.iSup_Iic /-
+/- warning: lower_set.supr_Iic -> LowerSet.iSup_Iic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (iSup.{u1, succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (fun (a : α) => iSup.{u1, 0} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasSup.{u1} α (Preorder.toHasLe.{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) => LowerSet.Iic.{u1} α _inst_1 a))) (lowerClosure.{u1} α _inst_1 s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (iSup.{u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instSupSetLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (fun (a : α) => iSup.{u1, 0} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instSupSetLowerSet.{u1} α (Preorder.toLE.{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) => LowerSet.Iic.{u1} α _inst_1 a))) (lowerClosure.{u1} α _inst_1 s)
+Case conversion may be inaccurate. Consider using '#align lower_set.supr_Iic LowerSet.iSup_Iicₓ'. -/
 @[simp]
 theorem LowerSet.iSup_Iic (s : Set α) : (⨆ a ∈ s, LowerSet.Iic a) = lowerClosure s :=
   by
   ext
   simp
 #align lower_set.supr_Iic LowerSet.iSup_Iic
--/
 
 #print gc_upperClosure_coe /-
 theorem gc_upperClosure_coe :
@@ -2301,7 +2481,7 @@ theorem gc_upperClosure_coe :
 
 /- warning: gc_lower_closure_coe -> gc_lowerClosure_coe is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], GaloisConnection.{u1, u1} (Set.{u1} α) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (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))))))) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))) (lowerClosure.{u1} α _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1))))))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], GaloisConnection.{u1, u1} (Set.{u1} α) (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (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))))))) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))) (lowerClosure.{u1} α _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], GaloisConnection.{u1, u1} (Set.{u1} α) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (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))))))) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1))))))) (lowerClosure.{u1} α _inst_1) (SetLike.coe.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.instSetLikeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))
 Case conversion may be inaccurate. Consider using '#align gc_lower_closure_coe gc_lowerClosure_coeₓ'. -/
@@ -2312,7 +2492,7 @@ theorem gc_lowerClosure_coe : GaloisConnection (lowerClosure : Set α → LowerS
 
 /- warning: gi_upper_closure_coe -> giUpperClosureCoe is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], GaloisInsertion.{u1, u1} (Set.{u1} α) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (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))))))) (OrderDual.preorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Function.comp.{succ u1, succ u1, succ u1} (Set.{u1} α) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (fun (_x : Equiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) => (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (Equiv.hasCoeToFun.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (OrderDual.toDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (upperClosure.{u1} α _inst_1)) (Function.comp.{succ u1, succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1)))))) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) => (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) -> (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderDual.ofDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], GaloisInsertion.{u1, u1} (Set.{u1} α) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (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))))))) (OrderDual.preorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (Function.comp.{succ u1, succ u1, succ u1} (Set.{u1} α) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))) (fun (_x : Equiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))) => (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))) (Equiv.hasCoeToFun.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))) (OrderDual.toDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))) (upperClosure.{u1} α _inst_1)) (Function.comp.{succ u1, succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) => (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) -> (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (OrderDual.ofDual.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], GaloisInsertion.{u1, u1} (Set.{u1} α) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (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))))))) (OrderDual.preorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Function.comp.{succ u1, succ u1, succ u1} (Set.{u1} α) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (OrderDual.toDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (upperClosure.{u1} α _inst_1)) (Function.comp.{succ u1, succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (fun (_x : OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) => UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderDual.ofDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align gi_upper_closure_coe giUpperClosureCoeₓ'. -/
@@ -2328,7 +2508,7 @@ def giUpperClosureCoe :
 
 /- warning: gi_lower_closure_coe -> giLowerClosureCoe is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], GaloisInsertion.{u1, u1} (Set.{u1} α) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (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))))))) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))) (lowerClosure.{u1} α _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1))))))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], GaloisInsertion.{u1, u1} (Set.{u1} α) (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (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))))))) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))) (lowerClosure.{u1} α _inst_1) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], GaloisInsertion.{u1, u1} (Set.{u1} α) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (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))))))) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1))))))) (lowerClosure.{u1} α _inst_1) (SetLike.coe.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.instSetLikeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))
 Case conversion may be inaccurate. Consider using '#align gi_lower_closure_coe giLowerClosureCoeₓ'. -/
@@ -2343,7 +2523,7 @@ def giLowerClosureCoe : GaloisInsertion (lowerClosure : Set α → LowerSet α)
 
 /- warning: upper_closure_anti -> upperClosure_anti is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Antitone.{u1, u1} (Set.{u1} α) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (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))))))) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))) (upperClosure.{u1} α _inst_1)
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Antitone.{u1, u1} (Set.{u1} α) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (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))))))) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))) (upperClosure.{u1} α _inst_1)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Antitone.{u1, u1} (Set.{u1} α) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (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))))))) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))))))) (upperClosure.{u1} α _inst_1)
 Case conversion may be inaccurate. Consider using '#align upper_closure_anti upperClosure_antiₓ'. -/
@@ -2353,7 +2533,7 @@ theorem upperClosure_anti : Antitone (upperClosure : Set α → UpperSet α) :=
 
 /- warning: lower_closure_mono -> lowerClosure_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Monotone.{u1, u1} (Set.{u1} α) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (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))))))) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))) (lowerClosure.{u1} α _inst_1)
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Monotone.{u1, u1} (Set.{u1} α) (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (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))))))) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))))) (lowerClosure.{u1} α _inst_1)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Monotone.{u1, u1} (Set.{u1} α) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (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))))))) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1))))))) (lowerClosure.{u1} α _inst_1)
 Case conversion may be inaccurate. Consider using '#align lower_closure_mono lowerClosure_monoₓ'. -/
@@ -2361,57 +2541,86 @@ theorem lowerClosure_mono : Monotone (lowerClosure : Set α → LowerSet α) :=
   gc_lowerClosure_coe.monotone_l
 #align lower_closure_mono lowerClosure_mono
 
-#print upperClosure_empty /-
+/- warning: upper_closure_empty -> upperClosure_empty is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (Top.top.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (Top.top.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instTopUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align upper_closure_empty upperClosure_emptyₓ'. -/
 @[simp]
 theorem upperClosure_empty : upperClosure (∅ : Set α) = ⊤ :=
   by
   ext
   simp
 #align upper_closure_empty upperClosure_empty
--/
 
-#print lowerClosure_empty /-
+/- warning: lower_closure_empty -> lowerClosure_empty is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (Bot.bot.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (Bot.bot.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instBotLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align lower_closure_empty lowerClosure_emptyₓ'. -/
 @[simp]
 theorem lowerClosure_empty : lowerClosure (∅ : Set α) = ⊥ :=
   by
   ext
   simp
 #align lower_closure_empty lowerClosure_empty
--/
 
-#print upperClosure_singleton /-
+/- warning: upper_closure_singleton -> upperClosure_singleton is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)) (UpperSet.Ici.{u1} α _inst_1 a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)) (UpperSet.Ici.{u1} α _inst_1 a)
+Case conversion may be inaccurate. Consider using '#align upper_closure_singleton upperClosure_singletonₓ'. -/
 @[simp]
 theorem upperClosure_singleton (a : α) : upperClosure ({a} : Set α) = UpperSet.Ici a :=
   by
   ext
   simp
 #align upper_closure_singleton upperClosure_singleton
--/
 
-#print lowerClosure_singleton /-
+/- warning: lower_closure_singleton -> lowerClosure_singleton is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)) (LowerSet.Iic.{u1} α _inst_1 a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (a : α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)) (LowerSet.Iic.{u1} α _inst_1 a)
+Case conversion may be inaccurate. Consider using '#align lower_closure_singleton lowerClosure_singletonₓ'. -/
 @[simp]
 theorem lowerClosure_singleton (a : α) : lowerClosure ({a} : Set α) = LowerSet.Iic a :=
   by
   ext
   simp
 #align lower_closure_singleton lowerClosure_singleton
--/
 
-#print upperClosure_univ /-
+/- warning: upper_closure_univ -> upperClosure_univ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Set.univ.{u1} α)) (Bot.bot.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Set.univ.{u1} α)) (Bot.bot.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instBotUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align upper_closure_univ upperClosure_univₓ'. -/
 @[simp]
 theorem upperClosure_univ : upperClosure (univ : Set α) = ⊥ :=
   le_bot_iff.1 subset_upperClosure
 #align upper_closure_univ upperClosure_univ
--/
 
-#print lowerClosure_univ /-
+/- warning: lower_closure_univ -> lowerClosure_univ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Set.univ.{u1} α)) (Top.top.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Set.univ.{u1} α)) (Top.top.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instTopLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align lower_closure_univ lowerClosure_univₓ'. -/
 @[simp]
 theorem lowerClosure_univ : lowerClosure (univ : Set α) = ⊤ :=
   top_le_iff.1 subset_lowerClosure
 #align lower_closure_univ lowerClosure_univ
--/
 
-#print upperClosure_eq_top_iff /-
+/- warning: upper_closure_eq_top_iff -> upperClosure_eq_top_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 s) (Top.top.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))) (Eq.{succ u1} (Set.{u1} α) s (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 s) (Top.top.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instTopUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (Eq.{succ u1} (Set.{u1} α) s (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α)))
+Case conversion may be inaccurate. Consider using '#align upper_closure_eq_top_iff upperClosure_eq_top_iffₓ'. -/
 @[simp]
 theorem upperClosure_eq_top_iff : upperClosure s = ⊤ ↔ s = ∅ :=
   ⟨fun h => subset_empty_iff.1 <| subset_upperClosure.trans (congr_arg coe h).Subset,
@@ -2419,9 +2628,13 @@ theorem upperClosure_eq_top_iff : upperClosure s = ⊤ ↔ s = ∅ :=
     rintro rfl
     exact upperClosure_empty⟩
 #align upper_closure_eq_top_iff upperClosure_eq_top_iff
--/
 
-#print lowerClosure_eq_bot_iff /-
+/- warning: lower_closure_eq_bot_iff -> lowerClosure_eq_bot_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 s) (Bot.bot.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))) (Eq.{succ u1} (Set.{u1} α) s (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 s) (Bot.bot.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instBotLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (Eq.{succ u1} (Set.{u1} α) s (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α)))
+Case conversion may be inaccurate. Consider using '#align lower_closure_eq_bot_iff lowerClosure_eq_bot_iffₓ'. -/
 @[simp]
 theorem lowerClosure_eq_bot_iff : lowerClosure s = ⊥ ↔ s = ∅ :=
   ⟨fun h => subset_empty_iff.1 <| subset_lowerClosure.trans (congr_arg coe h).Subset,
@@ -2429,11 +2642,10 @@ theorem lowerClosure_eq_bot_iff : lowerClosure s = ⊥ ↔ s = ∅ :=
     rintro rfl
     exact lowerClosure_empty⟩
 #align lower_closure_eq_bot_iff lowerClosure_eq_bot_iff
--/
 
 /- warning: upper_closure_union -> upperClosure_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Inf.inf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 s) (upperClosure.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Inf.inf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 s) (upperClosure.{u1} α _inst_1 t))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Inf.inf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instInfUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 s) (upperClosure.{u1} α _inst_1 t))
 Case conversion may be inaccurate. Consider using '#align upper_closure_union upperClosure_unionₓ'. -/
@@ -2446,7 +2658,7 @@ theorem upperClosure_union (s t : Set α) : upperClosure (s ∪ t) = upperClosur
 
 /- warning: lower_closure_union -> lowerClosure_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Sup.sup.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasSup.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 s) (lowerClosure.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Sup.sup.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 s) (lowerClosure.{u1} α _inst_1 t))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Sup.sup.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instSupLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 s) (lowerClosure.{u1} α _inst_1 t))
 Case conversion may be inaccurate. Consider using '#align lower_closure_union lowerClosure_unionₓ'. -/
@@ -2459,7 +2671,7 @@ theorem lowerClosure_union (s t : Set α) : lowerClosure (s ∪ t) = lowerClosur
 
 /- warning: upper_closure_Union -> upperClosure_iUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Preorder.{u1} α] (f : ι -> (Set.{u1} α)), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Set.iUnion.{u1, u2} α ι (fun (i : ι) => f i))) (iInf.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) ι (fun (i : ι) => upperClosure.{u1} α _inst_1 (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Preorder.{u1} α] (f : ι -> (Set.{u1} α)), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Set.iUnion.{u1, u2} α ι (fun (i : ι) => f i))) (iInf.{u1, u2} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) ι (fun (i : ι) => upperClosure.{u1} α _inst_1 (f i)))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : Preorder.{u2} α] (f : ι -> (Set.{u2} α)), Eq.{succ u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (upperClosure.{u2} α _inst_1 (Set.iUnion.{u2, u1} α ι (fun (i : ι) => f i))) (iInf.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instInfSetUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) ι (fun (i : ι) => upperClosure.{u2} α _inst_1 (f i)))
 Case conversion may be inaccurate. Consider using '#align upper_closure_Union upperClosure_iUnionₓ'. -/
@@ -2472,7 +2684,7 @@ theorem upperClosure_iUnion (f : ι → Set α) : upperClosure (⋃ i, f i) = 
 
 /- warning: lower_closure_Union -> lowerClosure_iUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Preorder.{u1} α] (f : ι -> (Set.{u1} α)), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Set.iUnion.{u1, u2} α ι (fun (i : ι) => f i))) (iSup.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasSup.{u1} α (Preorder.toLE.{u1} α _inst_1)) ι (fun (i : ι) => lowerClosure.{u1} α _inst_1 (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Preorder.{u1} α] (f : ι -> (Set.{u1} α)), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Set.iUnion.{u1, u2} α ι (fun (i : ι) => f i))) (iSup.{u1, u2} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) ι (fun (i : ι) => lowerClosure.{u1} α _inst_1 (f i)))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : Preorder.{u2} α] (f : ι -> (Set.{u2} α)), Eq.{succ u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (lowerClosure.{u2} α _inst_1 (Set.iUnion.{u2, u1} α ι (fun (i : ι) => f i))) (iSup.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instSupSetLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) ι (fun (i : ι) => lowerClosure.{u2} α _inst_1 (f i)))
 Case conversion may be inaccurate. Consider using '#align lower_closure_Union lowerClosure_iUnionₓ'. -/
@@ -2485,7 +2697,7 @@ theorem lowerClosure_iUnion (f : ι → Set α) : lowerClosure (⋃ i, f i) = 
 
 /- warning: upper_closure_sUnion -> upperClosure_sUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (S : Set.{u1} (Set.{u1} α)), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Set.sUnion.{u1} α S)) (iInf.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => iInf.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) s S) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) s S) => upperClosure.{u1} α _inst_1 s)))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (S : Set.{u1} (Set.{u1} α)), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Set.sUnion.{u1} α S)) (iInf.{u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => iInf.{u1, 0} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) s S) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) s S) => upperClosure.{u1} α _inst_1 s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (S : Set.{u1} (Set.{u1} α)), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Set.sUnion.{u1} α S)) (iInf.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instInfSetUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => iInf.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instInfSetUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) s S) (fun (H : Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) s S) => upperClosure.{u1} α _inst_1 s)))
 Case conversion may be inaccurate. Consider using '#align upper_closure_sUnion upperClosure_sUnionₓ'. -/
@@ -2494,16 +2706,20 @@ theorem upperClosure_sUnion (S : Set (Set α)) : upperClosure (⋃₀ S) = ⨅ s
   simp_rw [sUnion_eq_bUnion, upperClosure_iUnion]
 #align upper_closure_sUnion upperClosure_sUnion
 
-#print lowerClosure_sUnion /-
+/- warning: lower_closure_sUnion -> lowerClosure_sUnion is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (S : Set.{u1} (Set.{u1} α)), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Set.sUnion.{u1} α S)) (iSup.{u1, succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => iSup.{u1, 0} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) s S) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) s S) => lowerClosure.{u1} α _inst_1 s)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (S : Set.{u1} (Set.{u1} α)), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Set.sUnion.{u1} α S)) (iSup.{u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instSupSetLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => iSup.{u1, 0} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instSupSetLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) s S) (fun (H : Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) s S) => lowerClosure.{u1} α _inst_1 s)))
+Case conversion may be inaccurate. Consider using '#align lower_closure_sUnion lowerClosure_sUnionₓ'. -/
 @[simp]
 theorem lowerClosure_sUnion (S : Set (Set α)) : lowerClosure (⋃₀ S) = ⨆ s ∈ S, lowerClosure s := by
   simp_rw [sUnion_eq_bUnion, lowerClosure_iUnion]
 #align lower_closure_sUnion lowerClosure_sUnion
--/
 
 /- warning: set.ord_connected.upper_closure_inter_lower_closure -> Set.OrdConnected.upperClosure_inter_lowerClosure is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, (Set.OrdConnected.{u1} α _inst_1 s) -> (Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1))))) (upperClosure.{u1} α _inst_1 s)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1))))) (lowerClosure.{u1} α _inst_1 s))) s)
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, (Set.OrdConnected.{u1} α _inst_1 s) -> (Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))) (upperClosure.{u1} α _inst_1 s)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))) (lowerClosure.{u1} α _inst_1 s))) s)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, (Set.OrdConnected.{u1} α _inst_1 s) -> (Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 s)) (SetLike.coe.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.instSetLikeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 s))) s)
 Case conversion may be inaccurate. Consider using '#align set.ord_connected.upper_closure_inter_lower_closure Set.OrdConnected.upperClosure_inter_lowerClosureₓ'. -/
@@ -2515,7 +2731,7 @@ theorem Set.OrdConnected.upperClosure_inter_lowerClosure (h : s.OrdConnected) :
 
 /- warning: ord_connected_iff_upper_closure_inter_lower_closure -> ordConnected_iff_upperClosure_inter_lowerClosure is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, Iff (Set.OrdConnected.{u1} α _inst_1 s) (Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1))))) (upperClosure.{u1} α _inst_1 s)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1))))) (lowerClosure.{u1} α _inst_1 s))) s)
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, Iff (Set.OrdConnected.{u1} α _inst_1 s) (Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))) (upperClosure.{u1} α _inst_1 s)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))) (lowerClosure.{u1} α _inst_1 s))) s)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s : Set.{u1} α}, Iff (Set.OrdConnected.{u1} α _inst_1 s) (Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 s)) (SetLike.coe.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.instSetLikeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 s))) s)
 Case conversion may be inaccurate. Consider using '#align ord_connected_iff_upper_closure_inter_lower_closure ordConnected_iff_upperClosure_inter_lowerClosureₓ'. -/
@@ -2580,7 +2796,7 @@ variable {s : Set α} {t : Set β} {x : α × β}
 
 /- warning: is_upper_set.prod -> IsUpperSet.prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u2} β}, (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (IsUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2) t) -> (IsUpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (Set.prod.{u1, u2} α β s t))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u2} β}, (IsUpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (IsUpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2) t) -> (IsUpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (Set.prod.{u1, u2} α β s t))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {t : Set.{u1} β}, (IsUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1) s) -> (IsUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2) t) -> (IsUpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (Set.prod.{u2, u1} α β s t))
 Case conversion may be inaccurate. Consider using '#align is_upper_set.prod IsUpperSet.prodₓ'. -/
@@ -2591,7 +2807,7 @@ theorem IsUpperSet.prod (hs : IsUpperSet s) (ht : IsUpperSet t) : IsUpperSet (s
 
 /- warning: is_lower_set.prod -> IsLowerSet.prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u2} β}, (IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (IsLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2) t) -> (IsLowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (Set.prod.{u1, u2} α β s t))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u2} β}, (IsLowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1) s) -> (IsLowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2) t) -> (IsLowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)) (Set.prod.{u1, u2} α β s t))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {t : Set.{u1} β}, (IsLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1) s) -> (IsLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2) t) -> (IsLowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (Set.prod.{u2, u1} α β s t))
 Case conversion may be inaccurate. Consider using '#align is_lower_set.prod IsLowerSet.prodₓ'. -/
@@ -2606,20 +2822,24 @@ namespace UpperSet
 
 variable (s s₁ s₂ : UpperSet α) (t t₁ t₂ : UpperSet β) {x : α × β}
 
+/- warning: upper_set.prod -> UpperSet.prod is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β], (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) -> (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β], (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) -> (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)))
+Case conversion may be inaccurate. Consider using '#align upper_set.prod UpperSet.prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-#print UpperSet.prod /-
 /-- The product of two upper sets as an upper set. -/
 def prod : UpperSet (α × β) :=
   ⟨s ×ˢ t, s.2.Prod t.2⟩
 #align upper_set.prod UpperSet.prod
--/
 
 -- mathport name: upper_set.prod
 infixr:82 " ×ˢ " => prod
 
 /- warning: upper_set.coe_prod -> UpperSet.coe_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (Set.{max u1 u2} (Prod.{u1, u2} α β)) ((fun (a : Type.{max u1 u2}) (b : Type.{max u1 u2}) [self : HasLiftT.{succ (max u1 u2), succ (max u1 u2)} a b] => self.0) (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Set.{max u1 u2} (Prod.{u1, u2} α β)) (HasLiftT.mk.{succ (max u1 u2), succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Set.{max u1 u2} (Prod.{u1, u2} α β)) (CoeTCₓ.coe.{succ (max u1 u2), succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Set.{max u1 u2} (Prod.{u1, u2} α β)) (SetLike.Set.hasCoeT.{max u1 u2, max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Prod.{u1, u2} α β) (UpperSet.setLike.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)))))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t)) (Set.prod.{u1, u2} α β ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1))))) s) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Set.{u2} β) (SetLike.Set.hasCoeT.{u2, u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (UpperSet.setLike.{u2} β (Preorder.toLE.{u2} β _inst_2))))) t))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (t : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (Set.{max u1 u2} (Prod.{u1, u2} α β)) ((fun (a : Type.{max u1 u2}) (b : Type.{max u1 u2}) [self : HasLiftT.{succ (max u1 u2), succ (max u1 u2)} a b] => self.0) (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Set.{max u1 u2} (Prod.{u1, u2} α β)) (HasLiftT.mk.{succ (max u1 u2), succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Set.{max u1 u2} (Prod.{u1, u2} α β)) (CoeTCₓ.coe.{succ (max u1 u2), succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Set.{max u1 u2} (Prod.{u1, u2} α β)) (SetLike.Set.hasCoeT.{max u1 u2, max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Prod.{u1, u2} α β) (UpperSet.setLike.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)))))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t)) (Set.prod.{u1, u2} α β ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))) s) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Set.{u2} β) (SetLike.Set.hasCoeT.{u2, u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) β (UpperSet.setLike.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))) t))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (Set.{max u2 u1} (Prod.{u2, u1} α β)) (SetLike.coe.{max u2 u1, max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Prod.{u2, u1} α β) (UpperSet.instSetLikeUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s t)) (Set.prod.{u2, u1} α β (SetLike.coe.{u2, u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s) (SetLike.coe.{u1, u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) β (UpperSet.instSetLikeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t))
 Case conversion may be inaccurate. Consider using '#align upper_set.coe_prod UpperSet.coe_prodₓ'. -/
@@ -2632,7 +2852,7 @@ theorem coe_prod : (↑(s ×ˢ t) : Set (α × β)) = s ×ˢ t :=
 
 /- warning: upper_set.mem_prod -> UpperSet.mem_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {x : Prod.{u1, u2} α β} {s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, Iff (Membership.Mem.{max u1 u2, max u1 u2} (Prod.{u1, u2} α β) (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (SetLike.hasMem.{max u1 u2, max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Prod.{u1, u2} α β) (UpperSet.setLike.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)))) x (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t)) (And (Membership.Mem.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1))) (Prod.fst.{u1, u2} α β x) s) (Membership.Mem.{u2, u2} β (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (SetLike.hasMem.{u2, u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (UpperSet.setLike.{u2} β (Preorder.toLE.{u2} β _inst_2))) (Prod.snd.{u1, u2} α β x) t))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {x : Prod.{u1, u2} α β} {s : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {t : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)}, Iff (Membership.Mem.{max u1 u2, max u1 u2} (Prod.{u1, u2} α β) (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (SetLike.hasMem.{max u1 u2, max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Prod.{u1, u2} α β) (UpperSet.setLike.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)))) x (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t)) (And (Membership.Mem.{u1, u1} α (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (Prod.fst.{u1, u2} α β x) s) (Membership.Mem.{u2, u2} β (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (SetLike.hasMem.{u2, u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) β (UpperSet.setLike.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) (Prod.snd.{u1, u2} α β x) t))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {x : Prod.{u2, u1} α β} {s : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {t : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)}, Iff (Membership.mem.{max u2 u1, max u1 u2} (Prod.{u2, u1} α β) (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (SetLike.instMembership.{max u2 u1, max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Prod.{u2, u1} α β) (UpperSet.instSetLikeUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)))) x (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s t)) (And (Membership.mem.{u2, u2} α (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (SetLike.instMembership.{u2, u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1))) (Prod.fst.{u2, u1} α β x) s) (Membership.mem.{u1, u1} β (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) β (UpperSet.instSetLikeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (Prod.snd.{u2, u1} α β x) t))
 Case conversion may be inaccurate. Consider using '#align upper_set.mem_prod UpperSet.mem_prodₓ'. -/
@@ -2644,7 +2864,7 @@ theorem mem_prod {s : UpperSet α} {t : UpperSet β} : x ∈ s ×ˢ t ↔ x.1 
 
 /- warning: upper_set.Ici_prod -> UpperSet.Ici_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (x : Prod.{u1, u2} α β), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Preorder.toLE.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2))) (UpperSet.Ici.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2) x) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (UpperSet.Ici.{u1} α _inst_1 (Prod.fst.{u1, u2} α β x)) (UpperSet.Ici.{u2} β _inst_2 (Prod.snd.{u1, u2} α β x)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (x : Prod.{u1, u2} α β), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Preorder.toHasLe.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2))) (UpperSet.Ici.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2) x) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (UpperSet.Ici.{u1} α _inst_1 (Prod.fst.{u1, u2} α β x)) (UpperSet.Ici.{u2} β _inst_2 (Prod.snd.{u1, u2} α β x)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (x : Prod.{u2, u1} α β), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Preorder.toLE.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instPreorderProd.{u2, u1} α β _inst_1 _inst_2))) (UpperSet.Ici.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instPreorderProd.{u2, u1} α β _inst_1 _inst_2) x) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 (UpperSet.Ici.{u2} α _inst_1 (Prod.fst.{u2, u1} α β x)) (UpperSet.Ici.{u1} β _inst_2 (Prod.snd.{u2, u1} α β x)))
 Case conversion may be inaccurate. Consider using '#align upper_set.Ici_prod UpperSet.Ici_prodₓ'. -/
@@ -2655,7 +2875,7 @@ theorem Ici_prod (x : α × β) : Ici x = Ici x.1 ×ˢ Ici x.2 :=
 
 /- warning: upper_set.Ici_prod_Ici -> UpperSet.Ici_prod_Ici is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (a : α) (b : β), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (UpperSet.Ici.{u1} α _inst_1 a) (UpperSet.Ici.{u2} β _inst_2 b)) (UpperSet.Ici.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2) (Prod.mk.{u1, u2} α β a b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (a : α) (b : β), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (UpperSet.Ici.{u1} α _inst_1 a) (UpperSet.Ici.{u2} β _inst_2 b)) (UpperSet.Ici.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2) (Prod.mk.{u1, u2} α β a b))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (a : α) (b : β), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 (UpperSet.Ici.{u2} α _inst_1 a) (UpperSet.Ici.{u1} β _inst_2 b)) (UpperSet.Ici.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instPreorderProd.{u2, u1} α β _inst_1 _inst_2) (Prod.mk.{u2, u1} α β a b))
 Case conversion may be inaccurate. Consider using '#align upper_set.Ici_prod_Ici UpperSet.Ici_prod_Iciₓ'. -/
@@ -2667,7 +2887,7 @@ theorem Ici_prod_Ici (a : α) (b : β) : Ici a ×ˢ Ici b = Ici (a, b) :=
 
 /- warning: upper_set.prod_top -> UpperSet.prod_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s (Top.top.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.hasTop.{u2} β (Preorder.toLE.{u2} β _inst_2)))) (Top.top.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasTop.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s (Top.top.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.hasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))) (Top.top.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.hasTop.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s (Top.top.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instTopUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))) (Top.top.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instTopUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))))
 Case conversion may be inaccurate. Consider using '#align upper_set.prod_top UpperSet.prod_topₓ'. -/
@@ -2679,7 +2899,7 @@ theorem prod_top : s ×ˢ (⊤ : UpperSet β) = ⊤ :=
 
 /- warning: upper_set.top_prod -> UpperSet.top_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (t : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (Top.top.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasTop.{u1} α (Preorder.toLE.{u1} α _inst_1))) t) (Top.top.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasTop.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (t : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (Top.top.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) t) (Top.top.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.hasTop.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (t : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 (Top.top.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instTopUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1))) t) (Top.top.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instTopUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))))
 Case conversion may be inaccurate. Consider using '#align upper_set.top_prod UpperSet.top_prodₓ'. -/
@@ -2691,7 +2911,7 @@ theorem top_prod : (⊤ : UpperSet α) ×ˢ t = ⊤ :=
 
 /- warning: upper_set.bot_prod_bot -> UpperSet.bot_prod_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β], Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (Bot.bot.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasBot.{u1} α (Preorder.toLE.{u1} α _inst_1))) (Bot.bot.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.hasBot.{u2} β (Preorder.toLE.{u2} β _inst_2)))) (Bot.bot.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasBot.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β], Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (Bot.bot.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (Bot.bot.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.hasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))) (Bot.bot.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.hasBot.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β], Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 (Bot.bot.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instBotUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1))) (Bot.bot.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instBotUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))) (Bot.bot.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instBotUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))))
 Case conversion may be inaccurate. Consider using '#align upper_set.bot_prod_bot UpperSet.bot_prod_botₓ'. -/
@@ -2703,7 +2923,7 @@ theorem bot_prod_bot : (⊥ : UpperSet α) ×ˢ (⊥ : UpperSet β) = ⊥ :=
 
 /- warning: upper_set.sup_prod -> UpperSet.sup_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (s₂ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (Sup.sup.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α _inst_1)) s₁ s₂) t) (Sup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (s₂ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (t : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (Sup.sup.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) s₁ s₂) t) (Sup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 (Sup.sup.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instSupUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) t) (Sup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instSupUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t))
 Case conversion may be inaccurate. Consider using '#align upper_set.sup_prod UpperSet.sup_prodₓ'. -/
@@ -2717,7 +2937,7 @@ theorem sup_prod : (s₁ ⊔ s₂) ×ˢ t = s₁ ×ˢ t ⊔ s₂ ×ˢ t :=
 
 /- warning: upper_set.prod_sup -> UpperSet.prod_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t₁ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (t₂ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s (Sup.sup.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.hasSup.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ t₂)) (Sup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (t₁ : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (t₂ : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s (Sup.sup.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.hasSup.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) t₁ t₂)) (Sup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t₁ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (t₂ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s (Sup.sup.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instSupUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ t₂)) (Sup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instSupUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₂))
 Case conversion may be inaccurate. Consider using '#align upper_set.prod_sup UpperSet.prod_supₓ'. -/
@@ -2731,7 +2951,7 @@ theorem prod_sup : s ×ˢ (t₁ ⊔ t₂) = s ×ˢ t₁ ⊔ s ×ˢ t₂ :=
 
 /- warning: upper_set.inf_prod -> UpperSet.inf_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (s₂ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (Inf.inf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) s₁ s₂) t) (Inf.inf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (s₂ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (t : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (Inf.inf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) s₁ s₂) t) (Inf.inf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.hasInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 (Inf.inf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instInfUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) t) (Inf.inf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instInfUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t))
 Case conversion may be inaccurate. Consider using '#align upper_set.inf_prod UpperSet.inf_prodₓ'. -/
@@ -2745,7 +2965,7 @@ theorem inf_prod : (s₁ ⊓ s₂) ×ˢ t = s₁ ×ˢ t ⊓ s₂ ×ˢ t :=
 
 /- warning: upper_set.prod_inf -> UpperSet.prod_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t₁ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (t₂ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s (Inf.inf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.hasInf.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ t₂)) (Inf.inf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (t₁ : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (t₂ : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s (Inf.inf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.hasInf.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) t₁ t₂)) (Inf.inf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.hasInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t₁ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (t₂ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s (Inf.inf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instInfUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ t₂)) (Inf.inf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instInfUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₂))
 Case conversion may be inaccurate. Consider using '#align upper_set.prod_inf UpperSet.prod_infₓ'. -/
@@ -2759,7 +2979,7 @@ theorem prod_inf : s ×ˢ (t₁ ⊓ t₂) = s ×ˢ t₁ ⊓ s ×ˢ t₂ :=
 
 /- warning: upper_set.prod_sup_prod -> UpperSet.prod_sup_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (s₂ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t₁ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (t₂ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Sup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (Sup.sup.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α _inst_1)) s₁ s₂) (Sup.sup.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.hasSup.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ t₂))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (s₂ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (t₁ : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (t₂ : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Sup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (Sup.sup.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) s₁ s₂) (Sup.sup.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.hasSup.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) t₁ t₂))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t₁ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (t₂ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Sup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instSupUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t₁) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t₂)) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 (Sup.sup.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instSupUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) (Sup.sup.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instSupUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ t₂))
 Case conversion may be inaccurate. Consider using '#align upper_set.prod_sup_prod UpperSet.prod_sup_prodₓ'. -/
@@ -2774,7 +2994,7 @@ variable {s s₁ s₂ t t₁ t₂}
 
 /- warning: upper_set.prod_mono -> UpperSet.prod_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t₁ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)} {t₂ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) s₁ s₂) -> (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) t₁ t₂) -> (LE.le.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Preorder.toLE.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {s₂ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {t₁ : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)} {t₂ : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)}, (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) s₁ s₂) -> (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))) t₁ t₂) -> (LE.le.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Preorder.toHasLe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))))))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s₁ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {s₂ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {t₁ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)} {t₂ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)}, (LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)))))))) s₁ s₂) -> (LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) t₁ t₂) -> (LE.le.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Preorder.toLE.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (PartialOrder.toPreorder.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instCompleteDistribLatticeUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))))))))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t₁) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t₂))
 Case conversion may be inaccurate. Consider using '#align upper_set.prod_mono UpperSet.prod_monoₓ'. -/
@@ -2786,7 +3006,7 @@ theorem prod_mono : s₁ ≤ s₂ → t₁ ≤ t₂ → s₁ ×ˢ t₁ ≤ s₂
 
 /- warning: upper_set.prod_mono_left -> UpperSet.prod_mono_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) s₁ s₂) -> (LE.le.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Preorder.toLE.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {s₂ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {t : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)}, (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) s₁ s₂) -> (LE.le.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Preorder.toHasLe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))))))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s₁ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {s₂ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {t : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)}, (LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)))))))) s₁ s₂) -> (LE.le.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Preorder.toLE.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (PartialOrder.toPreorder.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instCompleteDistribLatticeUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))))))))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t))
 Case conversion may be inaccurate. Consider using '#align upper_set.prod_mono_left UpperSet.prod_mono_leftₓ'. -/
@@ -2798,7 +3018,7 @@ theorem prod_mono_left : s₁ ≤ s₂ → s₁ ×ˢ t ≤ s₂ ×ˢ t :=
 
 /- warning: upper_set.prod_mono_right -> UpperSet.prod_mono_right is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t₁ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)} {t₂ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) t₁ t₂) -> (LE.le.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Preorder.toLE.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {t₁ : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)} {t₂ : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)}, (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))) t₁ t₂) -> (LE.le.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Preorder.toHasLe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))))))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t₁ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)} {t₂ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) t₁ t₂) -> (LE.le.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Preorder.toLE.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.instCompleteDistribLatticeUpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
 Case conversion may be inaccurate. Consider using '#align upper_set.prod_mono_right UpperSet.prod_mono_rightₓ'. -/
@@ -2810,7 +3030,7 @@ theorem prod_mono_right : t₁ ≤ t₂ → s ×ˢ t₁ ≤ s ×ˢ t₂ :=
 
 /- warning: upper_set.prod_self_le_prod_self -> UpperSet.prod_self_le_prod_self is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s₁ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)}, Iff (LE.le.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (Preorder.toLE.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (UpperSet.completeDistribLattice.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))))))))) (UpperSet.prod.{u1, u1} α α _inst_1 _inst_1 s₁ s₁) (UpperSet.prod.{u1, u1} α α _inst_1 _inst_1 s₂ s₂)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) s₁ s₂)
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s₁ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {s₂ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)}, Iff (LE.le.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (Preorder.toHasLe.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (UpperSet.completeDistribLattice.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))))))))) (UpperSet.prod.{u1, u1} α α _inst_1 _inst_1 s₁ s₁) (UpperSet.prod.{u1, u1} α α _inst_1 _inst_1 s₂ s₂)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) s₁ s₂)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s₁ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)}, Iff (LE.le.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (Preorder.toLE.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))))))))) (UpperSet.prod.{u1, u1} α α _inst_1 _inst_1 s₁ s₁) (UpperSet.prod.{u1, u1} α α _inst_1 _inst_1 s₂ s₂)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) s₁ s₂)
 Case conversion may be inaccurate. Consider using '#align upper_set.prod_self_le_prod_self UpperSet.prod_self_le_prod_selfₓ'. -/
@@ -2823,7 +3043,7 @@ theorem prod_self_le_prod_self : s₁ ×ˢ s₁ ≤ s₂ ×ˢ s₂ ↔ s₁ ≤
 
 /- warning: upper_set.prod_self_lt_prod_self -> UpperSet.prod_self_lt_prod_self is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s₁ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)}, Iff (LT.lt.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (Preorder.toLT.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (UpperSet.completeDistribLattice.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))))))))) (UpperSet.prod.{u1, u1} α α _inst_1 _inst_1 s₁ s₁) (UpperSet.prod.{u1, u1} α α _inst_1 _inst_1 s₂ s₂)) (LT.lt.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLT.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) s₁ s₂)
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s₁ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {s₂ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)}, Iff (LT.lt.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (Preorder.toHasLt.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (UpperSet.completeDistribLattice.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))))))))) (UpperSet.prod.{u1, u1} α α _inst_1 _inst_1 s₁ s₁) (UpperSet.prod.{u1, u1} α α _inst_1 _inst_1 s₂ s₂)) (LT.lt.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLt.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) s₁ s₂)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s₁ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)}, Iff (LT.lt.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (Preorder.toLT.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))))))))) (UpperSet.prod.{u1, u1} α α _inst_1 _inst_1 s₁ s₁) (UpperSet.prod.{u1, u1} α α _inst_1 _inst_1 s₂ s₂)) (LT.lt.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLT.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) s₁ s₂)
 Case conversion may be inaccurate. Consider using '#align upper_set.prod_self_lt_prod_self UpperSet.prod_self_lt_prod_selfₓ'. -/
@@ -2836,7 +3056,7 @@ theorem prod_self_lt_prod_self : s₁ ×ˢ s₁ < s₂ ×ˢ s₂ ↔ s₁ < s₂
 
 /- warning: upper_set.prod_le_prod_iff -> UpperSet.prod_le_prod_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t₁ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)} {t₂ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, Iff (LE.le.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Preorder.toLE.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (Or (And (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) s₁ s₂) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) t₁ t₂)) (Or (Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) s₂ (Top.top.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasTop.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (Eq.{succ u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₂ (Top.top.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.hasTop.{u2} β (Preorder.toLE.{u2} β _inst_2))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {s₂ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {t₁ : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)} {t₂ : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)}, Iff (LE.le.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Preorder.toHasLe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))))))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (Or (And (LE.le.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) s₁ s₂) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))) t₁ t₂)) (Or (Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) s₂ (Top.top.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))) (Eq.{succ u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) t₂ (Top.top.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.hasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s₁ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {s₂ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {t₁ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)} {t₂ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)}, Iff (LE.le.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Preorder.toLE.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (PartialOrder.toPreorder.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instCompleteDistribLatticeUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))))))))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t₁) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t₂)) (Or (And (LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)))))))) s₁ s₂) (LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) t₁ t₂)) (Or (Eq.{succ u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₂ (Top.top.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instTopUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)))) (Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₂ (Top.top.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instTopUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align upper_set.prod_le_prod_iff UpperSet.prod_le_prod_iffₓ'. -/
@@ -2848,7 +3068,7 @@ theorem prod_le_prod_iff : s₁ ×ˢ t₁ ≤ s₂ ×ˢ t₂ ↔ s₁ ≤ s₂ 
 
 /- warning: upper_set.prod_eq_top -> UpperSet.prod_eq_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, Iff (Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t) (Top.top.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasTop.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))) (Or (Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) s (Top.top.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasTop.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (Eq.{succ u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) t (Top.top.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.hasTop.{u2} β (Preorder.toLE.{u2} β _inst_2)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {t : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)}, Iff (Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t) (Top.top.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.hasTop.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))) (Or (Eq.{succ u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) s (Top.top.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.hasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))) (Eq.{succ u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) t (Top.top.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.hasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {t : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)}, Iff (Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s t) (Top.top.{max u2 u1} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instTopUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))))) (Or (Eq.{succ u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s (Top.top.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instTopUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)))) (Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t (Top.top.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instTopUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align upper_set.prod_eq_top UpperSet.prod_eq_topₓ'. -/
@@ -2862,7 +3082,7 @@ theorem prod_eq_top : s ×ˢ t = ⊤ ↔ s = ⊤ ∨ t = ⊤ :=
 
 /- warning: upper_set.codisjoint_prod -> UpperSet.codisjoint_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t₁ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)} {t₂ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, Iff (Codisjoint.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))) (BoundedOrder.toOrderTop.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Preorder.toLE.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))))) (CompleteLattice.toBoundedOrder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (Or (Codisjoint.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))) (BoundedOrder.toOrderTop.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (CompleteLattice.toBoundedOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))) s₁ s₂) (Codisjoint.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))) (BoundedOrder.toOrderTop.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) (CompleteLattice.toBoundedOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))) t₁ t₂))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {s₂ : UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {t₁ : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)} {t₂ : UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)}, Iff (Codisjoint.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))))) (BoundedOrder.toOrderTop.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Preorder.toHasLe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))))))) (CompleteLattice.toBoundedOrder.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (UpperSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (Or (Codisjoint.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))) (BoundedOrder.toOrderTop.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (CompleteLattice.toBoundedOrder.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))) s₁ s₂) (Codisjoint.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))) (BoundedOrder.toOrderTop.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))) (CompleteLattice.toBoundedOrder.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))) t₁ t₂))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t₁ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)} {t₂ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, Iff (Codisjoint.{max u2 u1} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.instCompleteDistribLatticeUpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))) (BoundedOrder.toOrderTop.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Preorder.toLE.{max u2 u1} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u2 u1} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.instCompleteDistribLatticeUpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))))) (CompleteLattice.toBoundedOrder.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (UpperSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.instCompleteDistribLatticeUpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (Or (Codisjoint.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))) (BoundedOrder.toOrderTop.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (CompleteLattice.toBoundedOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))) s₁ s₂) (Codisjoint.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))) (BoundedOrder.toOrderTop.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) (CompleteLattice.toBoundedOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))) t₁ t₂))
 Case conversion may be inaccurate. Consider using '#align upper_set.codisjoint_prod UpperSet.codisjoint_prodₓ'. -/
@@ -2879,20 +3099,24 @@ namespace LowerSet
 
 variable (s s₁ s₂ : LowerSet α) (t t₁ t₂ : LowerSet β) {x : α × β}
 
+/- warning: lower_set.prod -> LowerSet.prod is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β], (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) -> (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) -> (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β], (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) -> (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)))
+Case conversion may be inaccurate. Consider using '#align lower_set.prod LowerSet.prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-#print LowerSet.prod /-
 /-- The product of two lower sets as a lower set. -/
 def prod : LowerSet (α × β) :=
   ⟨s ×ˢ t, s.2.Prod t.2⟩
 #align lower_set.prod LowerSet.prod
--/
 
 -- mathport name: lower_set.prod
 infixr:82 " ×ˢ " => LowerSet.prod
 
 /- warning: lower_set.coe_prod -> LowerSet.coe_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (Set.{max u1 u2} (Prod.{u1, u2} α β)) ((fun (a : Type.{max u1 u2}) (b : Type.{max u1 u2}) [self : HasLiftT.{succ (max u1 u2), succ (max u1 u2)} a b] => self.0) (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Set.{max u1 u2} (Prod.{u1, u2} α β)) (HasLiftT.mk.{succ (max u1 u2), succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Set.{max u1 u2} (Prod.{u1, u2} α β)) (CoeTCₓ.coe.{succ (max u1 u2), succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Set.{max u1 u2} (Prod.{u1, u2} α β)) (SetLike.Set.hasCoeT.{max u1 u2, max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Prod.{u1, u2} α β) (LowerSet.setLike.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)))))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t)) (Set.prod.{u1, u2} α β ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1))))) s) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Set.{u2} β) (SetLike.Set.hasCoeT.{u2, u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (LowerSet.setLike.{u2} β (Preorder.toLE.{u2} β _inst_2))))) t))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (t : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (Set.{max u1 u2} (Prod.{u1, u2} α β)) ((fun (a : Type.{max u1 u2}) (b : Type.{max u1 u2}) [self : HasLiftT.{succ (max u1 u2), succ (max u1 u2)} a b] => self.0) (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Set.{max u1 u2} (Prod.{u1, u2} α β)) (HasLiftT.mk.{succ (max u1 u2), succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Set.{max u1 u2} (Prod.{u1, u2} α β)) (CoeTCₓ.coe.{succ (max u1 u2), succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Set.{max u1 u2} (Prod.{u1, u2} α β)) (SetLike.Set.hasCoeT.{max u1 u2, max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Prod.{u1, u2} α β) (LowerSet.setLike.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)))))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t)) (Set.prod.{u1, u2} α β ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))))) s) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Set.{u2} β) (SetLike.Set.hasCoeT.{u2, u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) β (LowerSet.setLike.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))) t))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (Set.{max u2 u1} (Prod.{u2, u1} α β)) (SetLike.coe.{max u2 u1, max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Prod.{u2, u1} α β) (LowerSet.instSetLikeLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s t)) (Set.prod.{u2, u1} α β (SetLike.coe.{u2, u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) α (LowerSet.instSetLikeLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s) (SetLike.coe.{u1, u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) β (LowerSet.instSetLikeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t))
 Case conversion may be inaccurate. Consider using '#align lower_set.coe_prod LowerSet.coe_prodₓ'. -/
@@ -2905,7 +3129,7 @@ theorem coe_prod : (↑(s ×ˢ t) : Set (α × β)) = s ×ˢ t :=
 
 /- warning: lower_set.mem_prod -> LowerSet.mem_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {x : Prod.{u1, u2} α β} {s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, Iff (Membership.Mem.{max u1 u2, max u1 u2} (Prod.{u1, u2} α β) (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (SetLike.hasMem.{max u1 u2, max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Prod.{u1, u2} α β) (LowerSet.setLike.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)))) x (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t)) (And (Membership.Mem.{u1, u1} α (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1))) (Prod.fst.{u1, u2} α β x) s) (Membership.Mem.{u2, u2} β (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (SetLike.hasMem.{u2, u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (LowerSet.setLike.{u2} β (Preorder.toLE.{u2} β _inst_2))) (Prod.snd.{u1, u2} α β x) t))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {x : Prod.{u1, u2} α β} {s : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {t : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)}, Iff (Membership.Mem.{max u1 u2, max u1 u2} (Prod.{u1, u2} α β) (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (SetLike.hasMem.{max u1 u2, max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Prod.{u1, u2} α β) (LowerSet.setLike.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2)))) x (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t)) (And (Membership.Mem.{u1, u1} α (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (Prod.fst.{u1, u2} α β x) s) (Membership.Mem.{u2, u2} β (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (SetLike.hasMem.{u2, u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) β (LowerSet.setLike.{u2} β (Preorder.toHasLe.{u2} β _inst_2))) (Prod.snd.{u1, u2} α β x) t))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {x : Prod.{u2, u1} α β} {s : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {t : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)}, Iff (Membership.mem.{max u2 u1, max u1 u2} (Prod.{u2, u1} α β) (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (SetLike.instMembership.{max u2 u1, max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Prod.{u2, u1} α β) (LowerSet.instSetLikeLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)))) x (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s t)) (And (Membership.mem.{u2, u2} α (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (SetLike.instMembership.{u2, u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) α (LowerSet.instSetLikeLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1))) (Prod.fst.{u2, u1} α β x) s) (Membership.mem.{u1, u1} β (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) β (LowerSet.instSetLikeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (Prod.snd.{u2, u1} α β x) t))
 Case conversion may be inaccurate. Consider using '#align lower_set.mem_prod LowerSet.mem_prodₓ'. -/
@@ -2917,7 +3141,7 @@ theorem mem_prod {s : LowerSet α} {t : LowerSet β} : x ∈ s ×ˢ t ↔ x.1 
 
