order.complete_lattice ⟷ Mathlib.Order.CompleteLattice

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

@@ -5,7 +5,7 @@ Authors: Johannes Hölzl
 -/
 import Data.Bool.Set
 import Data.Nat.Set
-import Data.Ulift
+import Data.ULift
 import Order.Bounds.Basic
 import Order.Hom.Basic
 

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

@@ -630,7 +630,7 @@ theorem sInf_eq_top : sInf s = ⊤ ↔ ∀ a ∈ s, a = ⊤ :=
 #print eq_singleton_bot_of_sSup_eq_bot_of_nonempty /-
 theorem eq_singleton_bot_of_sSup_eq_bot_of_nonempty {s : Set α} (h_sup : sSup s = ⊥)
     (hne : s.Nonempty) : s = {⊥} := by rw [Set.eq_singleton_iff_nonempty_unique_mem];
-  rw [sSup_eq_bot] at h_sup ; exact ⟨hne, h_sup⟩
+  rw [sSup_eq_bot] at h_sup; exact ⟨hne, h_sup⟩
 #align eq_singleton_bot_of_Sup_eq_bot_of_nonempty eq_singleton_bot_of_sSup_eq_bot_of_nonempty
 -/
 
@@ -1119,14 +1119,14 @@ theorem biInf_mono {p q : ι → Prop} (hpq : ∀ i, p i → q i) :
 #print iSup_le_iff /-
 @[simp]
 theorem iSup_le_iff : iSup f ≤ a ↔ ∀ i, f i ≤ a :=
-  (isLUB_le_iff isLUB_iSup).trans forall_range_iff
+  (isLUB_le_iff isLUB_iSup).trans forall_mem_range
 #align supr_le_iff iSup_le_iff
 -/
 
 #print le_iInf_iff /-
 @[simp]
 theorem le_iInf_iff : a ≤ iInf f ↔ ∀ i, a ≤ f i :=
-  (le_isGLB_iff isGLB_iInf).trans forall_range_iff
+  (le_isGLB_iff isGLB_iInf).trans forall_mem_range
 #align le_infi_iff le_iInf_iff
 -/
 
@@ -1354,14 +1354,14 @@ theorem iInf_top : (⨅ i : ι, ⊤ : α) = ⊤ :=
 #print iSup_eq_bot /-
 @[simp]
 theorem iSup_eq_bot : iSup s = ⊥ ↔ ∀ i, s i = ⊥ :=
-  sSup_eq_bot.trans forall_range_iff
+  sSup_eq_bot.trans forall_mem_range
 #align supr_eq_bot iSup_eq_bot
 -/
 
 #print iInf_eq_top /-
 @[simp]
 theorem iInf_eq_top : iInf s = ⊤ ↔ ∀ i, s i = ⊤ :=
-  sInf_eq_top.trans forall_range_iff
+  sInf_eq_top.trans forall_mem_range
 #align infi_eq_top iInf_eq_top
 -/
 
@@ -1416,7 +1416,7 @@ See `csupr_eq_of_forall_le_of_forall_lt_exists_gt` for a version in conditionall
 lattices. -/
 theorem iSup_eq_of_forall_le_of_forall_lt_exists_gt {f : ι → α} (h₁ : ∀ i, f i ≤ b)
     (h₂ : ∀ w, w < b → ∃ i, w < f i) : (⨆ i : ι, f i) = b :=
-  sSup_eq_of_forall_le_of_forall_lt_exists_gt (forall_range_iff.mpr h₁) fun w hw =>
+  sSup_eq_of_forall_le_of_forall_lt_exists_gt (forall_mem_range.mpr h₁) fun w hw =>
     exists_range_iff.mpr <| h₂ w hw
 #align supr_eq_of_forall_le_of_forall_lt_exists_gt iSup_eq_of_forall_le_of_forall_lt_exists_gt
 -/
@@ -2242,23 +2242,23 @@ end CompleteLinearOrder
 -/
 
 
-#print Prop.completeLattice /-
-instance Prop.completeLattice : CompleteLattice Prop :=
-  { Prop.boundedOrder,
-    Prop.distribLattice with
+#print Prop.instCompleteLattice /-
+instance Prop.instCompleteLattice : CompleteLattice Prop :=
+  { Prop.instBoundedOrder,
+    Prop.instDistribLattice with
     sSup := fun s => ∃ a ∈ s, a
     le_sup := fun s a h p => ⟨a, h, p⟩
     sup_le := fun s a h ⟨b, h', p⟩ => h b h' p
     sInf := fun s => ∀ a, a ∈ s → a
     inf_le := fun s a h p => p a h
     le_inf := fun s a h p b hb => h b hb p }
-#align Prop.complete_lattice Prop.completeLattice
+#align Prop.complete_lattice Prop.instCompleteLattice
 -/
 