 /- warning: lower_set.Iic_prod -> LowerSet.Iic_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (x : Prod.{u1, u2} α β), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Preorder.toLE.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2))) (LowerSet.Iic.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2) x) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (LowerSet.Iic.{u1} α _inst_1 (Prod.fst.{u1, u2} α β x)) (LowerSet.Iic.{u2} β _inst_2 (Prod.snd.{u1, u2} α β x)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (x : Prod.{u1, u2} α β), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Preorder.toHasLe.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2))) (LowerSet.Iic.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2) x) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (LowerSet.Iic.{u1} α _inst_1 (Prod.fst.{u1, u2} α β x)) (LowerSet.Iic.{u2} β _inst_2 (Prod.snd.{u1, u2} α β x)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (x : Prod.{u2, u1} α β), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Preorder.toLE.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instPreorderProd.{u2, u1} α β _inst_1 _inst_2))) (LowerSet.Iic.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instPreorderProd.{u2, u1} α β _inst_1 _inst_2) x) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 (LowerSet.Iic.{u2} α _inst_1 (Prod.fst.{u2, u1} α β x)) (LowerSet.Iic.{u1} β _inst_2 (Prod.snd.{u2, u1} α β x)))
 Case conversion may be inaccurate. Consider using '#align lower_set.Iic_prod LowerSet.Iic_prodₓ'. -/
@@ -2928,7 +3152,7 @@ theorem Iic_prod (x : α × β) : Iic x = Iic x.1 ×ˢ Iic x.2 :=
 
 /- warning: lower_set.Ici_prod_Ici -> LowerSet.Ici_prod_Ici is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (a : α) (b : β), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (LowerSet.Iic.{u1} α _inst_1 a) (LowerSet.Iic.{u2} β _inst_2 b)) (LowerSet.Iic.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2) (Prod.mk.{u1, u2} α β a b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (a : α) (b : β), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (LowerSet.Iic.{u1} α _inst_1 a) (LowerSet.Iic.{u2} β _inst_2 b)) (LowerSet.Iic.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2) (Prod.mk.{u1, u2} α β a b))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (a : α) (b : β), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 (LowerSet.Iic.{u2} α _inst_1 a) (LowerSet.Iic.{u1} β _inst_2 b)) (LowerSet.Iic.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instPreorderProd.{u2, u1} α β _inst_1 _inst_2) (Prod.mk.{u2, u1} α β a b))
 Case conversion may be inaccurate. Consider using '#align lower_set.Ici_prod_Ici LowerSet.Ici_prod_Iciₓ'. -/
@@ -2940,7 +3164,7 @@ theorem Ici_prod_Ici (a : α) (b : β) : Iic a ×ˢ Iic b = Iic (a, b) :=
 
 /- warning: lower_set.prod_bot -> LowerSet.prod_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s (Bot.bot.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.hasBot.{u2} β (Preorder.toLE.{u2} β _inst_2)))) (Bot.bot.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.hasBot.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s (Bot.bot.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.hasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))) (Bot.bot.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.hasBot.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s (Bot.bot.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instBotLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))) (Bot.bot.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instBotLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))))
 Case conversion may be inaccurate. Consider using '#align lower_set.prod_bot LowerSet.prod_botₓ'. -/
@@ -2952,7 +3176,7 @@ theorem prod_bot : s ×ˢ (⊥ : LowerSet β) = ⊥ :=
 
 /- warning: lower_set.bot_prod -> LowerSet.bot_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (t : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (Bot.bot.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasBot.{u1} α (Preorder.toLE.{u1} α _inst_1))) t) (Bot.bot.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.hasBot.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (t : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (Bot.bot.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) t) (Bot.bot.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.hasBot.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (t : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 (Bot.bot.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instBotLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1))) t) (Bot.bot.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instBotLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))))
 Case conversion may be inaccurate. Consider using '#align lower_set.bot_prod LowerSet.bot_prodₓ'. -/
@@ -2964,7 +3188,7 @@ theorem bot_prod : (⊥ : LowerSet α) ×ˢ t = ⊥ :=
 
 /- warning: lower_set.top_prod_top -> LowerSet.top_prod_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β], Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (Top.top.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasTop.{u1} α (Preorder.toLE.{u1} α _inst_1))) (Top.top.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.hasTop.{u2} β (Preorder.toLE.{u2} β _inst_2)))) (Top.top.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.hasTop.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β], Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (Top.top.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_1))) (Top.top.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.hasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))) (Top.top.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.hasTop.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β], Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 (Top.top.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instTopLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1))) (Top.top.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instTopLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))) (Top.top.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instTopLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))))
 Case conversion may be inaccurate. Consider using '#align lower_set.top_prod_top LowerSet.top_prod_topₓ'. -/
@@ -2976,7 +3200,7 @@ theorem top_prod_top : (⊤ : LowerSet α) ×ˢ (⊤ : LowerSet β) = ⊤ :=
 
 /- warning: lower_set.inf_prod -> LowerSet.inf_prod is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (s₂ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (t : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (Inf.inf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) s₁ s₂) t) (Inf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.hasInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 (Inf.inf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instInfLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) t) (Inf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instInfLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t))
 Case conversion may be inaccurate. Consider using '#align lower_set.inf_prod LowerSet.inf_prodₓ'. -/
@@ -2990,7 +3214,7 @@ theorem inf_prod : (s₁ ⊓ s₂) ×ˢ t = s₁ ×ˢ t ⊓ s₂ ×ˢ t :=
 
 /- warning: lower_set.prod_inf -> LowerSet.prod_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t₁ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (t₂ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s (Inf.inf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.hasInf.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ t₂)) (Inf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.hasInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (t₁ : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (t₂ : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s (Inf.inf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.hasInf.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) t₁ t₂)) (Inf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.hasInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t₁ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (t₂ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s (Inf.inf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instInfLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ t₂)) (Inf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instInfLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₁) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₂))
 Case conversion may be inaccurate. Consider using '#align lower_set.prod_inf LowerSet.prod_infₓ'. -/
@@ -3004,7 +3228,7 @@ theorem prod_inf : s ×ˢ (t₁ ⊓ t₂) = s ×ˢ t₁ ⊓ s ×ˢ t₂ :=
 
 /- warning: lower_set.sup_prod -> LowerSet.sup_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (Sup.sup.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasSup.{u1} α (Preorder.toLE.{u1} α _inst_1)) s₁ s₂) t) (Sup.sup.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (s₂ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (t : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (Sup.sup.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasSup.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) s₁ s₂) t) (Sup.sup.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 (Sup.sup.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instSupLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) t) (Sup.sup.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instSupLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t))
 Case conversion may be inaccurate. Consider using '#align lower_set.sup_prod LowerSet.sup_prodₓ'. -/
@@ -3018,7 +3242,7 @@ theorem sup_prod : (s₁ ⊔ s₂) ×ˢ t = s₁ ×ˢ t ⊔ s₂ ×ˢ t :=
 
 /- warning: lower_set.prod_sup -> LowerSet.prod_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t₁ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (t₂ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s (Sup.sup.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.hasSup.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ t₂)) (Sup.sup.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (t₁ : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (t₂ : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s (Sup.sup.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.hasSup.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) t₁ t₂)) (Sup.sup.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t₁ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (t₂ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s (Sup.sup.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instSupLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ t₂)) (Sup.sup.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instSupLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₁) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₂))
 Case conversion may be inaccurate. Consider using '#align lower_set.prod_sup LowerSet.prod_supₓ'. -/
@@ -3032,7 +3256,7 @@ theorem prod_sup : s ×ˢ (t₁ ⊔ t₂) = s ×ˢ t₁ ⊔ s ×ˢ t₂ :=
 
 /- warning: lower_set.prod_inf_prod -> LowerSet.prod_inf_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t₁ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (t₂ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Inf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.hasInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (Inf.inf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) s₁ s₂) (Inf.inf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.hasInf.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ t₂))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (s₂ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (t₁ : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (t₂ : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Inf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.hasInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (Inf.inf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasInf.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) s₁ s₂) (Inf.inf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.hasInf.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) t₁ t₂))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t₁ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (t₂ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Inf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instInfLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t₂)) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 (Inf.inf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instInfLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) (Inf.inf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instInfLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ t₂))
 Case conversion may be inaccurate. Consider using '#align lower_set.prod_inf_prod LowerSet.prod_inf_prodₓ'. -/
@@ -3047,7 +3271,7 @@ variable {s s₁ s₂ t t₁ t₂}
 
 /- warning: lower_set.prod_mono -> LowerSet.prod_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t₁ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)} {t₂ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) s₁ s₂) -> (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) t₁ t₂) -> (LE.le.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Preorder.toLE.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {s₂ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {t₁ : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)} {t₂ : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)}, (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) s₁ s₂) -> (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))) t₁ t₂) -> (LE.le.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Preorder.toHasLe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))))))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s₁ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {s₂ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {t₁ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)} {t₂ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)}, (LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)))))))) s₁ s₂) -> (LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) t₁ t₂) -> (LE.le.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Preorder.toLE.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (PartialOrder.toPreorder.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instCompleteDistribLatticeLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))))))))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t₂))
 Case conversion may be inaccurate. Consider using '#align lower_set.prod_mono LowerSet.prod_monoₓ'. -/
@@ -3059,7 +3283,7 @@ theorem prod_mono : s₁ ≤ s₂ → t₁ ≤ t₂ → s₁ ×ˢ t₁ ≤ s₂
 
 /- warning: lower_set.prod_mono_left -> LowerSet.prod_mono_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) s₁ s₂) -> (LE.le.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Preorder.toLE.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {s₂ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {t : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)}, (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) s₁ s₂) -> (LE.le.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Preorder.toHasLe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))))))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s₁ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {s₂ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {t : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)}, (LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)))))))) s₁ s₂) -> (LE.le.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Preorder.toLE.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (PartialOrder.toPreorder.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instCompleteDistribLatticeLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))))))))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t))
 Case conversion may be inaccurate. Consider using '#align lower_set.prod_mono_left LowerSet.prod_mono_leftₓ'. -/
@@ -3071,7 +3295,7 @@ theorem prod_mono_left : s₁ ≤ s₂ → s₁ ×ˢ t ≤ s₂ ×ˢ t :=
 
 /- warning: lower_set.prod_mono_right -> LowerSet.prod_mono_right is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t₁ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)} {t₂ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) t₁ t₂) -> (LE.le.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Preorder.toLE.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {t₁ : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)} {t₂ : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)}, (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))) t₁ t₂) -> (LE.le.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Preorder.toHasLe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))))))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t₁ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)} {t₂ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) t₁ t₂) -> (LE.le.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Preorder.toLE.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.instCompleteDistribLatticeLowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
 Case conversion may be inaccurate. Consider using '#align lower_set.prod_mono_right LowerSet.prod_mono_rightₓ'. -/
@@ -3083,7 +3307,7 @@ theorem prod_mono_right : t₁ ≤ t₂ → s ×ˢ t₁ ≤ s ×ˢ t₂ :=
 
 /- warning: lower_set.prod_self_le_prod_self -> LowerSet.prod_self_le_prod_self is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)}, Iff (LE.le.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (Preorder.toLE.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (LowerSet.completeDistribLattice.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))))))))) (LowerSet.prod.{u1, u1} α α _inst_1 _inst_1 s₁ s₁) (LowerSet.prod.{u1, u1} α α _inst_1 _inst_1 s₂ s₂)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) s₁ s₂)
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s₁ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {s₂ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)}, Iff (LE.le.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (Preorder.toHasLe.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (LowerSet.completeDistribLattice.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))))))))) (LowerSet.prod.{u1, u1} α α _inst_1 _inst_1 s₁ s₁) (LowerSet.prod.{u1, u1} α α _inst_1 _inst_1 s₂ s₂)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) s₁ s₂)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)}, Iff (LE.le.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (Preorder.toLE.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))))))))) (LowerSet.prod.{u1, u1} α α _inst_1 _inst_1 s₁ s₁) (LowerSet.prod.{u1, u1} α α _inst_1 _inst_1 s₂ s₂)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) s₁ s₂)
 Case conversion may be inaccurate. Consider using '#align lower_set.prod_self_le_prod_self LowerSet.prod_self_le_prod_selfₓ'. -/
@@ -3096,7 +3320,7 @@ theorem prod_self_le_prod_self : s₁ ×ˢ s₁ ≤ s₂ ×ˢ s₂ ↔ s₁ ≤
 
 /- warning: lower_set.prod_self_lt_prod_self -> LowerSet.prod_self_lt_prod_self is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)}, Iff (LT.lt.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (Preorder.toLT.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (LowerSet.completeDistribLattice.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))))))))) (LowerSet.prod.{u1, u1} α α _inst_1 _inst_1 s₁ s₁) (LowerSet.prod.{u1, u1} α α _inst_1 _inst_1 s₂ s₂)) (LT.lt.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLT.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) s₁ s₂)
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s₁ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {s₂ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)}, Iff (LT.lt.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (Preorder.toHasLt.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))) (LowerSet.completeDistribLattice.{u1} (Prod.{u1, u1} α α) (Prod.hasLe.{u1, u1} α α (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u1} α _inst_1))))))))) (LowerSet.prod.{u1, u1} α α _inst_1 _inst_1 s₁ s₁) (LowerSet.prod.{u1, u1} α α _inst_1 _inst_1 s₂ s₂)) (LT.lt.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLt.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) s₁ s₂)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] {s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)}, Iff (LT.lt.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (Preorder.toLT.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} (Prod.{u1, u1} α α) (Prod.instLEProd.{u1, u1} α α (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u1} α _inst_1))))))))) (LowerSet.prod.{u1, u1} α α _inst_1 _inst_1 s₁ s₁) (LowerSet.prod.{u1, u1} α α _inst_1 _inst_1 s₂ s₂)) (LT.lt.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLT.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) s₁ s₂)
 Case conversion may be inaccurate. Consider using '#align lower_set.prod_self_lt_prod_self LowerSet.prod_self_lt_prod_selfₓ'. -/
@@ -3109,7 +3333,7 @@ theorem prod_self_lt_prod_self : s₁ ×ˢ s₁ < s₂ ×ˢ s₂ ↔ s₁ < s₂
 
 /- warning: lower_set.prod_le_prod_iff -> LowerSet.prod_le_prod_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t₁ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)} {t₂ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, Iff (LE.le.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Preorder.toLE.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (Or (And (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) s₁ s₂) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) t₁ t₂)) (Or (Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) s₁ (Bot.bot.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasBot.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (Eq.{succ u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ (Bot.bot.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.hasBot.{u2} β (Preorder.toLE.{u2} β _inst_2))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {s₂ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {t₁ : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)} {t₂ : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)}, Iff (LE.le.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Preorder.toHasLe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))))))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (Or (And (LE.le.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) s₁ s₂) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))) t₁ t₂)) (Or (Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) s₁ (Bot.bot.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))) (Eq.{succ u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) t₁ (Bot.bot.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.hasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2))))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s₁ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {s₂ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {t₁ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)} {t₂ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)}, Iff (LE.le.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Preorder.toLE.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (PartialOrder.toPreorder.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instCompleteDistribLatticeLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))))))))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t₂)) (Or (And (LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)))))))) s₁ s₂) (LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) t₁ t₂)) (Or (Eq.{succ u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ (Bot.bot.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instBotLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)))) (Eq.{succ u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ (Bot.bot.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instBotLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align lower_set.prod_le_prod_iff LowerSet.prod_le_prod_iffₓ'. -/
@@ -3121,7 +3345,7 @@ theorem prod_le_prod_iff : s₁ ×ˢ t₁ ≤ s₂ ×ˢ t₂ ↔ s₁ ≤ s₂ 
 
 /- warning: lower_set.prod_eq_bot -> LowerSet.prod_eq_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, Iff (Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t) (Bot.bot.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.hasBot.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))) (Or (Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) s (Bot.bot.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasBot.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (Eq.{succ u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) t (Bot.bot.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.hasBot.{u2} β (Preorder.toLE.{u2} β _inst_2)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {t : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)}, Iff (Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t) (Bot.bot.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.hasBot.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))) (Or (Eq.{succ u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) s (Bot.bot.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.hasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))) (Eq.{succ u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) t (Bot.bot.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.hasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {t : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)}, Iff (Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s t) (Bot.bot.{max u2 u1} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instBotLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))))) (Or (Eq.{succ u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s (Bot.bot.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instBotLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)))) (Eq.{succ u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t (Bot.bot.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instBotLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align lower_set.prod_eq_bot LowerSet.prod_eq_botₓ'. -/
@@ -3135,7 +3359,7 @@ theorem prod_eq_bot : s ×ˢ t = ⊥ ↔ s = ⊥ ∨ t = ⊥ :=
 
 /- warning: lower_set.disjoint_prod -> LowerSet.disjoint_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t₁ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)} {t₂ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, Iff (Disjoint.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))) (BoundedOrder.toOrderBot.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Preorder.toLE.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))))) (CompleteLattice.toBoundedOrder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (Or (Disjoint.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))) (BoundedOrder.toOrderBot.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (CompleteLattice.toBoundedOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))) s₁ s₂) (Disjoint.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))) (BoundedOrder.toOrderBot.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) (CompleteLattice.toBoundedOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))) t₁ t₂))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {s₂ : LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)} {t₁ : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)} {t₂ : LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)}, Iff (Disjoint.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))))) (BoundedOrder.toOrderBot.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Preorder.toHasLe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))))))) (CompleteLattice.toBoundedOrder.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))) (LowerSet.completeDistribLattice.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toHasLe.{u1} α _inst_1) (Preorder.toHasLe.{u2} β _inst_2))))))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (Or (Disjoint.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))) (BoundedOrder.toOrderBot.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Preorder.toHasLe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))))) (CompleteLattice.toBoundedOrder.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toHasLe.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toHasLe.{u1} α _inst_1)))))) s₁ s₂) (Disjoint.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))) (BoundedOrder.toOrderBot.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Preorder.toHasLe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))))) (CompleteLattice.toBoundedOrder.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toHasLe.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toHasLe.{u2} β _inst_2)))))) t₁ t₂))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {t₁ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)} {t₂ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)}, Iff (Disjoint.{max u2 u1} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.instCompleteDistribLatticeLowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))) (BoundedOrder.toOrderBot.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Preorder.toLE.{max u2 u1} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (PartialOrder.toPreorder.{max u2 u1} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteSemilatticeInf.toPartialOrder.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteLattice.toCompleteSemilatticeInf.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.instCompleteDistribLatticeLowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))))) (CompleteLattice.toBoundedOrder.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Order.Coframe.toCompleteLattice.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (CompleteDistribLattice.toCoframe.{max u1 u2} (LowerSet.{max u2 u1} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.instCompleteDistribLatticeLowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.instLEProd.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))))))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (Or (Disjoint.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))) (BoundedOrder.toOrderBot.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (CompleteLattice.toBoundedOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))) s₁ s₂) (Disjoint.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))) (BoundedOrder.toOrderBot.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) (CompleteLattice.toBoundedOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))) t₁ t₂))
 Case conversion may be inaccurate. Consider using '#align lower_set.disjoint_prod LowerSet.disjoint_prodₓ'. -/
@@ -3150,7 +3374,7 @@ end LowerSet
 
 /- warning: upper_closure_prod -> upperClosure_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : Set.{u1} α) (t : Set.{u2} β), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Preorder.toLE.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2))) (upperClosure.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2) (Set.prod.{u1, u2} α β s t)) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (upperClosure.{u1} α _inst_1 s) (upperClosure.{u2} β _inst_2 t))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : Set.{u1} α) (t : Set.{u2} β), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Preorder.toHasLe.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2))) (upperClosure.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2) (Set.prod.{u1, u2} α β s t)) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (upperClosure.{u1} α _inst_1 s) (upperClosure.{u2} β _inst_2 t))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : Set.{u2} α) (t : Set.{u1} β), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Preorder.toLE.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instPreorderProd.{u2, u1} α β _inst_1 _inst_2))) (upperClosure.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instPreorderProd.{u2, u1} α β _inst_1 _inst_2) (Set.prod.{u2, u1} α β s t)) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 (upperClosure.{u2} α _inst_1 s) (upperClosure.{u1} β _inst_2 t))
 Case conversion may be inaccurate. Consider using '#align upper_closure_prod upperClosure_prodₓ'. -/
@@ -3166,7 +3390,7 @@ theorem upperClosure_prod (s : Set α) (t : Set β) :
 
 /- warning: lower_closure_prod -> lowerClosure_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : Set.{u1} α) (t : Set.{u2} β), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Preorder.toLE.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2))) (lowerClosure.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2) (Set.prod.{u1, u2} α β s t)) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (lowerClosure.{u1} α _inst_1 s) (lowerClosure.{u2} β _inst_2 t))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : Set.{u1} α) (t : Set.{u2} β), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Preorder.toHasLe.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2))) (lowerClosure.{max u1 u2} (Prod.{u1, u2} α β) (Prod.preorder.{u1, u2} α β _inst_1 _inst_2) (Set.prod.{u1, u2} α β s t)) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (lowerClosure.{u1} α _inst_1 s) (lowerClosure.{u2} β _inst_2 t))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : Set.{u2} α) (t : Set.{u1} β), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Preorder.toLE.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instPreorderProd.{u2, u1} α β _inst_1 _inst_2))) (lowerClosure.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instPreorderProd.{u2, u1} α β _inst_1 _inst_2) (Set.prod.{u2, u1} α β s t)) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 (lowerClosure.{u2} α _inst_1 s) (lowerClosure.{u1} β _inst_2 t))
 Case conversion may be inaccurate. Consider using '#align lower_closure_prod lowerClosure_prodₓ'. -/

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

@@ -181,116 +181,116 @@ theorem IsLowerSet.inter (hs : IsLowerSet s) (ht : IsLowerSet t) : IsLowerSet (s
   fun a b h => And.imp (hs h) (ht h)
 #align is_lower_set.inter IsLowerSet.inter
 
-/- warning: is_upper_set_Union -> isUpperSet_unionᵢ is a dubious translation:
+/- warning: is_upper_set_Union -> isUpperSet_iUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {f : ι -> (Set.{u1} α)}, (forall (i : ι), IsUpperSet.{u1} α _inst_1 (f i)) -> (IsUpperSet.{u1} α _inst_1 (Set.unionᵢ.{u1, u2} α ι (fun (i : ι) => f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {f : ι -> (Set.{u1} α)}, (forall (i : ι), IsUpperSet.{u1} α _inst_1 (f i)) -> (IsUpperSet.{u1} α _inst_1 (Set.iUnion.{u1, u2} α ι (fun (i : ι) => f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {f : ι -> (Set.{u2} α)}, (forall (i : ι), IsUpperSet.{u2} α _inst_1 (f i)) -> (IsUpperSet.{u2} α _inst_1 (Set.unionᵢ.{u2, u1} α ι (fun (i : ι) => f i)))
-Case conversion may be inaccurate. Consider using '#align is_upper_set_Union isUpperSet_unionᵢₓ'. -/
-theorem isUpperSet_unionᵢ {f : ι → Set α} (hf : ∀ i, IsUpperSet (f i)) : IsUpperSet (⋃ i, f i) :=
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {f : ι -> (Set.{u2} α)}, (forall (i : ι), IsUpperSet.{u2} α _inst_1 (f i)) -> (IsUpperSet.{u2} α _inst_1 (Set.iUnion.{u2, u1} α ι (fun (i : ι) => f i)))
+Case conversion may be inaccurate. Consider using '#align is_upper_set_Union isUpperSet_iUnionₓ'. -/
+theorem isUpperSet_iUnion {f : ι → Set α} (hf : ∀ i, IsUpperSet (f i)) : IsUpperSet (⋃ i, f i) :=
   fun a b h => Exists₂.imp <| forall_range_iff.2 fun i => hf i h
-#align is_upper_set_Union isUpperSet_unionᵢ
+#align is_upper_set_Union isUpperSet_iUnion
 
-/- warning: is_lower_set_Union -> isLowerSet_unionᵢ is a dubious translation:
+/- warning: is_lower_set_Union -> isLowerSet_iUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {f : ι -> (Set.{u1} α)}, (forall (i : ι), IsLowerSet.{u1} α _inst_1 (f i)) -> (IsLowerSet.{u1} α _inst_1 (Set.unionᵢ.{u1, u2} α ι (fun (i : ι) => f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {f : ι -> (Set.{u1} α)}, (forall (i : ι), IsLowerSet.{u1} α _inst_1 (f i)) -> (IsLowerSet.{u1} α _inst_1 (Set.iUnion.{u1, u2} α ι (fun (i : ι) => f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {f : ι -> (Set.{u2} α)}, (forall (i : ι), IsLowerSet.{u2} α _inst_1 (f i)) -> (IsLowerSet.{u2} α _inst_1 (Set.unionᵢ.{u2, u1} α ι (fun (i : ι) => f i)))
-Case conversion may be inaccurate. Consider using '#align is_lower_set_Union isLowerSet_unionᵢₓ'. -/
-theorem isLowerSet_unionᵢ {f : ι → Set α} (hf : ∀ i, IsLowerSet (f i)) : IsLowerSet (⋃ i, f i) :=
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {f : ι -> (Set.{u2} α)}, (forall (i : ι), IsLowerSet.{u2} α _inst_1 (f i)) -> (IsLowerSet.{u2} α _inst_1 (Set.iUnion.{u2, u1} α ι (fun (i : ι) => f i)))
+Case conversion may be inaccurate. Consider using '#align is_lower_set_Union isLowerSet_iUnionₓ'. -/
+theorem isLowerSet_iUnion {f : ι → Set α} (hf : ∀ i, IsLowerSet (f i)) : IsLowerSet (⋃ i, f i) :=
   fun a b h => Exists₂.imp <| forall_range_iff.2 fun i => hf i h
-#align is_lower_set_Union isLowerSet_unionᵢ
+#align is_lower_set_Union isLowerSet_iUnion
 
-/- warning: is_upper_set_Union₂ -> isUpperSet_unionᵢ₂ is a dubious translation:
+/- warning: is_upper_set_Union₂ -> isUpperSet_iUnion₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {f : forall (i : ι), (κ i) -> (Set.{u1} α)}, (forall (i : ι) (j : κ i), IsUpperSet.{u1} α _inst_1 (f i j)) -> (IsUpperSet.{u1} α _inst_1 (Set.unionᵢ.{u1, u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, u3} α (κ i) (fun (j : κ i) => f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {f : forall (i : ι), (κ i) -> (Set.{u1} α)}, (forall (i : ι) (j : κ i), IsUpperSet.{u1} α _inst_1 (f i j)) -> (IsUpperSet.{u1} α _inst_1 (Set.iUnion.{u1, u2} α ι (fun (i : ι) => Set.iUnion.{u1, u3} α (κ i) (fun (j : κ i) => f i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {f : forall (i : ι), (κ i) -> (Set.{u3} α)}, (forall (i : ι) (j : κ i), IsUpperSet.{u3} α _inst_1 (f i j)) -> (IsUpperSet.{u3} α _inst_1 (Set.unionᵢ.{u3, u2} α ι (fun (i : ι) => Set.unionᵢ.{u3, u1} α (κ i) (fun (j : κ i) => f i j))))
-Case conversion may be inaccurate. Consider using '#align is_upper_set_Union₂ isUpperSet_unionᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {f : forall (i : ι), (κ i) -> (Set.{u3} α)}, (forall (i : ι) (j : κ i), IsUpperSet.{u3} α _inst_1 (f i j)) -> (IsUpperSet.{u3} α _inst_1 (Set.iUnion.{u3, u2} α ι (fun (i : ι) => Set.iUnion.{u3, u1} α (κ i) (fun (j : κ i) => f i j))))
+Case conversion may be inaccurate. Consider using '#align is_upper_set_Union₂ isUpperSet_iUnion₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem isUpperSet_unionᵢ₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsUpperSet (f i j)) :
+theorem isUpperSet_iUnion₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsUpperSet (f i j)) :
     IsUpperSet (⋃ (i) (j), f i j) :=
-  isUpperSet_unionᵢ fun i => isUpperSet_unionᵢ <| hf i
-#align is_upper_set_Union₂ isUpperSet_unionᵢ₂
+  isUpperSet_iUnion fun i => isUpperSet_iUnion <| hf i
+#align is_upper_set_Union₂ isUpperSet_iUnion₂
 
-/- warning: is_lower_set_Union₂ -> isLowerSet_unionᵢ₂ is a dubious translation:
+/- warning: is_lower_set_Union₂ -> isLowerSet_iUnion₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {f : forall (i : ι), (κ i) -> (Set.{u1} α)}, (forall (i : ι) (j : κ i), IsLowerSet.{u1} α _inst_1 (f i j)) -> (IsLowerSet.{u1} α _inst_1 (Set.unionᵢ.{u1, u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, u3} α (κ i) (fun (j : κ i) => f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {f : forall (i : ι), (κ i) -> (Set.{u1} α)}, (forall (i : ι) (j : κ i), IsLowerSet.{u1} α _inst_1 (f i j)) -> (IsLowerSet.{u1} α _inst_1 (Set.iUnion.{u1, u2} α ι (fun (i : ι) => Set.iUnion.{u1, u3} α (κ i) (fun (j : κ i) => f i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {f : forall (i : ι), (κ i) -> (Set.{u3} α)}, (forall (i : ι) (j : κ i), IsLowerSet.{u3} α _inst_1 (f i j)) -> (IsLowerSet.{u3} α _inst_1 (Set.unionᵢ.{u3, u2} α ι (fun (i : ι) => Set.unionᵢ.{u3, u1} α (κ i) (fun (j : κ i) => f i j))))
-Case conversion may be inaccurate. Consider using '#align is_lower_set_Union₂ isLowerSet_unionᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {f : forall (i : ι), (κ i) -> (Set.{u3} α)}, (forall (i : ι) (j : κ i), IsLowerSet.{u3} α _inst_1 (f i j)) -> (IsLowerSet.{u3} α _inst_1 (Set.iUnion.{u3, u2} α ι (fun (i : ι) => Set.iUnion.{u3, u1} α (κ i) (fun (j : κ i) => f i j))))
+Case conversion may be inaccurate. Consider using '#align is_lower_set_Union₂ isLowerSet_iUnion₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem isLowerSet_unionᵢ₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsLowerSet (f i j)) :
+theorem isLowerSet_iUnion₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsLowerSet (f i j)) :
     IsLowerSet (⋃ (i) (j), f i j) :=
-  isLowerSet_unionᵢ fun i => isLowerSet_unionᵢ <| hf i
-#align is_lower_set_Union₂ isLowerSet_unionᵢ₂
+  isLowerSet_iUnion fun i => isLowerSet_iUnion <| hf i
+#align is_lower_set_Union₂ isLowerSet_iUnion₂
 
-#print isUpperSet_unionₛ /-
-theorem isUpperSet_unionₛ {S : Set (Set α)} (hf : ∀ s ∈ S, IsUpperSet s) : IsUpperSet (⋃₀ S) :=
+#print isUpperSet_sUnion /-
+theorem isUpperSet_sUnion {S : Set (Set α)} (hf : ∀ s ∈ S, IsUpperSet s) : IsUpperSet (⋃₀ S) :=
   fun a b h => Exists₂.imp fun s hs => hf s hs h
-#align is_upper_set_sUnion isUpperSet_unionₛ
+#align is_upper_set_sUnion isUpperSet_sUnion
 -/
 
-#print isLowerSet_unionₛ /-
-theorem isLowerSet_unionₛ {S : Set (Set α)} (hf : ∀ s ∈ S, IsLowerSet s) : IsLowerSet (⋃₀ S) :=
+#print isLowerSet_sUnion /-
+theorem isLowerSet_sUnion {S : Set (Set α)} (hf : ∀ s ∈ S, IsLowerSet s) : IsLowerSet (⋃₀ S) :=
   fun a b h => Exists₂.imp fun s hs => hf s hs h
-#align is_lower_set_sUnion isLowerSet_unionₛ
+#align is_lower_set_sUnion isLowerSet_sUnion
 -/
 
-/- warning: is_upper_set_Inter -> isUpperSet_interᵢ is a dubious translation:
+/- warning: is_upper_set_Inter -> isUpperSet_iInter is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {f : ι -> (Set.{u1} α)}, (forall (i : ι), IsUpperSet.{u1} α _inst_1 (f i)) -> (IsUpperSet.{u1} α _inst_1 (Set.interᵢ.{u1, u2} α ι (fun (i : ι) => f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {f : ι -> (Set.{u1} α)}, (forall (i : ι), IsUpperSet.{u1} α _inst_1 (f i)) -> (IsUpperSet.{u1} α _inst_1 (Set.iInter.{u1, u2} α ι (fun (i : ι) => f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {f : ι -> (Set.{u2} α)}, (forall (i : ι), IsUpperSet.{u2} α _inst_1 (f i)) -> (IsUpperSet.{u2} α _inst_1 (Set.interᵢ.{u2, u1} α ι (fun (i : ι) => f i)))
-Case conversion may be inaccurate. Consider using '#align is_upper_set_Inter isUpperSet_interᵢₓ'. -/
-theorem isUpperSet_interᵢ {f : ι → Set α} (hf : ∀ i, IsUpperSet (f i)) : IsUpperSet (⋂ i, f i) :=
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {f : ι -> (Set.{u2} α)}, (forall (i : ι), IsUpperSet.{u2} α _inst_1 (f i)) -> (IsUpperSet.{u2} α _inst_1 (Set.iInter.{u2, u1} α ι (fun (i : ι) => f i)))
+Case conversion may be inaccurate. Consider using '#align is_upper_set_Inter isUpperSet_iInterₓ'. -/
+theorem isUpperSet_iInter {f : ι → Set α} (hf : ∀ i, IsUpperSet (f i)) : IsUpperSet (⋂ i, f i) :=
   fun a b h => forall₂_imp <| forall_range_iff.2 fun i => hf i h
-#align is_upper_set_Inter isUpperSet_interᵢ
+#align is_upper_set_Inter isUpperSet_iInter
 
-/- warning: is_lower_set_Inter -> isLowerSet_interᵢ is a dubious translation:
+/- warning: is_lower_set_Inter -> isLowerSet_iInter is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {f : ι -> (Set.{u1} α)}, (forall (i : ι), IsLowerSet.{u1} α _inst_1 (f i)) -> (IsLowerSet.{u1} α _inst_1 (Set.interᵢ.{u1, u2} α ι (fun (i : ι) => f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {f : ι -> (Set.{u1} α)}, (forall (i : ι), IsLowerSet.{u1} α _inst_1 (f i)) -> (IsLowerSet.{u1} α _inst_1 (Set.iInter.{u1, u2} α ι (fun (i : ι) => f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {f : ι -> (Set.{u2} α)}, (forall (i : ι), IsLowerSet.{u2} α _inst_1 (f i)) -> (IsLowerSet.{u2} α _inst_1 (Set.interᵢ.{u2, u1} α ι (fun (i : ι) => f i)))
-Case conversion may be inaccurate. Consider using '#align is_lower_set_Inter isLowerSet_interᵢₓ'. -/
-theorem isLowerSet_interᵢ {f : ι → Set α} (hf : ∀ i, IsLowerSet (f i)) : IsLowerSet (⋂ i, f i) :=
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {f : ι -> (Set.{u2} α)}, (forall (i : ι), IsLowerSet.{u2} α _inst_1 (f i)) -> (IsLowerSet.{u2} α _inst_1 (Set.iInter.{u2, u1} α ι (fun (i : ι) => f i)))
+Case conversion may be inaccurate. Consider using '#align is_lower_set_Inter isLowerSet_iInterₓ'. -/
+theorem isLowerSet_iInter {f : ι → Set α} (hf : ∀ i, IsLowerSet (f i)) : IsLowerSet (⋂ i, f i) :=
   fun a b h => forall₂_imp <| forall_range_iff.2 fun i => hf i h
-#align is_lower_set_Inter isLowerSet_interᵢ
+#align is_lower_set_Inter isLowerSet_iInter
 
-/- warning: is_upper_set_Inter₂ -> isUpperSet_interᵢ₂ is a dubious translation:
+/- warning: is_upper_set_Inter₂ -> isUpperSet_iInter₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {f : forall (i : ι), (κ i) -> (Set.{u1} α)}, (forall (i : ι) (j : κ i), IsUpperSet.{u1} α _inst_1 (f i j)) -> (IsUpperSet.{u1} α _inst_1 (Set.interᵢ.{u1, u2} α ι (fun (i : ι) => Set.interᵢ.{u1, u3} α (κ i) (fun (j : κ i) => f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {f : forall (i : ι), (κ i) -> (Set.{u1} α)}, (forall (i : ι) (j : κ i), IsUpperSet.{u1} α _inst_1 (f i j)) -> (IsUpperSet.{u1} α _inst_1 (Set.iInter.{u1, u2} α ι (fun (i : ι) => Set.iInter.{u1, u3} α (κ i) (fun (j : κ i) => f i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {f : forall (i : ι), (κ i) -> (Set.{u3} α)}, (forall (i : ι) (j : κ i), IsUpperSet.{u3} α _inst_1 (f i j)) -> (IsUpperSet.{u3} α _inst_1 (Set.interᵢ.{u3, u2} α ι (fun (i : ι) => Set.interᵢ.{u3, u1} α (κ i) (fun (j : κ i) => f i j))))
-Case conversion may be inaccurate. Consider using '#align is_upper_set_Inter₂ isUpperSet_interᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {f : forall (i : ι), (κ i) -> (Set.{u3} α)}, (forall (i : ι) (j : κ i), IsUpperSet.{u3} α _inst_1 (f i j)) -> (IsUpperSet.{u3} α _inst_1 (Set.iInter.{u3, u2} α ι (fun (i : ι) => Set.iInter.{u3, u1} α (κ i) (fun (j : κ i) => f i j))))
+Case conversion may be inaccurate. Consider using '#align is_upper_set_Inter₂ isUpperSet_iInter₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem isUpperSet_interᵢ₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsUpperSet (f i j)) :
+theorem isUpperSet_iInter₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsUpperSet (f i j)) :
     IsUpperSet (⋂ (i) (j), f i j) :=
-  isUpperSet_interᵢ fun i => isUpperSet_interᵢ <| hf i
-#align is_upper_set_Inter₂ isUpperSet_interᵢ₂
+  isUpperSet_iInter fun i => isUpperSet_iInter <| hf i
+#align is_upper_set_Inter₂ isUpperSet_iInter₂
 
-/- warning: is_lower_set_Inter₂ -> isLowerSet_interᵢ₂ is a dubious translation:
+/- warning: is_lower_set_Inter₂ -> isLowerSet_iInter₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {f : forall (i : ι), (κ i) -> (Set.{u1} α)}, (forall (i : ι) (j : κ i), IsLowerSet.{u1} α _inst_1 (f i j)) -> (IsLowerSet.{u1} α _inst_1 (Set.interᵢ.{u1, u2} α ι (fun (i : ι) => Set.interᵢ.{u1, u3} α (κ i) (fun (j : κ i) => f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {f : forall (i : ι), (κ i) -> (Set.{u1} α)}, (forall (i : ι) (j : κ i), IsLowerSet.{u1} α _inst_1 (f i j)) -> (IsLowerSet.{u1} α _inst_1 (Set.iInter.{u1, u2} α ι (fun (i : ι) => Set.iInter.{u1, u3} α (κ i) (fun (j : κ i) => f i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {f : forall (i : ι), (κ i) -> (Set.{u3} α)}, (forall (i : ι) (j : κ i), IsLowerSet.{u3} α _inst_1 (f i j)) -> (IsLowerSet.{u3} α _inst_1 (Set.interᵢ.{u3, u2} α ι (fun (i : ι) => Set.interᵢ.{u3, u1} α (κ i) (fun (j : κ i) => f i j))))
-Case conversion may be inaccurate. Consider using '#align is_lower_set_Inter₂ isLowerSet_interᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {f : forall (i : ι), (κ i) -> (Set.{u3} α)}, (forall (i : ι) (j : κ i), IsLowerSet.{u3} α _inst_1 (f i j)) -> (IsLowerSet.{u3} α _inst_1 (Set.iInter.{u3, u2} α ι (fun (i : ι) => Set.iInter.{u3, u1} α (κ i) (fun (j : κ i) => f i j))))
+Case conversion may be inaccurate. Consider using '#align is_lower_set_Inter₂ isLowerSet_iInter₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem isLowerSet_interᵢ₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsLowerSet (f i j)) :
+theorem isLowerSet_iInter₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsLowerSet (f i j)) :
     IsLowerSet (⋂ (i) (j), f i j) :=
-  isLowerSet_interᵢ fun i => isLowerSet_interᵢ <| hf i
-#align is_lower_set_Inter₂ isLowerSet_interᵢ₂
+  isLowerSet_iInter fun i => isLowerSet_iInter <| hf i
+#align is_lower_set_Inter₂ isLowerSet_iInter₂
 
-#print isUpperSet_interₛ /-
-theorem isUpperSet_interₛ {S : Set (Set α)} (hf : ∀ s ∈ S, IsUpperSet s) : IsUpperSet (⋂₀ S) :=
+#print isUpperSet_sInter /-
+theorem isUpperSet_sInter {S : Set (Set α)} (hf : ∀ s ∈ S, IsUpperSet s) : IsUpperSet (⋂₀ S) :=
   fun a b h => forall₂_imp fun s hs => hf s hs h
-#align is_upper_set_sInter isUpperSet_interₛ
+#align is_upper_set_sInter isUpperSet_sInter
 -/
 
-#print isLowerSet_interₛ /-
-theorem isLowerSet_interₛ {S : Set (Set α)} (hf : ∀ s ∈ S, IsLowerSet s) : IsLowerSet (⋂₀ S) :=
+#print isLowerSet_sInter /-
+theorem isLowerSet_sInter {S : Set (Set α)} (hf : ∀ s ∈ S, IsLowerSet s) : IsLowerSet (⋂₀ S) :=
   fun a b h => forall₂_imp fun s hs => hf s hs h
-#align is_lower_set_sInter isLowerSet_interₛ
+#align is_lower_set_sInter isLowerSet_sInter
 -/
 
 #print isLowerSet_preimage_ofDual_iff /-
@@ -746,10 +746,10 @@ instance : Bot (UpperSet α) :=
   ⟨⟨univ, isUpperSet_univ⟩⟩
 
 instance : SupSet (UpperSet α) :=
-  ⟨fun S => ⟨⋂ s ∈ S, ↑s, isUpperSet_interᵢ₂ fun s _ => s.upper⟩⟩
+  ⟨fun S => ⟨⋂ s ∈ S, ↑s, isUpperSet_iInter₂ fun s _ => s.upper⟩⟩
 
 instance : InfSet (UpperSet α) :=
-  ⟨fun S => ⟨⋃ s ∈ S, ↑s, isUpperSet_unionᵢ₂ fun s _ => s.upper⟩⟩
+  ⟨fun S => ⟨⋃ s ∈ S, ↑s, isUpperSet_iUnion₂ fun s _ => s.upper⟩⟩
 
 instance : CompleteDistribLattice (UpperSet α) :=
   (toDual.Injective.comp <| SetLike.coe_injective).CompleteDistribLattice _ (fun _ _ => rfl)
@@ -817,73 +817,73 @@ theorem coe_inf (s t : UpperSet α) : (↑(s ⊓ t) : Set α) = s ∪ t :=
   rfl
 #align upper_set.coe_inf UpperSet.coe_inf
 
-/- warning: upper_set.coe_Sup -> UpperSet.coe_supₛ is a dubious translation:
+/- warning: upper_set.coe_Sup -> UpperSet.coe_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (SupSet.supₛ.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) S)) (Set.interᵢ.{u1, succ u1} α (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => Set.interᵢ.{u1, 0} α (Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) s)))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (SupSet.sSup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) S)) (Set.iInter.{u1, succ u1} α (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => Set.iInter.{u1, 0} α (Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) (SupSet.supₛ.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instSupSetUpperSet.{u1} α _inst_1) S)) (Set.interᵢ.{u1, succ u1} α (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => Set.interᵢ.{u1, 0} α (Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) => SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) s)))
-Case conversion may be inaccurate. Consider using '#align upper_set.coe_Sup UpperSet.coe_supₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) (SupSet.sSup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instSupSetUpperSet.{u1} α _inst_1) S)) (Set.iInter.{u1, succ u1} α (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => Set.iInter.{u1, 0} α (Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) => SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) s)))
+Case conversion may be inaccurate. Consider using '#align upper_set.coe_Sup UpperSet.coe_sSupₓ'. -/
 @[simp, norm_cast]
-theorem coe_supₛ (S : Set (UpperSet α)) : (↑(supₛ S) : Set α) = ⋂ s ∈ S, ↑s :=
+theorem coe_sSup (S : Set (UpperSet α)) : (↑(sSup S) : Set α) = ⋂ s ∈ S, ↑s :=
   rfl
-#align upper_set.coe_Sup UpperSet.coe_supₛ
+#align upper_set.coe_Sup UpperSet.coe_sSup
 
-/- warning: upper_set.coe_Inf -> UpperSet.coe_infₛ is a dubious translation:
+/- warning: upper_set.coe_Inf -> UpperSet.coe_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (InfSet.infₛ.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) S)) (Set.unionᵢ.{u1, succ u1} α (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) s)))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (InfSet.sInf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) S)) (Set.iUnion.{u1, succ u1} α (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => Set.iUnion.{u1, 0} α (Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) (InfSet.infₛ.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instInfSetUpperSet.{u1} α _inst_1) S)) (Set.unionᵢ.{u1, succ u1} α (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) => SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) s)))
-Case conversion may be inaccurate. Consider using '#align upper_set.coe_Inf UpperSet.coe_infₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) (InfSet.sInf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instInfSetUpperSet.{u1} α _inst_1) S)) (Set.iUnion.{u1, succ u1} α (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => Set.iUnion.{u1, 0} α (Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) => SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) s)))
+Case conversion may be inaccurate. Consider using '#align upper_set.coe_Inf UpperSet.coe_sInfₓ'. -/
 @[simp, norm_cast]
-theorem coe_infₛ (S : Set (UpperSet α)) : (↑(infₛ S) : Set α) = ⋃ s ∈ S, ↑s :=
+theorem coe_sInf (S : Set (UpperSet α)) : (↑(sInf S) : Set α) = ⋃ s ∈ S, ↑s :=
   rfl
-#align upper_set.coe_Inf UpperSet.coe_infₛ
+#align upper_set.coe_Inf UpperSet.coe_sInf
 
-/- warning: upper_set.coe_supr -> UpperSet.coe_supᵢ is a dubious translation:
+/- warning: upper_set.coe_supr -> UpperSet.coe_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] (f : ι -> (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (supᵢ.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (Set.interᵢ.{u1, u2} α ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] (f : ι -> (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (iSup.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (Set.iInter.{u1, u2} α ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] (f : ι -> (UpperSet.{u2} α _inst_1)), Eq.{succ u2} (Set.{u2} α) (SetLike.coe.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1) (supᵢ.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instSupSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (Set.interᵢ.{u2, u1} α ι (fun (i : ι) => SetLike.coe.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1) (f i)))
-Case conversion may be inaccurate. Consider using '#align upper_set.coe_supr UpperSet.coe_supᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] (f : ι -> (UpperSet.{u2} α _inst_1)), Eq.{succ u2} (Set.{u2} α) (SetLike.coe.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1) (iSup.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instSupSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (Set.iInter.{u2, u1} α ι (fun (i : ι) => SetLike.coe.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1) (f i)))
+Case conversion may be inaccurate. Consider using '#align upper_set.coe_supr UpperSet.coe_iSupₓ'. -/
 @[simp, norm_cast]
-theorem coe_supᵢ (f : ι → UpperSet α) : (↑(⨆ i, f i) : Set α) = ⋂ i, f i := by simp [supᵢ]
-#align upper_set.coe_supr UpperSet.coe_supᵢ
+theorem coe_iSup (f : ι → UpperSet α) : (↑(⨆ i, f i) : Set α) = ⋂ i, f i := by simp [iSup]
+#align upper_set.coe_supr UpperSet.coe_iSup
 
-/- warning: upper_set.coe_infi -> UpperSet.coe_infᵢ is a dubious translation:
+/- warning: upper_set.coe_infi -> UpperSet.coe_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] (f : ι -> (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (infᵢ.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (Set.unionᵢ.{u1, u2} α ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] (f : ι -> (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (iInf.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (Set.iUnion.{u1, u2} α ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] (f : ι -> (UpperSet.{u2} α _inst_1)), Eq.{succ u2} (Set.{u2} α) (SetLike.coe.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1) (infᵢ.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instInfSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (Set.unionᵢ.{u2, u1} α ι (fun (i : ι) => SetLike.coe.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1) (f i)))
-Case conversion may be inaccurate. Consider using '#align upper_set.coe_infi UpperSet.coe_infᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] (f : ι -> (UpperSet.{u2} α _inst_1)), Eq.{succ u2} (Set.{u2} α) (SetLike.coe.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1) (iInf.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instInfSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (Set.iUnion.{u2, u1} α ι (fun (i : ι) => SetLike.coe.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1) (f i)))
+Case conversion may be inaccurate. Consider using '#align upper_set.coe_infi UpperSet.coe_iInfₓ'. -/
 @[simp, norm_cast]
-theorem coe_infᵢ (f : ι → UpperSet α) : (↑(⨅ i, f i) : Set α) = ⋃ i, f i := by simp [infᵢ]
-#align upper_set.coe_infi UpperSet.coe_infᵢ
+theorem coe_iInf (f : ι → UpperSet α) : (↑(⨅ i, f i) : Set α) = ⋃ i, f i := by simp [iInf]
+#align upper_set.coe_infi UpperSet.coe_iInf
 
-/- warning: upper_set.coe_supr₂ -> UpperSet.coe_supᵢ₂ is a dubious translation:
+/- warning: upper_set.coe_supr₂ -> UpperSet.coe_iSup₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] (f : forall (i : ι), (κ i) -> (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (supᵢ.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, u3} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Set.interᵢ.{u1, u2} α ι (fun (i : ι) => Set.interᵢ.{u1, u3} α (κ i) (fun (j : κ i) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] (f : forall (i : ι), (κ i) -> (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (iSup.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, u3} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Set.iInter.{u1, u2} α ι (fun (i : ι) => Set.iInter.{u1, u3} α (κ i) (fun (j : κ i) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (f i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] (f : forall (i : ι), (κ i) -> (UpperSet.{u3} α _inst_1)), Eq.{succ u3} (Set.{u3} α) (SetLike.coe.{u3, u3} (UpperSet.{u3} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u3} α _inst_1) (supᵢ.{u3, u2} (UpperSet.{u3} α _inst_1) (UpperSet.instSupSetUpperSet.{u3} α _inst_1) ι (fun (i : ι) => supᵢ.{u3, u1} (UpperSet.{u3} α _inst_1) (UpperSet.instSupSetUpperSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Set.interᵢ.{u3, u2} α ι (fun (i : ι) => Set.interᵢ.{u3, u1} α (κ i) (fun (j : κ i) => SetLike.coe.{u3, u3} (UpperSet.{u3} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u3} α _inst_1) (f i j))))
-Case conversion may be inaccurate. Consider using '#align upper_set.coe_supr₂ UpperSet.coe_supᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] (f : forall (i : ι), (κ i) -> (UpperSet.{u3} α _inst_1)), Eq.{succ u3} (Set.{u3} α) (SetLike.coe.{u3, u3} (UpperSet.{u3} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u3} α _inst_1) (iSup.{u3, u2} (UpperSet.{u3} α _inst_1) (UpperSet.instSupSetUpperSet.{u3} α _inst_1) ι (fun (i : ι) => iSup.{u3, u1} (UpperSet.{u3} α _inst_1) (UpperSet.instSupSetUpperSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Set.iInter.{u3, u2} α ι (fun (i : ι) => Set.iInter.{u3, u1} α (κ i) (fun (j : κ i) => SetLike.coe.{u3, u3} (UpperSet.{u3} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u3} α _inst_1) (f i j))))
+Case conversion may be inaccurate. Consider using '#align upper_set.coe_supr₂ UpperSet.coe_iSup₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp, norm_cast]
-theorem coe_supᵢ₂ (f : ∀ i, κ i → UpperSet α) : (↑(⨆ (i) (j), f i j) : Set α) = ⋂ (i) (j), f i j :=
+theorem coe_iSup₂ (f : ∀ i, κ i → UpperSet α) : (↑(⨆ (i) (j), f i j) : Set α) = ⋂ (i) (j), f i j :=
   by simp_rw [coe_supr]
-#align upper_set.coe_supr₂ UpperSet.coe_supᵢ₂
+#align upper_set.coe_supr₂ UpperSet.coe_iSup₂
 
-/- warning: upper_set.coe_infi₂ -> UpperSet.coe_infᵢ₂ is a dubious translation:
+/- warning: upper_set.coe_infi₂ -> UpperSet.coe_iInf₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] (f : forall (i : ι), (κ i) -> (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (infᵢ.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, u3} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Set.unionᵢ.{u1, u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, u3} α (κ i) (fun (j : κ i) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] (f : forall (i : ι), (κ i) -> (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (iInf.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => iInf.{u1, u3} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Set.iUnion.{u1, u2} α ι (fun (i : ι) => Set.iUnion.{u1, u3} α (κ i) (fun (j : κ i) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (f i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] (f : forall (i : ι), (κ i) -> (UpperSet.{u3} α _inst_1)), Eq.{succ u3} (Set.{u3} α) (SetLike.coe.{u3, u3} (UpperSet.{u3} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u3} α _inst_1) (infᵢ.{u3, u2} (UpperSet.{u3} α _inst_1) (UpperSet.instInfSetUpperSet.{u3} α _inst_1) ι (fun (i : ι) => infᵢ.{u3, u1} (UpperSet.{u3} α _inst_1) (UpperSet.instInfSetUpperSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Set.unionᵢ.{u3, u2} α ι (fun (i : ι) => Set.unionᵢ.{u3, u1} α (κ i) (fun (j : κ i) => SetLike.coe.{u3, u3} (UpperSet.{u3} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u3} α _inst_1) (f i j))))
-Case conversion may be inaccurate. Consider using '#align upper_set.coe_infi₂ UpperSet.coe_infᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] (f : forall (i : ι), (κ i) -> (UpperSet.{u3} α _inst_1)), Eq.{succ u3} (Set.{u3} α) (SetLike.coe.{u3, u3} (UpperSet.{u3} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u3} α _inst_1) (iInf.{u3, u2} (UpperSet.{u3} α _inst_1) (UpperSet.instInfSetUpperSet.{u3} α _inst_1) ι (fun (i : ι) => iInf.{u3, u1} (UpperSet.{u3} α _inst_1) (UpperSet.instInfSetUpperSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Set.iUnion.{u3, u2} α ι (fun (i : ι) => Set.iUnion.{u3, u1} α (κ i) (fun (j : κ i) => SetLike.coe.{u3, u3} (UpperSet.{u3} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u3} α _inst_1) (f i j))))
+Case conversion may be inaccurate. Consider using '#align upper_set.coe_infi₂ UpperSet.coe_iInf₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp, norm_cast]
-theorem coe_infᵢ₂ (f : ∀ i, κ i → UpperSet α) : (↑(⨅ (i) (j), f i j) : Set α) = ⋃ (i) (j), f i j :=
+theorem coe_iInf₂ (f : ∀ i, κ i → UpperSet α) : (↑(⨅ (i) (j), f i j) : Set α) = ⋃ (i) (j), f i j :=
   by simp_rw [coe_infi]
-#align upper_set.coe_infi₂ UpperSet.coe_infᵢ₂
+#align upper_set.coe_infi₂ UpperSet.coe_iInf₂
 
 #print UpperSet.not_mem_top /-
 @[simp]
@@ -921,77 +921,77 @@ theorem mem_inf_iff : a ∈ s ⊓ t ↔ a ∈ s ∨ a ∈ t :=
   Iff.rfl
 #align upper_set.mem_inf_iff UpperSet.mem_inf_iff
 
-/- warning: upper_set.mem_Sup_iff -> UpperSet.mem_supₛ_iff is a dubious translation:
+/- warning: upper_set.mem_Sup_iff -> UpperSet.mem_sSup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {S : Set.{u1} (UpperSet.{u1} α _inst_1)} {a : α}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (SupSet.supₛ.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) S)) (forall (s : UpperSet.{u1} α _inst_1), (Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) -> (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a s))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {S : Set.{u1} (UpperSet.{u1} α _inst_1)} {a : α}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (SupSet.sSup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) S)) (forall (s : UpperSet.{u1} α _inst_1), (Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) -> (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {S : Set.{u1} (UpperSet.{u1} α _inst_1)} {a : α}, Iff (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a (SupSet.supₛ.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instSupSetUpperSet.{u1} α _inst_1) S)) (forall (s : UpperSet.{u1} α _inst_1), (Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) -> (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a s))
-Case conversion may be inaccurate. Consider using '#align upper_set.mem_Sup_iff UpperSet.mem_supₛ_iffₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {S : Set.{u1} (UpperSet.{u1} α _inst_1)} {a : α}, Iff (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a (SupSet.sSup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instSupSetUpperSet.{u1} α _inst_1) S)) (forall (s : UpperSet.{u1} α _inst_1), (Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) -> (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a s))
+Case conversion may be inaccurate. Consider using '#align upper_set.mem_Sup_iff UpperSet.mem_sSup_iffₓ'. -/
 @[simp]
-theorem mem_supₛ_iff : a ∈ supₛ S ↔ ∀ s ∈ S, a ∈ s :=
-  mem_interᵢ₂
-#align upper_set.mem_Sup_iff UpperSet.mem_supₛ_iff
+theorem mem_sSup_iff : a ∈ sSup S ↔ ∀ s ∈ S, a ∈ s :=
+  mem_iInter₂
+#align upper_set.mem_Sup_iff UpperSet.mem_sSup_iff
 
-/- warning: upper_set.mem_Inf_iff -> UpperSet.mem_infₛ_iff is a dubious translation:
+/- warning: upper_set.mem_Inf_iff -> UpperSet.mem_sInf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {S : Set.{u1} (UpperSet.{u1} α _inst_1)} {a : α}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (InfSet.infₛ.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) S)) (Exists.{succ u1} (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => Exists.{0} (Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) => Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a s)))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {S : Set.{u1} (UpperSet.{u1} α _inst_1)} {a : α}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (InfSet.sInf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) S)) (Exists.{succ u1} (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => Exists.{0} (Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) => Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {S : Set.{u1} (UpperSet.{u1} α _inst_1)} {a : α}, Iff (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a (InfSet.infₛ.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instInfSetUpperSet.{u1} α _inst_1) S)) (Exists.{succ u1} (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => And (Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a s)))
-Case conversion may be inaccurate. Consider using '#align upper_set.mem_Inf_iff UpperSet.mem_infₛ_iffₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {S : Set.{u1} (UpperSet.{u1} α _inst_1)} {a : α}, Iff (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a (InfSet.sInf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instInfSetUpperSet.{u1} α _inst_1) S)) (Exists.{succ u1} (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => And (Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a s)))
+Case conversion may be inaccurate. Consider using '#align upper_set.mem_Inf_iff UpperSet.mem_sInf_iffₓ'. -/
 @[simp]
-theorem mem_infₛ_iff : a ∈ infₛ S ↔ ∃ s ∈ S, a ∈ s :=
-  mem_unionᵢ₂
-#align upper_set.mem_Inf_iff UpperSet.mem_infₛ_iff
+theorem mem_sInf_iff : a ∈ sInf S ↔ ∃ s ∈ S, a ∈ s :=
+  mem_iUnion₂
+#align upper_set.mem_Inf_iff UpperSet.mem_sInf_iff
 
-/- warning: upper_set.mem_supr_iff -> UpperSet.mem_supᵢ_iff is a dubious translation:
+/- warning: upper_set.mem_supr_iff -> UpperSet.mem_iSup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {a : α} {f : ι -> (UpperSet.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (supᵢ.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (forall (i : ι), Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (f i))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {a : α} {f : ι -> (UpperSet.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (iSup.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (forall (i : ι), Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (f i))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {a : α} {f : ι -> (UpperSet.{u2} α _inst_1)}, Iff (Membership.mem.{u2, u2} α (UpperSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1)) a (supᵢ.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instSupSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (forall (i : ι), Membership.mem.{u2, u2} α (UpperSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1)) a (f i))
-Case conversion may be inaccurate. Consider using '#align upper_set.mem_supr_iff UpperSet.mem_supᵢ_iffₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {a : α} {f : ι -> (UpperSet.{u2} α _inst_1)}, Iff (Membership.mem.{u2, u2} α (UpperSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1)) a (iSup.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instSupSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (forall (i : ι), Membership.mem.{u2, u2} α (UpperSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1)) a (f i))
+Case conversion may be inaccurate. Consider using '#align upper_set.mem_supr_iff UpperSet.mem_iSup_iffₓ'. -/
 @[simp]
-theorem mem_supᵢ_iff {f : ι → UpperSet α} : (a ∈ ⨆ i, f i) ↔ ∀ i, a ∈ f i :=
+theorem mem_iSup_iff {f : ι → UpperSet α} : (a ∈ ⨆ i, f i) ↔ ∀ i, a ∈ f i :=
   by
   rw [← SetLike.mem_coe, coe_supr]
   exact mem_Inter
-#align upper_set.mem_supr_iff UpperSet.mem_supᵢ_iff
+#align upper_set.mem_supr_iff UpperSet.mem_iSup_iff
 
-/- warning: upper_set.mem_infi_iff -> UpperSet.mem_infᵢ_iff is a dubious translation:
+/- warning: upper_set.mem_infi_iff -> UpperSet.mem_iInf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {a : α} {f : ι -> (UpperSet.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (infᵢ.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (Exists.{u2} ι (fun (i : ι) => Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {a : α} {f : ι -> (UpperSet.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (iInf.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (Exists.{u2} ι (fun (i : ι) => Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {a : α} {f : ι -> (UpperSet.{u2} α _inst_1)}, Iff (Membership.mem.{u2, u2} α (UpperSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1)) a (infᵢ.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instInfSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (Exists.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} α (UpperSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1)) a (f i)))
-Case conversion may be inaccurate. Consider using '#align upper_set.mem_infi_iff UpperSet.mem_infᵢ_iffₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {a : α} {f : ι -> (UpperSet.{u2} α _inst_1)}, Iff (Membership.mem.{u2, u2} α (UpperSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1)) a (iInf.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instInfSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (Exists.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} α (UpperSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (UpperSet.{u2} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u2} α _inst_1)) a (f i)))
+Case conversion may be inaccurate. Consider using '#align upper_set.mem_infi_iff UpperSet.mem_iInf_iffₓ'. -/
 @[simp]
-theorem mem_infᵢ_iff {f : ι → UpperSet α} : (a ∈ ⨅ i, f i) ↔ ∃ i, a ∈ f i :=
+theorem mem_iInf_iff {f : ι → UpperSet α} : (a ∈ ⨅ i, f i) ↔ ∃ i, a ∈ f i :=
   by
   rw [← SetLike.mem_coe, coe_infi]
   exact mem_Union
-#align upper_set.mem_infi_iff UpperSet.mem_infᵢ_iff
+#align upper_set.mem_infi_iff UpperSet.mem_iInf_iff
 
-/- warning: upper_set.mem_supr₂_iff -> UpperSet.mem_supᵢ₂_iff is a dubious translation:
+/- warning: upper_set.mem_supr₂_iff -> UpperSet.mem_iSup₂_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> (UpperSet.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (supᵢ.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, u3} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (forall (i : ι) (j : κ i), Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (f i j))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> (UpperSet.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (iSup.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, u3} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (forall (i : ι) (j : κ i), Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (f i j))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> (UpperSet.{u3} α _inst_1)}, Iff (Membership.mem.{u3, u3} α (UpperSet.{u3} α _inst_1) (SetLike.instMembership.{u3, u3} (UpperSet.{u3} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u3} α _inst_1)) a (supᵢ.{u3, u2} (UpperSet.{u3} α _inst_1) (UpperSet.instSupSetUpperSet.{u3} α _inst_1) ι (fun (i : ι) => supᵢ.{u3, u1} (UpperSet.{u3} α _inst_1) (UpperSet.instSupSetUpperSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (forall (i : ι) (j : κ i), Membership.mem.{u3, u3} α (UpperSet.{u3} α _inst_1) (SetLike.instMembership.{u3, u3} (UpperSet.{u3} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u3} α _inst_1)) a (f i j))
-Case conversion may be inaccurate. Consider using '#align upper_set.mem_supr₂_iff UpperSet.mem_supᵢ₂_iffₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> (UpperSet.{u3} α _inst_1)}, Iff (Membership.mem.{u3, u3} α (UpperSet.{u3} α _inst_1) (SetLike.instMembership.{u3, u3} (UpperSet.{u3} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u3} α _inst_1)) a (iSup.{u3, u2} (UpperSet.{u3} α _inst_1) (UpperSet.instSupSetUpperSet.{u3} α _inst_1) ι (fun (i : ι) => iSup.{u3, u1} (UpperSet.{u3} α _inst_1) (UpperSet.instSupSetUpperSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (forall (i : ι) (j : κ i), Membership.mem.{u3, u3} α (UpperSet.{u3} α _inst_1) (SetLike.instMembership.{u3, u3} (UpperSet.{u3} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u3} α _inst_1)) a (f i j))
+Case conversion may be inaccurate. Consider using '#align upper_set.mem_supr₂_iff UpperSet.mem_iSup₂_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
-theorem mem_supᵢ₂_iff {f : ∀ i, κ i → UpperSet α} : (a ∈ ⨆ (i) (j), f i j) ↔ ∀ i j, a ∈ f i j := by
+theorem mem_iSup₂_iff {f : ∀ i, κ i → UpperSet α} : (a ∈ ⨆ (i) (j), f i j) ↔ ∀ i j, a ∈ f i j := by
   simp_rw [mem_supr_iff]
-#align upper_set.mem_supr₂_iff UpperSet.mem_supᵢ₂_iff
+#align upper_set.mem_supr₂_iff UpperSet.mem_iSup₂_iff
 
-/- warning: upper_set.mem_infi₂_iff -> UpperSet.mem_infᵢ₂_iff is a dubious translation:
+/- warning: upper_set.mem_infi₂_iff -> UpperSet.mem_iInf₂_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> (UpperSet.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (infᵢ.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, u3} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Exists.{u2} ι (fun (i : ι) => Exists.{u3} (κ i) (fun (j : κ i) => Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> (UpperSet.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (iInf.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => iInf.{u1, u3} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Exists.{u2} ι (fun (i : ι) => Exists.{u3} (κ i) (fun (j : κ i) => Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (f i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> (UpperSet.{u3} α _inst_1)}, Iff (Membership.mem.{u3, u3} α (UpperSet.{u3} α _inst_1) (SetLike.instMembership.{u3, u3} (UpperSet.{u3} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u3} α _inst_1)) a (infᵢ.{u3, u2} (UpperSet.{u3} α _inst_1) (UpperSet.instInfSetUpperSet.{u3} α _inst_1) ι (fun (i : ι) => infᵢ.{u3, u1} (UpperSet.{u3} α _inst_1) (UpperSet.instInfSetUpperSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Exists.{u2} ι (fun (i : ι) => Exists.{u1} (κ i) (fun (j : κ i) => Membership.mem.{u3, u3} α (UpperSet.{u3} α _inst_1) (SetLike.instMembership.{u3, u3} (UpperSet.{u3} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u3} α _inst_1)) a (f i j))))
-Case conversion may be inaccurate. Consider using '#align upper_set.mem_infi₂_iff UpperSet.mem_infᵢ₂_iffₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> (UpperSet.{u3} α _inst_1)}, Iff (Membership.mem.{u3, u3} α (UpperSet.{u3} α _inst_1) (SetLike.instMembership.{u3, u3} (UpperSet.{u3} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u3} α _inst_1)) a (iInf.{u3, u2} (UpperSet.{u3} α _inst_1) (UpperSet.instInfSetUpperSet.{u3} α _inst_1) ι (fun (i : ι) => iInf.{u3, u1} (UpperSet.{u3} α _inst_1) (UpperSet.instInfSetUpperSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Exists.{u2} ι (fun (i : ι) => Exists.{u1} (κ i) (fun (j : κ i) => Membership.mem.{u3, u3} α (UpperSet.{u3} α _inst_1) (SetLike.instMembership.{u3, u3} (UpperSet.{u3} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u3} α _inst_1)) a (f i j))))
+Case conversion may be inaccurate. Consider using '#align upper_set.mem_infi₂_iff UpperSet.mem_iInf₂_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
-theorem mem_infᵢ₂_iff {f : ∀ i, κ i → UpperSet α} : (a ∈ ⨅ (i) (j), f i j) ↔ ∃ i j, a ∈ f i j := by
+theorem mem_iInf₂_iff {f : ∀ i, κ i → UpperSet α} : (a ∈ ⨅ (i) (j), f i j) ↔ ∃ i j, a ∈ f i j := by
   simp_rw [mem_infi_iff]
-#align upper_set.mem_infi₂_iff UpperSet.mem_infᵢ₂_iff
+#align upper_set.mem_infi₂_iff UpperSet.mem_iInf₂_iff
 
 /- warning: upper_set.codisjoint_coe -> UpperSet.codisjoint_coe is a dubious translation:
 lean 3 declaration is
@@ -1023,10 +1023,10 @@ instance : Bot (LowerSet α) :=
   ⟨⟨∅, fun a b h => id⟩⟩
 
 instance : SupSet (LowerSet α) :=
-  ⟨fun S => ⟨⋃ s ∈ S, ↑s, isLowerSet_unionᵢ₂ fun s _ => s.lower⟩⟩
+  ⟨fun S => ⟨⋃ s ∈ S, ↑s, isLowerSet_iUnion₂ fun s _ => s.lower⟩⟩
 
 instance : InfSet (LowerSet α) :=
-  ⟨fun S => ⟨⋂ s ∈ S, ↑s, isLowerSet_interᵢ₂ fun s _ => s.lower⟩⟩
+  ⟨fun S => ⟨⋂ s ∈ S, ↑s, isLowerSet_iInter₂ fun s _ => s.lower⟩⟩
 
 instance : CompleteDistribLattice (LowerSet α) :=
   SetLike.coe_injective.CompleteDistribLattice _ (fun _ _ => rfl) (fun _ _ => rfl) (fun _ => rfl)
@@ -1094,75 +1094,75 @@ theorem coe_inf (s t : LowerSet α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
   rfl
 #align lower_set.coe_inf LowerSet.coe_inf
 
-/- warning: lower_set.coe_Sup -> LowerSet.coe_supₛ is a dubious translation:
+/- warning: lower_set.coe_Sup -> LowerSet.coe_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (SupSet.supₛ.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) S)) (Set.unionᵢ.{u1, succ u1} α (LowerSet.{u1} α _inst_1) (fun (s : LowerSet.{u1} α _inst_1) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.hasMem.{u1} (LowerSet.{u1} α _inst_1)) s S) (fun (H : Membership.Mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.hasMem.{u1} (LowerSet.{u1} α _inst_1)) s S) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) s)))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (SupSet.sSup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) S)) (Set.iUnion.{u1, succ u1} α (LowerSet.{u1} α _inst_1) (fun (s : LowerSet.{u1} α _inst_1) => Set.iUnion.{u1, 0} α (Membership.Mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.hasMem.{u1} (LowerSet.{u1} α _inst_1)) s S) (fun (H : Membership.Mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.hasMem.{u1} (LowerSet.{u1} α _inst_1)) s S) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) (SupSet.supₛ.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instSupSetLowerSet.{u1} α _inst_1) S)) (Set.unionᵢ.{u1, succ u1} α (LowerSet.{u1} α _inst_1) (fun (s : LowerSet.{u1} α _inst_1) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (LowerSet.{u1} α _inst_1)) s S) (fun (H : Membership.mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (LowerSet.{u1} α _inst_1)) s S) => SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) s)))
-Case conversion may be inaccurate. Consider using '#align lower_set.coe_Sup LowerSet.coe_supₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) (SupSet.sSup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instSupSetLowerSet.{u1} α _inst_1) S)) (Set.iUnion.{u1, succ u1} α (LowerSet.{u1} α _inst_1) (fun (s : LowerSet.{u1} α _inst_1) => Set.iUnion.{u1, 0} α (Membership.mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (LowerSet.{u1} α _inst_1)) s S) (fun (H : Membership.mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (LowerSet.{u1} α _inst_1)) s S) => SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) s)))
+Case conversion may be inaccurate. Consider using '#align lower_set.coe_Sup LowerSet.coe_sSupₓ'. -/
 @[simp, norm_cast]
-theorem coe_supₛ (S : Set (LowerSet α)) : (↑(supₛ S) : Set α) = ⋃ s ∈ S, ↑s :=
+theorem coe_sSup (S : Set (LowerSet α)) : (↑(sSup S) : Set α) = ⋃ s ∈ S, ↑s :=
   rfl
-#align lower_set.coe_Sup LowerSet.coe_supₛ
+#align lower_set.coe_Sup LowerSet.coe_sSup
 
-/- warning: lower_set.coe_Inf -> LowerSet.coe_infₛ is a dubious translation:
+/- warning: lower_set.coe_Inf -> LowerSet.coe_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (InfSet.infₛ.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) S)) (Set.interᵢ.{u1, succ u1} α (LowerSet.{u1} α _inst_1) (fun (s : LowerSet.{u1} α _inst_1) => Set.interᵢ.{u1, 0} α (Membership.Mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.hasMem.{u1} (LowerSet.{u1} α _inst_1)) s S) (fun (H : Membership.Mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.hasMem.{u1} (LowerSet.{u1} α _inst_1)) s S) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) s)))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (InfSet.sInf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) S)) (Set.iInter.{u1, succ u1} α (LowerSet.{u1} α _inst_1) (fun (s : LowerSet.{u1} α _inst_1) => Set.iInter.{u1, 0} α (Membership.Mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.hasMem.{u1} (LowerSet.{u1} α _inst_1)) s S) (fun (H : Membership.Mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.hasMem.{u1} (LowerSet.{u1} α _inst_1)) s S) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) (InfSet.infₛ.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instInfSetLowerSet.{u1} α _inst_1) S)) (Set.interᵢ.{u1, succ u1} α (LowerSet.{u1} α _inst_1) (fun (s : LowerSet.{u1} α _inst_1) => Set.interᵢ.{u1, 0} α (Membership.mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (LowerSet.{u1} α _inst_1)) s S) (fun (H : Membership.mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (LowerSet.{u1} α _inst_1)) s S) => SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) s)))
-Case conversion may be inaccurate. Consider using '#align lower_set.coe_Inf LowerSet.coe_infₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) (InfSet.sInf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instInfSetLowerSet.{u1} α _inst_1) S)) (Set.iInter.{u1, succ u1} α (LowerSet.{u1} α _inst_1) (fun (s : LowerSet.{u1} α _inst_1) => Set.iInter.{u1, 0} α (Membership.mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (LowerSet.{u1} α _inst_1)) s S) (fun (H : Membership.mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (LowerSet.{u1} α _inst_1)) s S) => SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) s)))
+Case conversion may be inaccurate. Consider using '#align lower_set.coe_Inf LowerSet.coe_sInfₓ'. -/
 @[simp, norm_cast]
-theorem coe_infₛ (S : Set (LowerSet α)) : (↑(infₛ S) : Set α) = ⋂ s ∈ S, ↑s :=
+theorem coe_sInf (S : Set (LowerSet α)) : (↑(sInf S) : Set α) = ⋂ s ∈ S, ↑s :=
   rfl
-#align lower_set.coe_Inf LowerSet.coe_infₛ
+#align lower_set.coe_Inf LowerSet.coe_sInf
 
-/- warning: lower_set.coe_supr -> LowerSet.coe_supᵢ is a dubious translation:
+/- warning: lower_set.coe_supr -> LowerSet.coe_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] (f : ι -> (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (supᵢ.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (Set.unionᵢ.{u1, u2} α ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] (f : ι -> (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (iSup.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (Set.iUnion.{u1, u2} α ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] (f : ι -> (LowerSet.{u2} α _inst_1)), Eq.{succ u2} (Set.{u2} α) (SetLike.coe.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1) (supᵢ.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instSupSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (Set.unionᵢ.{u2, u1} α ι (fun (i : ι) => SetLike.coe.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1) (f i)))
-Case conversion may be inaccurate. Consider using '#align lower_set.coe_supr LowerSet.coe_supᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] (f : ι -> (LowerSet.{u2} α _inst_1)), Eq.{succ u2} (Set.{u2} α) (SetLike.coe.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1) (iSup.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instSupSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (Set.iUnion.{u2, u1} α ι (fun (i : ι) => SetLike.coe.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1) (f i)))
+Case conversion may be inaccurate. Consider using '#align lower_set.coe_supr LowerSet.coe_iSupₓ'. -/
 @[simp, norm_cast]
-theorem coe_supᵢ (f : ι → LowerSet α) : (↑(⨆ i, f i) : Set α) = ⋃ i, f i := by
-  simp_rw [supᵢ, coe_Sup, mem_range, Union_exists, Union_Union_eq']
-#align lower_set.coe_supr LowerSet.coe_supᵢ
+theorem coe_iSup (f : ι → LowerSet α) : (↑(⨆ i, f i) : Set α) = ⋃ i, f i := by
+  simp_rw [iSup, coe_Sup, mem_range, Union_exists, Union_Union_eq']
+#align lower_set.coe_supr LowerSet.coe_iSup
 
-/- warning: lower_set.coe_infi -> LowerSet.coe_infᵢ is a dubious translation:
+/- warning: lower_set.coe_infi -> LowerSet.coe_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] (f : ι -> (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (infᵢ.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (Set.interᵢ.{u1, u2} α ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] (f : ι -> (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (iInf.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (Set.iInter.{u1, u2} α ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] (f : ι -> (LowerSet.{u2} α _inst_1)), Eq.{succ u2} (Set.{u2} α) (SetLike.coe.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1) (infᵢ.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instInfSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (Set.interᵢ.{u2, u1} α ι (fun (i : ι) => SetLike.coe.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1) (f i)))
-Case conversion may be inaccurate. Consider using '#align lower_set.coe_infi LowerSet.coe_infᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] (f : ι -> (LowerSet.{u2} α _inst_1)), Eq.{succ u2} (Set.{u2} α) (SetLike.coe.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1) (iInf.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instInfSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (Set.iInter.{u2, u1} α ι (fun (i : ι) => SetLike.coe.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1) (f i)))
+Case conversion may be inaccurate. Consider using '#align lower_set.coe_infi LowerSet.coe_iInfₓ'. -/
 @[simp, norm_cast]
-theorem coe_infᵢ (f : ι → LowerSet α) : (↑(⨅ i, f i) : Set α) = ⋂ i, f i := by
-  simp_rw [infᵢ, coe_Inf, mem_range, Inter_exists, Inter_Inter_eq']
-#align lower_set.coe_infi LowerSet.coe_infᵢ
+theorem coe_iInf (f : ι → LowerSet α) : (↑(⨅ i, f i) : Set α) = ⋂ i, f i := by
+  simp_rw [iInf, coe_Inf, mem_range, Inter_exists, Inter_Inter_eq']
+#align lower_set.coe_infi LowerSet.coe_iInf
 
-/- warning: lower_set.coe_supr₂ -> LowerSet.coe_supᵢ₂ is a dubious translation:
+/- warning: lower_set.coe_supr₂ -> LowerSet.coe_iSup₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] (f : forall (i : ι), (κ i) -> (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (supᵢ.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, u3} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Set.unionᵢ.{u1, u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, u3} α (κ i) (fun (j : κ i) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] (f : forall (i : ι), (κ i) -> (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (iSup.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, u3} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Set.iUnion.{u1, u2} α ι (fun (i : ι) => Set.iUnion.{u1, u3} α (κ i) (fun (j : κ i) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (f i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] (f : forall (i : ι), (κ i) -> (LowerSet.{u3} α _inst_1)), Eq.{succ u3} (Set.{u3} α) (SetLike.coe.{u3, u3} (LowerSet.{u3} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u3} α _inst_1) (supᵢ.{u3, u2} (LowerSet.{u3} α _inst_1) (LowerSet.instSupSetLowerSet.{u3} α _inst_1) ι (fun (i : ι) => supᵢ.{u3, u1} (LowerSet.{u3} α _inst_1) (LowerSet.instSupSetLowerSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Set.unionᵢ.{u3, u2} α ι (fun (i : ι) => Set.unionᵢ.{u3, u1} α (κ i) (fun (j : κ i) => SetLike.coe.{u3, u3} (LowerSet.{u3} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u3} α _inst_1) (f i j))))
-Case conversion may be inaccurate. Consider using '#align lower_set.coe_supr₂ LowerSet.coe_supᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] (f : forall (i : ι), (κ i) -> (LowerSet.{u3} α _inst_1)), Eq.{succ u3} (Set.{u3} α) (SetLike.coe.{u3, u3} (LowerSet.{u3} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u3} α _inst_1) (iSup.{u3, u2} (LowerSet.{u3} α _inst_1) (LowerSet.instSupSetLowerSet.{u3} α _inst_1) ι (fun (i : ι) => iSup.{u3, u1} (LowerSet.{u3} α _inst_1) (LowerSet.instSupSetLowerSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Set.iUnion.{u3, u2} α ι (fun (i : ι) => Set.iUnion.{u3, u1} α (κ i) (fun (j : κ i) => SetLike.coe.{u3, u3} (LowerSet.{u3} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u3} α _inst_1) (f i j))))
+Case conversion may be inaccurate. Consider using '#align lower_set.coe_supr₂ LowerSet.coe_iSup₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp, norm_cast]
-theorem coe_supᵢ₂ (f : ∀ i, κ i → LowerSet α) : (↑(⨆ (i) (j), f i j) : Set α) = ⋃ (i) (j), f i j :=
+theorem coe_iSup₂ (f : ∀ i, κ i → LowerSet α) : (↑(⨆ (i) (j), f i j) : Set α) = ⋃ (i) (j), f i j :=
   by simp_rw [coe_supr]
-#align lower_set.coe_supr₂ LowerSet.coe_supᵢ₂
+#align lower_set.coe_supr₂ LowerSet.coe_iSup₂
 
-/- warning: lower_set.coe_infi₂ -> LowerSet.coe_infᵢ₂ is a dubious translation:
+/- warning: lower_set.coe_infi₂ -> LowerSet.coe_iInf₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] (f : forall (i : ι), (κ i) -> (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (infᵢ.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, u3} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Set.interᵢ.{u1, u2} α ι (fun (i : ι) => Set.interᵢ.{u1, u3} α (κ i) (fun (j : κ i) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] (f : forall (i : ι), (κ i) -> (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (iInf.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => iInf.{u1, u3} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Set.iInter.{u1, u2} α ι (fun (i : ι) => Set.iInter.{u1, u3} α (κ i) (fun (j : κ i) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (f i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] (f : forall (i : ι), (κ i) -> (LowerSet.{u3} α _inst_1)), Eq.{succ u3} (Set.{u3} α) (SetLike.coe.{u3, u3} (LowerSet.{u3} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u3} α _inst_1) (infᵢ.{u3, u2} (LowerSet.{u3} α _inst_1) (LowerSet.instInfSetLowerSet.{u3} α _inst_1) ι (fun (i : ι) => infᵢ.{u3, u1} (LowerSet.{u3} α _inst_1) (LowerSet.instInfSetLowerSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Set.interᵢ.{u3, u2} α ι (fun (i : ι) => Set.interᵢ.{u3, u1} α (κ i) (fun (j : κ i) => SetLike.coe.{u3, u3} (LowerSet.{u3} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u3} α _inst_1) (f i j))))
-Case conversion may be inaccurate. Consider using '#align lower_set.coe_infi₂ LowerSet.coe_infᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] (f : forall (i : ι), (κ i) -> (LowerSet.{u3} α _inst_1)), Eq.{succ u3} (Set.{u3} α) (SetLike.coe.{u3, u3} (LowerSet.{u3} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u3} α _inst_1) (iInf.{u3, u2} (LowerSet.{u3} α _inst_1) (LowerSet.instInfSetLowerSet.{u3} α _inst_1) ι (fun (i : ι) => iInf.{u3, u1} (LowerSet.{u3} α _inst_1) (LowerSet.instInfSetLowerSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Set.iInter.{u3, u2} α ι (fun (i : ι) => Set.iInter.{u3, u1} α (κ i) (fun (j : κ i) => SetLike.coe.{u3, u3} (LowerSet.{u3} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u3} α _inst_1) (f i j))))
+Case conversion may be inaccurate. Consider using '#align lower_set.coe_infi₂ LowerSet.coe_iInf₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp, norm_cast]
-theorem coe_infᵢ₂ (f : ∀ i, κ i → LowerSet α) : (↑(⨅ (i) (j), f i j) : Set α) = ⋂ (i) (j), f i j :=
+theorem coe_iInf₂ (f : ∀ i, κ i → LowerSet α) : (↑(⨅ (i) (j), f i j) : Set α) = ⋂ (i) (j), f i j :=
   by simp_rw [coe_infi]
-#align lower_set.coe_infi₂ LowerSet.coe_infᵢ₂
+#align lower_set.coe_infi₂ LowerSet.coe_iInf₂
 
 #print LowerSet.mem_top /-
 @[simp]
@@ -1200,77 +1200,77 @@ theorem mem_inf_iff : a ∈ s ⊓ t ↔ a ∈ s ∧ a ∈ t :=
   Iff.rfl
 #align lower_set.mem_inf_iff LowerSet.mem_inf_iff
 
-/- warning: lower_set.mem_Sup_iff -> LowerSet.mem_supₛ_iff is a dubious translation:
+/- warning: lower_set.mem_Sup_iff -> LowerSet.mem_sSup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {S : Set.{u1} (LowerSet.{u1} α _inst_1)} {a : α}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (SupSet.supₛ.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) S)) (Exists.{succ u1} (LowerSet.{u1} α _inst_1) (fun (s : LowerSet.{u1} α _inst_1) => Exists.{0} (Membership.Mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.hasMem.{u1} (LowerSet.{u1} α _inst_1)) s S) (fun (H : Membership.Mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.hasMem.{u1} (LowerSet.{u1} α _inst_1)) s S) => Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a s)))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {S : Set.{u1} (LowerSet.{u1} α _inst_1)} {a : α}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (SupSet.sSup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) S)) (Exists.{succ u1} (LowerSet.{u1} α _inst_1) (fun (s : LowerSet.{u1} α _inst_1) => Exists.{0} (Membership.Mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.hasMem.{u1} (LowerSet.{u1} α _inst_1)) s S) (fun (H : Membership.Mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.hasMem.{u1} (LowerSet.{u1} α _inst_1)) s S) => Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {S : Set.{u1} (LowerSet.{u1} α _inst_1)} {a : α}, Iff (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a (SupSet.supₛ.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instSupSetLowerSet.{u1} α _inst_1) S)) (Exists.{succ u1} (LowerSet.{u1} α _inst_1) (fun (s : LowerSet.{u1} α _inst_1) => And (Membership.mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (LowerSet.{u1} α _inst_1)) s S) (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a s)))
-Case conversion may be inaccurate. Consider using '#align lower_set.mem_Sup_iff LowerSet.mem_supₛ_iffₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {S : Set.{u1} (LowerSet.{u1} α _inst_1)} {a : α}, Iff (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a (SupSet.sSup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instSupSetLowerSet.{u1} α _inst_1) S)) (Exists.{succ u1} (LowerSet.{u1} α _inst_1) (fun (s : LowerSet.{u1} α _inst_1) => And (Membership.mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (LowerSet.{u1} α _inst_1)) s S) (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a s)))
+Case conversion may be inaccurate. Consider using '#align lower_set.mem_Sup_iff LowerSet.mem_sSup_iffₓ'. -/
 @[simp]
-theorem mem_supₛ_iff : a ∈ supₛ S ↔ ∃ s ∈ S, a ∈ s :=
-  mem_unionᵢ₂
-#align lower_set.mem_Sup_iff LowerSet.mem_supₛ_iff
+theorem mem_sSup_iff : a ∈ sSup S ↔ ∃ s ∈ S, a ∈ s :=
+  mem_iUnion₂
+#align lower_set.mem_Sup_iff LowerSet.mem_sSup_iff
 
-/- warning: lower_set.mem_Inf_iff -> LowerSet.mem_infₛ_iff is a dubious translation:
+/- warning: lower_set.mem_Inf_iff -> LowerSet.mem_sInf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {S : Set.{u1} (LowerSet.{u1} α _inst_1)} {a : α}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (InfSet.infₛ.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) S)) (forall (s : LowerSet.{u1} α _inst_1), (Membership.Mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.hasMem.{u1} (LowerSet.{u1} α _inst_1)) s S) -> (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a s))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {S : Set.{u1} (LowerSet.{u1} α _inst_1)} {a : α}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (InfSet.sInf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) S)) (forall (s : LowerSet.{u1} α _inst_1), (Membership.Mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.hasMem.{u1} (LowerSet.{u1} α _inst_1)) s S) -> (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {S : Set.{u1} (LowerSet.{u1} α _inst_1)} {a : α}, Iff (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a (InfSet.infₛ.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instInfSetLowerSet.{u1} α _inst_1) S)) (forall (s : LowerSet.{u1} α _inst_1), (Membership.mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (LowerSet.{u1} α _inst_1)) s S) -> (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a s))
-Case conversion may be inaccurate. Consider using '#align lower_set.mem_Inf_iff LowerSet.mem_infₛ_iffₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {S : Set.{u1} (LowerSet.{u1} α _inst_1)} {a : α}, Iff (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a (InfSet.sInf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instInfSetLowerSet.{u1} α _inst_1) S)) (forall (s : LowerSet.{u1} α _inst_1), (Membership.mem.{u1, u1} (LowerSet.{u1} α _inst_1) (Set.{u1} (LowerSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (LowerSet.{u1} α _inst_1)) s S) -> (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a s))
+Case conversion may be inaccurate. Consider using '#align lower_set.mem_Inf_iff LowerSet.mem_sInf_iffₓ'. -/
 @[simp]
-theorem mem_infₛ_iff : a ∈ infₛ S ↔ ∀ s ∈ S, a ∈ s :=
-  mem_interᵢ₂
-#align lower_set.mem_Inf_iff LowerSet.mem_infₛ_iff
+theorem mem_sInf_iff : a ∈ sInf S ↔ ∀ s ∈ S, a ∈ s :=
+  mem_iInter₂
+#align lower_set.mem_Inf_iff LowerSet.mem_sInf_iff
 
-/- warning: lower_set.mem_supr_iff -> LowerSet.mem_supᵢ_iff is a dubious translation:
+/- warning: lower_set.mem_supr_iff -> LowerSet.mem_iSup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {a : α} {f : ι -> (LowerSet.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (supᵢ.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (Exists.{u2} ι (fun (i : ι) => Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {a : α} {f : ι -> (LowerSet.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (iSup.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (Exists.{u2} ι (fun (i : ι) => Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {a : α} {f : ι -> (LowerSet.{u2} α _inst_1)}, Iff (Membership.mem.{u2, u2} α (LowerSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1)) a (supᵢ.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instSupSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (Exists.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} α (LowerSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1)) a (f i)))
-Case conversion may be inaccurate. Consider using '#align lower_set.mem_supr_iff LowerSet.mem_supᵢ_iffₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {a : α} {f : ι -> (LowerSet.{u2} α _inst_1)}, Iff (Membership.mem.{u2, u2} α (LowerSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1)) a (iSup.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instSupSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (Exists.{u1} ι (fun (i : ι) => Membership.mem.{u2, u2} α (LowerSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1)) a (f i)))
+Case conversion may be inaccurate. Consider using '#align lower_set.mem_supr_iff LowerSet.mem_iSup_iffₓ'. -/
 @[simp]
-theorem mem_supᵢ_iff {f : ι → LowerSet α} : (a ∈ ⨆ i, f i) ↔ ∃ i, a ∈ f i :=
+theorem mem_iSup_iff {f : ι → LowerSet α} : (a ∈ ⨆ i, f i) ↔ ∃ i, a ∈ f i :=
   by
   rw [← SetLike.mem_coe, coe_supr]
   exact mem_Union
-#align lower_set.mem_supr_iff LowerSet.mem_supᵢ_iff
+#align lower_set.mem_supr_iff LowerSet.mem_iSup_iff
 
-/- warning: lower_set.mem_infi_iff -> LowerSet.mem_infᵢ_iff is a dubious translation:
+/- warning: lower_set.mem_infi_iff -> LowerSet.mem_iInf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {a : α} {f : ι -> (LowerSet.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (infᵢ.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (forall (i : ι), Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (f i))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] {a : α} {f : ι -> (LowerSet.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (iInf.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (forall (i : ι), Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (f i))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {a : α} {f : ι -> (LowerSet.{u2} α _inst_1)}, Iff (Membership.mem.{u2, u2} α (LowerSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1)) a (infᵢ.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instInfSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (forall (i : ι), Membership.mem.{u2, u2} α (LowerSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1)) a (f i))
-Case conversion may be inaccurate. Consider using '#align lower_set.mem_infi_iff LowerSet.mem_infᵢ_iffₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] {a : α} {f : ι -> (LowerSet.{u2} α _inst_1)}, Iff (Membership.mem.{u2, u2} α (LowerSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1)) a (iInf.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instInfSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (forall (i : ι), Membership.mem.{u2, u2} α (LowerSet.{u2} α _inst_1) (SetLike.instMembership.{u2, u2} (LowerSet.{u2} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u2} α _inst_1)) a (f i))
+Case conversion may be inaccurate. Consider using '#align lower_set.mem_infi_iff LowerSet.mem_iInf_iffₓ'. -/
 @[simp]
-theorem mem_infᵢ_iff {f : ι → LowerSet α} : (a ∈ ⨅ i, f i) ↔ ∀ i, a ∈ f i :=
+theorem mem_iInf_iff {f : ι → LowerSet α} : (a ∈ ⨅ i, f i) ↔ ∀ i, a ∈ f i :=
   by
   rw [← SetLike.mem_coe, coe_infi]
   exact mem_Inter
-#align lower_set.mem_infi_iff LowerSet.mem_infᵢ_iff
+#align lower_set.mem_infi_iff LowerSet.mem_iInf_iff
 
-/- warning: lower_set.mem_supr₂_iff -> LowerSet.mem_supᵢ₂_iff is a dubious translation:
+/- warning: lower_set.mem_supr₂_iff -> LowerSet.mem_iSup₂_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> (LowerSet.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (supᵢ.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, u3} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Exists.{u2} ι (fun (i : ι) => Exists.{u3} (κ i) (fun (j : κ i) => Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> (LowerSet.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (iSup.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, u3} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Exists.{u2} ι (fun (i : ι) => Exists.{u3} (κ i) (fun (j : κ i) => Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (f i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> (LowerSet.{u3} α _inst_1)}, Iff (Membership.mem.{u3, u3} α (LowerSet.{u3} α _inst_1) (SetLike.instMembership.{u3, u3} (LowerSet.{u3} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u3} α _inst_1)) a (supᵢ.{u3, u2} (LowerSet.{u3} α _inst_1) (LowerSet.instSupSetLowerSet.{u3} α _inst_1) ι (fun (i : ι) => supᵢ.{u3, u1} (LowerSet.{u3} α _inst_1) (LowerSet.instSupSetLowerSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Exists.{u2} ι (fun (i : ι) => Exists.{u1} (κ i) (fun (j : κ i) => Membership.mem.{u3, u3} α (LowerSet.{u3} α _inst_1) (SetLike.instMembership.{u3, u3} (LowerSet.{u3} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u3} α _inst_1)) a (f i j))))
-Case conversion may be inaccurate. Consider using '#align lower_set.mem_supr₂_iff LowerSet.mem_supᵢ₂_iffₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> (LowerSet.{u3} α _inst_1)}, Iff (Membership.mem.{u3, u3} α (LowerSet.{u3} α _inst_1) (SetLike.instMembership.{u3, u3} (LowerSet.{u3} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u3} α _inst_1)) a (iSup.{u3, u2} (LowerSet.{u3} α _inst_1) (LowerSet.instSupSetLowerSet.{u3} α _inst_1) ι (fun (i : ι) => iSup.{u3, u1} (LowerSet.{u3} α _inst_1) (LowerSet.instSupSetLowerSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (Exists.{u2} ι (fun (i : ι) => Exists.{u1} (κ i) (fun (j : κ i) => Membership.mem.{u3, u3} α (LowerSet.{u3} α _inst_1) (SetLike.instMembership.{u3, u3} (LowerSet.{u3} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u3} α _inst_1)) a (f i j))))
+Case conversion may be inaccurate. Consider using '#align lower_set.mem_supr₂_iff LowerSet.mem_iSup₂_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
-theorem mem_supᵢ₂_iff {f : ∀ i, κ i → LowerSet α} : (a ∈ ⨆ (i) (j), f i j) ↔ ∃ i j, a ∈ f i j := by
+theorem mem_iSup₂_iff {f : ∀ i, κ i → LowerSet α} : (a ∈ ⨆ (i) (j), f i j) ↔ ∃ i j, a ∈ f i j := by
   simp_rw [mem_supr_iff]
-#align lower_set.mem_supr₂_iff LowerSet.mem_supᵢ₂_iff
+#align lower_set.mem_supr₂_iff LowerSet.mem_iSup₂_iff
 
-/- warning: lower_set.mem_infi₂_iff -> LowerSet.mem_infᵢ₂_iff is a dubious translation:
+/- warning: lower_set.mem_infi₂_iff -> LowerSet.mem_iInf₂_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> (LowerSet.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (infᵢ.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, u3} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (forall (i : ι) (j : κ i), Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (f i j))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> (LowerSet.{u1} α _inst_1)}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (iInf.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => iInf.{u1, u3} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (forall (i : ι) (j : κ i), Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (f i j))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> (LowerSet.{u3} α _inst_1)}, Iff (Membership.mem.{u3, u3} α (LowerSet.{u3} α _inst_1) (SetLike.instMembership.{u3, u3} (LowerSet.{u3} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u3} α _inst_1)) a (infᵢ.{u3, u2} (LowerSet.{u3} α _inst_1) (LowerSet.instInfSetLowerSet.{u3} α _inst_1) ι (fun (i : ι) => infᵢ.{u3, u1} (LowerSet.{u3} α _inst_1) (LowerSet.instInfSetLowerSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (forall (i : ι) (j : κ i), Membership.mem.{u3, u3} α (LowerSet.{u3} α _inst_1) (SetLike.instMembership.{u3, u3} (LowerSet.{u3} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u3} α _inst_1)) a (f i j))
-Case conversion may be inaccurate. Consider using '#align lower_set.mem_infi₂_iff LowerSet.mem_infᵢ₂_iffₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> (LowerSet.{u3} α _inst_1)}, Iff (Membership.mem.{u3, u3} α (LowerSet.{u3} α _inst_1) (SetLike.instMembership.{u3, u3} (LowerSet.{u3} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u3} α _inst_1)) a (iInf.{u3, u2} (LowerSet.{u3} α _inst_1) (LowerSet.instInfSetLowerSet.{u3} α _inst_1) ι (fun (i : ι) => iInf.{u3, u1} (LowerSet.{u3} α _inst_1) (LowerSet.instInfSetLowerSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (forall (i : ι) (j : κ i), Membership.mem.{u3, u3} α (LowerSet.{u3} α _inst_1) (SetLike.instMembership.{u3, u3} (LowerSet.{u3} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u3} α _inst_1)) a (f i j))
+Case conversion may be inaccurate. Consider using '#align lower_set.mem_infi₂_iff LowerSet.mem_iInf₂_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
-theorem mem_infᵢ₂_iff {f : ∀ i, κ i → LowerSet α} : (a ∈ ⨅ (i) (j), f i j) ↔ ∀ i j, a ∈ f i j := by
+theorem mem_iInf₂_iff {f : ∀ i, κ i → LowerSet α} : (a ∈ ⨅ (i) (j), f i j) ↔ ∀ i j, a ∈ f i j := by
   simp_rw [mem_infi_iff]
-#align lower_set.mem_infi₂_iff LowerSet.mem_infᵢ₂_iff
+#align lower_set.mem_infi₂_iff LowerSet.mem_iInf₂_iff
 