-#print Prop.completeLinearOrder /-
-noncomputable instance Prop.completeLinearOrder : CompleteLinearOrder Prop :=
-  { Prop.completeLattice, Prop.linearOrder with }
-#align Prop.complete_linear_order Prop.completeLinearOrder
+#print Prop.instCompleteLinearOrder /-
+noncomputable instance Prop.instCompleteLinearOrder : CompleteLinearOrder Prop :=
+  { Prop.instCompleteLattice, Prop.linearOrder with }
+#align Prop.complete_linear_order Prop.instCompleteLinearOrder
 -/
 
 #print sSup_Prop_eq /-
@@ -2302,8 +2302,8 @@ instance Pi.infSet {α : Type _} {β : α → Type _} [∀ i, InfSet (β i)] : I
 #align pi.has_Inf Pi.infSet
 -/
 
-#print Pi.completeLattice /-
-instance Pi.completeLattice {α : Type _} {β : α → Type _} [∀ i, CompleteLattice (β i)] :
+#print Pi.instCompleteLattice /-
+instance Pi.instCompleteLattice {α : Type _} {β : α → Type _} [∀ i, CompleteLattice (β i)] :
     CompleteLattice (∀ i, β i) :=
   { Pi.boundedOrder, Pi.lattice with
     sSup := sSup
@@ -2312,7 +2312,7 @@ instance Pi.completeLattice {α : Type _} {β : α → Type _} [∀ i, CompleteL
     inf_le := fun s f hf i => iInf_le (fun f : s => (f : ∀ i, β i) i) ⟨f, hf⟩
     sup_le := fun s f hf i => iSup_le fun g => hf g g.2 i
     le_inf := fun s f hf i => le_iInf fun g => hf g g.2 i }
-#align pi.complete_lattice Pi.completeLattice
+#align pi.complete_lattice Pi.instCompleteLattice
 -/
 
 #print sSup_apply /-

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

@@ -414,10 +414,10 @@ def completeLatticeOfCompleteSemilatticeSup (α : Type _) [CompleteSemilatticeSu
 -/
 
 #print CompleteLinearOrder /-
-/- ./././Mathport/Syntax/Translate/Command.lean:433:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:429:11: unsupported: advanced extends in structure -/
 /-- A complete linear order is a linear order whose lattice structure is complete. -/
 class CompleteLinearOrder (α : Type _) extends CompleteLattice α,
-    "./././Mathport/Syntax/Translate/Command.lean:433:11: unsupported: advanced extends in structure"
+    "./././Mathport/Syntax/Translate/Command.lean:429:11: unsupported: advanced extends in structure"
 #align complete_linear_order CompleteLinearOrder
 -/
 
@@ -1968,10 +1968,10 @@ theorem iSup_of_empty' {α ι} [SupSet α] [IsEmpty ι] (f : ι → α) : iSup f
 #align supr_of_empty' iSup_of_empty'
 -/
 
-#print iInf_of_empty' /-
-theorem iInf_of_empty' {α ι} [InfSet α] [IsEmpty ι] (f : ι → α) : iInf f = sInf (∅ : Set α) :=
+#print iInf_of_isEmpty /-
+theorem iInf_of_isEmpty {α ι} [InfSet α] [IsEmpty ι] (f : ι → α) : iInf f = sInf (∅ : Set α) :=
   congr_arg sInf (range_eq_empty f)
-#align infi_of_empty' iInf_of_empty'
+#align infi_of_empty' iInf_of_isEmpty
 -/
 
 #print iSup_of_empty /-

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

@@ -414,10 +414,10 @@ def completeLatticeOfCompleteSemilatticeSup (α : Type _) [CompleteSemilatticeSu
 -/
 
 #print CompleteLinearOrder /-
-/- ./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:433:11: unsupported: advanced extends in structure -/
 /-- A complete linear order is a linear order whose lattice structure is complete. -/
 class CompleteLinearOrder (α : Type _) extends CompleteLattice α,
-    "./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure"
+    "./././Mathport/Syntax/Translate/Command.lean:433:11: unsupported: advanced extends in structure"
 #align complete_linear_order CompleteLinearOrder
 -/
 