 /- warning: lower_set.disjoint_coe -> LowerSet.disjoint_coe is a dubious translation:
 lean 3 declaration is
@@ -1378,75 +1378,75 @@ protected theorem compl_bot : (⊥ : UpperSet α).compl = ⊥ :=
 #align upper_set.compl_bot UpperSet.compl_bot
 -/
 
-/- warning: upper_set.compl_Sup -> UpperSet.compl_supₛ is a dubious translation:
+/- warning: upper_set.compl_Sup -> UpperSet.compl_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (SupSet.supₛ.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) S)) (supᵢ.{u1, succ u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => supᵢ.{u1, 0} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) (Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) => UpperSet.compl.{u1} α _inst_1 s)))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (SupSet.sSup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) S)) (iSup.{u1, succ u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => iSup.{u1, 0} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) (Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) => UpperSet.compl.{u1} α _inst_1 s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (SupSet.supₛ.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instSupSetUpperSet.{u1} α _inst_1) S)) (supᵢ.{u1, succ u1} (LowerSet.{u1} α _inst_1) (LowerSet.instSupSetLowerSet.{u1} α _inst_1) (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => supᵢ.{u1, 0} (LowerSet.{u1} α _inst_1) (LowerSet.instSupSetLowerSet.{u1} α _inst_1) (Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) => UpperSet.compl.{u1} α _inst_1 s)))
-Case conversion may be inaccurate. Consider using '#align upper_set.compl_Sup UpperSet.compl_supₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (SupSet.sSup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instSupSetUpperSet.{u1} α _inst_1) S)) (iSup.{u1, succ u1} (LowerSet.{u1} α _inst_1) (LowerSet.instSupSetLowerSet.{u1} α _inst_1) (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => iSup.{u1, 0} (LowerSet.{u1} α _inst_1) (LowerSet.instSupSetLowerSet.{u1} α _inst_1) (Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) => UpperSet.compl.{u1} α _inst_1 s)))
+Case conversion may be inaccurate. Consider using '#align upper_set.compl_Sup UpperSet.compl_sSupₓ'. -/
 @[simp]
-protected theorem compl_supₛ (S : Set (UpperSet α)) : (supₛ S).compl = ⨆ s ∈ S, UpperSet.compl s :=
-  LowerSet.ext <| by simp only [coe_compl, coe_Sup, compl_Inter₂, LowerSet.coe_supᵢ₂]
-#align upper_set.compl_Sup UpperSet.compl_supₛ
+protected theorem compl_sSup (S : Set (UpperSet α)) : (sSup S).compl = ⨆ s ∈ S, UpperSet.compl s :=
+  LowerSet.ext <| by simp only [coe_compl, coe_Sup, compl_Inter₂, LowerSet.coe_iSup₂]
+#align upper_set.compl_Sup UpperSet.compl_sSup
 
-/- warning: upper_set.compl_Inf -> UpperSet.compl_infₛ is a dubious translation:
+/- warning: upper_set.compl_Inf -> UpperSet.compl_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (InfSet.infₛ.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) S)) (infᵢ.{u1, succ u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => infᵢ.{u1, 0} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) (Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) => UpperSet.compl.{u1} α _inst_1 s)))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (InfSet.sInf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) S)) (iInf.{u1, succ u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => iInf.{u1, 0} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) (Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.Mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.hasMem.{u1} (UpperSet.{u1} α _inst_1)) s S) => UpperSet.compl.{u1} α _inst_1 s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (InfSet.infₛ.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instInfSetUpperSet.{u1} α _inst_1) S)) (infᵢ.{u1, succ u1} (LowerSet.{u1} α _inst_1) (LowerSet.instInfSetLowerSet.{u1} α _inst_1) (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => infᵢ.{u1, 0} (LowerSet.{u1} α _inst_1) (LowerSet.instInfSetLowerSet.{u1} α _inst_1) (Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) => UpperSet.compl.{u1} α _inst_1 s)))
-Case conversion may be inaccurate. Consider using '#align upper_set.compl_Inf UpperSet.compl_infₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (S : Set.{u1} (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (InfSet.sInf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instInfSetUpperSet.{u1} α _inst_1) S)) (iInf.{u1, succ u1} (LowerSet.{u1} α _inst_1) (LowerSet.instInfSetLowerSet.{u1} α _inst_1) (UpperSet.{u1} α _inst_1) (fun (s : UpperSet.{u1} α _inst_1) => iInf.{u1, 0} (LowerSet.{u1} α _inst_1) (LowerSet.instInfSetLowerSet.{u1} α _inst_1) (Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) (fun (H : Membership.mem.{u1, u1} (UpperSet.{u1} α _inst_1) (Set.{u1} (UpperSet.{u1} α _inst_1)) (Set.instMembershipSet.{u1} (UpperSet.{u1} α _inst_1)) s S) => UpperSet.compl.{u1} α _inst_1 s)))
+Case conversion may be inaccurate. Consider using '#align upper_set.compl_Inf UpperSet.compl_sInfₓ'. -/
 @[simp]
-protected theorem compl_infₛ (S : Set (UpperSet α)) : (infₛ S).compl = ⨅ s ∈ S, UpperSet.compl s :=
-  LowerSet.ext <| by simp only [coe_compl, coe_Inf, compl_Union₂, LowerSet.coe_infᵢ₂]
-#align upper_set.compl_Inf UpperSet.compl_infₛ
+protected theorem compl_sInf (S : Set (UpperSet α)) : (sInf S).compl = ⨅ s ∈ S, UpperSet.compl s :=
+  LowerSet.ext <| by simp only [coe_compl, coe_Inf, compl_Union₂, LowerSet.coe_iInf₂]
+#align upper_set.compl_Inf UpperSet.compl_sInf
 
-/- warning: upper_set.compl_supr -> UpperSet.compl_supᵢ is a dubious translation:
+/- warning: upper_set.compl_supr -> UpperSet.compl_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] (f : ι -> (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (supᵢ.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (supᵢ.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => UpperSet.compl.{u1} α _inst_1 (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] (f : ι -> (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (iSup.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => UpperSet.compl.{u1} α _inst_1 (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] (f : ι -> (UpperSet.{u2} α _inst_1)), Eq.{succ u2} (LowerSet.{u2} α _inst_1) (UpperSet.compl.{u2} α _inst_1 (supᵢ.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instSupSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (supᵢ.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instSupSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => UpperSet.compl.{u2} α _inst_1 (f i)))
-Case conversion may be inaccurate. Consider using '#align upper_set.compl_supr UpperSet.compl_supᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] (f : ι -> (UpperSet.{u2} α _inst_1)), Eq.{succ u2} (LowerSet.{u2} α _inst_1) (UpperSet.compl.{u2} α _inst_1 (iSup.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instSupSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instSupSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => UpperSet.compl.{u2} α _inst_1 (f i)))
+Case conversion may be inaccurate. Consider using '#align upper_set.compl_supr UpperSet.compl_iSupₓ'. -/
 @[simp]
-protected theorem compl_supᵢ (f : ι → UpperSet α) : (⨆ i, f i).compl = ⨆ i, (f i).compl :=
-  LowerSet.ext <| by simp only [coe_compl, coe_supr, compl_Inter, LowerSet.coe_supᵢ]
-#align upper_set.compl_supr UpperSet.compl_supᵢ
+protected theorem compl_iSup (f : ι → UpperSet α) : (⨆ i, f i).compl = ⨆ i, (f i).compl :=
+  LowerSet.ext <| by simp only [coe_compl, coe_supr, compl_Inter, LowerSet.coe_iSup]
+#align upper_set.compl_supr UpperSet.compl_iSup
 
-/- warning: upper_set.compl_infi -> UpperSet.compl_infᵢ is a dubious translation:
+/- warning: upper_set.compl_infi -> UpperSet.compl_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] (f : ι -> (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (infᵢ.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (infᵢ.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => UpperSet.compl.{u1} α _inst_1 (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] (f : ι -> (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (iInf.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => UpperSet.compl.{u1} α _inst_1 (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] (f : ι -> (UpperSet.{u2} α _inst_1)), Eq.{succ u2} (LowerSet.{u2} α _inst_1) (UpperSet.compl.{u2} α _inst_1 (infᵢ.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instInfSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (infᵢ.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instInfSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => UpperSet.compl.{u2} α _inst_1 (f i)))
-Case conversion may be inaccurate. Consider using '#align upper_set.compl_infi UpperSet.compl_infᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] (f : ι -> (UpperSet.{u2} α _inst_1)), Eq.{succ u2} (LowerSet.{u2} α _inst_1) (UpperSet.compl.{u2} α _inst_1 (iInf.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instInfSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instInfSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => UpperSet.compl.{u2} α _inst_1 (f i)))
+Case conversion may be inaccurate. Consider using '#align upper_set.compl_infi UpperSet.compl_iInfₓ'. -/
 @[simp]
-protected theorem compl_infᵢ (f : ι → UpperSet α) : (⨅ i, f i).compl = ⨅ i, (f i).compl :=
-  LowerSet.ext <| by simp only [coe_compl, coe_infi, compl_Union, LowerSet.coe_infᵢ]
-#align upper_set.compl_infi UpperSet.compl_infᵢ
+protected theorem compl_iInf (f : ι → UpperSet α) : (⨅ i, f i).compl = ⨅ i, (f i).compl :=
+  LowerSet.ext <| by simp only [coe_compl, coe_infi, compl_Union, LowerSet.coe_iInf]
+#align upper_set.compl_infi UpperSet.compl_iInf
 
-/- warning: upper_set.compl_supr₂ -> UpperSet.compl_supᵢ₂ is a dubious translation:
+/- warning: upper_set.compl_supr₂ -> UpperSet.compl_iSup₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] (f : forall (i : ι), (κ i) -> (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (supᵢ.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, u3} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (supᵢ.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, u3} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) (κ i) (fun (j : κ i) => UpperSet.compl.{u1} α _inst_1 (f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] (f : forall (i : ι), (κ i) -> (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (iSup.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, u3} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (iSup.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, u3} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) (κ i) (fun (j : κ i) => UpperSet.compl.{u1} α _inst_1 (f i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] (f : forall (i : ι), (κ i) -> (UpperSet.{u3} α _inst_1)), Eq.{succ u3} (LowerSet.{u3} α _inst_1) (UpperSet.compl.{u3} α _inst_1 (supᵢ.{u3, u2} (UpperSet.{u3} α _inst_1) (UpperSet.instSupSetUpperSet.{u3} α _inst_1) ι (fun (i : ι) => supᵢ.{u3, u1} (UpperSet.{u3} α _inst_1) (UpperSet.instSupSetUpperSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (supᵢ.{u3, u2} (LowerSet.{u3} α _inst_1) (LowerSet.instSupSetLowerSet.{u3} α _inst_1) ι (fun (i : ι) => supᵢ.{u3, u1} (LowerSet.{u3} α _inst_1) (LowerSet.instSupSetLowerSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => UpperSet.compl.{u3} α _inst_1 (f i j))))
-Case conversion may be inaccurate. Consider using '#align upper_set.compl_supr₂ UpperSet.compl_supᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] (f : forall (i : ι), (κ i) -> (UpperSet.{u3} α _inst_1)), Eq.{succ u3} (LowerSet.{u3} α _inst_1) (UpperSet.compl.{u3} α _inst_1 (iSup.{u3, u2} (UpperSet.{u3} α _inst_1) (UpperSet.instSupSetUpperSet.{u3} α _inst_1) ι (fun (i : ι) => iSup.{u3, u1} (UpperSet.{u3} α _inst_1) (UpperSet.instSupSetUpperSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (iSup.{u3, u2} (LowerSet.{u3} α _inst_1) (LowerSet.instSupSetLowerSet.{u3} α _inst_1) ι (fun (i : ι) => iSup.{u3, u1} (LowerSet.{u3} α _inst_1) (LowerSet.instSupSetLowerSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => UpperSet.compl.{u3} α _inst_1 (f i j))))
+Case conversion may be inaccurate. Consider using '#align upper_set.compl_supr₂ UpperSet.compl_iSup₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
-theorem compl_supᵢ₂ (f : ∀ i, κ i → UpperSet α) :
-    (⨆ (i) (j), f i j).compl = ⨆ (i) (j), (f i j).compl := by simp_rw [UpperSet.compl_supᵢ]
-#align upper_set.compl_supr₂ UpperSet.compl_supᵢ₂
+theorem compl_iSup₂ (f : ∀ i, κ i → UpperSet α) :
+    (⨆ (i) (j), f i j).compl = ⨆ (i) (j), (f i j).compl := by simp_rw [UpperSet.compl_iSup]
+#align upper_set.compl_supr₂ UpperSet.compl_iSup₂
 
-/- warning: upper_set.compl_infi₂ -> UpperSet.compl_infᵢ₂ is a dubious translation:
+/- warning: upper_set.compl_infi₂ -> UpperSet.compl_iInf₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] (f : forall (i : ι), (κ i) -> (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (infᵢ.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, u3} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (infᵢ.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, u3} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) (κ i) (fun (j : κ i) => UpperSet.compl.{u1} α _inst_1 (f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] (f : forall (i : ι), (κ i) -> (UpperSet.{u1} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (iInf.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => iInf.{u1, u3} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (iInf.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => iInf.{u1, u3} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) (κ i) (fun (j : κ i) => UpperSet.compl.{u1} α _inst_1 (f i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] (f : forall (i : ι), (κ i) -> (UpperSet.{u3} α _inst_1)), Eq.{succ u3} (LowerSet.{u3} α _inst_1) (UpperSet.compl.{u3} α _inst_1 (infᵢ.{u3, u2} (UpperSet.{u3} α _inst_1) (UpperSet.instInfSetUpperSet.{u3} α _inst_1) ι (fun (i : ι) => infᵢ.{u3, u1} (UpperSet.{u3} α _inst_1) (UpperSet.instInfSetUpperSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (infᵢ.{u3, u2} (LowerSet.{u3} α _inst_1) (LowerSet.instInfSetLowerSet.{u3} α _inst_1) ι (fun (i : ι) => infᵢ.{u3, u1} (LowerSet.{u3} α _inst_1) (LowerSet.instInfSetLowerSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => UpperSet.compl.{u3} α _inst_1 (f i j))))
-Case conversion may be inaccurate. Consider using '#align upper_set.compl_infi₂ UpperSet.compl_infᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] (f : forall (i : ι), (κ i) -> (UpperSet.{u3} α _inst_1)), Eq.{succ u3} (LowerSet.{u3} α _inst_1) (UpperSet.compl.{u3} α _inst_1 (iInf.{u3, u2} (UpperSet.{u3} α _inst_1) (UpperSet.instInfSetUpperSet.{u3} α _inst_1) ι (fun (i : ι) => iInf.{u3, u1} (UpperSet.{u3} α _inst_1) (UpperSet.instInfSetUpperSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (iInf.{u3, u2} (LowerSet.{u3} α _inst_1) (LowerSet.instInfSetLowerSet.{u3} α _inst_1) ι (fun (i : ι) => iInf.{u3, u1} (LowerSet.{u3} α _inst_1) (LowerSet.instInfSetLowerSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => UpperSet.compl.{u3} α _inst_1 (f i j))))
+Case conversion may be inaccurate. Consider using '#align upper_set.compl_infi₂ UpperSet.compl_iInf₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
-theorem compl_infᵢ₂ (f : ∀ i, κ i → UpperSet α) :
-    (⨅ (i) (j), f i j).compl = ⨅ (i) (j), (f i j).compl := by simp_rw [UpperSet.compl_infᵢ]
-#align upper_set.compl_infi₂ UpperSet.compl_infᵢ₂
+theorem compl_iInf₂ (f : ∀ i, κ i → UpperSet α) :
+    (⨅ (i) (j), f i j).compl = ⨅ (i) (j), (f i j).compl := by simp_rw [UpperSet.compl_iInf]
+#align upper_set.compl_infi₂ UpperSet.compl_iInf₂
 
 end UpperSet
 
@@ -1522,63 +1522,63 @@ protected theorem compl_bot : (⊥ : LowerSet α).compl = ⊥ :=
 #align lower_set.compl_bot LowerSet.compl_bot
 -/
 
-#print LowerSet.compl_supₛ /-
-protected theorem compl_supₛ (S : Set (LowerSet α)) : (supₛ S).compl = ⨆ s ∈ S, LowerSet.compl s :=
-  UpperSet.ext <| by simp only [coe_compl, coe_Sup, compl_Union₂, UpperSet.coe_supᵢ₂]
-#align lower_set.compl_Sup LowerSet.compl_supₛ
+#print LowerSet.compl_sSup /-
+protected theorem compl_sSup (S : Set (LowerSet α)) : (sSup S).compl = ⨆ s ∈ S, LowerSet.compl s :=
+  UpperSet.ext <| by simp only [coe_compl, coe_Sup, compl_Union₂, UpperSet.coe_iSup₂]
+#align lower_set.compl_Sup LowerSet.compl_sSup
 -/
 
-#print LowerSet.compl_infₛ /-
-protected theorem compl_infₛ (S : Set (LowerSet α)) : (infₛ S).compl = ⨅ s ∈ S, LowerSet.compl s :=
-  UpperSet.ext <| by simp only [coe_compl, coe_Inf, compl_Inter₂, UpperSet.coe_infᵢ₂]
-#align lower_set.compl_Inf LowerSet.compl_infₛ
+#print LowerSet.compl_sInf /-
+protected theorem compl_sInf (S : Set (LowerSet α)) : (sInf S).compl = ⨅ s ∈ S, LowerSet.compl s :=
+  UpperSet.ext <| by simp only [coe_compl, coe_Inf, compl_Inter₂, UpperSet.coe_iInf₂]
+#align lower_set.compl_Inf LowerSet.compl_sInf
 -/
 
-/- warning: lower_set.compl_supr -> LowerSet.compl_supᵢ is a dubious translation:
+/- warning: lower_set.compl_supr -> LowerSet.compl_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] (f : ι -> (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (UpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 (supᵢ.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (supᵢ.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => LowerSet.compl.{u1} α _inst_1 (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] (f : ι -> (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (UpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 (iSup.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => LowerSet.compl.{u1} α _inst_1 (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] (f : ι -> (LowerSet.{u2} α _inst_1)), Eq.{succ u2} (UpperSet.{u2} α _inst_1) (LowerSet.compl.{u2} α _inst_1 (supᵢ.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instSupSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (supᵢ.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instSupSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => LowerSet.compl.{u2} α _inst_1 (f i)))
-Case conversion may be inaccurate. Consider using '#align lower_set.compl_supr LowerSet.compl_supᵢₓ'. -/
-protected theorem compl_supᵢ (f : ι → LowerSet α) : (⨆ i, f i).compl = ⨆ i, (f i).compl :=
-  UpperSet.ext <| by simp only [coe_compl, coe_supr, compl_Union, UpperSet.coe_supᵢ]
-#align lower_set.compl_supr LowerSet.compl_supᵢ
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] (f : ι -> (LowerSet.{u2} α _inst_1)), Eq.{succ u2} (UpperSet.{u2} α _inst_1) (LowerSet.compl.{u2} α _inst_1 (iSup.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instSupSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instSupSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => LowerSet.compl.{u2} α _inst_1 (f i)))
+Case conversion may be inaccurate. Consider using '#align lower_set.compl_supr LowerSet.compl_iSupₓ'. -/
+protected theorem compl_iSup (f : ι → LowerSet α) : (⨆ i, f i).compl = ⨆ i, (f i).compl :=
+  UpperSet.ext <| by simp only [coe_compl, coe_supr, compl_Union, UpperSet.coe_iSup]
+#align lower_set.compl_supr LowerSet.compl_iSup
 
-/- warning: lower_set.compl_infi -> LowerSet.compl_infᵢ is a dubious translation:
+/- warning: lower_set.compl_infi -> LowerSet.compl_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] (f : ι -> (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (UpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 (infᵢ.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (infᵢ.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => LowerSet.compl.{u1} α _inst_1 (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : LE.{u1} α] (f : ι -> (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (UpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 (iInf.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => LowerSet.compl.{u1} α _inst_1 (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] (f : ι -> (LowerSet.{u2} α _inst_1)), Eq.{succ u2} (UpperSet.{u2} α _inst_1) (LowerSet.compl.{u2} α _inst_1 (infᵢ.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instInfSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (infᵢ.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instInfSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => LowerSet.compl.{u2} α _inst_1 (f i)))
-Case conversion may be inaccurate. Consider using '#align lower_set.compl_infi LowerSet.compl_infᵢₓ'. -/
-protected theorem compl_infᵢ (f : ι → LowerSet α) : (⨅ i, f i).compl = ⨅ i, (f i).compl :=
-  UpperSet.ext <| by simp only [coe_compl, coe_infi, compl_Inter, UpperSet.coe_infᵢ]
-#align lower_set.compl_infi LowerSet.compl_infᵢ
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : LE.{u2} α] (f : ι -> (LowerSet.{u2} α _inst_1)), Eq.{succ u2} (UpperSet.{u2} α _inst_1) (LowerSet.compl.{u2} α _inst_1 (iInf.{u2, u1} (LowerSet.{u2} α _inst_1) (LowerSet.instInfSetLowerSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u2, u1} (UpperSet.{u2} α _inst_1) (UpperSet.instInfSetUpperSet.{u2} α _inst_1) ι (fun (i : ι) => LowerSet.compl.{u2} α _inst_1 (f i)))
+Case conversion may be inaccurate. Consider using '#align lower_set.compl_infi LowerSet.compl_iInfₓ'. -/
+protected theorem compl_iInf (f : ι → LowerSet α) : (⨅ i, f i).compl = ⨅ i, (f i).compl :=
+  UpperSet.ext <| by simp only [coe_compl, coe_infi, compl_Inter, UpperSet.coe_iInf]
+#align lower_set.compl_infi LowerSet.compl_iInf
 
-/- warning: lower_set.compl_supr₂ -> LowerSet.compl_supᵢ₂ is a dubious translation:
+/- warning: lower_set.compl_supr₂ -> LowerSet.compl_iSup₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] (f : forall (i : ι), (κ i) -> (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (UpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 (supᵢ.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, u3} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (supᵢ.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, u3} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) (κ i) (fun (j : κ i) => LowerSet.compl.{u1} α _inst_1 (f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] (f : forall (i : ι), (κ i) -> (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (UpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 (iSup.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, u3} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (iSup.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, u3} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) (κ i) (fun (j : κ i) => LowerSet.compl.{u1} α _inst_1 (f i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] (f : forall (i : ι), (κ i) -> (LowerSet.{u3} α _inst_1)), Eq.{succ u3} (UpperSet.{u3} α _inst_1) (LowerSet.compl.{u3} α _inst_1 (supᵢ.{u3, u2} (LowerSet.{u3} α _inst_1) (LowerSet.instSupSetLowerSet.{u3} α _inst_1) ι (fun (i : ι) => supᵢ.{u3, u1} (LowerSet.{u3} α _inst_1) (LowerSet.instSupSetLowerSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (supᵢ.{u3, u2} (UpperSet.{u3} α _inst_1) (UpperSet.instSupSetUpperSet.{u3} α _inst_1) ι (fun (i : ι) => supᵢ.{u3, u1} (UpperSet.{u3} α _inst_1) (UpperSet.instSupSetUpperSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => LowerSet.compl.{u3} α _inst_1 (f i j))))
-Case conversion may be inaccurate. Consider using '#align lower_set.compl_supr₂ LowerSet.compl_supᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] (f : forall (i : ι), (κ i) -> (LowerSet.{u3} α _inst_1)), Eq.{succ u3} (UpperSet.{u3} α _inst_1) (LowerSet.compl.{u3} α _inst_1 (iSup.{u3, u2} (LowerSet.{u3} α _inst_1) (LowerSet.instSupSetLowerSet.{u3} α _inst_1) ι (fun (i : ι) => iSup.{u3, u1} (LowerSet.{u3} α _inst_1) (LowerSet.instSupSetLowerSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (iSup.{u3, u2} (UpperSet.{u3} α _inst_1) (UpperSet.instSupSetUpperSet.{u3} α _inst_1) ι (fun (i : ι) => iSup.{u3, u1} (UpperSet.{u3} α _inst_1) (UpperSet.instSupSetUpperSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => LowerSet.compl.{u3} α _inst_1 (f i j))))
+Case conversion may be inaccurate. Consider using '#align lower_set.compl_supr₂ LowerSet.compl_iSup₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
-theorem compl_supᵢ₂ (f : ∀ i, κ i → LowerSet α) :
-    (⨆ (i) (j), f i j).compl = ⨆ (i) (j), (f i j).compl := by simp_rw [LowerSet.compl_supᵢ]
-#align lower_set.compl_supr₂ LowerSet.compl_supᵢ₂
+theorem compl_iSup₂ (f : ∀ i, κ i → LowerSet α) :
+    (⨆ (i) (j), f i j).compl = ⨆ (i) (j), (f i j).compl := by simp_rw [LowerSet.compl_iSup]
+#align lower_set.compl_supr₂ LowerSet.compl_iSup₂
 
-/- warning: lower_set.compl_infi₂ -> LowerSet.compl_infᵢ₂ is a dubious translation:
+/- warning: lower_set.compl_infi₂ -> LowerSet.compl_iInf₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] (f : forall (i : ι), (κ i) -> (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (UpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 (infᵢ.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, u3} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (infᵢ.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, u3} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) (κ i) (fun (j : κ i) => LowerSet.compl.{u1} α _inst_1 (f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : LE.{u1} α] (f : forall (i : ι), (κ i) -> (LowerSet.{u1} α _inst_1)), Eq.{succ u1} (UpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 (iInf.{u1, u2} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => iInf.{u1, u3} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (iInf.{u1, u2} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) ι (fun (i : ι) => iInf.{u1, u3} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) (κ i) (fun (j : κ i) => LowerSet.compl.{u1} α _inst_1 (f i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] (f : forall (i : ι), (κ i) -> (LowerSet.{u3} α _inst_1)), Eq.{succ u3} (UpperSet.{u3} α _inst_1) (LowerSet.compl.{u3} α _inst_1 (infᵢ.{u3, u2} (LowerSet.{u3} α _inst_1) (LowerSet.instInfSetLowerSet.{u3} α _inst_1) ι (fun (i : ι) => infᵢ.{u3, u1} (LowerSet.{u3} α _inst_1) (LowerSet.instInfSetLowerSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (infᵢ.{u3, u2} (UpperSet.{u3} α _inst_1) (UpperSet.instInfSetUpperSet.{u3} α _inst_1) ι (fun (i : ι) => infᵢ.{u3, u1} (UpperSet.{u3} α _inst_1) (UpperSet.instInfSetUpperSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => LowerSet.compl.{u3} α _inst_1 (f i j))))
-Case conversion may be inaccurate. Consider using '#align lower_set.compl_infi₂ LowerSet.compl_infᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : LE.{u3} α] (f : forall (i : ι), (κ i) -> (LowerSet.{u3} α _inst_1)), Eq.{succ u3} (UpperSet.{u3} α _inst_1) (LowerSet.compl.{u3} α _inst_1 (iInf.{u3, u2} (LowerSet.{u3} α _inst_1) (LowerSet.instInfSetLowerSet.{u3} α _inst_1) ι (fun (i : ι) => iInf.{u3, u1} (LowerSet.{u3} α _inst_1) (LowerSet.instInfSetLowerSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (iInf.{u3, u2} (UpperSet.{u3} α _inst_1) (UpperSet.instInfSetUpperSet.{u3} α _inst_1) ι (fun (i : ι) => iInf.{u3, u1} (UpperSet.{u3} α _inst_1) (UpperSet.instInfSetUpperSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => LowerSet.compl.{u3} α _inst_1 (f i j))))
+Case conversion may be inaccurate. Consider using '#align lower_set.compl_infi₂ LowerSet.compl_iInf₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
-theorem compl_infᵢ₂ (f : ∀ i, κ i → LowerSet α) :
-    (⨅ (i) (j), f i j).compl = ⨅ (i) (j), (f i j).compl := by simp_rw [LowerSet.compl_infᵢ]
-#align lower_set.compl_infi₂ LowerSet.compl_infᵢ₂
+theorem compl_iInf₂ (f : ∀ i, κ i → LowerSet α) :
+    (⨅ (i) (j), f i j).compl = ⨅ (i) (j), (f i j).compl := by simp_rw [LowerSet.compl_iInf]
+#align lower_set.compl_infi₂ LowerSet.compl_iInf₂
 
 end LowerSet
 
@@ -1936,40 +1936,40 @@ section CompleteLattice
 
 variable [CompleteLattice α]
 
-/- warning: upper_set.Ici_Sup -> UpperSet.Ici_supₛ is a dubious translation:
+/- warning: upper_set.Ici_Sup -> UpperSet.Ici_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (S : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) S)) (supᵢ.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) α (fun (a : α) => supᵢ.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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) => UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) a)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (S : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) S)) (iSup.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) α (fun (a : α) => iSup.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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) => UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (S : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) S)) (supᵢ.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.instSupSetUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) α (fun (a : α) => supᵢ.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.instSupSetUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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) => UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) a)))
-Case conversion may be inaccurate. Consider using '#align upper_set.Ici_Sup UpperSet.Ici_supₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (S : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) S)) (iSup.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.instSupSetUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) α (fun (a : α) => iSup.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.instSupSetUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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) => UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) a)))
+Case conversion may be inaccurate. Consider using '#align upper_set.Ici_Sup UpperSet.Ici_sSupₓ'. -/
 @[simp]
-theorem Ici_supₛ (S : Set α) : Ici (supₛ S) = ⨆ a ∈ S, Ici a :=
-  SetLike.ext fun c => by simp only [mem_Ici_iff, mem_supr_iff, supₛ_le_iff]
-#align upper_set.Ici_Sup UpperSet.Ici_supₛ
+theorem Ici_sSup (S : Set α) : Ici (sSup S) = ⨆ a ∈ S, Ici a :=
+  SetLike.ext fun c => by simp only [mem_Ici_iff, mem_supr_iff, sSup_le_iff]
+#align upper_set.Ici_Sup UpperSet.Ici_sSup
 
-/- warning: upper_set.Ici_supr -> UpperSet.Ici_supᵢ is a dubious translation:
+/- warning: upper_set.Ici_supr -> UpperSet.Ici_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i))) (supᵢ.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) ι (fun (i : ι) => UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i))) (iSup.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) ι (fun (i : ι) => UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α), Eq.{succ u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) (UpperSet.Ici.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (supᵢ.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) (UpperSet.instSupSetUpperSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) ι (fun (i : ι) => UpperSet.Ici.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (f i)))
-Case conversion may be inaccurate. Consider using '#align upper_set.Ici_supr UpperSet.Ici_supᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α), Eq.{succ u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) (UpperSet.Ici.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) (UpperSet.instSupSetUpperSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) ι (fun (i : ι) => UpperSet.Ici.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (f i)))
+Case conversion may be inaccurate. Consider using '#align upper_set.Ici_supr UpperSet.Ici_iSupₓ'. -/
 @[simp]
-theorem Ici_supᵢ (f : ι → α) : Ici (⨆ i, f i) = ⨆ i, Ici (f i) :=
-  SetLike.ext fun c => by simp only [mem_Ici_iff, mem_supr_iff, supᵢ_le_iff]
-#align upper_set.Ici_supr UpperSet.Ici_supᵢ
+theorem Ici_iSup (f : ι → α) : Ici (⨆ i, f i) = ⨆ i, Ici (f i) :=
+  SetLike.ext fun c => by simp only [mem_Ici_iff, mem_supr_iff, iSup_le_iff]
+#align upper_set.Ici_supr UpperSet.Ici_iSup
 
-/- warning: upper_set.Ici_supr₂ -> UpperSet.Ici_supᵢ₂ is a dubious translation:
+/- warning: upper_set.Ici_supr₂ -> UpperSet.Ici_iSup₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] (f : forall (i : ι), (κ i) -> α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ i) (fun (j : κ i) => f i j)))) (supᵢ.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) ι (fun (i : ι) => supᵢ.{u1, u3} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (κ i) (fun (j : κ i) => UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] (f : forall (i : ι), (κ i) -> α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ i) (fun (j : κ i) => f i j)))) (iSup.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) ι (fun (i : ι) => iSup.{u1, u3} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (κ i) (fun (j : κ i) => UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (f i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] (f : forall (i : ι), (κ i) -> α), Eq.{succ u3} (UpperSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (UpperSet.Ici.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (supᵢ.{u3, u2} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => supᵢ.{u3, u1} α (CompleteLattice.toSupSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (supᵢ.{u3, u2} (UpperSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (UpperSet.instSupSetUpperSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) ι (fun (i : ι) => supᵢ.{u3, u1} (UpperSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (UpperSet.instSupSetUpperSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (κ i) (fun (j : κ i) => UpperSet.Ici.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (f i j))))
-Case conversion may be inaccurate. Consider using '#align upper_set.Ici_supr₂ UpperSet.Ici_supᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] (f : forall (i : ι), (κ i) -> α), Eq.{succ u3} (UpperSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (UpperSet.Ici.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (iSup.{u3, u2} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => iSup.{u3, u1} α (CompleteLattice.toSupSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (iSup.{u3, u2} (UpperSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (UpperSet.instSupSetUpperSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) ι (fun (i : ι) => iSup.{u3, u1} (UpperSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (UpperSet.instSupSetUpperSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (κ i) (fun (j : κ i) => UpperSet.Ici.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (f i j))))
+Case conversion may be inaccurate. Consider using '#align upper_set.Ici_supr₂ UpperSet.Ici_iSup₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
-theorem Ici_supᵢ₂ (f : ∀ i, κ i → α) : Ici (⨆ (i) (j), f i j) = ⨆ (i) (j), Ici (f i j) := by
+theorem Ici_iSup₂ (f : ∀ i, κ i → α) : Ici (⨆ (i) (j), f i j) = ⨆ (i) (j), Ici (f i j) := by
   simp_rw [Ici_supr]
-#align upper_set.Ici_supr₂ UpperSet.Ici_supᵢ₂
+#align upper_set.Ici_supr₂ UpperSet.Ici_iSup₂
 
 end CompleteLattice
 
@@ -2095,40 +2095,40 @@ section CompleteLattice
 
 variable [CompleteLattice α]
 
-/- warning: lower_set.Iic_Inf -> LowerSet.Iic_infₛ is a dubious translation:
+/- warning: lower_set.Iic_Inf -> LowerSet.Iic_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (S : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) S)) (infᵢ.{u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) α (fun (a : α) => infᵢ.{u1, 0} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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) => LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) a)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (S : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) S)) (iInf.{u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) α (fun (a : α) => iInf.{u1, 0} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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) => LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (S : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) S)) (infᵢ.{u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.instInfSetLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) α (fun (a : α) => infᵢ.{u1, 0} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.instInfSetLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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) => LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) a)))
-Case conversion may be inaccurate. Consider using '#align lower_set.Iic_Inf LowerSet.Iic_infₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (S : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) S)) (iInf.{u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.instInfSetLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) α (fun (a : α) => iInf.{u1, 0} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.instInfSetLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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) => LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) a)))
+Case conversion may be inaccurate. Consider using '#align lower_set.Iic_Inf LowerSet.Iic_sInfₓ'. -/
 @[simp]
-theorem Iic_infₛ (S : Set α) : Iic (infₛ S) = ⨅ a ∈ S, Iic a :=
-  SetLike.ext fun c => by simp only [mem_Iic_iff, mem_infi₂_iff, le_infₛ_iff]
-#align lower_set.Iic_Inf LowerSet.Iic_infₛ
+theorem Iic_sInf (S : Set α) : Iic (sInf S) = ⨅ a ∈ S, Iic a :=
+  SetLike.ext fun c => by simp only [mem_Iic_iff, mem_infi₂_iff, le_sInf_iff]
+#align lower_set.Iic_Inf LowerSet.Iic_sInf
 
-/- warning: lower_set.Iic_infi -> LowerSet.Iic_infᵢ is a dubious translation:
+/- warning: lower_set.Iic_infi -> LowerSet.Iic_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => f i))) (infᵢ.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) ι (fun (i : ι) => LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => f i))) (iInf.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) ι (fun (i : ι) => LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α), Eq.{succ u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) (LowerSet.Iic.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (infᵢ.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) (LowerSet.instInfSetLowerSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) ι (fun (i : ι) => LowerSet.Iic.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (f i)))
-Case conversion may be inaccurate. Consider using '#align lower_set.Iic_infi LowerSet.Iic_infᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α), Eq.{succ u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) (LowerSet.Iic.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) (LowerSet.instInfSetLowerSet.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))))) ι (fun (i : ι) => LowerSet.Iic.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (f i)))
+Case conversion may be inaccurate. Consider using '#align lower_set.Iic_infi LowerSet.Iic_iInfₓ'. -/
 @[simp]
-theorem Iic_infᵢ (f : ι → α) : Iic (⨅ i, f i) = ⨅ i, Iic (f i) :=
-  SetLike.ext fun c => by simp only [mem_Iic_iff, mem_infi_iff, le_infᵢ_iff]
-#align lower_set.Iic_infi LowerSet.Iic_infᵢ
+theorem Iic_iInf (f : ι → α) : Iic (⨅ i, f i) = ⨅ i, Iic (f i) :=
+  SetLike.ext fun c => by simp only [mem_Iic_iff, mem_infi_iff, le_iInf_iff]
+#align lower_set.Iic_infi LowerSet.Iic_iInf
 
-/- warning: lower_set.Iic_infi₂ -> LowerSet.Iic_infᵢ₂ is a dubious translation:
+/- warning: lower_set.Iic_infi₂ -> LowerSet.Iic_iInf₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] (f : forall (i : ι), (κ i) -> α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ i) (fun (j : κ i) => f i j)))) (infᵢ.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) ι (fun (i : ι) => infᵢ.{u1, u3} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (κ i) (fun (j : κ i) => LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (f i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] (f : forall (i : ι), (κ i) -> α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ i) (fun (j : κ i) => f i j)))) (iInf.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) ι (fun (i : ι) => iInf.{u1, u3} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (κ i) (fun (j : κ i) => LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (f i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] (f : forall (i : ι), (κ i) -> α), Eq.{succ u3} (LowerSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (LowerSet.Iic.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (infᵢ.{u3, u2} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => infᵢ.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (infᵢ.{u3, u2} (LowerSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (LowerSet.instInfSetLowerSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) ι (fun (i : ι) => infᵢ.{u3, u1} (LowerSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (LowerSet.instInfSetLowerSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (κ i) (fun (j : κ i) => LowerSet.Iic.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (f i j))))
-Case conversion may be inaccurate. Consider using '#align lower_set.Iic_infi₂ LowerSet.Iic_infᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] (f : forall (i : ι), (κ i) -> α), Eq.{succ u3} (LowerSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (LowerSet.Iic.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (iInf.{u3, u2} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => iInf.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j)))) (iInf.{u3, u2} (LowerSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (LowerSet.instInfSetLowerSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) ι (fun (i : ι) => iInf.{u3, u1} (LowerSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (LowerSet.instInfSetLowerSet.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))))) (κ i) (fun (j : κ i) => LowerSet.Iic.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (f i j))))
+Case conversion may be inaccurate. Consider using '#align lower_set.Iic_infi₂ LowerSet.Iic_iInf₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
-theorem Iic_infᵢ₂ (f : ∀ i, κ i → α) : Iic (⨅ (i) (j), f i j) = ⨅ (i) (j), Iic (f i j) := by
+theorem Iic_iInf₂ (f : ∀ i, κ i → α) : Iic (⨅ (i) (j), f i j) = ⨅ (i) (j), Iic (f i j) := by
   simp_rw [Iic_infi]
-#align lower_set.Iic_infi₂ LowerSet.Iic_infᵢ₂
+#align lower_set.Iic_infi₂ LowerSet.Iic_iInf₂
 
 end CompleteLattice
 
@@ -2269,26 +2269,26 @@ theorem lowerClosure_image (f : α ≃o β) : lowerClosure (f '' s) = LowerSet.m
   simp [-LowerSet.symm_map, LowerSet.map, OrderIso.symm, ← f.symm_apply_le]
 #align lower_closure_image lowerClosure_image
 
-/- warning: upper_set.infi_Ici -> UpperSet.infᵢ_Ici is a dubious translation:
+/- warning: upper_set.infi_Ici -> UpperSet.iInf_Ici is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (infᵢ.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (fun (a : α) => infᵢ.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{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) => UpperSet.Ici.{u1} α _inst_1 a))) (upperClosure.{u1} α _inst_1 s)
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (iInf.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (fun (a : α) => iInf.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{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) => UpperSet.Ici.{u1} α _inst_1 a))) (upperClosure.{u1} α _inst_1 s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (infᵢ.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instInfSetUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (fun (a : α) => infᵢ.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instInfSetUpperSet.{u1} α (Preorder.toLE.{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) => UpperSet.Ici.{u1} α _inst_1 a))) (upperClosure.{u1} α _inst_1 s)
-Case conversion may be inaccurate. Consider using '#align upper_set.infi_Ici UpperSet.infᵢ_Iciₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (iInf.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instInfSetUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (fun (a : α) => iInf.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instInfSetUpperSet.{u1} α (Preorder.toLE.{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) => UpperSet.Ici.{u1} α _inst_1 a))) (upperClosure.{u1} α _inst_1 s)
+Case conversion may be inaccurate. Consider using '#align upper_set.infi_Ici UpperSet.iInf_Iciₓ'. -/
 @[simp]
-theorem UpperSet.infᵢ_Ici (s : Set α) : (⨅ a ∈ s, UpperSet.Ici a) = upperClosure s :=
+theorem UpperSet.iInf_Ici (s : Set α) : (⨅ a ∈ s, UpperSet.Ici a) = upperClosure s :=
   by
   ext
   simp
-#align upper_set.infi_Ici UpperSet.infᵢ_Ici
+#align upper_set.infi_Ici UpperSet.iInf_Ici
 
-#print LowerSet.supᵢ_Iic /-
+#print LowerSet.iSup_Iic /-
 @[simp]
-theorem LowerSet.supᵢ_Iic (s : Set α) : (⨆ a ∈ s, LowerSet.Iic a) = lowerClosure s :=
+theorem LowerSet.iSup_Iic (s : Set α) : (⨆ a ∈ s, LowerSet.Iic a) = lowerClosure s :=
   by
   ext
   simp
-#align lower_set.supr_Iic LowerSet.supᵢ_Iic
+#align lower_set.supr_Iic LowerSet.iSup_Iic
 -/
 
 #print gc_upperClosure_coe /-
@@ -2457,48 +2457,48 @@ theorem lowerClosure_union (s t : Set α) : lowerClosure (s ∪ t) = lowerClosur
   simp [or_and_right, exists_or]
 #align lower_closure_union lowerClosure_union
 
-/- warning: upper_closure_Union -> upperClosure_unionᵢ is a dubious translation:
+/- warning: upper_closure_Union -> upperClosure_iUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Preorder.{u1} α] (f : ι -> (Set.{u1} α)), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Set.unionᵢ.{u1, u2} α ι (fun (i : ι) => f i))) (infᵢ.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) ι (fun (i : ι) => upperClosure.{u1} α _inst_1 (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Preorder.{u1} α] (f : ι -> (Set.{u1} α)), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Set.iUnion.{u1, u2} α ι (fun (i : ι) => f i))) (iInf.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) ι (fun (i : ι) => upperClosure.{u1} α _inst_1 (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : Preorder.{u2} α] (f : ι -> (Set.{u2} α)), Eq.{succ u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (upperClosure.{u2} α _inst_1 (Set.unionᵢ.{u2, u1} α ι (fun (i : ι) => f i))) (infᵢ.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instInfSetUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) ι (fun (i : ι) => upperClosure.{u2} α _inst_1 (f i)))
-Case conversion may be inaccurate. Consider using '#align upper_closure_Union upperClosure_unionᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : Preorder.{u2} α] (f : ι -> (Set.{u2} α)), Eq.{succ u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (upperClosure.{u2} α _inst_1 (Set.iUnion.{u2, u1} α ι (fun (i : ι) => f i))) (iInf.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instInfSetUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) ι (fun (i : ι) => upperClosure.{u2} α _inst_1 (f i)))
+Case conversion may be inaccurate. Consider using '#align upper_closure_Union upperClosure_iUnionₓ'. -/
 @[simp]
-theorem upperClosure_unionᵢ (f : ι → Set α) : upperClosure (⋃ i, f i) = ⨅ i, upperClosure (f i) :=
+theorem upperClosure_iUnion (f : ι → Set α) : upperClosure (⋃ i, f i) = ⨅ i, upperClosure (f i) :=
   by
   ext
   simp [← exists_and_right, @exists_comm α]
-#align upper_closure_Union upperClosure_unionᵢ
+#align upper_closure_Union upperClosure_iUnion
 
-/- warning: lower_closure_Union -> lowerClosure_unionᵢ is a dubious translation:
+/- warning: lower_closure_Union -> lowerClosure_iUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Preorder.{u1} α] (f : ι -> (Set.{u1} α)), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Set.unionᵢ.{u1, u2} α ι (fun (i : ι) => f i))) (supᵢ.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasSup.{u1} α (Preorder.toLE.{u1} α _inst_1)) ι (fun (i : ι) => lowerClosure.{u1} α _inst_1 (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Preorder.{u1} α] (f : ι -> (Set.{u1} α)), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Set.iUnion.{u1, u2} α ι (fun (i : ι) => f i))) (iSup.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasSup.{u1} α (Preorder.toLE.{u1} α _inst_1)) ι (fun (i : ι) => lowerClosure.{u1} α _inst_1 (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : Preorder.{u2} α] (f : ι -> (Set.{u2} α)), Eq.{succ u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (lowerClosure.{u2} α _inst_1 (Set.unionᵢ.{u2, u1} α ι (fun (i : ι) => f i))) (supᵢ.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instSupSetLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) ι (fun (i : ι) => lowerClosure.{u2} α _inst_1 (f i)))
-Case conversion may be inaccurate. Consider using '#align lower_closure_Union lowerClosure_unionᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : Preorder.{u2} α] (f : ι -> (Set.{u2} α)), Eq.{succ u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (lowerClosure.{u2} α _inst_1 (Set.iUnion.{u2, u1} α ι (fun (i : ι) => f i))) (iSup.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instSupSetLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) ι (fun (i : ι) => lowerClosure.{u2} α _inst_1 (f i)))
+Case conversion may be inaccurate. Consider using '#align lower_closure_Union lowerClosure_iUnionₓ'. -/
 @[simp]
-theorem lowerClosure_unionᵢ (f : ι → Set α) : lowerClosure (⋃ i, f i) = ⨆ i, lowerClosure (f i) :=
+theorem lowerClosure_iUnion (f : ι → Set α) : lowerClosure (⋃ i, f i) = ⨆ i, lowerClosure (f i) :=
   by
   ext
   simp [← exists_and_right, @exists_comm α]
-#align lower_closure_Union lowerClosure_unionᵢ
+#align lower_closure_Union lowerClosure_iUnion
 