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

@@ -3,11 +3,11 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 -/
-import Mathbin.Data.Bool.Set
-import Mathbin.Data.Nat.Set
-import Mathbin.Data.Ulift
-import Mathbin.Order.Bounds.Basic
-import Mathbin.Order.Hom.Basic
+import Data.Bool.Set
+import Data.Nat.Set
+import Data.Ulift
+import Order.Bounds.Basic
+import Order.Hom.Basic
 
 #align_import order.complete_lattice from "leanprover-community/mathlib"@"5709b0d8725255e76f47debca6400c07b5c2d8e6"
 
@@ -414,10 +414,10 @@ def completeLatticeOfCompleteSemilatticeSup (α : Type _) [CompleteSemilatticeSu
 -/
 
 #print CompleteLinearOrder /-
-/- ./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure -/
 /-- A complete linear order is a linear order whose lattice structure is complete. -/
 class CompleteLinearOrder (α : Type _) extends CompleteLattice α,
-    "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure"
+    "./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure"
 #align complete_linear_order CompleteLinearOrder
 -/
 

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

@@ -434,7 +434,7 @@ instance [CompleteLattice α] : CompleteLattice αᵒᵈ :=
     le_inf := @CompleteLattice.sup_le α _ }
 
 instance [CompleteLinearOrder α] : CompleteLinearOrder αᵒᵈ :=
-  { OrderDual.completeLattice α, OrderDual.linearOrder α with }
+  { OrderDual.completeLattice α, OrderDual.instLinearOrder α with }
 
 end OrderDual
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module order.complete_lattice
-! leanprover-community/mathlib commit 5709b0d8725255e76f47debca6400c07b5c2d8e6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Bool.Set
 import Mathbin.Data.Nat.Set
@@ -14,6 +9,8 @@ import Mathbin.Data.Ulift
 import Mathbin.Order.Bounds.Basic
 import Mathbin.Order.Hom.Basic
 
+#align_import order.complete_lattice from "leanprover-community/mathlib"@"5709b0d8725255e76f47debca6400c07b5c2d8e6"
+
 /-!
 # Theory of complete lattices
 

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

@@ -104,10 +104,8 @@ instance (priority := 50) supSet_to_nonempty (α) [SupSet α] : Nonempty α :=
 #align has_Sup_to_nonempty supSet_to_nonempty
 -/
 
--- mathport name: «expr⨆ , »
 notation3"⨆ "(...)", "r:(scoped f => iSup f) => r
 
--- mathport name: «expr⨅ , »
 notation3"⨅ "(...)", "r:(scoped f => iInf f) => r
 
 instance (α) [InfSet α] : SupSet αᵒᵈ :=
@@ -132,55 +130,77 @@ section
 
 variable [CompleteSemilatticeSup α] {s t : Set α} {a b : α}
 
+#print le_sSup /-
 @[ematch]
 theorem le_sSup : a ∈ s → a ≤ sSup s :=
   CompleteSemilatticeSup.le_sup s a
 #align le_Sup le_sSup
+-/
 
+#print sSup_le /-
 theorem sSup_le : (∀ b ∈ s, b ≤ a) → sSup s ≤ a :=
   CompleteSemilatticeSup.sup_le s a
 #align Sup_le sSup_le
+-/
 
+#print isLUB_sSup /-
 theorem isLUB_sSup (s : Set α) : IsLUB s (sSup s) :=
   ⟨fun x => le_sSup, fun x => sSup_le⟩
 #align is_lub_Sup isLUB_sSup
+-/
 
+#print IsLUB.sSup_eq /-
 theorem IsLUB.sSup_eq (h : IsLUB s a) : sSup s = a :=
   (isLUB_sSup s).unique h
 #align is_lub.Sup_eq IsLUB.sSup_eq
+-/
 
+#print le_sSup_of_le /-
 theorem le_sSup_of_le (hb : b ∈ s) (h : a ≤ b) : a ≤ sSup s :=
   le_trans h (le_sSup hb)
 #align le_Sup_of_le le_sSup_of_le
+-/
 
+#print sSup_le_sSup /-
 theorem sSup_le_sSup (h : s ⊆ t) : sSup s ≤ sSup t :=
   (isLUB_sSup s).mono (isLUB_sSup t) h
 #align Sup_le_Sup sSup_le_sSup
+-/
 
+#print sSup_le_iff /-
 @[simp]
 theorem sSup_le_iff : sSup s ≤ a ↔ ∀ b ∈ s, b ≤ a :=
   isLUB_le_iff (isLUB_sSup s)
 #align Sup_le_iff sSup_le_iff
+-/
 