-/- warning: upper_closure_sUnion -> upperClosure_unionₛ is a dubious translation:
+/- warning: upper_closure_sUnion -> upperClosure_sUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (S : Set.{u1} (Set.{u1} α)), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Set.unionₛ.{u1} α S)) (infᵢ.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => infᵢ.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) s S) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) s S) => upperClosure.{u1} α _inst_1 s)))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (S : Set.{u1} (Set.{u1} α)), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Set.sUnion.{u1} α S)) (iInf.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => iInf.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) s S) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) s S) => upperClosure.{u1} α _inst_1 s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (S : Set.{u1} (Set.{u1} α)), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Set.unionₛ.{u1} α S)) (infᵢ.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instInfSetUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => infᵢ.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instInfSetUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) s S) (fun (H : Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) s S) => upperClosure.{u1} α _inst_1 s)))
-Case conversion may be inaccurate. Consider using '#align upper_closure_sUnion upperClosure_unionₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (S : Set.{u1} (Set.{u1} α)), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Set.sUnion.{u1} α S)) (iInf.{u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instInfSetUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (fun (s : Set.{u1} α) => iInf.{u1, 0} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instInfSetUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) s S) (fun (H : Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) s S) => upperClosure.{u1} α _inst_1 s)))
+Case conversion may be inaccurate. Consider using '#align upper_closure_sUnion upperClosure_sUnionₓ'. -/
 @[simp]
-theorem upperClosure_unionₛ (S : Set (Set α)) : upperClosure (⋃₀ S) = ⨅ s ∈ S, upperClosure s := by
-  simp_rw [sUnion_eq_bUnion, upperClosure_unionᵢ]
-#align upper_closure_sUnion upperClosure_unionₛ
+theorem upperClosure_sUnion (S : Set (Set α)) : upperClosure (⋃₀ S) = ⨅ s ∈ S, upperClosure s := by
+  simp_rw [sUnion_eq_bUnion, upperClosure_iUnion]
+#align upper_closure_sUnion upperClosure_sUnion
 
-#print lowerClosure_unionₛ /-
+#print lowerClosure_sUnion /-
 @[simp]
-theorem lowerClosure_unionₛ (S : Set (Set α)) : lowerClosure (⋃₀ S) = ⨆ s ∈ S, lowerClosure s := by
-  simp_rw [sUnion_eq_bUnion, lowerClosure_unionᵢ]
-#align lower_closure_sUnion lowerClosure_unionₛ
+theorem lowerClosure_sUnion (S : Set (Set α)) : lowerClosure (⋃₀ S) = ⨆ s ∈ S, lowerClosure s := by
+  simp_rw [sUnion_eq_bUnion, lowerClosure_iUnion]
+#align lower_closure_sUnion lowerClosure_sUnion
 -/
 
 /- warning: set.ord_connected.upper_closure_inter_lower_closure -> Set.OrdConnected.upperClosure_inter_lowerClosure is a dubious translation:

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

@@ -413,7 +413,7 @@ theorem IsLowerSet.preimage (hs : IsLowerSet s) {f : β → α} (hf : Monotone f
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α}, (IsUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (forall (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)), IsUpperSet.{u2} β (Preorder.toLE.{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 _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) f) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α}, (IsUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1) s) -> (forall (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), IsUpperSet.{u1} β (Preorder.toLE.{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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f))) s))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α}, (IsUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1) s) -> (forall (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), IsUpperSet.{u1} β (Preorder.toLE.{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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) s))
 Case conversion may be inaccurate. Consider using '#align is_upper_set.image IsUpperSet.imageₓ'. -/
 theorem IsUpperSet.image (hs : IsUpperSet s) (f : α ≃o β) : IsUpperSet (f '' s : Set β) :=
   by
@@ -426,7 +426,7 @@ theorem IsUpperSet.image (hs : IsUpperSet s) (f : α ≃o β) : IsUpperSet (f ''
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α}, (IsLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1) s) -> (forall (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)), IsLowerSet.{u2} β (Preorder.toLE.{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 _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) f) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α}, (IsLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1) s) -> (forall (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), IsLowerSet.{u1} β (Preorder.toLE.{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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f))) s))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α}, (IsLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1) s) -> (forall (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), IsLowerSet.{u1} β (Preorder.toLE.{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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) s))
 Case conversion may be inaccurate. Consider using '#align is_lower_set.image IsLowerSet.imageₓ'. -/
 theorem IsLowerSet.image (hs : IsLowerSet s) (f : α ≃o β) : IsLowerSet (f '' s : Set β) :=
   by
@@ -1643,7 +1643,7 @@ theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)} {s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {b : β}, Iff (Membership.Mem.{u2, u2} β (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (SetLike.hasMem.{u2, u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (UpperSet.setLike.{u2} β (Preorder.toLE.{u2} β _inst_2))) b (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) => (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (Membership.Mem.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderIso.{u2, u1} β α (Preorder.toLE.{u2} β _inst_2) (Preorder.toLE.{u1} α _inst_1)) (fun (_x : RelIso.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1))) => β -> α) (RelIso.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderIso.symm.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2) f) b) s)
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)} {s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {b : β}, Iff (Membership.mem.{u2, u2} β ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) s) (SetLike.instMembership.{u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) s) β (UpperSet.instSetLikeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) b (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))) (RelEmbedding.toEmbedding.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f))) s)) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) b) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β α) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} β α) β α (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} β α)) (RelEmbedding.toEmbedding.{u2, u1} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (OrderIso.symm.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2) f))) b) s)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)} {s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {b : β}, Iff (Membership.mem.{u2, u2} β (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (SetLike.instMembership.{u2, u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (UpperSet.instSetLikeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) b (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (Membership.mem.{u1, u1} α (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β (fun (_x : β) => α) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (OrderIso.symm.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2) f) b) s)
 Case conversion may be inaccurate. Consider using '#align upper_set.mem_map UpperSet.mem_mapₓ'. -/
 @[simp]
 theorem mem_map : b ∈ map f s ↔ f.symm b ∈ s :=
@@ -1669,7 +1669,7 @@ theorem map_refl : map (OrderIso.refl α) = OrderIso.refl _ :=
 lean 3 declaration is
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 but is expected to have type
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u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α 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(Preorder.toLE.{u2} γ _inst_3)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u1, u2} α γ _inst_1 _inst_3 (OrderIso.trans.{u1, u3, u2} α β γ (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) f g)) s)
 Case conversion may be inaccurate. Consider using '#align upper_set.map_map UpperSet.map_mapₓ'. -/
 @[simp]
 theorem map_map (g : β ≃o γ) (f : α ≃o β) : map g (map f s) = map (f.trans g) s :=
@@ -1684,7 +1684,7 @@ variable (f s t)
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)), Eq.{succ u2} (Set.{u2} β) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Set.{u2} β) (SetLike.Set.hasCoeT.{u2, u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (UpperSet.setLike.{u2} β (Preorder.toLE.{u2} β _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) => (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (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 _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1))))) s))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)), Eq.{succ u2} (Set.{u2} β) (SetLike.coe.{u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) s) β (UpperSet.instSetLikeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))) (RelEmbedding.toEmbedding.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f))) s)) (Set.image.{u1, u2} α β (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u1, succ u2} α β)) (RelEmbedding.toEmbedding.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f))) (SetLike.coe.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)), Eq.{succ u2} (Set.{u2} β) (SetLike.coe.{u2, u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (UpperSet.instSetLikeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (Set.image.{u1, u2} α β (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) (SetLike.coe.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) s))
 Case conversion may be inaccurate. Consider using '#align upper_set.coe_map UpperSet.coe_mapₓ'. -/
 @[simp, norm_cast]
 theorem coe_map : (map f s : Set β) = f '' s :=
@@ -1728,7 +1728,7 @@ theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)} {f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)} {b : β}, Iff (Membership.Mem.{u2, u2} β (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (SetLike.hasMem.{u2, u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (LowerSet.setLike.{u2} β (Preorder.toLE.{u2} β _inst_2))) b (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) => (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (Membership.Mem.{u1, u1} α (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderIso.{u2, u1} β α (Preorder.toLE.{u2} β _inst_2) (Preorder.toLE.{u1} α _inst_1)) (fun (_x : RelIso.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1))) => β -> α) (RelIso.hasCoeToFun.{u2, u1} β α (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderIso.symm.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2) f) b) s)
 but is expected to have type
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=> (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))) (RelEmbedding.toEmbedding.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) 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u1, succ u2} (Function.Embedding.{succ u1, succ u2} β α) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} β α) β α (Function.instEmbeddingLikeEmbedding.{succ u1, succ u2} β α)) (RelEmbedding.toEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u2} β α (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (OrderIso.symm.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) f))) b) s)
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)} {f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)} {b : β}, Iff (Membership.mem.{u1, u1} β (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) β (LowerSet.instSetLikeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) 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(Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) s)) (Membership.mem.{u2, u2} α (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (SetLike.instMembership.{u2, u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) α (LowerSet.instSetLikeLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1))) 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x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (OrderIso.symm.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2) f) b) s)
 Case conversion may be inaccurate. Consider using '#align lower_set.mem_map LowerSet.mem_mapₓ'. -/
 @[simp]
 theorem mem_map {f : α ≃o β} {b : β} : b ∈ map f s ↔ f.symm b ∈ s :=
@@ -1754,7 +1754,7 @@ theorem map_refl : map (OrderIso.refl α) = OrderIso.refl _ :=
 lean 3 declaration is
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 but is expected to have type
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(CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) => LE.le.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Preorder.toLE.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} γ (Preorder.toLE.{u2} γ _inst_3)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u1, u2} α γ _inst_1 _inst_3 (OrderIso.trans.{u1, u3, u2} α β γ (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u3} β _inst_2) (Preorder.toLE.{u2} γ _inst_3) f g)) s)
 Case conversion may be inaccurate. Consider using '#align lower_set.map_map LowerSet.map_mapₓ'. -/
 @[simp]
 theorem map_map (g : β ≃o γ) (f : α ≃o β) : map g (map f s) = map (f.trans g) s :=
@@ -1769,7 +1769,7 @@ variable (f s t)
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)), Eq.{succ u2} (Set.{u2} β) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Set.{u2} β) (SetLike.Set.hasCoeT.{u2, u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (LowerSet.setLike.{u2} β (Preorder.toLE.{u2} β _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) => (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (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 _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) f) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1))))) s))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)), Eq.{succ u2} (Set.{u2} β) (SetLike.coe.{u2, u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) s) β (LowerSet.instSetLikeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))) (RelEmbedding.toEmbedding.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f))) s)) (Set.image.{u1, u2} α β (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u1, succ u2} (Function.Embedding.{succ u1, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u1, succ u2} α β)) (RelEmbedding.toEmbedding.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f))) (SetLike.coe.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.instSetLikeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)), Eq.{succ u2} (Set.{u2} β) (SetLike.coe.{u2, u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) β (LowerSet.instSetLikeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) => LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (Set.image.{u1, u2} α β (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u1, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) (SetLike.coe.{u1, u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (LowerSet.instSetLikeLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) s))
 Case conversion may be inaccurate. Consider using '#align lower_set.coe_map LowerSet.coe_mapₓ'. -/
 @[simp, norm_cast]
 theorem coe_map : (map f s : Set β) = f '' s :=
@@ -1784,7 +1784,7 @@ namespace UpperSet
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)), Eq.{succ u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.compl.{u2} β (Preorder.toLE.{u2} β _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} 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(UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} α 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(CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) => (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} 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(CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) (UpperSet.compl.{u1} α (Preorder.toLE.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (s : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)), Eq.{succ u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.compl.{u1} β (Preorder.toLE.{u1} β _inst_2) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β 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_inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β 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(Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β 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(Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) (UpperSet.compl.{u2} α (Preorder.toLE.{u2} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align upper_set.compl_map UpperSet.compl_mapₓ'. -/
 @[simp]
 theorem compl_map (f : α ≃o β) (s : UpperSet α) : (map f s).compl = LowerSet.map f s.compl :=
@@ -1799,7 +1799,7 @@ namespace LowerSet
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)), Eq.{succ u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.compl.{u2} β (Preorder.toLE.{u2} β _inst_2) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) => (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) s)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} α 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(CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) => (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) (LowerSet.compl.{u1} α (Preorder.toLE.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (s : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.compl.{u1} β (Preorder.toLE.{u1} β _inst_2) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))) (RelEmbedding.toEmbedding.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α 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(Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f))) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))) (RelEmbedding.toEmbedding.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f))) (LowerSet.compl.{u2} α (Preorder.toLE.{u2} α _inst_1) s))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (s : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.compl.{u1} β (Preorder.toLE.{u1} β _inst_2) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) 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(PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β 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(x._@.Mathlib.Order.Hom.Basic._hyg.1296 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f) (LowerSet.compl.{u2} α (Preorder.toLE.{u2} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align lower_set.compl_map LowerSet.compl_mapₓ'. -/
 @[simp]
 theorem compl_map (f : α ≃o β) (s : LowerSet α) : (map f s).compl = UpperSet.map f s.compl :=
@@ -1865,7 +1865,7 @@ theorem mem_Ioi_iff : b ∈ Ioi a ↔ a < b :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (a : α), Eq.{succ u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) => (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) (UpperSet.Ici.{u1} α _inst_1 a)) (UpperSet.Ici.{u2} β _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) f a))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.Ici.{u2} α _inst_1 a)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))) (RelEmbedding.toEmbedding.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f))) (UpperSet.Ici.{u2} α _inst_1 a)) (UpperSet.Ici.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) _inst_2 (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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f)) a))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f) (UpperSet.Ici.{u2} α _inst_1 a)) (UpperSet.Ici.{u1} β _inst_2 (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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a))
 Case conversion may be inaccurate. Consider using '#align upper_set.map_Ici UpperSet.map_Iciₓ'. -/
 @[simp]
 theorem map_Ici (f : α ≃o β) (a : α) : map f (Ici a) = Ici (f a) :=
@@ -1878,7 +1878,7 @@ theorem map_Ici (f : α ≃o β) (a : α) : map f (Ici a) = Ici (f a) :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (a : α), Eq.{succ u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) => (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) (UpperSet.Ioi.{u1} α _inst_1 a)) (UpperSet.Ioi.{u2} β _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) f a))
 but is expected to have type
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α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))) (RelEmbedding.toEmbedding.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f))) (UpperSet.Ioi.{u2} α _inst_1 a)) (UpperSet.Ioi.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) _inst_2 (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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f)) a))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f) (UpperSet.Ioi.{u2} α _inst_1 a)) (UpperSet.Ioi.{u1} β _inst_2 (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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a))
 Case conversion may be inaccurate. Consider using '#align upper_set.map_Ioi UpperSet.map_Ioiₓ'. -/
 @[simp]
 theorem map_Ioi (f : α ≃o β) (a : α) : map f (Ioi a) = Ioi (f a) :=
@@ -2028,7 +2028,7 @@ theorem mem_Iio_iff : b ∈ Iio a ↔ b < a :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (a : α), Eq.{succ u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) => (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) (LowerSet.Iic.{u1} α _inst_1 a)) (LowerSet.Iic.{u2} β _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) f a))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.Iic.{u2} α _inst_1 a)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))) (RelEmbedding.toEmbedding.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α 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(LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f))) (LowerSet.Iic.{u2} α _inst_1 a)) (LowerSet.Iic.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) _inst_2 (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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f)) a))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) (LowerSet.Iic.{u2} α _inst_1 a)) (LowerSet.Iic.{u1} β _inst_2 (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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a))
 Case conversion may be inaccurate. Consider using '#align lower_set.map_Iic LowerSet.map_Iicₓ'. -/
 @[simp]
 theorem map_Iic (f : α ≃o β) (a : α) : map f (Iic a) = Iic (f a) :=
@@ -2041,7 +2041,7 @@ theorem map_Iic (f : α ≃o β) (a : α) : map f (Iic a) = Iic (f a) :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (a : α), Eq.{succ u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) => (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) (LowerSet.Iio.{u1} α _inst_1 a)) (LowerSet.Iio.{u2} β _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) f a))
 but is expected to have type
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α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))) (RelEmbedding.toEmbedding.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f))) (LowerSet.Iio.{u2} α _inst_1 a)) (LowerSet.Iio.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) a) _inst_2 (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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f)) a))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)) (a : α), Eq.{succ u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) (LowerSet.Iio.{u2} α _inst_1 a)) (LowerSet.Iio.{u1} β _inst_2 (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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a))
 Case conversion may be inaccurate. Consider using '#align lower_set.map_Iio LowerSet.map_Iioₓ'. -/
 @[simp]
 theorem map_Iio (f : α ≃o β) (a : α) : map f (Iio a) = Iio (f a) :=
@@ -2245,7 +2245,7 @@ protected theorem LowerSet.lowerClosure (s : LowerSet α) : lowerClosure (s : Se
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)), Eq.{succ u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (upperClosure.{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 _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) f) s)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) => (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) (UpperSet.map.{u1, u2} α β _inst_1 _inst_2 f) (upperClosure.{u1} α _inst_1 s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (upperClosure.{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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f))) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))) (RelEmbedding.toEmbedding.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f))) (upperClosure.{u2} α _inst_1 s))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} (f : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2)), Eq.{succ u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (upperClosure.{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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u2} α (Preorder.toLE.{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 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (UpperSet.map.{u2, u1} α β _inst_1 _inst_2 f) (upperClosure.{u2} α _inst_1 s))
 Case conversion may be inaccurate. Consider using '#align upper_closure_image upperClosure_imageₓ'. -/
 @[simp]
 theorem upperClosure_image (f : α ≃o β) : upperClosure (f '' s) = UpperSet.map f (upperClosure s) :=
@@ -2259,7 +2259,7 @@ theorem upperClosure_image (f : α ≃o β) : upperClosure (f '' s) = UpperSet.m
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2)), Eq.{succ u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (lowerClosure.{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 _inst_1) (Preorder.toLE.{u2} β _inst_2)) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2))) f) s)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2))))))))) (fun (_x : RelIso.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) => (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2))) (RelIso.hasCoeToFun.{u1, u2} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LE.le.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Preorder.toLE.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1))))))))) (LE.le.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Preorder.toLE.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.completeDistribLattice.{u2} β (Preorder.toLE.{u2} β _inst_2)))))))))) (LowerSet.map.{u1, u2} α β _inst_1 _inst_2 f) (lowerClosure.{u1} α _inst_1 s))
 but is expected to have type
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(x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{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 _inst_1) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.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 _inst_2) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f))) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (fun (_x : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2))) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))) (RelEmbedding.toEmbedding.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f))) (lowerClosure.{u2} α _inst_1 s))
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(Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) 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_inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) => LE.le.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Preorder.toLE.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (PartialOrder.toPreorder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (Order.Coframe.toCompleteLattice.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (CompleteDistribLattice.toCoframe.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instCompleteDistribLatticeLowerSet.{u2} α (Preorder.toLE.{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 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) => LE.le.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Preorder.toLE.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (PartialOrder.toPreorder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteSemilatticeInf.toPartialOrder.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (Order.Coframe.toCompleteLattice.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (CompleteDistribLattice.toCoframe.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instCompleteDistribLatticeLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)))))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) (LowerSet.map.{u2, u1} α β _inst_1 _inst_2 f) (lowerClosure.{u2} α _inst_1 s))
 Case conversion may be inaccurate. Consider using '#align lower_closure_image lowerClosure_imageₓ'. -/
 @[simp]
 theorem lowerClosure_image (f : α ≃o β) : lowerClosure (f '' s) = LowerSet.map f (lowerClosure s) :=

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

@@ -2527,25 +2527,33 @@ theorem ordConnected_iff_upperClosure_inter_lowerClosure :
   exact (UpperSet.upper _).OrdConnected.inter (LowerSet.lower _).OrdConnected
 #align ord_connected_iff_upper_closure_inter_lower_closure ordConnected_iff_upperClosure_inter_lowerClosure
 
+#print upperBounds_lowerClosure /-
 @[simp]
 theorem upperBounds_lowerClosure : upperBounds (lowerClosure s : Set α) = upperBounds s :=
   (upperBounds_mono_set subset_lowerClosure).antisymm fun a ha b ⟨c, hc, hcb⟩ => hcb.trans <| ha hc
 #align upper_bounds_lower_closure upperBounds_lowerClosure
+-/
 
+#print lowerBounds_upperClosure /-
 @[simp]
 theorem lowerBounds_upperClosure : lowerBounds (upperClosure s : Set α) = lowerBounds s :=
   (lowerBounds_mono_set subset_upperClosure).antisymm fun a ha b ⟨c, hc, hcb⟩ => (ha hc).trans hcb
 #align lower_bounds_upper_closure lowerBounds_upperClosure
+-/
 
+#print bddAbove_lowerClosure /-
 @[simp]
 theorem bddAbove_lowerClosure : BddAbove (lowerClosure s : Set α) ↔ BddAbove s := by
   simp_rw [BddAbove, upperBounds_lowerClosure]
 #align bdd_above_lower_closure bddAbove_lowerClosure
+-/
 
+#print bddBelow_upperClosure /-
 @[simp]
 theorem bddBelow_upperClosure : BddBelow (upperClosure s : Set α) ↔ BddBelow s := by
   simp_rw [BddBelow, lowerBounds_upperClosure]
 #align bdd_below_upper_closure bddBelow_upperClosure
+-/
 
 alias bddAbove_lowerClosure ↔ BddAbove.of_lowerClosure BddAbove.lowerClosure
 #align bdd_above.of_lower_closure BddAbove.of_lowerClosure

mathlib commit https://github.com/leanprover-community/mathlib/commit/d11893b411025250c8e61ff2f12ccbd7ee35ab15

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Sara Rousta
 
 ! This file was ported from Lean 3 source module order.upper_lower.basic
-! leanprover-community/mathlib commit f16e7a22e11fc09c71f25446ac1db23a24e8a0bd
+! leanprover-community/mathlib commit e9ce88cd0d54891c714c604076084f763dd480ed
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -2527,6 +2527,36 @@ theorem ordConnected_iff_upperClosure_inter_lowerClosure :
   exact (UpperSet.upper _).OrdConnected.inter (LowerSet.lower _).OrdConnected
 #align ord_connected_iff_upper_closure_inter_lower_closure ordConnected_iff_upperClosure_inter_lowerClosure
 
+@[simp]
+theorem upperBounds_lowerClosure : upperBounds (lowerClosure s : Set α) = upperBounds s :=
+  (upperBounds_mono_set subset_lowerClosure).antisymm fun a ha b ⟨c, hc, hcb⟩ => hcb.trans <| ha hc
+#align upper_bounds_lower_closure upperBounds_lowerClosure
+
+@[simp]
+theorem lowerBounds_upperClosure : lowerBounds (upperClosure s : Set α) = lowerBounds s :=
+  (lowerBounds_mono_set subset_upperClosure).antisymm fun a ha b ⟨c, hc, hcb⟩ => (ha hc).trans hcb
+#align lower_bounds_upper_closure lowerBounds_upperClosure
+
+@[simp]
+theorem bddAbove_lowerClosure : BddAbove (lowerClosure s : Set α) ↔ BddAbove s := by
+  simp_rw [BddAbove, upperBounds_lowerClosure]
+#align bdd_above_lower_closure bddAbove_lowerClosure
+
+@[simp]
+theorem bddBelow_upperClosure : BddBelow (upperClosure s : Set α) ↔ BddBelow s := by
+  simp_rw [BddBelow, lowerBounds_upperClosure]
+#align bdd_below_upper_closure bddBelow_upperClosure
+
+alias bddAbove_lowerClosure ↔ BddAbove.of_lowerClosure BddAbove.lowerClosure
+#align bdd_above.of_lower_closure BddAbove.of_lowerClosure
+#align bdd_above.lower_closure BddAbove.lowerClosure
+
+alias bddBelow_upperClosure ↔ BddBelow.of_upperClosure BddBelow.upperClosure
+#align bdd_below.of_upper_closure BddBelow.of_upperClosure
+#align bdd_below.upper_closure BddBelow.upperClosure
+
+attribute [protected] BddAbove.lowerClosure BddBelow.upperClosure
+
 end closure
 
 /-! ### Product -/

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

@@ -2314,7 +2314,7 @@ theorem gc_lowerClosure_coe : GaloisConnection (lowerClosure : Set α → LowerS
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], GaloisInsertion.{u1, u1} (Set.{u1} α) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (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))))))) (OrderDual.preorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.completeDistribLattice.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Function.comp.{succ u1, succ u1, succ u1} (Set.{u1} α) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (fun (_x : Equiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) => (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) -> (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (Equiv.hasCoeToFun.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (OrderDual.toDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (upperClosure.{u1} α _inst_1)) (Function.comp.{succ u1, succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.setLike.{u1} α (Preorder.toLE.{u1} α _inst_1)))))) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) => (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) -> (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderDual.ofDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], GaloisInsertion.{u1, u1} (Set.{u1} α) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (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))))))) (OrderDual.preorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Function.comp.{succ u1, succ u1, succ u1} (Set.{u1} α) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (OrderDual.toDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (upperClosure.{u1} α _inst_1)) (Function.comp.{succ u1, succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (fun (_x : OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) => UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderDual.ofDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α], GaloisInsertion.{u1, u1} (Set.{u1} α) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (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))))))) (OrderDual.preorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (PartialOrder.toPreorder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteSemilatticeInf.toPartialOrder.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Order.Coframe.toCompleteLattice.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (CompleteDistribLattice.toCoframe.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instCompleteDistribLatticeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))))) (Function.comp.{succ u1, succ u1, succ u1} (Set.{u1} α) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (fun (_x : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) => OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (OrderDual.toDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))) (upperClosure.{u1} α _inst_1)) (Function.comp.{succ u1, succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (Set.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) α (UpperSet.instSetLikeUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (fun (_x : OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) => UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1))) (OrderDual.ofDual.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align gi_upper_closure_coe giUpperClosureCoeₓ'. -/
 /-- `upper_closure` forms a reversed Galois insertion with the coercion from upper sets to sets. -/
 def giUpperClosureCoe :

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

@@ -733,10 +733,10 @@ namespace UpperSet
 
 variable {S : Set (UpperSet α)} {s t : UpperSet α} {a : α}
 
-instance : HasSup (UpperSet α) :=
+instance : Sup (UpperSet α) :=
   ⟨fun s t => ⟨s ∩ t, s.upper.inter t.upper⟩⟩
 
-instance : HasInf (UpperSet α) :=
+instance : Inf (UpperSet α) :=
   ⟨fun s t => ⟨s ∪ t, s.upper.union t.upper⟩⟩
 
 instance : Top (UpperSet α) :=
@@ -797,9 +797,9 @@ theorem coe_eq_empty : (s : Set α) = ∅ ↔ s = ⊤ := by simp [SetLike.ext'_i
 
 /- warning: upper_set.coe_sup -> UpperSet.coe_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : UpperSet.{u1} α _inst_1) (t : UpperSet.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (HasSup.sup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : UpperSet.{u1} α _inst_1) (t : UpperSet.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (Sup.sup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : UpperSet.{u1} α _inst_1) (t : UpperSet.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) (HasSup.sup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instHasSupUpperSet.{u1} α _inst_1) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : UpperSet.{u1} α _inst_1) (t : UpperSet.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) (Sup.sup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instSupUpperSet.{u1} α _inst_1) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align upper_set.coe_sup UpperSet.coe_supₓ'. -/
 @[simp, norm_cast]
 theorem coe_sup (s t : UpperSet α) : (↑(s ⊔ t) : Set α) = s ∩ t :=
@@ -808,9 +808,9 @@ theorem coe_sup (s t : UpperSet α) : (↑(s ⊔ t) : Set α) = s ∩ t :=
 
 /- warning: upper_set.coe_inf -> UpperSet.coe_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : UpperSet.{u1} α _inst_1) (t : UpperSet.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (HasInf.inf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : UpperSet.{u1} α _inst_1) (t : UpperSet.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) (Inf.inf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (UpperSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (UpperSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)))) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : UpperSet.{u1} α _inst_1) (t : UpperSet.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) (HasInf.inf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instHasInfUpperSet.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : UpperSet.{u1} α _inst_1) (t : UpperSet.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) (Inf.inf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instInfUpperSet.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align upper_set.coe_inf UpperSet.coe_infₓ'. -/
 @[simp, norm_cast]
 theorem coe_inf (s t : UpperSet α) : (↑(s ⊓ t) : Set α) = s ∪ t :=
@@ -901,9 +901,9 @@ theorem mem_bot : a ∈ (⊥ : UpperSet α) :=
 
 /- warning: upper_set.mem_sup_iff -> UpperSet.mem_sup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1} {a : α}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (HasSup.sup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) s t)) (And (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a s) (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1} {a : α}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (Sup.sup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) s t)) (And (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a s) (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1} {a : α}, Iff (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a (HasSup.sup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instHasSupUpperSet.{u1} α _inst_1) s t)) (And (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a s) (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1} {a : α}, Iff (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a (Sup.sup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instSupUpperSet.{u1} α _inst_1) s t)) (And (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a s) (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a t))
 Case conversion may be inaccurate. Consider using '#align upper_set.mem_sup_iff UpperSet.mem_sup_iffₓ'. -/
 @[simp]
 theorem mem_sup_iff : a ∈ s ⊔ t ↔ a ∈ s ∧ a ∈ t :=
@@ -912,9 +912,9 @@ theorem mem_sup_iff : a ∈ s ⊔ t ↔ a ∈ s ∧ a ∈ t :=
 
 /- warning: upper_set.mem_inf_iff -> UpperSet.mem_inf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1} {a : α}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (HasInf.inf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) s t)) (Or (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a s) (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1} {a : α}, Iff (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a (Inf.inf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) s t)) (Or (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a s) (Membership.Mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.setLike.{u1} α _inst_1)) a t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1} {a : α}, Iff (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a (HasInf.inf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instHasInfUpperSet.{u1} α _inst_1) s t)) (Or (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a s) (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : UpperSet.{u1} α _inst_1} {t : UpperSet.{u1} α _inst_1} {a : α}, Iff (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a (Inf.inf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instInfUpperSet.{u1} α _inst_1) s t)) (Or (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a s) (Membership.mem.{u1, u1} α (UpperSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (UpperSet.{u1} α _inst_1) α (UpperSet.instSetLikeUpperSet.{u1} α _inst_1)) a t))
 Case conversion may be inaccurate. Consider using '#align upper_set.mem_inf_iff UpperSet.mem_inf_iffₓ'. -/
 @[simp]
 theorem mem_inf_iff : a ∈ s ⊓ t ↔ a ∈ s ∨ a ∈ t :=
@@ -1010,10 +1010,10 @@ namespace LowerSet
 
 variable {S : Set (LowerSet α)} {s t : LowerSet α} {a : α}
 
-instance : HasSup (LowerSet α) :=
+instance : Sup (LowerSet α) :=
   ⟨fun s t => ⟨s ∪ t, fun a b h => Or.imp (s.lower h) (t.lower h)⟩⟩
 
-instance : HasInf (LowerSet α) :=
+instance : Inf (LowerSet α) :=
   ⟨fun s t => ⟨s ∩ t, fun a b h => And.imp (s.lower h) (t.lower h)⟩⟩
 
 instance : Top (LowerSet α) :=
@@ -1074,9 +1074,9 @@ theorem coe_eq_empty : (s : Set α) = ∅ ↔ s = ⊥ := by simp [SetLike.ext'_i
 
 /- warning: lower_set.coe_sup -> LowerSet.coe_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : LowerSet.{u1} α _inst_1) (t : LowerSet.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (HasSup.sup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : LowerSet.{u1} α _inst_1) (t : LowerSet.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (Sup.sup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : LowerSet.{u1} α _inst_1) (t : LowerSet.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) (HasSup.sup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instHasSupLowerSet.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : LowerSet.{u1} α _inst_1) (t : LowerSet.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) (Sup.sup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instSupLowerSet.{u1} α _inst_1) s t)) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align lower_set.coe_sup LowerSet.coe_supₓ'. -/
 @[simp, norm_cast]
 theorem coe_sup (s t : LowerSet α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
@@ -1085,9 +1085,9 @@ theorem coe_sup (s t : LowerSet α) : (↑(s ⊔ t) : Set α) = s ∪ t :=
 
 /- warning: lower_set.coe_inf -> LowerSet.coe_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : LowerSet.{u1} α _inst_1) (t : LowerSet.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (HasInf.inf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : LowerSet.{u1} α _inst_1) (t : LowerSet.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) (Inf.inf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (LowerSet.{u1} α _inst_1) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (LowerSet.{u1} α _inst_1) (Set.{u1} α) (SetLike.Set.hasCoeT.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)))) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : LowerSet.{u1} α _inst_1) (t : LowerSet.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) (HasInf.inf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instHasInfLowerSet.{u1} α _inst_1) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : LowerSet.{u1} α _inst_1) (t : LowerSet.{u1} α _inst_1), Eq.{succ u1} (Set.{u1} α) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) (Inf.inf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instInfLowerSet.{u1} α _inst_1) s t)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) s) (SetLike.coe.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align lower_set.coe_inf LowerSet.coe_infₓ'. -/
 @[simp, norm_cast]
 theorem coe_inf (s t : LowerSet α) : (↑(s ⊓ t) : Set α) = s ∩ t :=
@@ -1180,9 +1180,9 @@ theorem not_mem_bot : a ∉ (⊥ : LowerSet α) :=
 
 /- warning: lower_set.mem_sup_iff -> LowerSet.mem_sup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1} {a : α}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (HasSup.sup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) s t)) (Or (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a s) (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1} {a : α}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (Sup.sup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) s t)) (Or (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a s) (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1} {a : α}, Iff (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a (HasSup.sup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instHasSupLowerSet.{u1} α _inst_1) s t)) (Or (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a s) (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1} {a : α}, Iff (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a (Sup.sup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instSupLowerSet.{u1} α _inst_1) s t)) (Or (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a s) (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a t))
 Case conversion may be inaccurate. Consider using '#align lower_set.mem_sup_iff LowerSet.mem_sup_iffₓ'. -/
 @[simp]
 theorem mem_sup_iff : a ∈ s ⊔ t ↔ a ∈ s ∨ a ∈ t :=
@@ -1191,9 +1191,9 @@ theorem mem_sup_iff : a ∈ s ⊔ t ↔ a ∈ s ∨ a ∈ t :=
 
 /- warning: lower_set.mem_inf_iff -> LowerSet.mem_inf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1} {a : α}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (HasInf.inf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) s t)) (And (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a s) (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1} {a : α}, Iff (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a (Inf.inf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) s t)) (And (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a s) (Membership.Mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.hasMem.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.setLike.{u1} α _inst_1)) a t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1} {a : α}, Iff (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a (HasInf.inf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instHasInfLowerSet.{u1} α _inst_1) s t)) (And (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a s) (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] {s : LowerSet.{u1} α _inst_1} {t : LowerSet.{u1} α _inst_1} {a : α}, Iff (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a (Inf.inf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instInfLowerSet.{u1} α _inst_1) s t)) (And (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a s) (Membership.mem.{u1, u1} α (LowerSet.{u1} α _inst_1) (SetLike.instMembership.{u1, u1} (LowerSet.{u1} α _inst_1) α (LowerSet.instSetLikeLowerSet.{u1} α _inst_1)) a t))
 Case conversion may be inaccurate. Consider using '#align lower_set.mem_inf_iff LowerSet.mem_inf_iffₓ'. -/
 @[simp]
 theorem mem_inf_iff : a ∈ s ⊓ t ↔ a ∈ s ∧ a ∈ t :=
@@ -1344,9 +1344,9 @@ theorem compl_le_compl : s.compl ≤ t.compl ↔ s ≤ t :=
 
 /- warning: upper_set.compl_sup -> UpperSet.compl_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : UpperSet.{u1} α _inst_1) (t : UpperSet.{u1} α _inst_1), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (HasSup.sup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) s t)) (HasSup.sup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 s) (UpperSet.compl.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : UpperSet.{u1} α _inst_1) (t : UpperSet.{u1} α _inst_1), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (Sup.sup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) s t)) (Sup.sup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 s) (UpperSet.compl.{u1} α _inst_1 t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : UpperSet.{u1} α _inst_1) (t : UpperSet.{u1} α _inst_1), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (HasSup.sup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instHasSupUpperSet.{u1} α _inst_1) s t)) (HasSup.sup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instHasSupLowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 s) (UpperSet.compl.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : UpperSet.{u1} α _inst_1) (t : UpperSet.{u1} α _inst_1), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (Sup.sup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instSupUpperSet.{u1} α _inst_1) s t)) (Sup.sup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instSupLowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 s) (UpperSet.compl.{u1} α _inst_1 t))
 Case conversion may be inaccurate. Consider using '#align upper_set.compl_sup UpperSet.compl_supₓ'. -/
 @[simp]
 protected theorem compl_sup (s t : UpperSet α) : (s ⊔ t).compl = s.compl ⊔ t.compl :=
@@ -1355,9 +1355,9 @@ protected theorem compl_sup (s t : UpperSet α) : (s ⊔ t).compl = s.compl ⊔
 
 /- warning: upper_set.compl_inf -> UpperSet.compl_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : UpperSet.{u1} α _inst_1) (t : UpperSet.{u1} α _inst_1), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (HasInf.inf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) s t)) (HasInf.inf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 s) (UpperSet.compl.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : UpperSet.{u1} α _inst_1) (t : UpperSet.{u1} α _inst_1), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (Inf.inf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) s t)) (Inf.inf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 s) (UpperSet.compl.{u1} α _inst_1 t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : UpperSet.{u1} α _inst_1) (t : UpperSet.{u1} α _inst_1), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (HasInf.inf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instHasInfUpperSet.{u1} α _inst_1) s t)) (HasInf.inf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instHasInfLowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 s) (UpperSet.compl.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : UpperSet.{u1} α _inst_1) (t : UpperSet.{u1} α _inst_1), Eq.{succ u1} (LowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 (Inf.inf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instInfUpperSet.{u1} α _inst_1) s t)) (Inf.inf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instInfLowerSet.{u1} α _inst_1) (UpperSet.compl.{u1} α _inst_1 s) (UpperSet.compl.{u1} α _inst_1 t))
 Case conversion may be inaccurate. Consider using '#align upper_set.compl_inf UpperSet.compl_infₓ'. -/
 @[simp]
 protected theorem compl_inf (s t : UpperSet α) : (s ⊓ t).compl = s.compl ⊓ t.compl :=
@@ -1492,9 +1492,9 @@ theorem compl_le_compl : s.compl ≤ t.compl ↔ s ≤ t :=
 
 /- warning: lower_set.compl_sup -> LowerSet.compl_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : LowerSet.{u1} α _inst_1) (t : LowerSet.{u1} α _inst_1), Eq.{succ u1} (UpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 (HasSup.sup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) s t)) (HasSup.sup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 s) (LowerSet.compl.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : LowerSet.{u1} α _inst_1) (t : LowerSet.{u1} α _inst_1), Eq.{succ u1} (UpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 (Sup.sup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasSup.{u1} α _inst_1) s t)) (Sup.sup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasSup.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 s) (LowerSet.compl.{u1} α _inst_1 t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : LowerSet.{u1} α _inst_1) (t : LowerSet.{u1} α _inst_1), Eq.{succ u1} (UpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 (HasSup.sup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instHasSupLowerSet.{u1} α _inst_1) s t)) (HasSup.sup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instHasSupUpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 s) (LowerSet.compl.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : LowerSet.{u1} α _inst_1) (t : LowerSet.{u1} α _inst_1), Eq.{succ u1} (UpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 (Sup.sup.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instSupLowerSet.{u1} α _inst_1) s t)) (Sup.sup.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instSupUpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 s) (LowerSet.compl.{u1} α _inst_1 t))
 Case conversion may be inaccurate. Consider using '#align lower_set.compl_sup LowerSet.compl_supₓ'. -/
 protected theorem compl_sup (s t : LowerSet α) : (s ⊔ t).compl = s.compl ⊔ t.compl :=
   UpperSet.ext compl_sup
@@ -1502,9 +1502,9 @@ protected theorem compl_sup (s t : LowerSet α) : (s ⊔ t).compl = s.compl ⊔
 
 /- warning: lower_set.compl_inf -> LowerSet.compl_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : LowerSet.{u1} α _inst_1) (t : LowerSet.{u1} α _inst_1), Eq.{succ u1} (UpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 (HasInf.inf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) s t)) (HasInf.inf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 s) (LowerSet.compl.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : LowerSet.{u1} α _inst_1) (t : LowerSet.{u1} α _inst_1), Eq.{succ u1} (UpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 (Inf.inf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.hasInf.{u1} α _inst_1) s t)) (Inf.inf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.hasInf.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 s) (LowerSet.compl.{u1} α _inst_1 t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : LowerSet.{u1} α _inst_1) (t : LowerSet.{u1} α _inst_1), Eq.{succ u1} (UpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 (HasInf.inf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instHasInfLowerSet.{u1} α _inst_1) s t)) (HasInf.inf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instHasInfUpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 s) (LowerSet.compl.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : LE.{u1} α] (s : LowerSet.{u1} α _inst_1) (t : LowerSet.{u1} α _inst_1), Eq.{succ u1} (UpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 (Inf.inf.{u1} (LowerSet.{u1} α _inst_1) (LowerSet.instInfLowerSet.{u1} α _inst_1) s t)) (Inf.inf.{u1} (UpperSet.{u1} α _inst_1) (UpperSet.instInfUpperSet.{u1} α _inst_1) (LowerSet.compl.{u1} α _inst_1 s) (LowerSet.compl.{u1} α _inst_1 t))
 Case conversion may be inaccurate. Consider using '#align lower_set.compl_inf LowerSet.compl_infₓ'. -/
 protected theorem compl_inf (s t : LowerSet α) : (s ⊓ t).compl = s.compl ⊓ t.compl :=
   UpperSet.ext compl_inf
@@ -1923,9 +1923,9 @@ end Preorder
 
 /- warning: upper_set.Ici_sup -> UpperSet.Ici_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α] (a : α) (b : α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) a b)) (HasSup.sup.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) a) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) b))
+  forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α] (a : α) (b : α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) a b)) (Sup.sup.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) a) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) b))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α] (a : α) (b : α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α _inst_1) a b)) (HasSup.sup.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.instHasSupUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) a) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) b))
+  forall {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u1} α] (a : α) (b : α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α _inst_1) a b)) (Sup.sup.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.instSupUpperSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)))) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) a) (UpperSet.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeSup.toPartialOrder.{u1} α _inst_1)) b))
 Case conversion may be inaccurate. Consider using '#align upper_set.Ici_sup UpperSet.Ici_supₓ'. -/
 @[simp]
 theorem Ici_sup [SemilatticeSup α] (a b : α) : Ici (a ⊔ b) = Ici a ⊔ Ici b :=
@@ -2082,9 +2082,9 @@ end Preorder
 
 /- warning: lower_set.Iic_inf -> LowerSet.Iic_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] (a : α) (b : α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) a b)) (HasInf.inf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) a) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) b))
+  forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] (a : α) (b : α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) a b)) (Inf.inf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) a) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) b))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] (a : α) (b : α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α _inst_1) a b)) (HasInf.inf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.instHasInfLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) a) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) b))
+  forall {α : Type.{u1}} [_inst_1 : SemilatticeInf.{u1} α] (a : α) (b : α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) (Inf.inf.{u1} α (SemilatticeInf.toInf.{u1} α _inst_1) a b)) (Inf.inf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.instInfLowerSet.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)))) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) a) (LowerSet.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α _inst_1)) b))
 Case conversion may be inaccurate. Consider using '#align lower_set.Iic_inf LowerSet.Iic_infₓ'. -/
 @[simp]
 theorem Iic_inf [SemilatticeInf α] (a b : α) : Iic (a ⊓ b) = Iic a ⊓ Iic b :=
@@ -2433,9 +2433,9 @@ theorem lowerClosure_eq_bot_iff : lowerClosure s = ⊥ ↔ s = ∅ :=
 
 /- warning: upper_closure_union -> upperClosure_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (HasInf.inf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 s) (upperClosure.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Inf.inf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 s) (upperClosure.{u1} α _inst_1 t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (HasInf.inf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instHasInfUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 s) (upperClosure.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Inf.inf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.instInfUpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (upperClosure.{u1} α _inst_1 s) (upperClosure.{u1} α _inst_1 t))
 Case conversion may be inaccurate. Consider using '#align upper_closure_union upperClosure_unionₓ'. -/
 @[simp]
 theorem upperClosure_union (s t : Set α) : upperClosure (s ∪ t) = upperClosure s ⊓ upperClosure t :=
@@ -2446,9 +2446,9 @@ theorem upperClosure_union (s t : Set α) : upperClosure (s ∪ t) = upperClosur
 
 /- warning: lower_closure_union -> lowerClosure_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (HasSup.sup.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasSup.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 s) (lowerClosure.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Sup.sup.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasSup.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 s) (lowerClosure.{u1} α _inst_1 t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (HasSup.sup.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instHasSupLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 s) (lowerClosure.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α), Eq.{succ u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Sup.sup.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.instSupLowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (lowerClosure.{u1} α _inst_1 s) (lowerClosure.{u1} α _inst_1 t))
 Case conversion may be inaccurate. Consider using '#align lower_closure_union lowerClosure_unionₓ'. -/
 @[simp]
 theorem lowerClosure_union (s t : Set α) : lowerClosure (s ∪ t) = lowerClosure s ⊔ lowerClosure t :=
@@ -2665,9 +2665,9 @@ theorem bot_prod_bot : (⊥ : UpperSet α) ×ˢ (⊥ : UpperSet β) = ⊥ :=
 
 /- warning: upper_set.sup_prod -> UpperSet.sup_prod is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (s₂ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (Sup.sup.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α _inst_1)) s₁ s₂) t) (Sup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 (HasSup.sup.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instHasSupUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) t) (HasSup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instHasSupUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 (Sup.sup.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instSupUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) t) (Sup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instSupUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t))
 Case conversion may be inaccurate. Consider using '#align upper_set.sup_prod UpperSet.sup_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -2679,9 +2679,9 @@ theorem sup_prod : (s₁ ⊔ s₂) ×ˢ t = s₁ ×ˢ t ⊔ s₂ ×ˢ t :=
 
 /- warning: upper_set.prod_sup -> UpperSet.prod_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t₁ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (t₂ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s (HasSup.sup.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.hasSup.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ t₂)) (HasSup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t₁ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (t₂ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s (Sup.sup.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.hasSup.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ t₂)) (Sup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t₁ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (t₂ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s (HasSup.sup.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instHasSupUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ t₂)) (HasSup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instHasSupUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₂))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t₁ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (t₂ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s (Sup.sup.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instSupUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ t₂)) (Sup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instSupUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₂))
 Case conversion may be inaccurate. Consider using '#align upper_set.prod_sup UpperSet.prod_supₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -2693,9 +2693,9 @@ theorem prod_sup : s ×ˢ (t₁ ⊔ t₂) = s ×ˢ t₁ ⊔ s ×ˢ t₂ :=
 
 /- warning: upper_set.inf_prod -> UpperSet.inf_prod is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (s₂ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (Inf.inf.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) s₁ s₂) t) (Inf.inf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 (HasInf.inf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instHasInfUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) t) (HasInf.inf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instHasInfUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 (Inf.inf.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instInfUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) t) (Inf.inf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instInfUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t))
 Case conversion may be inaccurate. Consider using '#align upper_set.inf_prod UpperSet.inf_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -2707,9 +2707,9 @@ theorem inf_prod : (s₁ ⊓ s₂) ×ˢ t = s₁ ×ˢ t ⊓ s₂ ×ˢ t :=
 
 /- warning: upper_set.prod_inf -> UpperSet.prod_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t₁ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (t₂ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s (HasInf.inf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.hasInf.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ t₂)) (HasInf.inf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t₁ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (t₂ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s (Inf.inf.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.hasInf.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ t₂)) (Inf.inf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t₁ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (t₂ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s (HasInf.inf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instHasInfUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ t₂)) (HasInf.inf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instHasInfUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₂))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t₁ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (t₂ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s (Inf.inf.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instInfUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ t₂)) (Inf.inf.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instInfUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₁) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₂))
 Case conversion may be inaccurate. Consider using '#align upper_set.prod_inf UpperSet.prod_infₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -2721,9 +2721,9 @@ theorem prod_inf : s ×ˢ (t₁ ⊓ t₂) = s ×ˢ t₁ ⊓ s ×ˢ t₂ :=
 
 /- warning: upper_set.prod_sup_prod -> UpperSet.prod_sup_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (s₂ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t₁ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (t₂ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (HasSup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (HasSup.sup.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α _inst_1)) s₁ s₂) (HasSup.sup.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.hasSup.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ t₂))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (s₂ : UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t₁ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (t₂ : UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Sup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (UpperSet.prod.{u1, u2} α β _inst_1 _inst_2 (Sup.sup.{u1} (UpperSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (UpperSet.hasSup.{u1} α (Preorder.toLE.{u1} α _inst_1)) s₁ s₂) (Sup.sup.{u2} (UpperSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (UpperSet.hasSup.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ t₂))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t₁ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (t₂ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (HasSup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instHasSupUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t₁) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t₂)) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 (HasSup.sup.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instHasSupUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) (HasSup.sup.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instHasSupUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ t₂))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t₁ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (t₂ : UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Sup.sup.{max u1 u2} (UpperSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.instSupUpperSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t₁) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t₂)) (UpperSet.prod.{u2, u1} α β _inst_1 _inst_2 (Sup.sup.{u2} (UpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (UpperSet.instSupUpperSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) (Sup.sup.{u1} (UpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (UpperSet.instSupUpperSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ t₂))
 Case conversion may be inaccurate. Consider using '#align upper_set.prod_sup_prod UpperSet.prod_sup_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -2938,9 +2938,9 @@ theorem top_prod_top : (⊤ : LowerSet α) ×ˢ (⊤ : LowerSet β) = ⊤ :=
 
 /- warning: lower_set.inf_prod -> LowerSet.inf_prod is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (Inf.inf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) s₁ s₂) t) (Inf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.hasInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 (HasInf.inf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instHasInfLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) t) (HasInf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instHasInfLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 (Inf.inf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instInfLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) t) (Inf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instInfLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t))
 Case conversion may be inaccurate. Consider using '#align lower_set.inf_prod LowerSet.inf_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -2952,9 +2952,9 @@ theorem inf_prod : (s₁ ⊓ s₂) ×ˢ t = s₁ ×ˢ t ⊓ s₂ ×ˢ t :=
 
 /- warning: lower_set.prod_inf -> LowerSet.prod_inf is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t₁ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (t₂ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s (Inf.inf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.hasInf.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ t₂)) (Inf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.hasInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t₁ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (t₂ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s (HasInf.inf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instHasInfLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ t₂)) (HasInf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instHasInfLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₁) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₂))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t₁ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (t₂ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s (Inf.inf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instInfLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ t₂)) (Inf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instInfLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₁) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₂))
 Case conversion may be inaccurate. Consider using '#align lower_set.prod_inf LowerSet.prod_infₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -2966,9 +2966,9 @@ theorem prod_inf : s ×ˢ (t₁ ⊓ t₂) = s ×ˢ t₁ ⊓ s ×ˢ t₂ :=
 
 /- warning: lower_set.sup_prod -> LowerSet.sup_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (HasSup.sup.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasSup.{u1} α (Preorder.toLE.{u1} α _inst_1)) s₁ s₂) t) (HasSup.sup.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (Sup.sup.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasSup.{u1} α (Preorder.toLE.{u1} α _inst_1)) s₁ s₂) t) (Sup.sup.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 (HasSup.sup.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instHasSupLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) t) (HasSup.sup.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instHasSupLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 (Sup.sup.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instSupLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) t) (Sup.sup.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instSupLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t))
 Case conversion may be inaccurate. Consider using '#align lower_set.sup_prod LowerSet.sup_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -2980,9 +2980,9 @@ theorem sup_prod : (s₁ ⊔ s₂) ×ˢ t = s₁ ×ˢ t ⊔ s₂ ×ˢ t :=
 
 /- warning: lower_set.prod_sup -> LowerSet.prod_sup is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t₁ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (t₂ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s (Sup.sup.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.hasSup.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ t₂)) (Sup.sup.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.hasSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s t₂))
 but is expected to have type
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+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t₁ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (t₂ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s (Sup.sup.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instSupLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ t₂)) (Sup.sup.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instSupLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₁) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s t₂))
 Case conversion may be inaccurate. Consider using '#align lower_set.prod_sup LowerSet.prod_supₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -2994,9 +2994,9 @@ theorem prod_sup : s ×ˢ (t₁ ⊔ t₂) = s ×ˢ t₁ ⊔ s ×ˢ t₂ :=
 
 /- warning: lower_set.prod_inf_prod -> LowerSet.prod_inf_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t₁ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (t₂ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (HasInf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.hasInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (HasInf.inf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) s₁ s₂) (HasInf.inf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.hasInf.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ t₂))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (s₁ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (s₂ : LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (t₁ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (t₂ : LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)), Eq.{succ (max u1 u2)} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (Inf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.hasInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasLe.{u1, u2} α β (Preorder.toLE.{u1} α _inst_1) (Preorder.toLE.{u2} β _inst_2))) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 s₂ t₂)) (LowerSet.prod.{u1, u2} α β _inst_1 _inst_2 (Inf.inf.{u1} (LowerSet.{u1} α (Preorder.toLE.{u1} α _inst_1)) (LowerSet.hasInf.{u1} α (Preorder.toLE.{u1} α _inst_1)) s₁ s₂) (Inf.inf.{u2} (LowerSet.{u2} β (Preorder.toLE.{u2} β _inst_2)) (LowerSet.hasInf.{u2} β (Preorder.toLE.{u2} β _inst_2)) t₁ t₂))
 but is expected to have type
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+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : Preorder.{u1} β] (s₁ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (s₂ : LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (t₁ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (t₂ : LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)), Eq.{max (succ u2) (succ u1)} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (Inf.inf.{max u1 u2} (LowerSet.{max u1 u2} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.instInfLowerSet.{max u2 u1} (Prod.{u2, u1} α β) (Prod.instLEProd.{u2, u1} α β (Preorder.toLE.{u2} α _inst_1) (Preorder.toLE.{u1} β _inst_2))) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₁ t₁) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 s₂ t₂)) (LowerSet.prod.{u2, u1} α β _inst_1 _inst_2 (Inf.inf.{u2} (LowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) (LowerSet.instInfLowerSet.{u2} α (Preorder.toLE.{u2} α _inst_1)) s₁ s₂) (Inf.inf.{u1} (LowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) (LowerSet.instInfLowerSet.{u1} β (Preorder.toLE.{u1} β _inst_2)) t₁ t₂))
 Case conversion may be inaccurate. Consider using '#align lower_set.prod_inf_prod LowerSet.prod_inf_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/

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

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.

@@ -4,8 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Sara Rousta
 -/
 import Mathlib.Data.SetLike.Basic
-import Mathlib.Data.Set.Intervals.OrdConnected
-import Mathlib.Data.Set.Intervals.OrderIso
+import Mathlib.Order.Interval.Set.OrdConnected
+import Mathlib.Order.Interval.Set.OrderIso
 import Mathlib.Data.Set.Lattice
 
 #align_import order.upper_lower.basic from "leanprover-community/mathlib"@"c0c52abb75074ed8b73a948341f50521fbf43b4c"

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

Notes

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

@@ -1615,12 +1615,14 @@ theorem ordConnected_iff_upperClosure_inter_lowerClosure :
 
 @[simp]
 theorem upperBounds_lowerClosure : upperBounds (lowerClosure s : Set α) = upperBounds s :=
-  (upperBounds_mono_set subset_lowerClosure).antisymm λ _a ha _b ⟨_c, hc, hcb⟩ => hcb.trans <| ha hc
+  (upperBounds_mono_set subset_lowerClosure).antisymm
+    fun _a ha _b ⟨_c, hc, hcb⟩ ↦ hcb.trans <| ha hc
 #align upper_bounds_lower_closure upperBounds_lowerClosure
 
 @[simp]
 theorem lowerBounds_upperClosure : lowerBounds (upperClosure s : Set α) = lowerBounds s :=
-  (lowerBounds_mono_set subset_upperClosure).antisymm λ _a ha _b ⟨_c, hc, hcb⟩ => (ha hc).trans hcb
+  (lowerBounds_mono_set subset_upperClosure).antisymm
+    fun _a ha _b ⟨_c, hc, hcb⟩ ↦ (ha hc).trans hcb
 #align lower_bounds_upper_closure lowerBounds_upperClosure
 
 @[simp]

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

@@ -1395,7 +1395,7 @@ def lowerClosure (s : Set α) : LowerSet α :=
   ⟨{ x | ∃ a ∈ s, x ≤ a }, fun _ _ hle h => h.imp fun _x hx => ⟨hx.1, hle.trans hx.2⟩⟩
 #align lower_closure lowerClosure
 
--- Porting note: todo: move `GaloisInsertion`s up, use them to prove lemmas
+-- Porting note (#11215): TODO: move `GaloisInsertion`s up, use them to prove lemmas
 
 @[simp]
 theorem mem_upperClosure : x ∈ upperClosure s ↔ ∃ a ∈ s, a ≤ x :=

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

@@ -126,11 +126,11 @@ theorem isLowerSet_sUnion {S : Set (Set α)} (hf : ∀ s ∈ S, IsLowerSet s) :
 #align is_lower_set_sUnion isLowerSet_sUnion
 
 theorem isUpperSet_iUnion {f : ι → Set α} (hf : ∀ i, IsUpperSet (f i)) : IsUpperSet (⋃ i, f i) :=
-  isUpperSet_sUnion <| forall_range_iff.2 hf
+  isUpperSet_sUnion <| forall_mem_range.2 hf
 #align is_upper_set_Union isUpperSet_iUnion
 
 theorem isLowerSet_iUnion {f : ι → Set α} (hf : ∀ i, IsLowerSet (f i)) : IsLowerSet (⋃ i, f i) :=
-  isLowerSet_sUnion <| forall_range_iff.2 hf
+  isLowerSet_sUnion <| forall_mem_range.2 hf
 #align is_lower_set_Union isLowerSet_iUnion
 
 theorem isUpperSet_iUnion₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsUpperSet (f i j)) :
@@ -152,11 +152,11 @@ theorem isLowerSet_sInter {S : Set (Set α)} (hf : ∀ s ∈ S, IsLowerSet s) :
 #align is_lower_set_sInter isLowerSet_sInter
 
 theorem isUpperSet_iInter {f : ι → Set α} (hf : ∀ i, IsUpperSet (f i)) : IsUpperSet (⋂ i, f i) :=
-  isUpperSet_sInter <| forall_range_iff.2 hf
+  isUpperSet_sInter <| forall_mem_range.2 hf
 #align is_upper_set_Inter isUpperSet_iInter
 
 theorem isLowerSet_iInter {f : ι → Set α} (hf : ∀ i, IsLowerSet (f i)) : IsLowerSet (⋂ i, f i) :=
-  isLowerSet_sInter <| forall_range_iff.2 hf
+  isLowerSet_sInter <| forall_mem_range.2 hf
 #align is_lower_set_Inter isLowerSet_iInter
 
 theorem isUpperSet_iInter₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsUpperSet (f i j)) :

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -627,12 +627,12 @@ theorem coe_iSup (f : ι → UpperSet α) : (↑(⨆ i, f i) : Set α) = ⋂ i,
 theorem coe_iInf (f : ι → UpperSet α) : (↑(⨅ i, f i) : Set α) = ⋃ i, f i := by simp [iInf]
 #align upper_set.coe_infi UpperSet.coe_iInf
 
-@[norm_cast] -- porting note: no longer a `simp`
+@[norm_cast] -- Porting note: no longer a `simp`
 theorem coe_iSup₂ (f : ∀ i, κ i → UpperSet α) : (↑(⨆ (i) (j), f i j) : Set α) = ⋂ (i) (j), f i j :=
   by simp_rw [coe_iSup]
 #align upper_set.coe_supr₂ UpperSet.coe_iSup₂
 
-@[norm_cast] -- porting note: no longer a `simp`
+@[norm_cast] -- Porting note: no longer a `simp`
 theorem coe_iInf₂ (f : ∀ i, κ i → UpperSet α) : (↑(⨅ (i) (j), f i j) : Set α) = ⋃ (i) (j), f i j :=
   by simp_rw [coe_iInf]
 #align upper_set.coe_infi₂ UpperSet.coe_iInf₂
@@ -679,12 +679,12 @@ theorem mem_iInf_iff {f : ι → UpperSet α} : (a ∈ ⨅ i, f i) ↔ ∃ i, a
   exact mem_iUnion
 #align upper_set.mem_infi_iff UpperSet.mem_iInf_iff
 
--- porting note: no longer a @[simp]
+-- Porting note: no longer a @[simp]
 theorem mem_iSup₂_iff {f : ∀ i, κ i → UpperSet α} : (a ∈ ⨆ (i) (j), f i j) ↔ ∀ i j, a ∈ f i j := by
   simp_rw [mem_iSup_iff]
 #align upper_set.mem_supr₂_iff UpperSet.mem_iSup₂_iff
 
--- porting note: no longer a @[simp]
+-- Porting note: no longer a @[simp]
 theorem mem_iInf₂_iff {f : ∀ i, κ i → UpperSet α} : (a ∈ ⨅ (i) (j), f i j) ↔ ∃ i j, a ∈ f i j := by
   simp_rw [mem_iInf_iff]
 #align upper_set.mem_infi₂_iff UpperSet.mem_iInf₂_iff
@@ -781,12 +781,12 @@ theorem coe_iInf (f : ι → LowerSet α) : (↑(⨅ i, f i) : Set α) = ⋂ i,
   simp_rw [iInf, coe_sInf, mem_range, iInter_exists, iInter_iInter_eq']
 #align lower_set.coe_infi LowerSet.coe_iInf
 
-@[norm_cast] -- porting note: no longer a `simp`
+@[norm_cast] -- Porting note: no longer a `simp`
 theorem coe_iSup₂ (f : ∀ i, κ i → LowerSet α) : (↑(⨆ (i) (j), f i j) : Set α) = ⋃ (i) (j), f i j :=
   by simp_rw [coe_iSup]
 #align lower_set.coe_supr₂ LowerSet.coe_iSup₂
 
-@[norm_cast] -- porting note: no longer a `simp`
+@[norm_cast] -- Porting note: no longer a `simp`
 theorem coe_iInf₂ (f : ∀ i, κ i → LowerSet α) : (↑(⨅ (i) (j), f i j) : Set α) = ⋂ (i) (j), f i j :=
   by simp_rw [coe_iInf]
 #align lower_set.coe_infi₂ LowerSet.coe_iInf₂
@@ -833,12 +833,12 @@ theorem mem_iInf_iff {f : ι → LowerSet α} : (a ∈ ⨅ i, f i) ↔ ∀ i, a
   exact mem_iInter
 #align lower_set.mem_infi_iff LowerSet.mem_iInf_iff
 
--- porting note: no longer a @[simp]
+-- Porting note: no longer a @[simp]
 theorem mem_iSup₂_iff {f : ∀ i, κ i → LowerSet α} : (a ∈ ⨆ (i) (j), f i j) ↔ ∃ i j, a ∈ f i j := by
   simp_rw [mem_iSup_iff]
 #align lower_set.mem_supr₂_iff LowerSet.mem_iSup₂_iff
 
--- porting note: no longer a @[simp]
+-- Porting note: no longer a @[simp]
 theorem mem_iInf₂_iff {f : ∀ i, κ i → LowerSet α} : (a ∈ ⨅ (i) (j), f i j) ↔ ∀ i j, a ∈ f i j := by
   simp_rw [mem_iInf_iff]
 #align lower_set.mem_infi₂_iff LowerSet.mem_iInf₂_iff
@@ -926,12 +926,12 @@ protected theorem compl_iInf (f : ι → UpperSet α) : (⨅ i, f i).compl = ⨅
   LowerSet.ext <| by simp only [coe_compl, coe_iInf, compl_iUnion, LowerSet.coe_iInf]
 #align upper_set.compl_infi UpperSet.compl_iInf
 
--- porting note: no longer a @[simp]
+-- Porting note: no longer a @[simp]
 theorem compl_iSup₂ (f : ∀ i, κ i → UpperSet α) :
     (⨆ (i) (j), f i j).compl = ⨆ (i) (j), (f i j).compl := by simp_rw [UpperSet.compl_iSup]
 #align upper_set.compl_supr₂ UpperSet.compl_iSup₂
 
--- porting note: no longer a @[simp]
+-- Porting note: no longer a @[simp]
 theorem compl_iInf₂ (f : ∀ i, κ i → UpperSet α) :
     (⨅ (i) (j), f i j).compl = ⨅ (i) (j), (f i j).compl := by simp_rw [UpperSet.compl_iInf]
 #align upper_set.compl_infi₂ UpperSet.compl_iInf₂
@@ -1263,7 +1263,7 @@ theorem Ici_iSup (f : ι → α) : Ici (⨆ i, f i) = ⨆ i, Ici (f i) :=
   SetLike.ext fun c => by simp only [mem_Ici_iff, mem_iSup_iff, iSup_le_iff]
 #align upper_set.Ici_supr UpperSet.Ici_iSup
 
--- porting note: no longer a @[simp]
+-- Porting note: no longer a @[simp]
 theorem Ici_iSup₂ (f : ∀ i, κ i → α) : Ici (⨆ (i) (j), f i j) = ⨆ (i) (j), Ici (f i j) := by
   simp_rw [Ici_iSup]
 #align upper_set.Ici_supr₂ UpperSet.Ici_iSup₂
@@ -1372,7 +1372,7 @@ theorem Iic_iInf (f : ι → α) : Iic (⨅ i, f i) = ⨅ i, Iic (f i) :=
   SetLike.ext fun c => by simp only [mem_Iic_iff, mem_iInf_iff, le_iInf_iff]
 #align lower_set.Iic_infi LowerSet.Iic_iInf
 
--- porting note: no longer a @[simp]
+-- Porting note: no longer a @[simp]
 theorem Iic_iInf₂ (f : ∀ i, κ i → α) : Iic (⨅ (i) (j), f i j) = ⨅ (i) (j), Iic (f i j) := by
   simp_rw [Iic_iInf]
 #align lower_set.Iic_infi₂ LowerSet.Iic_iInf₂
@@ -1395,7 +1395,7 @@ def lowerClosure (s : Set α) : LowerSet α :=
   ⟨{ x | ∃ a ∈ s, x ≤ a }, fun _ _ hle h => h.imp fun _x hx => ⟨hx.1, hle.trans hx.2⟩⟩
 #align lower_closure lowerClosure
 
--- porting note: todo: move `GaloisInsertion`s up, use them to prove lemmas
+-- Porting note: todo: move `GaloisInsertion`s up, use them to prove lemmas
 
 @[simp]
 theorem mem_upperClosure : x ∈ upperClosure s ↔ ∃ a ∈ s, a ≤ x :=

@@ -6,6 +6,7 @@ Authors: Yaël Dillies, Sara Rousta
 import Mathlib.Data.SetLike.Basic
 import Mathlib.Data.Set.Intervals.OrdConnected
 import Mathlib.Data.Set.Intervals.OrderIso
+import Mathlib.Data.Set.Lattice
 
 #align_import order.upper_lower.basic from "leanprover-community/mathlib"@"c0c52abb75074ed8b73a948341f50521fbf43b4c"
 

Also generalize IsUpperSet.Ioi_subset and IsLowerSet.Iio_subset from a PartialOrder to a Preorder.

@@ -258,6 +258,14 @@ alias ⟨IsUpperSet.Ici_subset, _⟩ := isUpperSet_iff_Ici_subset
 alias ⟨IsLowerSet.Iic_subset, _⟩ := isLowerSet_iff_Iic_subset
 #align is_lower_set.Iic_subset IsLowerSet.Iic_subset
 
+theorem IsUpperSet.Ioi_subset (h : IsUpperSet s) ⦃a⦄ (ha : a ∈ s) : Ioi a ⊆ s :=
+  Ioi_subset_Ici_self.trans <| h.Ici_subset ha
+#align is_upper_set.Ioi_subset IsUpperSet.Ioi_subset
+
+theorem IsLowerSet.Iio_subset (h : IsLowerSet s) ⦃a⦄ (ha : a ∈ s) : Iio a ⊆ s :=
+  h.toDual.Ioi_subset ha
+#align is_lower_set.Iio_subset IsLowerSet.Iio_subset
+
 theorem IsUpperSet.ordConnected (h : IsUpperSet s) : s.OrdConnected :=
   ⟨fun _ ha _ _ => Icc_subset_Ici_self.trans <| h.Ici_subset ha⟩
 #align is_upper_set.ord_connected IsUpperSet.ordConnected
@@ -286,6 +294,24 @@ theorem IsLowerSet.image (hs : IsLowerSet s) (f : α ≃o β) : IsLowerSet (f ''
   exact hs.preimage f.symm.monotone
 #align is_lower_set.image IsLowerSet.image
 
+theorem OrderEmbedding.image_Ici (e : α ↪o β) (he : IsUpperSet (range e)) (a : α) :
+    e '' Ici a = Ici (e a) := by
+  rw [← e.preimage_Ici, image_preimage_eq_inter_range,
+    inter_eq_left.2 <| he.Ici_subset (mem_range_self _)]
+
+theorem OrderEmbedding.image_Iic (e : α ↪o β) (he : IsLowerSet (range e)) (a : α) :
+    e '' Iic a = Iic (e a) :=
+  e.dual.image_Ici he a
+
+theorem OrderEmbedding.image_Ioi (e : α ↪o β) (he : IsUpperSet (range e)) (a : α) :
+    e '' Ioi a = Ioi (e a) := by
+  rw [← e.preimage_Ioi, image_preimage_eq_inter_range,
+    inter_eq_left.2 <| he.Ioi_subset (mem_range_self _)]
+
+theorem OrderEmbedding.image_Iio (e : α ↪o β) (he : IsLowerSet (range e)) (a : α) :
+    e '' Iio a = Iio (e a) :=
+  e.dual.image_Ioi he a
+
 @[simp]
 theorem Set.monotone_mem : Monotone (· ∈ s) ↔ IsUpperSet s :=
   Iff.rfl
@@ -410,12 +436,6 @@ theorem isLowerSet_iff_Iio_subset : IsLowerSet s ↔ ∀ ⦃a⦄, a ∈ s → Ii
   simp [isLowerSet_iff_forall_lt, subset_def, @forall_swap (_ ∈ s)]
 #align is_lower_set_iff_Iio_subset isLowerSet_iff_Iio_subset
 
-alias ⟨IsUpperSet.Ioi_subset, _⟩ := isUpperSet_iff_Ioi_subset
-#align is_upper_set.Ioi_subset IsUpperSet.Ioi_subset
-
-alias ⟨IsLowerSet.Iio_subset, _⟩ := isLowerSet_iff_Iio_subset
-#align is_lower_set.Iio_subset IsLowerSet.Iio_subset
-
 end PartialOrder
 
 section LinearOrder

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -1045,7 +1045,7 @@ def map (f : α ≃o β) : UpperSet α ≃o UpperSet β where
 
 @[simp]
 theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
-  FunLike.ext _ _ fun s => ext <| by convert Set.preimage_equiv_eq_image_symm s f.toEquiv
+  DFunLike.ext _ _ fun s => ext <| by convert Set.preimage_equiv_eq_image_symm s f.toEquiv
 #align upper_set.symm_map UpperSet.symm_map
 
 @[simp]
@@ -1090,7 +1090,7 @@ def map (f : α ≃o β) : LowerSet α ≃o LowerSet β where
 
 @[simp]
 theorem symm_map (f : α ≃o β) : (map f).symm = map f.symm :=
-  FunLike.ext _ _ fun s => ext <| by convert Set.preimage_equiv_eq_image_symm s f.toEquiv
+  DFunLike.ext _ _ fun s => ext <| by convert Set.preimage_equiv_eq_image_symm s f.toEquiv
 #align lower_set.symm_map LowerSet.symm_map
 
 @[simp]

See Zulip thread for the discussion.

@@ -208,23 +208,23 @@ lemma IsLowerSet.isUpperSet_preimage_coe (hs : IsLowerSet s) :
 
 lemma IsUpperSet.sdiff (hs : IsUpperSet s) (ht : ∀ b ∈ s, ∀ c ∈ t, b ≤ c → b ∈ t) :
     IsUpperSet (s \ t) :=
-  fun _b _c hbc hb ↦ ⟨hs hbc hb.1, fun hc ↦ hb.2 $ ht _ hb.1 _ hc hbc⟩
+  fun _b _c hbc hb ↦ ⟨hs hbc hb.1, fun hc ↦ hb.2 <| ht _ hb.1 _ hc hbc⟩
 
 lemma IsLowerSet.sdiff (hs : IsLowerSet s) (ht : ∀ b ∈ s, ∀ c ∈ t, c ≤ b → b ∈ t) :
     IsLowerSet (s \ t) :=
-  fun _b _c hcb hb ↦ ⟨hs hcb hb.1, fun hc ↦ hb.2 $ ht _ hb.1 _ hc hcb⟩
+  fun _b _c hcb hb ↦ ⟨hs hcb hb.1, fun hc ↦ hb.2 <| ht _ hb.1 _ hc hcb⟩
 
 lemma IsUpperSet.sdiff_of_isLowerSet (hs : IsUpperSet s) (ht : IsLowerSet t) : IsUpperSet (s \ t) :=
-  hs.sdiff $ by aesop
+  hs.sdiff <| by aesop
 
 lemma IsLowerSet.sdiff_of_isUpperSet (hs : IsLowerSet s) (ht : IsUpperSet t) : IsLowerSet (s \ t) :=
-  hs.sdiff $ by aesop
+  hs.sdiff <| by aesop
 
 lemma IsUpperSet.erase (hs : IsUpperSet s) (has : ∀ b ∈ s, b ≤ a → b = a) : IsUpperSet (s \ {a}) :=
-  hs.sdiff $ by simpa using has
+  hs.sdiff <| by simpa using has
 
 lemma IsLowerSet.erase (hs : IsLowerSet s) (has : ∀ b ∈ s, a ≤ b → b = a) : IsLowerSet (s \ {a}) :=
-  hs.sdiff $ by simpa using has
+  hs.sdiff <| by simpa using has
 
 end LE
 
@@ -1215,7 +1215,7 @@ section PartialOrder
 variable [PartialOrder α] {a b : α}
 
 nonrec lemma Ici_injective : Injective (Ici : α → UpperSet α) := fun _a _b hab ↦
-  Ici_injective $ congr_arg ((↑) : _ → Set α) hab
+  Ici_injective <| congr_arg ((↑) : _ → Set α) hab
 
 @[simp] lemma Ici_inj : Ici a = Ici b ↔ a = b := Ici_injective.eq_iff
 
@@ -1324,7 +1324,7 @@ section PartialOrder
 variable [PartialOrder α] {a b : α}
 
 nonrec lemma Iic_injective : Injective (Iic : α → LowerSet α) := fun _a _b hab ↦
-  Iic_injective $ congr_arg ((↑) : _ → Set α) hab
+  Iic_injective <| congr_arg ((↑) : _ → Set α) hab
 
 @[simp] lemma Iic_inj : Iic a = Iic b ↔ a = b := Iic_injective.eq_iff
 
@@ -1466,11 +1466,11 @@ theorem LowerSet.iSup_Iic (s : Set α) : ⨆ a ∈ s, LowerSet.Iic a = lowerClos
 #align lower_set.supr_Iic LowerSet.iSup_Iic
 
 @[simp] lemma lowerClosure_le {t : LowerSet α} : lowerClosure s ≤ t ↔ s ⊆ t :=
-  ⟨fun h ↦ subset_lowerClosure.trans $ LowerSet.coe_subset_coe.2 h,
+  ⟨fun h ↦ subset_lowerClosure.trans <| LowerSet.coe_subset_coe.2 h,
     fun h ↦ lowerClosure_min h t.lower⟩
 
 @[simp] lemma le_upperClosure {s : UpperSet α} : s ≤ upperClosure t ↔ t ⊆ s :=
-  ⟨fun h ↦ subset_upperClosure.trans $ UpperSet.coe_subset_coe.2 h,
+  ⟨fun h ↦ subset_upperClosure.trans <| UpperSet.coe_subset_coe.2 h,
     fun h ↦ upperClosure_min h s.upper⟩
 
 theorem gc_upperClosure_coe :
@@ -1624,7 +1624,7 @@ protected alias ⟨BddBelow.of_upperClosure, BddBelow.upperClosure⟩ := bddBelo
     Disjoint ↑(upperClosure s) t ↔ Disjoint s t := by
   refine ⟨Disjoint.mono_left subset_upperClosure, ?_⟩
   simp only [disjoint_left, SetLike.mem_coe, mem_upperClosure, forall_exists_index, and_imp]
-  exact fun h a b hb hba ha ↦ h hb $ ht hba ha
+  exact fun h a b hb hba ha ↦ h hb <| ht hba ha
 
 @[simp] lemma IsLowerSet.disjoint_upperClosure_right (hs : IsLowerSet s) :
     Disjoint s (upperClosure t) ↔ Disjoint s t := by
@@ -1683,12 +1683,12 @@ lemma erase_le : s.erase a ≤ s := diff_subset _ _
 
 lemma sdiff_sup_lowerClosure (hts : t ⊆ s) (hst : ∀ b ∈ s, ∀ c ∈ t, c ≤ b → b ∈ t) :
     s.sdiff t ⊔ lowerClosure t = s := by
-  refine' le_antisymm (sup_le sdiff_le_left $ lowerClosure_le.2 hts) fun a ha ↦ _
+  refine' le_antisymm (sup_le sdiff_le_left <| lowerClosure_le.2 hts) fun a ha ↦ _
   obtain hat | hat := em (a ∈ t)
   · exact subset_union_right _ _ (subset_lowerClosure hat)
   · refine subset_union_left _ _ ⟨ha, ?_⟩
     rintro ⟨b, hb, hba⟩
-    exact hat $ hst _ ha _ hb hba
+    exact hat <| hst _ ha _ hb hba
 
 lemma lowerClosure_sup_sdiff (hts : t ⊆ s) (hst : ∀ b ∈ s, ∀ c ∈ t, c ≤ b → b ∈ t) :
     lowerClosure t ⊔ s.sdiff t = s := by rw [sup_comm, sdiff_sup_lowerClosure hts hst]
@@ -1744,12 +1744,12 @@ lemma le_erase : s ≤ s.erase a := diff_subset _ _
 
 lemma sdiff_inf_upperClosure (hts : t ⊆ s) (hst : ∀ b ∈ s, ∀ c ∈ t, b ≤ c → b ∈ t) :
     s.sdiff t ⊓ upperClosure t = s := by
-  refine' ge_antisymm (le_inf le_sdiff_left $ le_upperClosure.2 hts) fun a ha ↦ _
+  refine' ge_antisymm (le_inf le_sdiff_left <| le_upperClosure.2 hts) fun a ha ↦ _
   obtain hat | hat := em (a ∈ t)
   · exact subset_union_right _ _ (subset_upperClosure hat)
   · refine subset_union_left _ _ ⟨ha, ?_⟩
     rintro ⟨b, hb, hab⟩
-    exact hat $ hst _ ha _ hb hab
+    exact hat <| hst _ ha _ hb hab
 
 lemma upperClosure_inf_sdiff (hts : t ⊆ s) (hst : ∀ b ∈ s, ∀ c ∈ t, b ≤ c → b ∈ t) :
     upperClosure t ⊓ s.sdiff t = s := by rw [inf_comm, sdiff_inf_upperClosure hts hst]

Introduce the Scott topology on a preorder, defined in terms of directed sets.

There is already a related notion of Scott topology defined in topology.omega_complete_partial_order, where it is defined on ω-complete partial orders in terms of ω-chains. In some circumstances the definition given here coincides with that given in topology.omega_complete_partial_order but in general they are different. Abramsky and Jung ([Domain Theory, 2.2.4][abramsky_gabbay_maibaum_1994]) argue that the ω-chain approach has pedagogical advantages, but the directed sets approach is more appropriate as a theoretical foundation.

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com> Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -306,6 +306,12 @@ theorem isLowerSet_setOf : IsLowerSet { a | p a } ↔ Antitone p :=
   forall_swap
 #align is_lower_set_set_of isLowerSet_setOf
 
+lemma IsUpperSet.upperBounds_subset (hs : IsUpperSet s) : s.Nonempty → upperBounds s ⊆ s :=
+  fun ⟨_a, ha⟩ _b hb ↦ hs (hb ha) ha
+
+lemma IsLowerSet.lowerBounds_subset (hs : IsLowerSet s) : s.Nonempty → lowerBounds s ⊆ s :=
+  fun ⟨_a, ha⟩ _b hb ↦ hs (hb ha) ha
+
 section OrderTop
 
 variable [OrderTop α]

To fit with the "please try harder" convention of ! tactics.

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

@@ -416,7 +416,7 @@ section LinearOrder
 variable [LinearOrder α] {s t : Set α}
 
 theorem IsUpperSet.total (hs : IsUpperSet s) (ht : IsUpperSet t) : s ⊆ t ∨ t ⊆ s := by
-  by_contra' h
+  by_contra! h
   simp_rw [Set.not_subset] at h
   obtain ⟨⟨a, has, hat⟩, b, hbt, hbs⟩ := h
   obtain hab | hba := le_total a b

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

@@ -1660,9 +1660,9 @@ lemma sdiff_le_left : s.sdiff t ≤ s := diff_subset _ _
 lemma erase_le : s.erase a ≤ s := diff_subset _ _
 
 @[simp] protected lemma sdiff_eq_left : s.sdiff t = s ↔ Disjoint ↑s t := by
-  simp [←SetLike.coe_set_eq]
+  simp [← SetLike.coe_set_eq]
 
-@[simp] lemma erase_eq : s.erase a = s ↔ a ∉ s := by rw [←sdiff_singleton]; simp [-sdiff_singleton]
+@[simp] lemma erase_eq : s.erase a = s ↔ a ∉ s := by rw [← sdiff_singleton]; simp [-sdiff_singleton]
 
 @[simp] lemma sdiff_lt_left : s.sdiff t < s ↔ ¬ Disjoint ↑s t :=
   sdiff_le_left.lt_iff_ne.trans LowerSet.sdiff_eq_left.not
@@ -1688,7 +1688,7 @@ lemma lowerClosure_sup_sdiff (hts : t ⊆ s) (hst : ∀ b ∈ s, ∀ c ∈ t, c
     lowerClosure t ⊔ s.sdiff t = s := by rw [sup_comm, sdiff_sup_lowerClosure hts hst]
 
 lemma erase_sup_Iic (ha : a ∈ s) (has : ∀ b ∈ s, a ≤ b → b = a) : s.erase a ⊔ Iic a = s := by
-  rw [←lowerClosure_singleton, ←sdiff_singleton, sdiff_sup_lowerClosure] <;> simpa
+  rw [← lowerClosure_singleton, ← sdiff_singleton, sdiff_sup_lowerClosure] <;> simpa
 
 lemma Iic_sup_erase (ha : a ∈ s) (has : ∀ b ∈ s, a ≤ b → b = a) : Iic a ⊔ s.erase a = s := by
   rw [sup_comm, erase_sup_Iic ha has]
@@ -1721,9 +1721,9 @@ lemma le_sdiff_left : s ≤ s.sdiff t := diff_subset _ _
 lemma le_erase : s ≤ s.erase a := diff_subset _ _
 
 @[simp] protected lemma sdiff_eq_left : s.sdiff t = s ↔ Disjoint ↑s t := by
-  simp [←SetLike.coe_set_eq]
+  simp [← SetLike.coe_set_eq]
 
-@[simp] lemma erase_eq : s.erase a = s ↔ a ∉ s := by rw [←sdiff_singleton]; simp [-sdiff_singleton]
+@[simp] lemma erase_eq : s.erase a = s ↔ a ∉ s := by rw [← sdiff_singleton]; simp [-sdiff_singleton]
 
 @[simp] lemma lt_sdiff_left : s < s.sdiff t ↔ ¬ Disjoint ↑s t :=
   le_sdiff_left.gt_iff_ne.trans UpperSet.sdiff_eq_left.not
@@ -1749,7 +1749,7 @@ lemma upperClosure_inf_sdiff (hts : t ⊆ s) (hst : ∀ b ∈ s, ∀ c ∈ t, b
     upperClosure t ⊓ s.sdiff t = s := by rw [inf_comm, sdiff_inf_upperClosure hts hst]
 
 lemma erase_inf_Ici (ha : a ∈ s) (has : ∀ b ∈ s, b ≤ a → b = a) : s.erase a ⊓ Ici a = s := by
-  rw [←upperClosure_singleton, ←sdiff_singleton, sdiff_inf_upperClosure] <;> simpa
+  rw [← upperClosure_singleton, ← sdiff_singleton, sdiff_inf_upperClosure] <;> simpa
 
 lemma Ici_inf_erase (ha : a ∈ s) (has : ∀ b ∈ s, b ≤ a → b = a) : Ici a ⊓ s.erase a = s := by
   rw [inf_comm, erase_inf_Ici ha has]

If a set t is an upper set inside a lower set s, then s \ t is a lower set.

@@ -43,8 +43,7 @@ makes them order-isomorphic to lower sets and antichains, and matches the conven
 Lattice structure on antichains. Order equivalence between upper/lower sets and antichains.
 -/
 
-
-open OrderDual Set
+open Function OrderDual Set
 
 variable {α β γ : Type*} {ι : Sort*} {κ : ι → Sort*}
 
@@ -53,16 +52,18 @@ variable {α β γ : Type*} {ι : Sort*} {κ : ι → Sort*}
 
 section LE
 
-variable [LE α] [LE β] {s t : Set α}
+variable [LE α] [LE β] {s t : Set α} {a : α}
 
 /-- An upper set in an order `α` is a set such that any element greater than one of its members is
 also a member. Also called up-set, upward-closed set. -/
+@[aesop norm unfold]
 def IsUpperSet (s : Set α) : Prop :=
   ∀ ⦃a b : α⦄, a ≤ b → a ∈ s → b ∈ s
 #align is_upper_set IsUpperSet
 
 /-- A lower set in an order `α` is a set such that any element less than one of its members is also
 a member. Also called down-set, downward-closed set. -/
+@[aesop norm unfold]
 def IsLowerSet (s : Set α) : Prop :=
   ∀ ⦃a b : α⦄, b ≤ a → a ∈ s → b ∈ s
 #align is_lower_set IsLowerSet
@@ -199,6 +200,32 @@ alias ⟨_, IsUpperSet.ofDual⟩ := isLowerSet_preimage_toDual_iff
 alias ⟨_, IsLowerSet.ofDual⟩ := isUpperSet_preimage_toDual_iff
 #align is_lower_set.of_dual IsLowerSet.ofDual
 
+lemma IsUpperSet.isLowerSet_preimage_coe (hs : IsUpperSet s) :
+    IsLowerSet ((↑) ⁻¹' t : Set s) ↔ ∀ b ∈ s, ∀ c ∈ t, b ≤ c → b ∈ t := by aesop
+
+lemma IsLowerSet.isUpperSet_preimage_coe (hs : IsLowerSet s) :
+    IsUpperSet ((↑) ⁻¹' t : Set s) ↔ ∀ b ∈ s, ∀ c ∈ t, c ≤ b → b ∈ t := by aesop
+
+lemma IsUpperSet.sdiff (hs : IsUpperSet s) (ht : ∀ b ∈ s, ∀ c ∈ t, b ≤ c → b ∈ t) :
+    IsUpperSet (s \ t) :=
+  fun _b _c hbc hb ↦ ⟨hs hbc hb.1, fun hc ↦ hb.2 $ ht _ hb.1 _ hc hbc⟩
+
+lemma IsLowerSet.sdiff (hs : IsLowerSet s) (ht : ∀ b ∈ s, ∀ c ∈ t, c ≤ b → b ∈ t) :
+    IsLowerSet (s \ t) :=
+  fun _b _c hcb hb ↦ ⟨hs hcb hb.1, fun hc ↦ hb.2 $ ht _ hb.1 _ hc hcb⟩
+
+lemma IsUpperSet.sdiff_of_isLowerSet (hs : IsUpperSet s) (ht : IsLowerSet t) : IsUpperSet (s \ t) :=
+  hs.sdiff $ by aesop
+
+lemma IsLowerSet.sdiff_of_isUpperSet (hs : IsLowerSet s) (ht : IsUpperSet t) : IsLowerSet (s \ t) :=
+  hs.sdiff $ by aesop
+
+lemma IsUpperSet.erase (hs : IsUpperSet s) (has : ∀ b ∈ s, b ≤ a → b = a) : IsUpperSet (s \ {a}) :=
+  hs.sdiff $ by simpa using has
+
+lemma IsLowerSet.erase (hs : IsLowerSet s) (has : ∀ b ∈ s, a ≤ b → b = a) : IsLowerSet (s \ {a}) :=
+  hs.sdiff $ by simpa using has
+
 end LE
 
 section Preorder
@@ -432,28 +459,26 @@ instance : SetLike (UpperSet α) α where
   coe := UpperSet.carrier
   coe_injective' s t h := by cases s; cases t; congr
 
-@[ext]
-theorem ext {s t : UpperSet α} : (s : Set α) = t → s = t :=
-  SetLike.ext'
-#align upper_set.ext UpperSet.ext
-
 /-- See Note [custom simps projection]. -/
 def Simps.coe (s : UpperSet α) : Set α := s
 
 initialize_simps_projections UpperSet (carrier → coe)
 
+@[ext]
+theorem ext {s t : UpperSet α} : (s : Set α) = t → s = t :=
+  SetLike.ext'
+#align upper_set.ext UpperSet.ext
+
 @[simp]
 theorem carrier_eq_coe (s : UpperSet α) : s.carrier = s :=
   rfl
 #align upper_set.carrier_eq_coe UpperSet.carrier_eq_coe
 
-protected theorem upper (s : UpperSet α) : IsUpperSet (s : Set α) :=
-  s.upper'
+@[simp] protected lemma upper (s : UpperSet α) : IsUpperSet (s : Set α) := s.upper'
 #align upper_set.upper UpperSet.upper
 
-@[simp]
-theorem mem_mk (carrier : Set α) (upper') {a : α} : a ∈ mk carrier upper' ↔ a ∈ carrier :=
-  Iff.rfl
+@[simp, norm_cast] lemma coe_mk (s : Set α) (hs) : mk s hs = s := rfl
+@[simp] lemma mem_mk {s : Set α} (hs) {a : α} : a ∈ mk s hs ↔ a ∈ s := Iff.rfl
 #align upper_set.mem_mk UpperSet.mem_mk
 
 end UpperSet
@@ -479,13 +504,11 @@ theorem carrier_eq_coe (s : LowerSet α) : s.carrier = s :=
   rfl
 #align lower_set.carrier_eq_coe LowerSet.carrier_eq_coe
 
-protected theorem lower (s : LowerSet α) : IsLowerSet (s : Set α) :=
-  s.lower'
+@[simp] protected lemma lower (s : LowerSet α) : IsLowerSet (s : Set α) := s.lower'
 #align lower_set.lower LowerSet.lower
 
-@[simp]
-theorem mem_mk (carrier : Set α) (lower') {a : α} : a ∈ mk carrier lower' ↔ a ∈ carrier :=
-  Iff.rfl
+@[simp, norm_cast] lemma coe_mk (s : Set α) (hs) : mk s hs = s := rfl
+@[simp] lemma mem_mk {s : Set α} (hs) {a : α} : a ∈ mk s hs ↔ a ∈ s := Iff.rfl
 #align lower_set.mem_mk LowerSet.mem_mk
 
 end LowerSet
@@ -526,6 +549,8 @@ theorem coe_subset_coe : (s : Set α) ⊆ t ↔ t ≤ s :=
   Iff.rfl
 #align upper_set.coe_subset_coe UpperSet.coe_subset_coe
 
+@[simp 1100, norm_cast] lemma coe_ssubset_coe : (s : Set α) ⊂ t ↔ t < s := Iff.rfl
+
 @[simp, norm_cast]
 theorem coe_top : ((⊤ : UpperSet α) : Set α) = ∅ :=
   rfl
@@ -544,6 +569,9 @@ theorem coe_eq_univ : (s : Set α) = univ ↔ s = ⊥ := by simp [SetLike.ext'_i
 theorem coe_eq_empty : (s : Set α) = ∅ ↔ s = ⊤ := by simp [SetLike.ext'_iff]
 #align upper_set.coe_eq_empty UpperSet.coe_eq_empty
 
+@[simp, norm_cast] lemma coe_nonempty : (s : Set α).Nonempty ↔ s ≠ ⊤ :=
+  nonempty_iff_ne_empty.trans coe_eq_empty.not
+
 @[simp, norm_cast]
 theorem coe_sup (s t : UpperSet α) : (↑(s ⊔ t) : Set α) = (s : Set α) ∩ t :=
   rfl
@@ -670,11 +698,11 @@ instance completelyDistribLattice : CompletelyDistribLattice (LowerSet α) :=
 instance : Inhabited (LowerSet α) :=
   ⟨⊥⟩
 
-@[norm_cast] -- porting note: no longer a `simp`
-theorem coe_subset_coe : (s : Set α) ⊆ t ↔ s ≤ t :=
-  Iff.rfl
+@[norm_cast] lemma coe_subset_coe : (s : Set α) ⊆ t ↔ s ≤ t := Iff.rfl
 #align lower_set.coe_subset_coe LowerSet.coe_subset_coe
 
+@[norm_cast] lemma coe_ssubset_coe : (s : Set α) ⊂ t ↔ s < t := Iff.rfl
+
 @[simp, norm_cast]
 theorem coe_top : ((⊤ : LowerSet α) : Set α) = univ :=
   rfl
@@ -693,6 +721,9 @@ theorem coe_eq_univ : (s : Set α) = univ ↔ s = ⊤ := by simp [SetLike.ext'_i
 theorem coe_eq_empty : (s : Set α) = ∅ ↔ s = ⊥ := by simp [SetLike.ext'_iff]
 #align lower_set.coe_eq_empty LowerSet.coe_eq_empty
 
+@[simp, norm_cast] lemma coe_nonempty : (s : Set α).Nonempty ↔ s ≠ ⊥ :=
+  nonempty_iff_ne_empty.trans coe_eq_empty.not
+
 @[simp, norm_cast]
 theorem coe_sup (s t : LowerSet α) : (↑(s ⊔ t) : Set α) = (s : Set α) ∪ t :=
   rfl
@@ -1158,18 +1189,34 @@ theorem Ici_le_Ioi (a : α) : Ici a ≤ Ioi a :=
   Ioi_subset_Ici_self
 #align upper_set.Ici_le_Ioi UpperSet.Ici_le_Ioi
 
+@[simp]
+nonrec theorem Ici_bot [OrderBot α] : Ici (⊥ : α) = ⊥ :=
+  SetLike.coe_injective Ici_bot
+#align upper_set.Ici_bot UpperSet.Ici_bot
+
 @[simp]
 nonrec theorem Ioi_top [OrderTop α] : Ioi (⊤ : α) = ⊤ :=
   SetLike.coe_injective Ioi_top
 #align upper_set.Ioi_top UpperSet.Ioi_top
 
-@[simp]
-nonrec theorem Ici_bot [OrderBot α] : Ici (⊥ : α) = ⊥ :=
-  SetLike.coe_injective Ici_bot
-#align upper_set.Ici_bot UpperSet.Ici_bot
+@[simp] lemma Ici_ne_top : Ici a ≠ ⊤ := SetLike.coe_ne_coe.1 nonempty_Ici.ne_empty
+@[simp] lemma Ici_lt_top : Ici a < ⊤ := lt_top_iff_ne_top.2 Ici_ne_top
+@[simp] lemma le_Ici : s ≤ Ici a ↔ a ∈ s := ⟨fun h ↦ h le_rfl, fun ha ↦ s.upper.Ici_subset ha⟩
 
 end Preorder
 
+section PartialOrder
+variable [PartialOrder α] {a b : α}
+
+nonrec lemma Ici_injective : Injective (Ici : α → UpperSet α) := fun _a _b hab ↦
+  Ici_injective $ congr_arg ((↑) : _ → Set α) hab
+
+@[simp] lemma Ici_inj : Ici a = Ici b ↔ a = b := Ici_injective.eq_iff
+
+lemma Ici_ne_Ici : Ici a ≠ Ici b ↔ a ≠ b := Ici_inj.not
+
+end PartialOrder
+
 @[simp]
 theorem Ici_sup [SemilatticeSup α] (a b : α) : Ici (a ⊔ b) = Ici a ⊔ Ici b :=
   ext Ici_inter_Ici.symm
@@ -1261,8 +1308,24 @@ nonrec theorem Iio_bot [OrderBot α] : Iio (⊥ : α) = ⊥ :=
   SetLike.coe_injective Iio_bot
 #align lower_set.Iio_bot LowerSet.Iio_bot
 
+@[simp] lemma Iic_ne_bot : Iic a ≠ ⊥ := SetLike.coe_ne_coe.1 nonempty_Iic.ne_empty
+@[simp] lemma bot_lt_Iic : ⊥ < Iic a := bot_lt_iff_ne_bot.2 Iic_ne_bot
+@[simp] lemma Iic_le : Iic a ≤ s ↔ a ∈ s := ⟨fun h ↦ h le_rfl, fun ha ↦ s.lower.Iic_subset ha⟩
+
 end Preorder
 
+section PartialOrder
+variable [PartialOrder α] {a b : α}
+
+nonrec lemma Iic_injective : Injective (Iic : α → LowerSet α) := fun _a _b hab ↦
+  Iic_injective $ congr_arg ((↑) : _ → Set α) hab
+
+@[simp] lemma Iic_inj : Iic a = Iic b ↔ a = b := Iic_injective.eq_iff
+
+lemma Iic_ne_Iic : Iic a ≠ Iic b ↔ a ≠ b := Iic_inj.not
+
+end PartialOrder
+
 @[simp]
 theorem Iic_inf [SemilatticeInf α] (a b : α) : Iic (a ⊓ b) = Iic a ⊓ Iic b :=
   SetLike.coe_injective Iic_inter_Iic.symm
@@ -1396,16 +1459,21 @@ theorem LowerSet.iSup_Iic (s : Set α) : ⨆ a ∈ s, LowerSet.Iic a = lowerClos
   simp
 #align lower_set.supr_Iic LowerSet.iSup_Iic
 