+#print le_sSup_iff /-
 theorem le_sSup_iff : a ≤ sSup s ↔ ∀ b ∈ upperBounds s, a ≤ b :=
   ⟨fun h b hb => le_trans h (sSup_le hb), fun hb => hb _ fun x => le_sSup⟩
 #align le_Sup_iff le_sSup_iff
+-/
 
+#print le_iSup_iff /-
 theorem le_iSup_iff {s : ι → α} : a ≤ iSup s ↔ ∀ b, (∀ i, s i ≤ b) → a ≤ b := by
   simp [iSup, le_sSup_iff, upperBounds]
 #align le_supr_iff le_iSup_iff
+-/
 
+#print sSup_le_sSup_of_forall_exists_le /-
 theorem sSup_le_sSup_of_forall_exists_le (h : ∀ x ∈ s, ∃ y ∈ t, x ≤ y) : sSup s ≤ sSup t :=
   le_sSup_iff.2 fun b hb =>
     sSup_le fun a ha =>
       let ⟨c, hct, hac⟩ := h a ha
       hac.trans (hb hct)
 #align Sup_le_Sup_of_forall_exists_le sSup_le_sSup_of_forall_exists_le
+-/
 
+#print sSup_singleton /-
 -- We will generalize this to conditionally complete lattices in `cSup_singleton`.
 theorem sSup_singleton {a : α} : sSup {a} = a :=
   isLUB_singleton.sSup_eq
 #align Sup_singleton sSup_singleton
+-/
 
 end
 
@@ -200,44 +220,63 @@ section
 
 variable [CompleteSemilatticeInf α] {s t : Set α} {a b : α}
 
+#print sInf_le /-
 @[ematch]
 theorem sInf_le : a ∈ s → sInf s ≤ a :=
   CompleteSemilatticeInf.inf_le s a
 #align Inf_le sInf_le
+-/
 
+#print le_sInf /-
 theorem le_sInf : (∀ b ∈ s, a ≤ b) → a ≤ sInf s :=
   CompleteSemilatticeInf.le_inf s a
 #align le_Inf le_sInf
+-/
 
+#print isGLB_sInf /-
 theorem isGLB_sInf (s : Set α) : IsGLB s (sInf s) :=
   ⟨fun a => sInf_le, fun a => le_sInf⟩
 #align is_glb_Inf isGLB_sInf
+-/
 
+#print IsGLB.sInf_eq /-
 theorem IsGLB.sInf_eq (h : IsGLB s a) : sInf s = a :=
   (isGLB_sInf s).unique h
 #align is_glb.Inf_eq IsGLB.sInf_eq
+-/
 
+#print sInf_le_of_le /-
 theorem sInf_le_of_le (hb : b ∈ s) (h : b ≤ a) : sInf s ≤ a :=
   le_trans (sInf_le hb) h
 #align Inf_le_of_le sInf_le_of_le
+-/
 
+#print sInf_le_sInf /-
 theorem sInf_le_sInf (h : s ⊆ t) : sInf t ≤ sInf s :=
   (isGLB_sInf s).mono (isGLB_sInf t) h
 #align Inf_le_Inf sInf_le_sInf
+-/
 
+#print le_sInf_iff /-
 @[simp]
 theorem le_sInf_iff : a ≤ sInf s ↔ ∀ b ∈ s, a ≤ b :=
   le_isGLB_iff (isGLB_sInf s)
 #align le_Inf_iff le_sInf_iff
+-/
 
+#print sInf_le_iff /-
 theorem sInf_le_iff : sInf s ≤ a ↔ ∀ b ∈ lowerBounds s, b ≤ a :=
   ⟨fun h b hb => le_trans (le_sInf hb) h, fun hb => hb _ fun x => sInf_le⟩
 #align Inf_le_iff sInf_le_iff
+-/
 
+#print iInf_le_iff /-
 theorem iInf_le_iff {s : ι → α} : iInf s ≤ a ↔ ∀ b, (∀ i, b ≤ s i) → b ≤ a := by
   simp [iInf, sInf_le_iff, lowerBounds]
 #align infi_le_iff iInf_le_iff
+-/
 
+#print sInf_le_sInf_of_forall_exists_le /-
 theorem sInf_le_sInf_of_forall_exists_le (h : ∀ x ∈ s, ∃ y ∈ t, y ≤ x) : sInf t ≤ sInf s :=
   le_of_forall_le
     (by
@@ -246,11 +285,14 @@ theorem sInf_le_sInf_of_forall_exists_le (h : ∀ x ∈ s, ∃ y ∈ t, y ≤ x)
       rcases h _ h₁ with ⟨y, hy, hy'⟩
       solve_by_elim [le_trans _ hy'])
 #align Inf_le_Inf_of_forall_exists_le sInf_le_sInf_of_forall_exists_le
+-/
 