+@[simp] lemma lowerClosure_le {t : LowerSet α} : lowerClosure s ≤ t ↔ s ⊆ t :=
+  ⟨fun h ↦ subset_lowerClosure.trans $ LowerSet.coe_subset_coe.2 h,
+    fun h ↦ lowerClosure_min h t.lower⟩
+
+@[simp] lemma le_upperClosure {s : UpperSet α} : s ≤ upperClosure t ↔ t ⊆ s :=
+  ⟨fun h ↦ subset_upperClosure.trans $ UpperSet.coe_subset_coe.2 h,
+    fun h ↦ upperClosure_min h s.upper⟩
+
 theorem gc_upperClosure_coe :
-    GaloisConnection (toDual ∘ upperClosure : Set α → (UpperSet α)ᵒᵈ) ((↑) ∘ ofDual) := fun _s t =>
-  ⟨fun h => subset_upperClosure.trans <| UpperSet.coe_subset_coe.2 h, fun h =>
-    upperClosure_min h t.upper⟩
+    GaloisConnection (toDual ∘ upperClosure : Set α → (UpperSet α)ᵒᵈ) ((↑) ∘ ofDual) :=
+  fun _s _t ↦ le_upperClosure
 #align gc_upper_closure_coe gc_upperClosure_coe
 
 theorem gc_lowerClosure_coe :
-    GaloisConnection (lowerClosure : Set α → LowerSet α) (↑) := fun _s t =>
-  ⟨fun h => subset_lowerClosure.trans <| LowerSet.coe_subset_coe.2 h, fun h =>
-    lowerClosure_min h t.lower⟩
+    GaloisConnection (lowerClosure : Set α → LowerSet α) (↑) := fun _s _t ↦ lowerClosure_le
 #align gc_lower_closure_coe gc_lowerClosure_coe
 
 /-- `upperClosure` forms a reversed Galois insertion with the coercion from upper sets to sets. -/
@@ -1538,19 +1606,156 @@ theorem bddBelow_upperClosure : BddBelow (upperClosure s : Set α) ↔ BddBelow
   simp_rw [BddBelow, lowerBounds_upperClosure]
 #align bdd_below_upper_closure bddBelow_upperClosure
 
-alias ⟨BddAbove.of_lowerClosure, BddAbove.lowerClosure⟩ := bddAbove_lowerClosure
+protected alias ⟨BddAbove.of_lowerClosure, BddAbove.lowerClosure⟩ := bddAbove_lowerClosure
 #align bdd_above.of_lower_closure BddAbove.of_lowerClosure
 #align bdd_above.lower_closure BddAbove.lowerClosure
 
-alias ⟨BddBelow.of_upperClosure, BddBelow.upperClosure⟩ := bddBelow_upperClosure
+protected alias ⟨BddBelow.of_upperClosure, BddBelow.upperClosure⟩ := bddBelow_upperClosure
 #align bdd_below.of_upper_closure BddBelow.of_upperClosure
 #align bdd_below.upper_closure BddBelow.upperClosure
 
--- Porting note: attribute [protected] doesn't work
--- attribute protected BddAbove.lowerClosure BddBelow.upperClosure
+@[simp] lemma IsLowerSet.disjoint_upperClosure_left (ht : IsLowerSet t) :
+    Disjoint ↑(upperClosure s) t ↔ Disjoint s t := by
+  refine ⟨Disjoint.mono_left subset_upperClosure, ?_⟩
+  simp only [disjoint_left, SetLike.mem_coe, mem_upperClosure, forall_exists_index, and_imp]
+  exact fun h a b hb hba ha ↦ h hb $ ht hba ha
+
+@[simp] lemma IsLowerSet.disjoint_upperClosure_right (hs : IsLowerSet s) :
+    Disjoint s (upperClosure t) ↔ Disjoint s t := by
+  simpa only [disjoint_comm] using hs.disjoint_upperClosure_left
+
+@[simp] lemma IsUpperSet.disjoint_lowerClosure_left (ht : IsUpperSet t) :
+    Disjoint ↑(lowerClosure s) t ↔ Disjoint s t := ht.toDual.disjoint_upperClosure_left
+
+@[simp] lemma IsUpperSet.disjoint_lowerClosure_right (hs : IsUpperSet s) :
+    Disjoint s (lowerClosure t) ↔ Disjoint s t := hs.toDual.disjoint_upperClosure_right
 
 end closure
 
+/-! ### Set Difference -/
+
+namespace LowerSet
+variable [Preorder α] {s : LowerSet α} {t : Set α} {a : α}
+
+/-- The biggest lower subset of a lower set `s` disjoint from a set `t`. -/
+def sdiff (s : LowerSet α) (t : Set α) : LowerSet α where
+  carrier := s \ upperClosure t
+  lower' := s.lower.sdiff_of_isUpperSet (upperClosure t).upper
+
+/-- The biggest lower subset of a lower set `s` not containing an element `a`. -/
+def erase (s : LowerSet α) (a : α) : LowerSet α where
+  carrier := s \ UpperSet.Ici a
+  lower' := s.lower.sdiff_of_isUpperSet (UpperSet.Ici a).upper
+
+@[simp, norm_cast]
+lemma coe_sdiff (s : LowerSet α) (t : Set α) : s.sdiff t = (s : Set α) \ upperClosure t := rfl
+
+@[simp, norm_cast]
+lemma coe_erase (s : LowerSet α) (a : α) : s.erase a = (s : Set α) \ UpperSet.Ici a := rfl
+
+@[simp] lemma sdiff_singleton (s : LowerSet α) (a : α) : s.sdiff {a} = s.erase a := by
+  simp [sdiff, erase]
+
+lemma sdiff_le_left : s.sdiff t ≤ s := diff_subset _ _
+lemma erase_le : s.erase a ≤ s := diff_subset _ _
+
+@[simp] protected lemma sdiff_eq_left : s.sdiff t = s ↔ Disjoint ↑s t := by
+  simp [←SetLike.coe_set_eq]
+
+@[simp] lemma erase_eq : s.erase a = s ↔ a ∉ s := by rw [←sdiff_singleton]; simp [-sdiff_singleton]
+
+@[simp] lemma sdiff_lt_left : s.sdiff t < s ↔ ¬ Disjoint ↑s t :=
+  sdiff_le_left.lt_iff_ne.trans LowerSet.sdiff_eq_left.not
+
+@[simp] lemma erase_lt : s.erase a < s ↔ a ∈ s := erase_le.lt_iff_ne.trans erase_eq.not_left
+
+@[simp] protected lemma sdiff_idem (s : LowerSet α) (t : Set α) : (s.sdiff t).sdiff t = s.sdiff t :=
+  SetLike.coe_injective sdiff_idem
+
+@[simp] lemma erase_idem (s : LowerSet α) (a : α) : (s.erase a).erase a = s.erase a :=
+  SetLike.coe_injective sdiff_idem
+
+lemma sdiff_sup_lowerClosure (hts : t ⊆ s) (hst : ∀ b ∈ s, ∀ c ∈ t, c ≤ b → b ∈ t) :
+    s.sdiff t ⊔ lowerClosure t = s := by
+  refine' le_antisymm (sup_le sdiff_le_left $ lowerClosure_le.2 hts) fun a ha ↦ _
+  obtain hat | hat := em (a ∈ t)
+  · exact subset_union_right _ _ (subset_lowerClosure hat)
+  · refine subset_union_left _ _ ⟨ha, ?_⟩
+    rintro ⟨b, hb, hba⟩
+    exact hat $ hst _ ha _ hb hba
+
+lemma lowerClosure_sup_sdiff (hts : t ⊆ s) (hst : ∀ b ∈ s, ∀ c ∈ t, c ≤ b → b ∈ t) :
+    lowerClosure t ⊔ s.sdiff t = s := by rw [sup_comm, sdiff_sup_lowerClosure hts hst]
+
+lemma erase_sup_Iic (ha : a ∈ s) (has : ∀ b ∈ s, a ≤ b → b = a) : s.erase a ⊔ Iic a = s := by
+  rw [←lowerClosure_singleton, ←sdiff_singleton, sdiff_sup_lowerClosure] <;> simpa
+
+lemma Iic_sup_erase (ha : a ∈ s) (has : ∀ b ∈ s, a ≤ b → b = a) : Iic a ⊔ s.erase a = s := by
+  rw [sup_comm, erase_sup_Iic ha has]
+
+end LowerSet
+
+namespace UpperSet
+variable [Preorder α] {s : UpperSet α} {t : Set α} {a : α}
+
+/-- The biggest upper subset of a upper set `s` disjoint from a set `t`. -/
+def sdiff (s : UpperSet α) (t : Set α) : UpperSet α where
+  carrier := s \ lowerClosure t
+  upper' := s.upper.sdiff_of_isLowerSet (lowerClosure t).lower
+
+/-- The biggest upper subset of a upper set `s` not containing an element `a`. -/
+def erase (s : UpperSet α) (a : α) : UpperSet α where
+  carrier := s \ LowerSet.Iic a
+  upper' := s.upper.sdiff_of_isLowerSet (LowerSet.Iic a).lower
+
+@[simp, norm_cast]
+lemma coe_sdiff (s : UpperSet α) (t : Set α) : s.sdiff t = (s : Set α) \ lowerClosure t := rfl
+
+@[simp, norm_cast]
+lemma coe_erase (s : UpperSet α) (a : α) : s.erase a = (s : Set α) \ LowerSet.Iic a := rfl
+
+@[simp] lemma sdiff_singleton (s : UpperSet α) (a : α) : s.sdiff {a} = s.erase a := by
+  simp [sdiff, erase]
+
+lemma le_sdiff_left : s ≤ s.sdiff t := diff_subset _ _
+lemma le_erase : s ≤ s.erase a := diff_subset _ _
+
+@[simp] protected lemma sdiff_eq_left : s.sdiff t = s ↔ Disjoint ↑s t := by
+  simp [←SetLike.coe_set_eq]
+
+@[simp] lemma erase_eq : s.erase a = s ↔ a ∉ s := by rw [←sdiff_singleton]; simp [-sdiff_singleton]
+
+@[simp] lemma lt_sdiff_left : s < s.sdiff t ↔ ¬ Disjoint ↑s t :=
+  le_sdiff_left.gt_iff_ne.trans UpperSet.sdiff_eq_left.not
+
+@[simp] lemma lt_erase : s < s.erase a ↔ a ∈ s := le_erase.gt_iff_ne.trans erase_eq.not_left
+
+@[simp] protected lemma sdiff_idem (s : UpperSet α) (t : Set α) : (s.sdiff t).sdiff t = s.sdiff t :=
+  SetLike.coe_injective sdiff_idem
+
+@[simp] lemma erase_idem (s : UpperSet α) (a : α) : (s.erase a).erase a = s.erase a :=
+  SetLike.coe_injective sdiff_idem
+
+lemma sdiff_inf_upperClosure (hts : t ⊆ s) (hst : ∀ b ∈ s, ∀ c ∈ t, b ≤ c → b ∈ t) :
+    s.sdiff t ⊓ upperClosure t = s := by
+  refine' ge_antisymm (le_inf le_sdiff_left $ le_upperClosure.2 hts) fun a ha ↦ _
+  obtain hat | hat := em (a ∈ t)
+  · exact subset_union_right _ _ (subset_upperClosure hat)
+  · refine subset_union_left _ _ ⟨ha, ?_⟩
+    rintro ⟨b, hb, hab⟩
+    exact hat $ hst _ ha _ hb hab
+
+lemma upperClosure_inf_sdiff (hts : t ⊆ s) (hst : ∀ b ∈ s, ∀ c ∈ t, b ≤ c → b ∈ t) :
+    upperClosure t ⊓ s.sdiff t = s := by rw [inf_comm, sdiff_inf_upperClosure hts hst]
+
+lemma erase_inf_Ici (ha : a ∈ s) (has : ∀ b ∈ s, b ≤ a → b = a) : s.erase a ⊓ Ici a = s := by
+  rw [←upperClosure_singleton, ←sdiff_singleton, sdiff_inf_upperClosure] <;> simpa
+
+lemma Ici_inf_erase (ha : a ∈ s) (has : ∀ b ∈ s, b ≤ a → b = a) : Ici a ⊓ s.erase a = s := by
+  rw [inf_comm, erase_inf_Ici ha has]
+
+end UpperSet
+
 /-! ### Product -/
 
 

@@ -1330,6 +1330,12 @@ theorem coe_lowerClosure (s : Set α) : ↑(lowerClosure s) = ⋃ a ∈ s, Iic a
   simp
 #align coe_lower_closure coe_lowerClosure
 
+instance instDecidablePredMemUpperClosure [DecidablePred (∃ a ∈ s, a ≤ ·)] :
+    DecidablePred (· ∈ upperClosure s) := ‹DecidablePred _›
+
+instance instDecidablePredMemLowerClosure [DecidablePred (∃ a ∈ s, · ≤ a)] :
+    DecidablePred (· ∈ lowerClosure s) := ‹DecidablePred _›
+
 theorem subset_upperClosure : s ⊆ upperClosure s := fun x hx => ⟨x, hx, le_rfl⟩
 #align subset_upper_closure subset_upperClosure
 

Match https://github.com/leanprover-community/mathlib/pull/19068

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -7,7 +7,7 @@ import Mathlib.Data.SetLike.Basic
 import Mathlib.Data.Set.Intervals.OrdConnected
 import Mathlib.Data.Set.Intervals.OrderIso
 
-#align_import order.upper_lower.basic from "leanprover-community/mathlib"@"e9ce88cd0d54891c714c604076084f763dd480ed"
+#align_import order.upper_lower.basic from "leanprover-community/mathlib"@"c0c52abb75074ed8b73a948341f50521fbf43b4c"
 
 /-!
 # Up-sets and down-sets
@@ -187,18 +187,18 @@ theorem isUpperSet_preimage_toDual_iff {s : Set αᵒᵈ} : IsUpperSet (toDual 
   Iff.rfl
 #align is_upper_set_preimage_to_dual_iff isUpperSet_preimage_toDual_iff
 
-alias ⟨_, IsUpperSet.ofDual⟩ := isLowerSet_preimage_ofDual_iff
-#align is_upper_set.of_dual IsUpperSet.ofDual
-
-alias ⟨_, IsLowerSet.ofDual⟩ := isUpperSet_preimage_ofDual_iff
-#align is_lower_set.of_dual IsLowerSet.ofDual
-
-alias ⟨_, IsUpperSet.toDual⟩ := isLowerSet_preimage_toDual_iff
+alias ⟨_, IsUpperSet.toDual⟩ := isLowerSet_preimage_ofDual_iff
 #align is_upper_set.to_dual IsUpperSet.toDual
 
-alias ⟨_, IsLowerSet.toDual⟩ := isUpperSet_preimage_toDual_iff
+alias ⟨_, IsLowerSet.toDual⟩ := isUpperSet_preimage_ofDual_iff
 #align is_lower_set.to_dual IsLowerSet.toDual
 
+alias ⟨_, IsUpperSet.ofDual⟩ := isLowerSet_preimage_toDual_iff
+#align is_upper_set.of_dual IsUpperSet.ofDual
+
+alias ⟨_, IsLowerSet.ofDual⟩ := isUpperSet_preimage_toDual_iff
+#align is_lower_set.of_dual IsLowerSet.ofDual
+
 end LE
 
 section Preorder
@@ -385,6 +385,24 @@ alias ⟨IsLowerSet.Iio_subset, _⟩ := isLowerSet_iff_Iio_subset
 
 end PartialOrder
 
+section LinearOrder
+variable [LinearOrder α] {s t : Set α}
+
+theorem IsUpperSet.total (hs : IsUpperSet s) (ht : IsUpperSet t) : s ⊆ t ∨ t ⊆ s := by
+  by_contra' h
+  simp_rw [Set.not_subset] at h
+  obtain ⟨⟨a, has, hat⟩, b, hbt, hbs⟩ := h
+  obtain hab | hba := le_total a b
+  · exact hbs (hs hab has)
+  · exact hat (ht hba hbt)
+#align is_upper_set.total IsUpperSet.total
+
+theorem IsLowerSet.total (hs : IsLowerSet s) (ht : IsLowerSet t) : s ⊆ t ∨ t ⊆ s :=
+  hs.toDual.total ht.toDual
+#align is_lower_set.total IsLowerSet.total
+
+end LinearOrder
+
 /-! ### Bundled upper/lower sets -/
 
 
@@ -496,7 +514,7 @@ instance : SupSet (UpperSet α) :=
 instance : InfSet (UpperSet α) :=
   ⟨fun S => ⟨⋃ s ∈ S, ↑s, isUpperSet_iUnion₂ fun s _ => s.upper⟩⟩
 
-instance : CompletelyDistribLattice (UpperSet α) :=
+instance completelyDistribLattice : CompletelyDistribLattice (UpperSet α) :=
   (toDual.injective.comp SetLike.coe_injective).completelyDistribLattice _ (fun _ _ => rfl)
     (fun _ _ => rfl) (fun _ => rfl) (fun _ => rfl) rfl rfl
 
@@ -645,7 +663,7 @@ instance : SupSet (LowerSet α) :=
 instance : InfSet (LowerSet α) :=
   ⟨fun S => ⟨⋂ s ∈ S, ↑s, isLowerSet_iInter₂ fun s _ => s.lower⟩⟩
 
-instance : CompletelyDistribLattice (LowerSet α) :=
+instance completelyDistribLattice : CompletelyDistribLattice (LowerSet α) :=
   SetLike.coe_injective.completelyDistribLattice _ (fun _ _ => rfl) (fun _ _ => rfl) (fun _ => rfl)
     (fun _ => rfl) rfl rfl
 
@@ -943,6 +961,31 @@ def upperSetIsoLowerSet : UpperSet α ≃o LowerSet α
 
 end LE
 
+section LinearOrder
+variable [LinearOrder α]
+
+instance UpperSet.isTotal_le : IsTotal (UpperSet α) (· ≤ ·) := ⟨fun s t => t.upper.total s.upper⟩
+#align upper_set.is_total_le UpperSet.isTotal_le
+
+instance LowerSet.isTotal_le : IsTotal (LowerSet α) (· ≤ ·) := ⟨fun s t => s.lower.total t.lower⟩
+#align lower_set.is_total_le LowerSet.isTotal_le
+
+noncomputable instance : CompleteLinearOrder (UpperSet α) :=
+  { UpperSet.completelyDistribLattice with
+    le_total := IsTotal.total
+    decidableLE := Classical.decRel _
+    decidableEq := Classical.decRel _
+    decidableLT := Classical.decRel _ }
+
+noncomputable instance : CompleteLinearOrder (LowerSet α) :=
+  { LowerSet.completelyDistribLattice with
+    le_total := IsTotal.total
+    decidableLE := Classical.decRel _
+    decidableEq := Classical.decRel _
+    decidableLT := Classical.decRel _ }
+
+end LinearOrder
+
 /-! #### Map -/
 
 

@@ -187,16 +187,16 @@ theorem isUpperSet_preimage_toDual_iff {s : Set αᵒᵈ} : IsUpperSet (toDual 
   Iff.rfl
 #align is_upper_set_preimage_to_dual_iff isUpperSet_preimage_toDual_iff
 
-alias isLowerSet_preimage_ofDual_iff ↔ _ IsUpperSet.ofDual
+alias ⟨_, IsUpperSet.ofDual⟩ := isLowerSet_preimage_ofDual_iff
 #align is_upper_set.of_dual IsUpperSet.ofDual
 
-alias isUpperSet_preimage_ofDual_iff ↔ _ IsLowerSet.ofDual
+alias ⟨_, IsLowerSet.ofDual⟩ := isUpperSet_preimage_ofDual_iff
 #align is_lower_set.of_dual IsLowerSet.ofDual
 
-alias isLowerSet_preimage_toDual_iff ↔ _ IsUpperSet.toDual
+alias ⟨_, IsUpperSet.toDual⟩ := isLowerSet_preimage_toDual_iff
 #align is_upper_set.to_dual IsUpperSet.toDual
 
-alias isUpperSet_preimage_toDual_iff ↔ _ IsLowerSet.toDual
+alias ⟨_, IsLowerSet.toDual⟩ := isUpperSet_preimage_toDual_iff
 #align is_lower_set.to_dual IsLowerSet.toDual
 
 end LE
@@ -225,10 +225,10 @@ theorem isLowerSet_iff_Iic_subset : IsLowerSet s ↔ ∀ ⦃a⦄, a ∈ s → Ii
   simp [IsLowerSet, subset_def, @forall_swap (_ ∈ s)]
 #align is_lower_set_iff_Iic_subset isLowerSet_iff_Iic_subset
 
-alias isUpperSet_iff_Ici_subset ↔ IsUpperSet.Ici_subset _
+alias ⟨IsUpperSet.Ici_subset, _⟩ := isUpperSet_iff_Ici_subset
 #align is_upper_set.Ici_subset IsUpperSet.Ici_subset
 
-alias isLowerSet_iff_Iic_subset ↔ IsLowerSet.Iic_subset _
+alias ⟨IsLowerSet.Iic_subset, _⟩ := isLowerSet_iff_Iic_subset
 #align is_lower_set.Iic_subset IsLowerSet.Iic_subset
 
 theorem IsUpperSet.ordConnected (h : IsUpperSet s) : s.OrdConnected :=
@@ -377,10 +377,10 @@ theorem isLowerSet_iff_Iio_subset : IsLowerSet s ↔ ∀ ⦃a⦄, a ∈ s → Ii
   simp [isLowerSet_iff_forall_lt, subset_def, @forall_swap (_ ∈ s)]
 #align is_lower_set_iff_Iio_subset isLowerSet_iff_Iio_subset
 
-alias isUpperSet_iff_Ioi_subset ↔ IsUpperSet.Ioi_subset _
+alias ⟨IsUpperSet.Ioi_subset, _⟩ := isUpperSet_iff_Ioi_subset
 #align is_upper_set.Ioi_subset IsUpperSet.Ioi_subset
 
-alias isLowerSet_iff_Iio_subset ↔ IsLowerSet.Iio_subset _
+alias ⟨IsLowerSet.Iio_subset, _⟩ := isLowerSet_iff_Iio_subset
 #align is_lower_set.Iio_subset IsLowerSet.Iio_subset
 
 end PartialOrder
@@ -1489,11 +1489,11 @@ theorem bddBelow_upperClosure : BddBelow (upperClosure s : Set α) ↔ BddBelow
   simp_rw [BddBelow, lowerBounds_upperClosure]
 #align bdd_below_upper_closure bddBelow_upperClosure
 
-alias bddAbove_lowerClosure ↔ BddAbove.of_lowerClosure BddAbove.lowerClosure
+alias ⟨BddAbove.of_lowerClosure, BddAbove.lowerClosure⟩ := bddAbove_lowerClosure
 #align bdd_above.of_lower_closure BddAbove.of_lowerClosure
 #align bdd_above.lower_closure BddAbove.lowerClosure
 
-alias bddBelow_upperClosure ↔ BddBelow.of_upperClosure BddBelow.upperClosure
+alias ⟨BddBelow.of_upperClosure, BddBelow.upperClosure⟩ := bddBelow_upperClosure
 #align bdd_below.of_upper_closure BddBelow.of_upperClosure
 #align bdd_below.upper_closure BddBelow.upperClosure
 

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

This has nice performance benefits.

@@ -46,7 +46,7 @@ Lattice structure on antichains. Order equivalence between upper/lower sets and
 
 open OrderDual Set
 
-variable {α β γ : Type _} {ι : Sort _} {κ : ι → Sort _}
+variable {α β γ : Type*} {ι : Sort*} {κ : ι → Sort*}
 
 /-! ### Unbundled upper/lower sets -/
 
@@ -393,7 +393,7 @@ section LE
 variable [LE α]
 
 /-- The type of upper sets of an order. -/
-structure UpperSet (α : Type _) [LE α] where
+structure UpperSet (α : Type*) [LE α] where
   /-- The carrier of an `UpperSet`. -/
   carrier : Set α
   /-- The carrier of an `UpperSet` is an upper set. -/
@@ -401,7 +401,7 @@ structure UpperSet (α : Type _) [LE α] where
 #align upper_set UpperSet
 
 /-- The type of lower sets of an order. -/
-structure LowerSet (α : Type _) [LE α] where
+structure LowerSet (α : Type*) [LE α] where
   /-- The carrier of a `LowerSet`. -/
   carrier : Set α
   /-- The carrier of a `LowerSet` is a lower set. -/

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Sara Rousta
-
-! This file was ported from Lean 3 source module order.upper_lower.basic
-! leanprover-community/mathlib commit e9ce88cd0d54891c714c604076084f763dd480ed
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.SetLike.Basic
 import Mathlib.Data.Set.Intervals.OrdConnected
 import Mathlib.Data.Set.Intervals.OrderIso
 
+#align_import order.upper_lower.basic from "leanprover-community/mathlib"@"e9ce88cd0d54891c714c604076084f763dd480ed"
+
 /-!
 # Up-sets and down-sets
 

Adds new CompletelyDistribLattice/CompleteAtomicBooleanAlgebra classes for complete lattices / complete atomic Boolean algebras that are also completely distributive, and removes the misleading claim that CompleteDistribLattice/CompleteBooleanAlgebra are completely distributive.

• Product/pi/order dual instances for completely distributive lattices, etc.
• Every complete linear order is a completely distributive lattice.
• Every atomic complete Boolean algebra is a complete atomic Boolean algebra.
• Every complete atomic Boolean algebra is indeed (co)atom(ist)ic.
• Atom(ist)ic orders are closed under pis.
• All existing types with CompleteDistribLattice instances are upgraded to CompletelyDistribLattice.
• All existing types with CompleteBooleanAlgebra instances are upgraded to CompleteAtomicBooleanAlgebra.

See related discussion on Zulip.

@@ -499,8 +499,8 @@ instance : SupSet (UpperSet α) :=
 instance : InfSet (UpperSet α) :=
   ⟨fun S => ⟨⋃ s ∈ S, ↑s, isUpperSet_iUnion₂ fun s _ => s.upper⟩⟩
 
-instance : CompleteDistribLattice (UpperSet α) :=
-  (toDual.injective.comp SetLike.coe_injective).completeDistribLattice _ (fun _ _ => rfl)
+instance : CompletelyDistribLattice (UpperSet α) :=
+  (toDual.injective.comp SetLike.coe_injective).completelyDistribLattice _ (fun _ _ => rfl)
     (fun _ _ => rfl) (fun _ => rfl) (fun _ => rfl) rfl rfl
 
 instance : Inhabited (UpperSet α) :=
@@ -648,8 +648,8 @@ instance : SupSet (LowerSet α) :=
 instance : InfSet (LowerSet α) :=
   ⟨fun S => ⟨⋂ s ∈ S, ↑s, isLowerSet_iInter₂ fun s _ => s.lower⟩⟩
 
-instance : CompleteDistribLattice (LowerSet α) :=
-  SetLike.coe_injective.completeDistribLattice _ (fun _ _ => rfl) (fun _ _ => rfl) (fun _ => rfl)
+instance : CompletelyDistribLattice (LowerSet α) :=
+  SetLike.coe_injective.completelyDistribLattice _ (fun _ _ => rfl) (fun _ _ => rfl) (fun _ => rfl)
     (fun _ => rfl) rfl rfl
 
 instance : Inhabited (LowerSet α) :=

@@ -1339,13 +1339,13 @@ theorem lowerClosure_image (f : α ≃o β) :
 #align lower_closure_image lowerClosure_image
 
 @[simp]
-theorem UpperSet.iInf_Ici (s : Set α) : (⨅ a ∈ s, UpperSet.Ici a) = upperClosure s := by
+theorem UpperSet.iInf_Ici (s : Set α) : ⨅ a ∈ s, UpperSet.Ici a = upperClosure s := by
   ext
   simp
 #align upper_set.infi_Ici UpperSet.iInf_Ici
 
 @[simp]
-theorem LowerSet.iSup_Iic (s : Set α) : (⨆ a ∈ s, LowerSet.Iic a) = lowerClosure s := by
+theorem LowerSet.iSup_Iic (s : Set α) : ⨆ a ∈ s, LowerSet.Iic a = lowerClosure s := by
   ext
   simp
 #align lower_set.supr_Iic LowerSet.iSup_Iic

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

@@ -82,21 +82,21 @@ theorem isUpperSet_univ : IsUpperSet (univ : Set α) := fun _ _ _ => id
 theorem isLowerSet_univ : IsLowerSet (univ : Set α) := fun _ _ _ => id
 #align is_lower_set_univ isLowerSet_univ
 
-theorem IsUpperSet.compl (hs : IsUpperSet s) : IsLowerSet (sᶜ) := fun _a _b h hb ha => hb <| hs h ha
+theorem IsUpperSet.compl (hs : IsUpperSet s) : IsLowerSet sᶜ := fun _a _b h hb ha => hb <| hs h ha
 #align is_upper_set.compl IsUpperSet.compl
 
-theorem IsLowerSet.compl (hs : IsLowerSet s) : IsUpperSet (sᶜ) := fun _a _b h hb ha => hb <| hs h ha
+theorem IsLowerSet.compl (hs : IsLowerSet s) : IsUpperSet sᶜ := fun _a _b h hb ha => hb <| hs h ha
 #align is_lower_set.compl IsLowerSet.compl
 
 @[simp]
-theorem isUpperSet_compl : IsUpperSet (sᶜ) ↔ IsLowerSet s :=
+theorem isUpperSet_compl : IsUpperSet sᶜ ↔ IsLowerSet s :=
   ⟨fun h => by
     convert h.compl
     rw [compl_compl], IsLowerSet.compl⟩
 #align is_upper_set_compl isUpperSet_compl
 
 @[simp]
-theorem isLowerSet_compl : IsLowerSet (sᶜ) ↔ IsUpperSet s :=
+theorem isLowerSet_compl : IsLowerSet sᶜ ↔ IsUpperSet s :=
   ⟨fun h => by
     convert h.compl
     rw [compl_compl], IsUpperSet.compl⟩
@@ -794,7 +794,7 @@ namespace UpperSet
 variable {s t : UpperSet α} {a : α}
 
 @[simp]
-theorem coe_compl (s : UpperSet α) : (s.compl : Set α) = ↑sᶜ :=
+theorem coe_compl (s : UpperSet α) : (s.compl : Set α) = (↑s)ᶜ :=
   rfl
 #align upper_set.coe_compl UpperSet.coe_compl
 
@@ -870,7 +870,7 @@ namespace LowerSet
 variable {s t : LowerSet α} {a : α}
 
 @[simp]
-theorem coe_compl (s : LowerSet α) : (s.compl : Set α) = ↑sᶜ :=
+theorem coe_compl (s : LowerSet α) : (s.compl : Set α) = (↑s)ᶜ :=
   rfl
 #align lower_set.coe_compl LowerSet.coe_compl
 

Part 3 of #5001

@@ -29,8 +29,8 @@ This file defines upper and lower sets in an order.
 * `lowerClosure`: The least lower set containing a set.
 * `UpperSet.Ici`: Principal upper set. `Set.Ici` as an upper set.
 * `UpperSet.Ioi`: Strict principal upper set. `Set.Ioi` as an upper set.
-* `LowerSet.Iic`: Principal lower set. `Set.Iic` as an lower set.
-* `LowerSet.Iio`: Strict principal lower set. `Set.Iio` as an lower set.
+* `LowerSet.Iic`: Principal lower set. `Set.Iic` as a lower set.
+* `LowerSet.Iio`: Strict principal lower set. `Set.Iio` as a lower set.
 
 ## Notation
 

Currently, the following notations are changed from · ×ˢ · because Lean 4 can't deal with ambiguous notations. | Definition | Notation | | :

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

@@ -34,9 +34,7 @@ This file defines upper and lower sets in an order.
 
 ## Notation
 
-* `×ˢ` is notation for `Set.prod`, defined elsewhere;
-* `×ᵘˢ` is notation for `UpperSet.prod`;
-* `×ˡˢ` is notation for `LowerSet.prod`.
+* `×ˢ` is notation for `UpperSet.prod` / `LowerSet.prod`.
 
 ## Notes
 
@@ -1537,105 +1535,105 @@ def prod : UpperSet (α × β) :=
   ⟨s ×ˢ t, s.2.prod t.2⟩
 #align upper_set.prod UpperSet.prod
 
-@[inherit_doc]
-infixr:82 " ×ᵘˢ " => prod
+instance instSProd : SProd (UpperSet α) (UpperSet β) (UpperSet (α × β)) where
+  sprod := UpperSet.prod
 
 @[simp, norm_cast]
-theorem coe_prod : (↑(s ×ᵘˢ t) : Set (α × β)) = (s : Set α) ×ˢ t :=
+theorem coe_prod : ((s ×ˢ t : UpperSet (α × β)) : Set (α × β)) = (s : Set α) ×ˢ t :=
   rfl
 #align upper_set.coe_prod UpperSet.coe_prod
 
 @[simp]
-theorem mem_prod {s : UpperSet α} {t : UpperSet β} : x ∈ s ×ᵘˢ t ↔ x.1 ∈ s ∧ x.2 ∈ t :=
+theorem mem_prod {s : UpperSet α} {t : UpperSet β} : x ∈ s ×ˢ t ↔ x.1 ∈ s ∧ x.2 ∈ t :=
   Iff.rfl
 #align upper_set.mem_prod UpperSet.mem_prod
 
-theorem Ici_prod (x : α × β) : Ici x = Ici x.1 ×ᵘˢ Ici x.2 :=
+theorem Ici_prod (x : α × β) : Ici x = Ici x.1 ×ˢ Ici x.2 :=
   rfl
 #align upper_set.Ici_prod UpperSet.Ici_prod
 
 @[simp]
-theorem Ici_prod_Ici (a : α) (b : β) : Ici a ×ᵘˢ Ici b = Ici (a, b) :=
+theorem Ici_prod_Ici (a : α) (b : β) : Ici a ×ˢ Ici b = Ici (a, b) :=
   rfl
 #align upper_set.Ici_prod_Ici UpperSet.Ici_prod_Ici
 
 @[simp]
-theorem prod_top : s ×ᵘˢ (⊤ : UpperSet β) = ⊤ :=
+theorem prod_top : s ×ˢ (⊤ : UpperSet β) = ⊤ :=
   ext prod_empty
 #align upper_set.prod_top UpperSet.prod_top
 
 @[simp]
-theorem top_prod : (⊤ : UpperSet α) ×ᵘˢ t = ⊤ :=
+theorem top_prod : (⊤ : UpperSet α) ×ˢ t = ⊤ :=
   ext empty_prod
 #align upper_set.top_prod UpperSet.top_prod
 
 @[simp]
-theorem bot_prod_bot : (⊥ : UpperSet α) ×ᵘˢ (⊥ : UpperSet β) = ⊥ :=
+theorem bot_prod_bot : (⊥ : UpperSet α) ×ˢ (⊥ : UpperSet β) = ⊥ :=
   ext univ_prod_univ
 #align upper_set.bot_prod_bot UpperSet.bot_prod_bot
 
 @[simp]
-theorem sup_prod : (s₁ ⊔ s₂) ×ᵘˢ t = s₁ ×ᵘˢ t ⊔ s₂ ×ᵘˢ t :=
+theorem sup_prod : (s₁ ⊔ s₂) ×ˢ t = s₁ ×ˢ t ⊔ s₂ ×ˢ t :=
   ext inter_prod
 #align upper_set.sup_prod UpperSet.sup_prod
 
 @[simp]
-theorem prod_sup : s ×ᵘˢ (t₁ ⊔ t₂) = s ×ᵘˢ t₁ ⊔ s ×ᵘˢ t₂ :=
+theorem prod_sup : s ×ˢ (t₁ ⊔ t₂) = s ×ˢ t₁ ⊔ s ×ˢ t₂ :=
   ext prod_inter
 #align upper_set.prod_sup UpperSet.prod_sup
 
 @[simp]
-theorem inf_prod : (s₁ ⊓ s₂) ×ᵘˢ t = s₁ ×ᵘˢ t ⊓ s₂ ×ᵘˢ t :=
+theorem inf_prod : (s₁ ⊓ s₂) ×ˢ t = s₁ ×ˢ t ⊓ s₂ ×ˢ t :=
   ext union_prod
 #align upper_set.inf_prod UpperSet.inf_prod
 
 @[simp]
-theorem prod_inf : s ×ᵘˢ (t₁ ⊓ t₂) = s ×ᵘˢ t₁ ⊓ s ×ᵘˢ t₂ :=
+theorem prod_inf : s ×ˢ (t₁ ⊓ t₂) = s ×ˢ t₁ ⊓ s ×ˢ t₂ :=
   ext prod_union
 #align upper_set.prod_inf UpperSet.prod_inf
 
-theorem prod_sup_prod : s₁ ×ᵘˢ t₁ ⊔ s₂ ×ᵘˢ t₂ = (s₁ ⊔ s₂) ×ᵘˢ (t₁ ⊔ t₂) :=
+theorem prod_sup_prod : s₁ ×ˢ t₁ ⊔ s₂ ×ˢ t₂ = (s₁ ⊔ s₂) ×ˢ (t₁ ⊔ t₂) :=
   ext prod_inter_prod
 #align upper_set.prod_sup_prod UpperSet.prod_sup_prod
 
 variable {s s₁ s₂ t t₁ t₂}
 
 @[mono]
-theorem prod_mono : s₁ ≤ s₂ → t₁ ≤ t₂ → s₁ ×ᵘˢ t₁ ≤ s₂ ×ᵘˢ t₂ :=
+theorem prod_mono : s₁ ≤ s₂ → t₁ ≤ t₂ → s₁ ×ˢ t₁ ≤ s₂ ×ˢ t₂ :=
   Set.prod_mono
 #align upper_set.prod_mono UpperSet.prod_mono
 
-theorem prod_mono_left : s₁ ≤ s₂ → s₁ ×ᵘˢ t ≤ s₂ ×ᵘˢ t :=
+theorem prod_mono_left : s₁ ≤ s₂ → s₁ ×ˢ t ≤ s₂ ×ˢ t :=
   Set.prod_mono_left
 #align upper_set.prod_mono_left UpperSet.prod_mono_left
 
-theorem prod_mono_right : t₁ ≤ t₂ → s ×ᵘˢ t₁ ≤ s ×ᵘˢ t₂ :=
+theorem prod_mono_right : t₁ ≤ t₂ → s ×ˢ t₁ ≤ s ×ˢ t₂ :=
   Set.prod_mono_right
 #align upper_set.prod_mono_right UpperSet.prod_mono_right
 
 @[simp]
-theorem prod_self_le_prod_self : s₁ ×ᵘˢ s₁ ≤ s₂ ×ᵘˢ s₂ ↔ s₁ ≤ s₂ :=
+theorem prod_self_le_prod_self : s₁ ×ˢ s₁ ≤ s₂ ×ˢ s₂ ↔ s₁ ≤ s₂ :=
   prod_self_subset_prod_self
 #align upper_set.prod_self_le_prod_self UpperSet.prod_self_le_prod_self
 
 @[simp]
-theorem prod_self_lt_prod_self : s₁ ×ᵘˢ s₁ < s₂ ×ᵘˢ s₂ ↔ s₁ < s₂ :=
+theorem prod_self_lt_prod_self : s₁ ×ˢ s₁ < s₂ ×ˢ s₂ ↔ s₁ < s₂ :=
   prod_self_ssubset_prod_self
 #align upper_set.prod_self_lt_prod_self UpperSet.prod_self_lt_prod_self
 
-theorem prod_le_prod_iff : s₁ ×ᵘˢ t₁ ≤ s₂ ×ᵘˢ t₂ ↔ s₁ ≤ s₂ ∧ t₁ ≤ t₂ ∨ s₂ = ⊤ ∨ t₂ = ⊤ :=
+theorem prod_le_prod_iff : s₁ ×ˢ t₁ ≤ s₂ ×ˢ t₂ ↔ s₁ ≤ s₂ ∧ t₁ ≤ t₂ ∨ s₂ = ⊤ ∨ t₂ = ⊤ :=
   prod_subset_prod_iff.trans <| by simp
 #align upper_set.prod_le_prod_iff UpperSet.prod_le_prod_iff
 
 @[simp]
-theorem prod_eq_top : s ×ᵘˢ t = ⊤ ↔ s = ⊤ ∨ t = ⊤ := by
+theorem prod_eq_top : s ×ˢ t = ⊤ ↔ s = ⊤ ∨ t = ⊤ := by
   simp_rw [SetLike.ext'_iff]
   exact prod_eq_empty_iff
 #align upper_set.prod_eq_top UpperSet.prod_eq_top
 
 @[simp]
 theorem codisjoint_prod :
-    Codisjoint (s₁ ×ᵘˢ t₁) (s₂ ×ᵘˢ t₂) ↔ Codisjoint s₁ s₂ ∨ Codisjoint t₁ t₂ := by
+    Codisjoint (s₁ ×ˢ t₁) (s₂ ×ˢ t₂) ↔ Codisjoint s₁ s₂ ∨ Codisjoint t₁ t₂ := by
   simp_rw [codisjoint_iff, prod_sup_prod, prod_eq_top]
 #align upper_set.codisjoint_prod UpperSet.codisjoint_prod
 
@@ -1649,98 +1647,99 @@ variable (s s₁ s₂ : LowerSet α) (t t₁ t₂ : LowerSet β) {x : α × β}
 def prod : LowerSet (α × β) := ⟨s ×ˢ t, s.2.prod t.2⟩
 #align lower_set.prod LowerSet.prod
 
-@[inherit_doc]
-infixr:82 " ×ˡˢ " => LowerSet.prod
+instance instSProd : SProd (LowerSet α) (LowerSet β) (LowerSet (α × β)) where
+  sprod := LowerSet.prod
 
-@[simp, norm_cast] theorem coe_prod : (↑(s ×ˡˢ t) : Set (α × β)) = s ×ˢ t := rfl
+@[simp, norm_cast]
+theorem coe_prod : ((s ×ˢ t : LowerSet (α × β)) : Set (α × β)) = (s : Set α) ×ˢ t := rfl
 #align lower_set.coe_prod LowerSet.coe_prod
 
 @[simp]
-theorem mem_prod {s : LowerSet α} {t : LowerSet β} : x ∈ s ×ˡˢ t ↔ x.1 ∈ s ∧ x.2 ∈ t :=
+theorem mem_prod {s : LowerSet α} {t : LowerSet β} : x ∈ s ×ˢ t ↔ x.1 ∈ s ∧ x.2 ∈ t :=
   Iff.rfl
 #align lower_set.mem_prod LowerSet.mem_prod
 
-theorem Iic_prod (x : α × β) : Iic x = Iic x.1 ×ˡˢ Iic x.2 :=
+theorem Iic_prod (x : α × β) : Iic x = Iic x.1 ×ˢ Iic x.2 :=
   rfl
 #align lower_set.Iic_prod LowerSet.Iic_prod
 
 @[simp]
-theorem Ici_prod_Ici (a : α) (b : β) : Iic a ×ˡˢ Iic b = Iic (a, b) :=
+theorem Ici_prod_Ici (a : α) (b : β) : Iic a ×ˢ Iic b = Iic (a, b) :=
   rfl
 #align lower_set.Ici_prod_Ici LowerSet.Ici_prod_Ici
 
 @[simp]
-theorem prod_bot : s ×ˡˢ (⊥ : LowerSet β) = ⊥ :=
+theorem prod_bot : s ×ˢ (⊥ : LowerSet β) = ⊥ :=
   ext prod_empty
 #align lower_set.prod_bot LowerSet.prod_bot
 
 @[simp]
-theorem bot_prod : (⊥ : LowerSet α) ×ˡˢ t = ⊥ :=
+theorem bot_prod : (⊥ : LowerSet α) ×ˢ t = ⊥ :=
   ext empty_prod
 #align lower_set.bot_prod LowerSet.bot_prod
 
 @[simp]
-theorem top_prod_top : (⊤ : LowerSet α) ×ˡˢ (⊤ : LowerSet β) = ⊤ :=
+theorem top_prod_top : (⊤ : LowerSet α) ×ˢ (⊤ : LowerSet β) = ⊤ :=
   ext univ_prod_univ
 #align lower_set.top_prod_top LowerSet.top_prod_top
 
 @[simp]
-theorem inf_prod : (s₁ ⊓ s₂) ×ˡˢ t = s₁ ×ˡˢ t ⊓ s₂ ×ˡˢ t :=
+theorem inf_prod : (s₁ ⊓ s₂) ×ˢ t = s₁ ×ˢ t ⊓ s₂ ×ˢ t :=
   ext inter_prod
 #align lower_set.inf_prod LowerSet.inf_prod
 
 @[simp]
-theorem prod_inf : s ×ˡˢ (t₁ ⊓ t₂) = s ×ˡˢ t₁ ⊓ s ×ˡˢ t₂ :=
+theorem prod_inf : s ×ˢ (t₁ ⊓ t₂) = s ×ˢ t₁ ⊓ s ×ˢ t₂ :=
   ext prod_inter
 #align lower_set.prod_inf LowerSet.prod_inf
 
 @[simp]
-theorem sup_prod : (s₁ ⊔ s₂) ×ˡˢ t = s₁ ×ˡˢ t ⊔ s₂ ×ˡˢ t :=
+theorem sup_prod : (s₁ ⊔ s₂) ×ˢ t = s₁ ×ˢ t ⊔ s₂ ×ˢ t :=
   ext union_prod
 #align lower_set.sup_prod LowerSet.sup_prod
 
 @[simp]
-theorem prod_sup : s ×ˡˢ (t₁ ⊔ t₂) = s ×ˡˢ t₁ ⊔ s ×ˡˢ t₂ :=
+theorem prod_sup : s ×ˢ (t₁ ⊔ t₂) = s ×ˢ t₁ ⊔ s ×ˢ t₂ :=
   ext prod_union
 #align lower_set.prod_sup LowerSet.prod_sup
 
-theorem prod_inf_prod : s₁ ×ˡˢ t₁ ⊓ s₂ ×ˡˢ t₂ = (s₁ ⊓ s₂) ×ˡˢ (t₁ ⊓ t₂) :=
+theorem prod_inf_prod : s₁ ×ˢ t₁ ⊓ s₂ ×ˢ t₂ = (s₁ ⊓ s₂) ×ˢ (t₁ ⊓ t₂) :=
   ext prod_inter_prod
 #align lower_set.prod_inf_prod LowerSet.prod_inf_prod
 
 variable {s s₁ s₂ t t₁ t₂}
 
-theorem prod_mono : s₁ ≤ s₂ → t₁ ≤ t₂ → s₁ ×ˡˢ t₁ ≤ s₂ ×ˡˢ t₂ := Set.prod_mono
+theorem prod_mono : s₁ ≤ s₂ → t₁ ≤ t₂ → s₁ ×ˢ t₁ ≤ s₂ ×ˢ t₂ := Set.prod_mono
 #align lower_set.prod_mono LowerSet.prod_mono
 
-theorem prod_mono_left : s₁ ≤ s₂ → s₁ ×ˡˢ t ≤ s₂ ×ˡˢ t := Set.prod_mono_left
+theorem prod_mono_left : s₁ ≤ s₂ → s₁ ×ˢ t ≤ s₂ ×ˢ t := Set.prod_mono_left
 #align lower_set.prod_mono_left LowerSet.prod_mono_left
 
-theorem prod_mono_right : t₁ ≤ t₂ → s ×ˡˢ t₁ ≤ s ×ˡˢ t₂ := Set.prod_mono_right
+theorem prod_mono_right : t₁ ≤ t₂ → s ×ˢ t₁ ≤ s ×ˢ t₂ := Set.prod_mono_right
 #align lower_set.prod_mono_right LowerSet.prod_mono_right
 
 @[simp]
-theorem prod_self_le_prod_self : s₁ ×ˡˢ s₁ ≤ s₂ ×ˡˢ s₂ ↔ s₁ ≤ s₂ :=
+theorem prod_self_le_prod_self : s₁ ×ˢ s₁ ≤ s₂ ×ˢ s₂ ↔ s₁ ≤ s₂ :=
   prod_self_subset_prod_self
 #align lower_set.prod_self_le_prod_self LowerSet.prod_self_le_prod_self
 
 @[simp]
-theorem prod_self_lt_prod_self : s₁ ×ˡˢ s₁ < s₂ ×ˡˢ s₂ ↔ s₁ < s₂ :=
+theorem prod_self_lt_prod_self : s₁ ×ˢ s₁ < s₂ ×ˢ s₂ ↔ s₁ < s₂ :=
   prod_self_ssubset_prod_self
 #align lower_set.prod_self_lt_prod_self LowerSet.prod_self_lt_prod_self
 
-theorem prod_le_prod_iff : s₁ ×ˡˢ t₁ ≤ s₂ ×ˡˢ t₂ ↔ s₁ ≤ s₂ ∧ t₁ ≤ t₂ ∨ s₁ = ⊥ ∨ t₁ = ⊥ :=
+theorem prod_le_prod_iff : s₁ ×ˢ t₁ ≤ s₂ ×ˢ t₂ ↔ s₁ ≤ s₂ ∧ t₁ ≤ t₂ ∨ s₁ = ⊥ ∨ t₁ = ⊥ :=
   prod_subset_prod_iff.trans <| by simp
 #align lower_set.prod_le_prod_iff LowerSet.prod_le_prod_iff
 
 @[simp]
-theorem prod_eq_bot : s ×ˡˢ t = ⊥ ↔ s = ⊥ ∨ t = ⊥ := by
+theorem prod_eq_bot : s ×ˢ t = ⊥ ↔ s = ⊥ ∨ t = ⊥ := by
   simp_rw [SetLike.ext'_iff]
   exact prod_eq_empty_iff
 #align lower_set.prod_eq_bot LowerSet.prod_eq_bot
 
 @[simp]
-theorem disjoint_prod : Disjoint (s₁ ×ˡˢ t₁) (s₂ ×ˡˢ t₂) ↔ Disjoint s₁ s₂ ∨ Disjoint t₁ t₂ := by
+theorem disjoint_prod : Disjoint (s₁ ×ˢ t₁) (s₂ ×ˢ t₂) ↔ Disjoint s₁ s₂ ∨ Disjoint t₁ t₂ := by
   simp_rw [disjoint_iff, prod_inf_prod, prod_eq_bot]
 #align lower_set.disjoint_prod LowerSet.disjoint_prod
 
@@ -1748,14 +1747,14 @@ end LowerSet
 
 @[simp]
 theorem upperClosure_prod (s : Set α) (t : Set β) :
-    upperClosure (s ×ˢ t) = upperClosure s ×ᵘˢ upperClosure t := by
+    upperClosure (s ×ˢ t) = upperClosure s ×ˢ upperClosure t := by
   ext
   simp [Prod.le_def, @and_and_and_comm _ (_ ∈ t)]
 #align upper_closure_prod upperClosure_prod
 
 @[simp]
 theorem lowerClosure_prod (s : Set α) (t : Set β) :
-    lowerClosure (s ×ˢ t) = lowerClosure s ×ˡˢ lowerClosure t := by
+    lowerClosure (s ×ˢ t) = lowerClosure s ×ˢ lowerClosure t := by
   ext
   simp [Prod.le_def, @and_and_and_comm _ (_ ∈ t)]
 #align lower_closure_prod lowerClosure_prod

As discussed on Zulip

Renames

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

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

@@ -120,57 +120,57 @@ theorem IsLowerSet.inter (hs : IsLowerSet s) (ht : IsLowerSet t) : IsLowerSet (s
   fun _ _ h => And.imp (hs h) (ht h)
 #align is_lower_set.inter IsLowerSet.inter
 
-theorem isUpperSet_unionₛ {S : Set (Set α)} (hf : ∀ s ∈ S, IsUpperSet s) : IsUpperSet (⋃₀ S) :=
+theorem isUpperSet_sUnion {S : Set (Set α)} (hf : ∀ s ∈ S, IsUpperSet s) : IsUpperSet (⋃₀ S) :=
   fun _ _ h => Exists.imp fun _ hs => ⟨hs.1, hf _ hs.1 h hs.2⟩
-#align is_upper_set_sUnion isUpperSet_unionₛ
+#align is_upper_set_sUnion isUpperSet_sUnion
 
-theorem isLowerSet_unionₛ {S : Set (Set α)} (hf : ∀ s ∈ S, IsLowerSet s) : IsLowerSet (⋃₀ S) :=
+theorem isLowerSet_sUnion {S : Set (Set α)} (hf : ∀ s ∈ S, IsLowerSet s) : IsLowerSet (⋃₀ S) :=
   fun _ _ h => Exists.imp fun _ hs => ⟨hs.1, hf _ hs.1 h hs.2⟩
-#align is_lower_set_sUnion isLowerSet_unionₛ
+#align is_lower_set_sUnion isLowerSet_sUnion
 
-theorem isUpperSet_unionᵢ {f : ι → Set α} (hf : ∀ i, IsUpperSet (f i)) : IsUpperSet (⋃ i, f i) :=
-  isUpperSet_unionₛ <| forall_range_iff.2 hf
-#align is_upper_set_Union isUpperSet_unionᵢ
+theorem isUpperSet_iUnion {f : ι → Set α} (hf : ∀ i, IsUpperSet (f i)) : IsUpperSet (⋃ i, f i) :=
+  isUpperSet_sUnion <| forall_range_iff.2 hf
+#align is_upper_set_Union isUpperSet_iUnion
 
-theorem isLowerSet_unionᵢ {f : ι → Set α} (hf : ∀ i, IsLowerSet (f i)) : IsLowerSet (⋃ i, f i) :=
-  isLowerSet_unionₛ <| forall_range_iff.2 hf
-#align is_lower_set_Union isLowerSet_unionᵢ
+theorem isLowerSet_iUnion {f : ι → Set α} (hf : ∀ i, IsLowerSet (f i)) : IsLowerSet (⋃ i, f i) :=
+  isLowerSet_sUnion <| forall_range_iff.2 hf
+#align is_lower_set_Union isLowerSet_iUnion
 
-theorem isUpperSet_unionᵢ₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsUpperSet (f i j)) :
+theorem isUpperSet_iUnion₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsUpperSet (f i j)) :
     IsUpperSet (⋃ (i) (j), f i j) :=
-  isUpperSet_unionᵢ fun i => isUpperSet_unionᵢ <| hf i
-#align is_upper_set_Union₂ isUpperSet_unionᵢ₂
+  isUpperSet_iUnion fun i => isUpperSet_iUnion <| hf i
+#align is_upper_set_Union₂ isUpperSet_iUnion₂
 
-theorem isLowerSet_unionᵢ₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsLowerSet (f i j)) :
+theorem isLowerSet_iUnion₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsLowerSet (f i j)) :
     IsLowerSet (⋃ (i) (j), f i j) :=
-  isLowerSet_unionᵢ fun i => isLowerSet_unionᵢ <| hf i
-#align is_lower_set_Union₂ isLowerSet_unionᵢ₂
+  isLowerSet_iUnion fun i => isLowerSet_iUnion <| hf i
+#align is_lower_set_Union₂ isLowerSet_iUnion₂
 
-theorem isUpperSet_interₛ {S : Set (Set α)} (hf : ∀ s ∈ S, IsUpperSet s) : IsUpperSet (⋂₀ S) :=
+theorem isUpperSet_sInter {S : Set (Set α)} (hf : ∀ s ∈ S, IsUpperSet s) : IsUpperSet (⋂₀ S) :=
   fun _ _ h => forall₂_imp fun s hs => hf s hs h
-#align is_upper_set_sInter isUpperSet_interₛ
+#align is_upper_set_sInter isUpperSet_sInter
 
-theorem isLowerSet_interₛ {S : Set (Set α)} (hf : ∀ s ∈ S, IsLowerSet s) : IsLowerSet (⋂₀ S) :=
+theorem isLowerSet_sInter {S : Set (Set α)} (hf : ∀ s ∈ S, IsLowerSet s) : IsLowerSet (⋂₀ S) :=
   fun _ _ h => forall₂_imp fun s hs => hf s hs h
-#align is_lower_set_sInter isLowerSet_interₛ
+#align is_lower_set_sInter isLowerSet_sInter
 
-theorem isUpperSet_interᵢ {f : ι → Set α} (hf : ∀ i, IsUpperSet (f i)) : IsUpperSet (⋂ i, f i) :=
-  isUpperSet_interₛ <| forall_range_iff.2 hf
-#align is_upper_set_Inter isUpperSet_interᵢ
+theorem isUpperSet_iInter {f : ι → Set α} (hf : ∀ i, IsUpperSet (f i)) : IsUpperSet (⋂ i, f i) :=
+  isUpperSet_sInter <| forall_range_iff.2 hf
+#align is_upper_set_Inter isUpperSet_iInter
 
-theorem isLowerSet_interᵢ {f : ι → Set α} (hf : ∀ i, IsLowerSet (f i)) : IsLowerSet (⋂ i, f i) :=
-  isLowerSet_interₛ <| forall_range_iff.2 hf
-#align is_lower_set_Inter isLowerSet_interᵢ
+theorem isLowerSet_iInter {f : ι → Set α} (hf : ∀ i, IsLowerSet (f i)) : IsLowerSet (⋂ i, f i) :=
+  isLowerSet_sInter <| forall_range_iff.2 hf
+#align is_lower_set_Inter isLowerSet_iInter
 
-theorem isUpperSet_interᵢ₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsUpperSet (f i j)) :
+theorem isUpperSet_iInter₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsUpperSet (f i j)) :
     IsUpperSet (⋂ (i) (j), f i j) :=
-  isUpperSet_interᵢ fun i => isUpperSet_interᵢ <| hf i
-#align is_upper_set_Inter₂ isUpperSet_interᵢ₂
+  isUpperSet_iInter fun i => isUpperSet_iInter <| hf i
+#align is_upper_set_Inter₂ isUpperSet_iInter₂
 
-theorem isLowerSet_interᵢ₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsLowerSet (f i j)) :
+theorem isLowerSet_iInter₂ {f : ∀ i, κ i → Set α} (hf : ∀ i j, IsLowerSet (f i j)) :
     IsLowerSet (⋂ (i) (j), f i j) :=
-  isLowerSet_interᵢ fun i => isLowerSet_interᵢ <| hf i
-#align is_lower_set_Inter₂ isLowerSet_interᵢ₂
+  isLowerSet_iInter fun i => isLowerSet_iInter <| hf i
+#align is_lower_set_Inter₂ isLowerSet_iInter₂
 
 @[simp]
 theorem isLowerSet_preimage_ofDual_iff : IsLowerSet (ofDual ⁻¹' s) ↔ IsUpperSet s :=
@@ -496,10 +496,10 @@ instance : Bot (UpperSet α) :=
   ⟨⟨univ, isUpperSet_univ⟩⟩
 
 instance : SupSet (UpperSet α) :=
-  ⟨fun S => ⟨⋂ s ∈ S, ↑s, isUpperSet_interᵢ₂ fun s _ => s.upper⟩⟩
+  ⟨fun S => ⟨⋂ s ∈ S, ↑s, isUpperSet_iInter₂ fun s _ => s.upper⟩⟩
 
 instance : InfSet (UpperSet α) :=
-  ⟨fun S => ⟨⋃ s ∈ S, ↑s, isUpperSet_unionᵢ₂ fun s _ => s.upper⟩⟩
+  ⟨fun S => ⟨⋃ s ∈ S, ↑s, isUpperSet_iUnion₂ fun s _ => s.upper⟩⟩
 
 instance : CompleteDistribLattice (UpperSet α) :=
   (toDual.injective.comp SetLike.coe_injective).completeDistribLattice _ (fun _ _ => rfl)
@@ -542,32 +542,32 @@ theorem coe_inf (s t : UpperSet α) : (↑(s ⊓ t) : Set α) = (s : Set α) ∪
 #align upper_set.coe_inf UpperSet.coe_inf
 
 @[simp, norm_cast]
-theorem coe_supₛ (S : Set (UpperSet α)) : (↑(supₛ S) : Set α) = ⋂ s ∈ S, ↑s :=
+theorem coe_sSup (S : Set (UpperSet α)) : (↑(sSup S) : Set α) = ⋂ s ∈ S, ↑s :=
   rfl
-#align upper_set.coe_Sup UpperSet.coe_supₛ
+#align upper_set.coe_Sup UpperSet.coe_sSup
 
 @[simp, norm_cast]
-theorem coe_infₛ (S : Set (UpperSet α)) : (↑(infₛ S) : Set α) = ⋃ s ∈ S, ↑s :=
+theorem coe_sInf (S : Set (UpperSet α)) : (↑(sInf S) : Set α) = ⋃ s ∈ S, ↑s :=
   rfl
-#align upper_set.coe_Inf UpperSet.coe_infₛ
+#align upper_set.coe_Inf UpperSet.coe_sInf
 
 @[simp, norm_cast]
-theorem coe_supᵢ (f : ι → UpperSet α) : (↑(⨆ i, f i) : Set α) = ⋂ i, f i := by simp [supᵢ]
-#align upper_set.coe_supr UpperSet.coe_supᵢ
+theorem coe_iSup (f : ι → UpperSet α) : (↑(⨆ i, f i) : Set α) = ⋂ i, f i := by simp [iSup]
+#align upper_set.coe_supr UpperSet.coe_iSup
 
 @[simp, norm_cast]
-theorem coe_infᵢ (f : ι → UpperSet α) : (↑(⨅ i, f i) : Set α) = ⋃ i, f i := by simp [infᵢ]
-#align upper_set.coe_infi UpperSet.coe_infᵢ
+theorem coe_iInf (f : ι → UpperSet α) : (↑(⨅ i, f i) : Set α) = ⋃ i, f i := by simp [iInf]
+#align upper_set.coe_infi UpperSet.coe_iInf
 
 @[norm_cast] -- porting note: no longer a `simp`
-theorem coe_supᵢ₂ (f : ∀ i, κ i → UpperSet α) : (↑(⨆ (i) (j), f i j) : Set α) = ⋂ (i) (j), f i j :=
-  by simp_rw [coe_supᵢ]
-#align upper_set.coe_supr₂ UpperSet.coe_supᵢ₂
+theorem coe_iSup₂ (f : ∀ i, κ i → UpperSet α) : (↑(⨆ (i) (j), f i j) : Set α) = ⋂ (i) (j), f i j :=
+  by simp_rw [coe_iSup]
+#align upper_set.coe_supr₂ UpperSet.coe_iSup₂
 
 @[norm_cast] -- porting note: no longer a `simp`
-theorem coe_infᵢ₂ (f : ∀ i, κ i → UpperSet α) : (↑(⨅ (i) (j), f i j) : Set α) = ⋃ (i) (j), f i j :=
-  by simp_rw [coe_infᵢ]
-#align upper_set.coe_infi₂ UpperSet.coe_infᵢ₂
+theorem coe_iInf₂ (f : ∀ i, κ i → UpperSet α) : (↑(⨅ (i) (j), f i j) : Set α) = ⋃ (i) (j), f i j :=
+  by simp_rw [coe_iInf]
+#align upper_set.coe_infi₂ UpperSet.coe_iInf₂
 
 @[simp]
 theorem not_mem_top : a ∉ (⊤ : UpperSet α) :=
@@ -590,36 +590,36 @@ theorem mem_inf_iff : a ∈ s ⊓ t ↔ a ∈ s ∨ a ∈ t :=
 #align upper_set.mem_inf_iff UpperSet.mem_inf_iff
 
 @[simp]
-theorem mem_supₛ_iff : a ∈ supₛ S ↔ ∀ s ∈ S, a ∈ s :=
-  mem_interᵢ₂
-#align upper_set.mem_Sup_iff UpperSet.mem_supₛ_iff
+theorem mem_sSup_iff : a ∈ sSup S ↔ ∀ s ∈ S, a ∈ s :=
+  mem_iInter₂
+#align upper_set.mem_Sup_iff UpperSet.mem_sSup_iff
 
 @[simp]
-theorem mem_infₛ_iff : a ∈ infₛ S ↔ ∃ s ∈ S, a ∈ s :=
-  mem_unionᵢ₂.trans <| by simp only [exists_prop, SetLike.mem_coe]
-#align upper_set.mem_Inf_iff UpperSet.mem_infₛ_iff
+theorem mem_sInf_iff : a ∈ sInf S ↔ ∃ s ∈ S, a ∈ s :=
+  mem_iUnion₂.trans <| by simp only [exists_prop, SetLike.mem_coe]
+#align upper_set.mem_Inf_iff UpperSet.mem_sInf_iff
 
 @[simp]
-theorem mem_supᵢ_iff {f : ι → UpperSet α} : (a ∈ ⨆ i, f i) ↔ ∀ i, a ∈ f i := by
-  rw [← SetLike.mem_coe, coe_supᵢ]
-  exact mem_interᵢ
-#align upper_set.mem_supr_iff UpperSet.mem_supᵢ_iff
+theorem mem_iSup_iff {f : ι → UpperSet α} : (a ∈ ⨆ i, f i) ↔ ∀ i, a ∈ f i := by
+  rw [← SetLike.mem_coe, coe_iSup]
+  exact mem_iInter
+#align upper_set.mem_supr_iff UpperSet.mem_iSup_iff
 
 @[simp]
-theorem mem_infᵢ_iff {f : ι → UpperSet α} : (a ∈ ⨅ i, f i) ↔ ∃ i, a ∈ f i := by
-  rw [← SetLike.mem_coe, coe_infᵢ]
-  exact mem_unionᵢ
-#align upper_set.mem_infi_iff UpperSet.mem_infᵢ_iff
+theorem mem_iInf_iff {f : ι → UpperSet α} : (a ∈ ⨅ i, f i) ↔ ∃ i, a ∈ f i := by
+  rw [← SetLike.mem_coe, coe_iInf]
+  exact mem_iUnion
+#align upper_set.mem_infi_iff UpperSet.mem_iInf_iff
 
 -- porting note: no longer a @[simp]
-theorem mem_supᵢ₂_iff {f : ∀ i, κ i → UpperSet α} : (a ∈ ⨆ (i) (j), f i j) ↔ ∀ i j, a ∈ f i j := by
-  simp_rw [mem_supᵢ_iff]
-#align upper_set.mem_supr₂_iff UpperSet.mem_supᵢ₂_iff
+theorem mem_iSup₂_iff {f : ∀ i, κ i → UpperSet α} : (a ∈ ⨆ (i) (j), f i j) ↔ ∀ i j, a ∈ f i j := by
+  simp_rw [mem_iSup_iff]
+#align upper_set.mem_supr₂_iff UpperSet.mem_iSup₂_iff
 
 -- porting note: no longer a @[simp]
-theorem mem_infᵢ₂_iff {f : ∀ i, κ i → UpperSet α} : (a ∈ ⨅ (i) (j), f i j) ↔ ∃ i j, a ∈ f i j := by
-  simp_rw [mem_infᵢ_iff]
-#align upper_set.mem_infi₂_iff UpperSet.mem_infᵢ₂_iff
+theorem mem_iInf₂_iff {f : ∀ i, κ i → UpperSet α} : (a ∈ ⨅ (i) (j), f i j) ↔ ∃ i j, a ∈ f i j := by
+  simp_rw [mem_iInf_iff]
+#align upper_set.mem_infi₂_iff UpperSet.mem_iInf₂_iff
 
 @[simp, norm_cast]
 theorem codisjoint_coe : Codisjoint (s : Set α) t ↔ Disjoint s t := by
@@ -645,10 +645,10 @@ instance : Bot (LowerSet α) :=
   ⟨⟨∅, fun _ _ _ => id⟩⟩
 
 instance : SupSet (LowerSet α) :=
-  ⟨fun S => ⟨⋃ s ∈ S, ↑s, isLowerSet_unionᵢ₂ fun s _ => s.lower⟩⟩
+  ⟨fun S => ⟨⋃ s ∈ S, ↑s, isLowerSet_iUnion₂ fun s _ => s.lower⟩⟩
 
 instance : InfSet (LowerSet α) :=
-  ⟨fun S => ⟨⋂ s ∈ S, ↑s, isLowerSet_interᵢ₂ fun s _ => s.lower⟩⟩
+  ⟨fun S => ⟨⋂ s ∈ S, ↑s, isLowerSet_iInter₂ fun s _ => s.lower⟩⟩
 
 instance : CompleteDistribLattice (LowerSet α) :=
   SetLike.coe_injective.completeDistribLattice _ (fun _ _ => rfl) (fun _ _ => rfl) (fun _ => rfl)
@@ -691,34 +691,34 @@ theorem coe_inf (s t : LowerSet α) : (↑(s ⊓ t) : Set α) = (s : Set α) ∩
 #align lower_set.coe_inf LowerSet.coe_inf
 
 @[simp, norm_cast]
-theorem coe_supₛ (S : Set (LowerSet α)) : (↑(supₛ S) : Set α) = ⋃ s ∈ S, ↑s :=
+theorem coe_sSup (S : Set (LowerSet α)) : (↑(sSup S) : Set α) = ⋃ s ∈ S, ↑s :=
   rfl
-#align lower_set.coe_Sup LowerSet.coe_supₛ
+#align lower_set.coe_Sup LowerSet.coe_sSup
 
 @[simp, norm_cast]
-theorem coe_infₛ (S : Set (LowerSet α)) : (↑(infₛ S) : Set α) = ⋂ s ∈ S, ↑s :=
+theorem coe_sInf (S : Set (LowerSet α)) : (↑(sInf S) : Set α) = ⋂ s ∈ S, ↑s :=
   rfl
-#align lower_set.coe_Inf LowerSet.coe_infₛ
+#align lower_set.coe_Inf LowerSet.coe_sInf
 
 @[simp, norm_cast]
-theorem coe_supᵢ (f : ι → LowerSet α) : (↑(⨆ i, f i) : Set α) = ⋃ i, f i := by
-  simp_rw [supᵢ, coe_supₛ, mem_range, unionᵢ_exists, unionᵢ_unionᵢ_eq']
-#align lower_set.coe_supr LowerSet.coe_supᵢ
+theorem coe_iSup (f : ι → LowerSet α) : (↑(⨆ i, f i) : Set α) = ⋃ i, f i := by
+  simp_rw [iSup, coe_sSup, mem_range, iUnion_exists, iUnion_iUnion_eq']
+#align lower_set.coe_supr LowerSet.coe_iSup
 
 @[simp, norm_cast]
-theorem coe_infᵢ (f : ι → LowerSet α) : (↑(⨅ i, f i) : Set α) = ⋂ i, f i := by
-  simp_rw [infᵢ, coe_infₛ, mem_range, interᵢ_exists, interᵢ_interᵢ_eq']
-#align lower_set.coe_infi LowerSet.coe_infᵢ
+theorem coe_iInf (f : ι → LowerSet α) : (↑(⨅ i, f i) : Set α) = ⋂ i, f i := by
+  simp_rw [iInf, coe_sInf, mem_range, iInter_exists, iInter_iInter_eq']
+#align lower_set.coe_infi LowerSet.coe_iInf
 
 @[norm_cast] -- porting note: no longer a `simp`
-theorem coe_supᵢ₂ (f : ∀ i, κ i → LowerSet α) : (↑(⨆ (i) (j), f i j) : Set α) = ⋃ (i) (j), f i j :=
-  by simp_rw [coe_supᵢ]
-#align lower_set.coe_supr₂ LowerSet.coe_supᵢ₂
+theorem coe_iSup₂ (f : ∀ i, κ i → LowerSet α) : (↑(⨆ (i) (j), f i j) : Set α) = ⋃ (i) (j), f i j :=
+  by simp_rw [coe_iSup]
+#align lower_set.coe_supr₂ LowerSet.coe_iSup₂
 
 @[norm_cast] -- porting note: no longer a `simp`
-theorem coe_infᵢ₂ (f : ∀ i, κ i → LowerSet α) : (↑(⨅ (i) (j), f i j) : Set α) = ⋂ (i) (j), f i j :=
-  by simp_rw [coe_infᵢ]
-#align lower_set.coe_infi₂ LowerSet.coe_infᵢ₂
+theorem coe_iInf₂ (f : ∀ i, κ i → LowerSet α) : (↑(⨅ (i) (j), f i j) : Set α) = ⋂ (i) (j), f i j :=
+  by simp_rw [coe_iInf]
+#align lower_set.coe_infi₂ LowerSet.coe_iInf₂
 
 @[simp]
 theorem mem_top : a ∈ (⊤ : LowerSet α) :=
@@ -741,36 +741,36 @@ theorem mem_inf_iff : a ∈ s ⊓ t ↔ a ∈ s ∧ a ∈ t :=
 #align lower_set.mem_inf_iff LowerSet.mem_inf_iff
 
 @[simp]
-theorem mem_supₛ_iff : a ∈ supₛ S ↔ ∃ s ∈ S, a ∈ s :=
-  mem_unionᵢ₂.trans <| by simp only [exists_prop, SetLike.mem_coe]
-#align lower_set.mem_Sup_iff LowerSet.mem_supₛ_iff
+theorem mem_sSup_iff : a ∈ sSup S ↔ ∃ s ∈ S, a ∈ s :=
+  mem_iUnion₂.trans <| by simp only [exists_prop, SetLike.mem_coe]
+#align lower_set.mem_Sup_iff LowerSet.mem_sSup_iff
 
 @[simp]
-theorem mem_infₛ_iff : a ∈ infₛ S ↔ ∀ s ∈ S, a ∈ s :=
-  mem_interᵢ₂
-#align lower_set.mem_Inf_iff LowerSet.mem_infₛ_iff
+theorem mem_sInf_iff : a ∈ sInf S ↔ ∀ s ∈ S, a ∈ s :=
+  mem_iInter₂
+#align lower_set.mem_Inf_iff LowerSet.mem_sInf_iff
 
 @[simp]
-theorem mem_supᵢ_iff {f : ι → LowerSet α} : (a ∈ ⨆ i, f i) ↔ ∃ i, a ∈ f i := by
-  rw [← SetLike.mem_coe, coe_supᵢ]
-  exact mem_unionᵢ
-#align lower_set.mem_supr_iff LowerSet.mem_supᵢ_iff
+theorem mem_iSup_iff {f : ι → LowerSet α} : (a ∈ ⨆ i, f i) ↔ ∃ i, a ∈ f i := by
+  rw [← SetLike.mem_coe, coe_iSup]
+  exact mem_iUnion
+#align lower_set.mem_supr_iff LowerSet.mem_iSup_iff
 
 @[simp]
-theorem mem_infᵢ_iff {f : ι → LowerSet α} : (a ∈ ⨅ i, f i) ↔ ∀ i, a ∈ f i := by
-  rw [← SetLike.mem_coe, coe_infᵢ]
-  exact mem_interᵢ
-#align lower_set.mem_infi_iff LowerSet.mem_infᵢ_iff
+theorem mem_iInf_iff {f : ι → LowerSet α} : (a ∈ ⨅ i, f i) ↔ ∀ i, a ∈ f i := by
+  rw [← SetLike.mem_coe, coe_iInf]
+  exact mem_iInter
+#align lower_set.mem_infi_iff LowerSet.mem_iInf_iff
 
 -- porting note: no longer a @[simp]
-theorem mem_supᵢ₂_iff {f : ∀ i, κ i → LowerSet α} : (a ∈ ⨆ (i) (j), f i j) ↔ ∃ i j, a ∈ f i j := by
-  simp_rw [mem_supᵢ_iff]
-#align lower_set.mem_supr₂_iff LowerSet.mem_supᵢ₂_iff
+theorem mem_iSup₂_iff {f : ∀ i, κ i → LowerSet α} : (a ∈ ⨆ (i) (j), f i j) ↔ ∃ i j, a ∈ f i j := by
+  simp_rw [mem_iSup_iff]
+#align lower_set.mem_supr₂_iff LowerSet.mem_iSup₂_iff
 
 -- porting note: no longer a @[simp]
-theorem mem_infᵢ₂_iff {f : ∀ i, κ i → LowerSet α} : (a ∈ ⨅ (i) (j), f i j) ↔ ∀ i j, a ∈ f i j := by
-  simp_rw [mem_infᵢ_iff]
-#align lower_set.mem_infi₂_iff LowerSet.mem_infᵢ₂_iff
+theorem mem_iInf₂_iff {f : ∀ i, κ i → LowerSet α} : (a ∈ ⨅ (i) (j), f i j) ↔ ∀ i j, a ∈ f i j := by
+  simp_rw [mem_iInf_iff]
+#align lower_set.mem_infi₂_iff LowerSet.mem_iInf₂_iff
 
 @[simp, norm_cast]
 theorem disjoint_coe : Disjoint (s : Set α) t ↔ Disjoint s t := by
@@ -836,34 +836,34 @@ protected theorem compl_bot : (⊥ : UpperSet α).compl = ⊥ :=
 #align upper_set.compl_bot UpperSet.compl_bot
 
 @[simp]
-protected theorem compl_supₛ (S : Set (UpperSet α)) : (supₛ S).compl = ⨆ s ∈ S, UpperSet.compl s :=
-  LowerSet.ext <| by simp only [coe_compl, coe_supₛ, compl_interᵢ₂, LowerSet.coe_supᵢ₂]
-#align upper_set.compl_Sup UpperSet.compl_supₛ
+protected theorem compl_sSup (S : Set (UpperSet α)) : (sSup S).compl = ⨆ s ∈ S, UpperSet.compl s :=
+  LowerSet.ext <| by simp only [coe_compl, coe_sSup, compl_iInter₂, LowerSet.coe_iSup₂]
+#align upper_set.compl_Sup UpperSet.compl_sSup
 
 @[simp]
-protected theorem compl_infₛ (S : Set (UpperSet α)) : (infₛ S).compl = ⨅ s ∈ S, UpperSet.compl s :=
-  LowerSet.ext <| by simp only [coe_compl, coe_infₛ, compl_unionᵢ₂, LowerSet.coe_infᵢ₂]
-#align upper_set.compl_Inf UpperSet.compl_infₛ
+protected theorem compl_sInf (S : Set (UpperSet α)) : (sInf S).compl = ⨅ s ∈ S, UpperSet.compl s :=
+  LowerSet.ext <| by simp only [coe_compl, coe_sInf, compl_iUnion₂, LowerSet.coe_iInf₂]
+#align upper_set.compl_Inf UpperSet.compl_sInf
 
 @[simp]
-protected theorem compl_supᵢ (f : ι → UpperSet α) : (⨆ i, f i).compl = ⨆ i, (f i).compl :=
-  LowerSet.ext <| by simp only [coe_compl, coe_supᵢ, compl_interᵢ, LowerSet.coe_supᵢ]
-#align upper_set.compl_supr UpperSet.compl_supᵢ
+protected theorem compl_iSup (f : ι → UpperSet α) : (⨆ i, f i).compl = ⨆ i, (f i).compl :=
+  LowerSet.ext <| by simp only [coe_compl, coe_iSup, compl_iInter, LowerSet.coe_iSup]
+#align upper_set.compl_supr UpperSet.compl_iSup
 
 @[simp]
-protected theorem compl_infᵢ (f : ι → UpperSet α) : (⨅ i, f i).compl = ⨅ i, (f i).compl :=
-  LowerSet.ext <| by simp only [coe_compl, coe_infᵢ, compl_unionᵢ, LowerSet.coe_infᵢ]
-#align upper_set.compl_infi UpperSet.compl_infᵢ
+protected theorem compl_iInf (f : ι → UpperSet α) : (⨅ i, f i).compl = ⨅ i, (f i).compl :=
+  LowerSet.ext <| by simp only [coe_compl, coe_iInf, compl_iUnion, LowerSet.coe_iInf]
+#align upper_set.compl_infi UpperSet.compl_iInf
 
 -- porting note: no longer a @[simp]
-theorem compl_supᵢ₂ (f : ∀ i, κ i → UpperSet α) :
-    (⨆ (i) (j), f i j).compl = ⨆ (i) (j), (f i j).compl := by simp_rw [UpperSet.compl_supᵢ]
-#align upper_set.compl_supr₂ UpperSet.compl_supᵢ₂
+theorem compl_iSup₂ (f : ∀ i, κ i → UpperSet α) :
+    (⨆ (i) (j), f i j).compl = ⨆ (i) (j), (f i j).compl := by simp_rw [UpperSet.compl_iSup]
+#align upper_set.compl_supr₂ UpperSet.compl_iSup₂
 
 -- porting note: no longer a @[simp]
-theorem compl_infᵢ₂ (f : ∀ i, κ i → UpperSet α) :
-    (⨅ (i) (j), f i j).compl = ⨅ (i) (j), (f i j).compl := by simp_rw [UpperSet.compl_infᵢ]
-#align upper_set.compl_infi₂ UpperSet.compl_infᵢ₂
+theorem compl_iInf₂ (f : ∀ i, κ i → UpperSet α) :
+    (⨅ (i) (j), f i j).compl = ⨅ (i) (j), (f i j).compl := by simp_rw [UpperSet.compl_iInf]
+#align upper_set.compl_infi₂ UpperSet.compl_iInf₂
 
 end UpperSet
 
@@ -907,31 +907,31 @@ protected theorem compl_bot : (⊥ : LowerSet α).compl = ⊥ :=
   UpperSet.ext compl_empty
 #align lower_set.compl_bot LowerSet.compl_bot
 
-protected theorem compl_supₛ (S : Set (LowerSet α)) : (supₛ S).compl = ⨆ s ∈ S, LowerSet.compl s :=
-  UpperSet.ext <| by simp only [coe_compl, coe_supₛ, compl_unionᵢ₂, UpperSet.coe_supᵢ₂]
-#align lower_set.compl_Sup LowerSet.compl_supₛ
+protected theorem compl_sSup (S : Set (LowerSet α)) : (sSup S).compl = ⨆ s ∈ S, LowerSet.compl s :=
+  UpperSet.ext <| by simp only [coe_compl, coe_sSup, compl_iUnion₂, UpperSet.coe_iSup₂]
+#align lower_set.compl_Sup LowerSet.compl_sSup
 
-protected theorem compl_infₛ (S : Set (LowerSet α)) : (infₛ S).compl = ⨅ s ∈ S, LowerSet.compl s :=
-  UpperSet.ext <| by simp only [coe_compl, coe_infₛ, compl_interᵢ₂, UpperSet.coe_infᵢ₂]
-#align lower_set.compl_Inf LowerSet.compl_infₛ
+protected theorem compl_sInf (S : Set (LowerSet α)) : (sInf S).compl = ⨅ s ∈ S, LowerSet.compl s :=
+  UpperSet.ext <| by simp only [coe_compl, coe_sInf, compl_iInter₂, UpperSet.coe_iInf₂]
+#align lower_set.compl_Inf LowerSet.compl_sInf
 
-protected theorem compl_supᵢ (f : ι → LowerSet α) : (⨆ i, f i).compl = ⨆ i, (f i).compl :=
-  UpperSet.ext <| by simp only [coe_compl, coe_supᵢ, compl_unionᵢ, UpperSet.coe_supᵢ]
-#align lower_set.compl_supr LowerSet.compl_supᵢ
+protected theorem compl_iSup (f : ι → LowerSet α) : (⨆ i, f i).compl = ⨆ i, (f i).compl :=
+  UpperSet.ext <| by simp only [coe_compl, coe_iSup, compl_iUnion, UpperSet.coe_iSup]
+#align lower_set.compl_supr LowerSet.compl_iSup
 
-protected theorem compl_infᵢ (f : ι → LowerSet α) : (⨅ i, f i).compl = ⨅ i, (f i).compl :=
-  UpperSet.ext <| by simp only [coe_compl, coe_infᵢ, compl_interᵢ, UpperSet.coe_infᵢ]
-#align lower_set.compl_infi LowerSet.compl_infᵢ
+protected theorem compl_iInf (f : ι → LowerSet α) : (⨅ i, f i).compl = ⨅ i, (f i).compl :=
+  UpperSet.ext <| by simp only [coe_compl, coe_iInf, compl_iInter, UpperSet.coe_iInf]
+#align lower_set.compl_infi LowerSet.compl_iInf
 
 @[simp]
-theorem compl_supᵢ₂ (f : ∀ i, κ i → LowerSet α) :
-    (⨆ (i) (j), f i j).compl = ⨆ (i) (j), (f i j).compl := by simp_rw [LowerSet.compl_supᵢ]
-#align lower_set.compl_supr₂ LowerSet.compl_supᵢ₂
+theorem compl_iSup₂ (f : ∀ i, κ i → LowerSet α) :
+    (⨆ (i) (j), f i j).compl = ⨆ (i) (j), (f i j).compl := by simp_rw [LowerSet.compl_iSup]
+#align lower_set.compl_supr₂ LowerSet.compl_iSup₂
 
 @[simp]
-theorem compl_infᵢ₂ (f : ∀ i, κ i → LowerSet α) :
-    (⨅ (i) (j), f i j).compl = ⨅ (i) (j), (f i j).compl := by simp_rw [LowerSet.compl_infᵢ]
-#align lower_set.compl_infi₂ LowerSet.compl_infᵢ₂
+theorem compl_iInf₂ (f : ∀ i, κ i → LowerSet α) :
+    (⨅ (i) (j), f i j).compl = ⨅ (i) (j), (f i j).compl := by simp_rw [LowerSet.compl_iInf]
+#align lower_set.compl_infi₂ LowerSet.compl_iInf₂
 
 end LowerSet
 
@@ -1142,19 +1142,19 @@ section CompleteLattice
 variable [CompleteLattice α]
 
 @[simp]
-theorem Ici_supₛ (S : Set α) : Ici (supₛ S) = ⨆ a ∈ S, Ici a :=
-  SetLike.ext fun c => by simp only [mem_Ici_iff, mem_supᵢ_iff, supₛ_le_iff]
-#align upper_set.Ici_Sup UpperSet.Ici_supₛ
+theorem Ici_sSup (S : Set α) : Ici (sSup S) = ⨆ a ∈ S, Ici a :=
+  SetLike.ext fun c => by simp only [mem_Ici_iff, mem_iSup_iff, sSup_le_iff]
+#align upper_set.Ici_Sup UpperSet.Ici_sSup
 
 @[simp]
-theorem Ici_supᵢ (f : ι → α) : Ici (⨆ i, f i) = ⨆ i, Ici (f i) :=
-  SetLike.ext fun c => by simp only [mem_Ici_iff, mem_supᵢ_iff, supᵢ_le_iff]
-#align upper_set.Ici_supr UpperSet.Ici_supᵢ
+theorem Ici_iSup (f : ι → α) : Ici (⨆ i, f i) = ⨆ i, Ici (f i) :=
+  SetLike.ext fun c => by simp only [mem_Ici_iff, mem_iSup_iff, iSup_le_iff]
+#align upper_set.Ici_supr UpperSet.Ici_iSup
 
 -- porting note: no longer a @[simp]
-theorem Ici_supᵢ₂ (f : ∀ i, κ i → α) : Ici (⨆ (i) (j), f i j) = ⨆ (i) (j), Ici (f i j) := by
-  simp_rw [Ici_supᵢ]
-#align upper_set.Ici_supr₂ UpperSet.Ici_supᵢ₂
+theorem Ici_iSup₂ (f : ∀ i, κ i → α) : Ici (⨆ (i) (j), f i j) = ⨆ (i) (j), Ici (f i j) := by
+  simp_rw [Ici_iSup]
+#align upper_set.Ici_supr₂ UpperSet.Ici_iSup₂
 
 end CompleteLattice
 
@@ -1235,19 +1235,19 @@ section CompleteLattice
 variable [CompleteLattice α]
 
 @[simp]
-theorem Iic_infₛ (S : Set α) : Iic (infₛ S) = ⨅ a ∈ S, Iic a :=
-  SetLike.ext fun c => by simp only [mem_Iic_iff, mem_infᵢ₂_iff, le_infₛ_iff]
-#align lower_set.Iic_Inf LowerSet.Iic_infₛ
+theorem Iic_sInf (S : Set α) : Iic (sInf S) = ⨅ a ∈ S, Iic a :=
+  SetLike.ext fun c => by simp only [mem_Iic_iff, mem_iInf₂_iff, le_sInf_iff]
+#align lower_set.Iic_Inf LowerSet.Iic_sInf
 
 @[simp]
-theorem Iic_infᵢ (f : ι → α) : Iic (⨅ i, f i) = ⨅ i, Iic (f i) :=
-  SetLike.ext fun c => by simp only [mem_Iic_iff, mem_infᵢ_iff, le_infᵢ_iff]
-#align lower_set.Iic_infi LowerSet.Iic_infᵢ
+theorem Iic_iInf (f : ι → α) : Iic (⨅ i, f i) = ⨅ i, Iic (f i) :=
+  SetLike.ext fun c => by simp only [mem_Iic_iff, mem_iInf_iff, le_iInf_iff]
+#align lower_set.Iic_infi LowerSet.Iic_iInf
 
 -- porting note: no longer a @[simp]
-theorem Iic_infᵢ₂ (f : ∀ i, κ i → α) : Iic (⨅ (i) (j), f i j) = ⨅ (i) (j), Iic (f i j) := by
-  simp_rw [Iic_infᵢ]
-#align lower_set.Iic_infi₂ LowerSet.Iic_infᵢ₂
+theorem Iic_iInf₂ (f : ∀ i, κ i → α) : Iic (⨅ (i) (j), f i j) = ⨅ (i) (j), Iic (f i j) := by
+  simp_rw [Iic_iInf]
+#align lower_set.Iic_infi₂ LowerSet.Iic_iInf₂
 
 end CompleteLattice
 
@@ -1341,16 +1341,16 @@ theorem lowerClosure_image (f : α ≃o β) :
 #align lower_closure_image lowerClosure_image
 
 @[simp]
-theorem UpperSet.infᵢ_Ici (s : Set α) : (⨅ a ∈ s, UpperSet.Ici a) = upperClosure s := by
+theorem UpperSet.iInf_Ici (s : Set α) : (⨅ a ∈ s, UpperSet.Ici a) = upperClosure s := by
   ext
   simp
-#align upper_set.infi_Ici UpperSet.infᵢ_Ici
+#align upper_set.infi_Ici UpperSet.iInf_Ici
 
 @[simp]
-theorem LowerSet.supᵢ_Iic (s : Set α) : (⨆ a ∈ s, LowerSet.Iic a) = lowerClosure s := by
+theorem LowerSet.iSup_Iic (s : Set α) : (⨆ a ∈ s, LowerSet.Iic a) = lowerClosure s := by
   ext
   simp
-#align lower_set.supr_Iic LowerSet.supᵢ_Iic
+#align lower_set.supr_Iic LowerSet.iSup_Iic
 
 theorem gc_upperClosure_coe :
     GaloisConnection (toDual ∘ upperClosure : Set α → (UpperSet α)ᵒᵈ) ((↑) ∘ ofDual) := fun _s t =>
@@ -1442,24 +1442,24 @@ theorem lowerClosure_union (s t : Set α) : lowerClosure (s ∪ t) = lowerClosur
 #align lower_closure_union lowerClosure_union
 
 @[simp]
-theorem upperClosure_unionᵢ (f : ι → Set α) : upperClosure (⋃ i, f i) = ⨅ i, upperClosure (f i) :=
-  (@gc_upperClosure_coe α _).l_supᵢ
-#align upper_closure_Union upperClosure_unionᵢ
+theorem upperClosure_iUnion (f : ι → Set α) : upperClosure (⋃ i, f i) = ⨅ i, upperClosure (f i) :=
+  (@gc_upperClosure_coe α _).l_iSup
+#align upper_closure_Union upperClosure_iUnion
 
 @[simp]
-theorem lowerClosure_unionᵢ (f : ι → Set α) : lowerClosure (⋃ i, f i) = ⨆ i, lowerClosure (f i) :=
-  (@gc_lowerClosure_coe α _).l_supᵢ
-#align lower_closure_Union lowerClosure_unionᵢ
+theorem lowerClosure_iUnion (f : ι → Set α) : lowerClosure (⋃ i, f i) = ⨆ i, lowerClosure (f i) :=
+  (@gc_lowerClosure_coe α _).l_iSup
+#align lower_closure_Union lowerClosure_iUnion
 
 @[simp]
-theorem upperClosure_unionₛ (S : Set (Set α)) : upperClosure (⋃₀ S) = ⨅ s ∈ S, upperClosure s := by
-  simp_rw [unionₛ_eq_bunionᵢ, upperClosure_unionᵢ]
-#align upper_closure_sUnion upperClosure_unionₛ
+theorem upperClosure_sUnion (S : Set (Set α)) : upperClosure (⋃₀ S) = ⨅ s ∈ S, upperClosure s := by
+  simp_rw [sUnion_eq_biUnion, upperClosure_iUnion]
+#align upper_closure_sUnion upperClosure_sUnion
 
 @[simp]
-theorem lowerClosure_unionₛ (S : Set (Set α)) : lowerClosure (⋃₀ S) = ⨆ s ∈ S, lowerClosure s := by
-  simp_rw [unionₛ_eq_bunionᵢ, lowerClosure_unionᵢ]
-#align lower_closure_sUnion lowerClosure_unionₛ
+theorem lowerClosure_sUnion (S : Set (Set α)) : lowerClosure (⋃₀ S) = ⨆ s ∈ S, lowerClosure s := by
+  simp_rw [sUnion_eq_biUnion, lowerClosure_iUnion]
+#align lower_closure_sUnion lowerClosure_sUnion
 
 theorem Set.OrdConnected.upperClosure_inter_lowerClosure (h : s.OrdConnected) :
     ↑(upperClosure s) ∩ ↑(lowerClosure s) = s :=

Match https://github.com/leanprover-community/mathlib/pull/18637

order.upper_lower.basic@59694bd07f0a39c5beccba34bd9f413a160782bf..e9ce88cd0d54891c714c604076084f763dd480ed

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies, Sara Rousta
 
 ! This file was ported from Lean 3 source module order.upper_lower.basic
-! leanprover-community/mathlib commit 59694bd07f0a39c5beccba34bd9f413a160782bf
+! leanprover-community/mathlib commit e9ce88cd0d54891c714c604076084f763dd480ed
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1474,6 +1474,37 @@ theorem ordConnected_iff_upperClosure_inter_lowerClosure :
   exact (UpperSet.upper _).ordConnected.inter (LowerSet.lower _).ordConnected
 #align ord_connected_iff_upper_closure_inter_lower_closure ordConnected_iff_upperClosure_inter_lowerClosure
 
+@[simp]
+theorem upperBounds_lowerClosure : upperBounds (lowerClosure s : Set α) = upperBounds s :=
+  (upperBounds_mono_set subset_lowerClosure).antisymm λ _a ha _b ⟨_c, hc, hcb⟩ => hcb.trans <| ha hc
+#align upper_bounds_lower_closure upperBounds_lowerClosure
+
+@[simp]
+theorem lowerBounds_upperClosure : lowerBounds (upperClosure s : Set α) = lowerBounds s :=
+  (lowerBounds_mono_set subset_upperClosure).antisymm λ _a ha _b ⟨_c, hc, hcb⟩ => (ha hc).trans hcb
+#align lower_bounds_upper_closure lowerBounds_upperClosure
+
+@[simp]
+theorem bddAbove_lowerClosure : BddAbove (lowerClosure s : Set α) ↔ BddAbove s := by
+  simp_rw [BddAbove, upperBounds_lowerClosure]
+#align bdd_above_lower_closure bddAbove_lowerClosure
+
+@[simp]
+theorem bddBelow_upperClosure : BddBelow (upperClosure s : Set α) ↔ BddBelow s := by
+  simp_rw [BddBelow, lowerBounds_upperClosure]
+#align bdd_below_upper_closure bddBelow_upperClosure
+
+alias bddAbove_lowerClosure ↔ BddAbove.of_lowerClosure BddAbove.lowerClosure
+#align bdd_above.of_lower_closure BddAbove.of_lowerClosure
+#align bdd_above.lower_closure BddAbove.lowerClosure
+
+alias bddBelow_upperClosure ↔ BddBelow.of_upperClosure BddBelow.upperClosure
+#align bdd_below.of_upper_closure BddBelow.of_upperClosure
+#align bdd_below.upper_closure BddBelow.upperClosure
+
+-- Porting note: attribute [protected] doesn't work
+-- attribute protected BddAbove.lowerClosure BddBelow.upperClosure
+
 end closure
 
 /-! ### Product -/

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

I think I got all of the monos.

@@ -1569,7 +1569,7 @@ theorem prod_sup_prod : s₁ ×ᵘˢ t₁ ⊔ s₂ ×ᵘˢ t₂ = (s₁ ⊔ s₂
 
 variable {s s₁ s₂ t t₁ t₂}
 
--- porting note: todo: add `@[mono]`
+@[mono]
 theorem prod_mono : s₁ ≤ s₂ → t₁ ≤ t₂ → s₁ ×ᵘˢ t₁ ≤ s₂ ×ᵘˢ t₂ :=
   Set.prod_mono
 #align upper_set.prod_mono UpperSet.prod_mono

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

@@ -483,10 +483,10 @@ namespace UpperSet
 
 variable {S : Set (UpperSet α)} {s t : UpperSet α} {a : α}
 
-instance : HasSup (UpperSet α) :=
+instance : Sup (UpperSet α) :=
   ⟨fun s t => ⟨s ∩ t, s.upper.inter t.upper⟩⟩
 
-instance : HasInf (UpperSet α) :=
+instance : Inf (UpperSet α) :=
   ⟨fun s t => ⟨s ∪ t, s.upper.union t.upper⟩⟩
 
 instance : Top (UpperSet α) :=
@@ -632,10 +632,10 @@ namespace LowerSet
 
 variable {S : Set (LowerSet α)} {s t : LowerSet α} {a : α}
 
-instance : HasSup (LowerSet α) :=
+instance : Sup (LowerSet α) :=
   ⟨fun s t => ⟨s ∪ t, fun _ _ h => Or.imp (s.lower h) (t.lower h)⟩⟩
 
-instance : HasInf (LowerSet α) :=
+instance : Inf (LowerSet α) :=
   ⟨fun s t => ⟨s ∩ t, fun _ _ h => And.imp (s.lower h) (t.lower h)⟩⟩
 
 instance : Top (LowerSet α) :=

@@ -424,6 +424,11 @@ theorem ext {s t : UpperSet α} : (s : Set α) = t → s = t :=
   SetLike.ext'
 #align upper_set.ext UpperSet.ext
 
+/-- See Note [custom simps projection]. -/
+def Simps.coe (s : UpperSet α) : Set α := s
+
+initialize_simps_projections UpperSet (carrier → coe)
+
 @[simp]
 theorem carrier_eq_coe (s : UpperSet α) : s.carrier = s :=
   rfl
@@ -446,6 +451,11 @@ instance : SetLike (LowerSet α) α where
   coe := LowerSet.carrier
   coe_injective' s t h := by cases s; cases t; congr
 
+/-- See Note [custom simps projection]. -/
+def Simps.coe (s : LowerSet α) : Set α := s
+
+initialize_simps_projections LowerSet (carrier → coe)
+
 @[ext]
 theorem ext {s t : LowerSet α} : (s : Set α) = t → s = t :=
   SetLike.ext'