+#print sInf_singleton /-
 -- We will generalize this to conditionally complete lattices in `cInf_singleton`.
 theorem sInf_singleton {a : α} : sInf {a} = a :=
   isGLB_singleton.sInf_eq
 #align Inf_singleton sInf_singleton
+-/
 
 end
 
@@ -375,10 +417,10 @@ def completeLatticeOfCompleteSemilatticeSup (α : Type _) [CompleteSemilatticeSu
 -/
 
 #print CompleteLinearOrder /-
-/- ./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure -/
 /-- A complete linear order is a linear order whose lattice structure is complete. -/
 class CompleteLinearOrder (α : Type _) extends CompleteLattice α,
-    "./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure"
+    "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure"
 #align complete_linear_order CompleteLinearOrder
 -/
 
@@ -433,124 +475,175 @@ theorem ofDual_sInf (s : Set αᵒᵈ) : ofDual (sInf s) = sSup (toDual ⁻¹' s
 #align of_dual_Inf ofDual_sInf
 -/
 
+#print toDual_iSup /-
 @[simp]
 theorem toDual_iSup (f : ι → α) : toDual (⨆ i, f i) = ⨅ i, toDual (f i) :=
   rfl
 #align to_dual_supr toDual_iSup
+-/
 
+#print toDual_iInf /-
 @[simp]
 theorem toDual_iInf (f : ι → α) : toDual (⨅ i, f i) = ⨆ i, toDual (f i) :=
   rfl
 #align to_dual_infi toDual_iInf
+-/
 
+#print ofDual_iSup /-
 @[simp]
 theorem ofDual_iSup (f : ι → αᵒᵈ) : ofDual (⨆ i, f i) = ⨅ i, ofDual (f i) :=
   rfl
 #align of_dual_supr ofDual_iSup
+-/
 
+#print ofDual_iInf /-
 @[simp]
 theorem ofDual_iInf (f : ι → αᵒᵈ) : ofDual (⨅ i, f i) = ⨆ i, ofDual (f i) :=
   rfl
 #align of_dual_infi ofDual_iInf
+-/
 
+#print sInf_le_sSup /-
 theorem sInf_le_sSup (hs : s.Nonempty) : sInf s ≤ sSup s :=
   isGLB_le_isLUB (isGLB_sInf s) (isLUB_sSup s) hs
 #align Inf_le_Sup sInf_le_sSup
+-/
 
+#print sSup_union /-
 theorem sSup_union {s t : Set α} : sSup (s ∪ t) = sSup s ⊔ sSup t :=
   ((isLUB_sSup s).union (isLUB_sSup t)).sSup_eq
 #align Sup_union sSup_union
+-/
 
+#print sInf_union /-
 theorem sInf_union {s t : Set α} : sInf (s ∪ t) = sInf s ⊓ sInf t :=
   ((isGLB_sInf s).union (isGLB_sInf t)).sInf_eq
 #align Inf_union sInf_union
+-/
 
+#print sSup_inter_le /-
 theorem sSup_inter_le {s t : Set α} : sSup (s ∩ t) ≤ sSup s ⊓ sSup t :=
   sSup_le fun b hb => le_inf (le_sSup hb.1) (le_sSup hb.2)
 #align Sup_inter_le sSup_inter_le
+-/
 
+#print le_sInf_inter /-
 theorem le_sInf_inter {s t : Set α} : sInf s ⊔ sInf t ≤ sInf (s ∩ t) :=
   @sSup_inter_le αᵒᵈ _ _ _
 #align le_Inf_inter le_sInf_inter
+-/
 
+#print sSup_empty /-
 @[simp]
 theorem sSup_empty : sSup ∅ = (⊥ : α) :=
   (@isLUB_empty α _ _).sSup_eq
 #align Sup_empty sSup_empty
+-/
 
+#print sInf_empty /-
 @[simp]
 theorem sInf_empty : sInf ∅ = (⊤ : α) :=
   (@isGLB_empty α _ _).sInf_eq
 #align Inf_empty sInf_empty
+-/
 
+#print sSup_univ /-
 @[simp]
 theorem sSup_univ : sSup univ = (⊤ : α) :=
   (@isLUB_univ α _ _).sSup_eq
 #align Sup_univ sSup_univ
+-/
 
+#print sInf_univ /-
 @[simp]
 theorem sInf_univ : sInf univ = (⊥ : α) :=
   (@isGLB_univ α _ _).sInf_eq
 #align Inf_univ sInf_univ
+-/
 
+#print sSup_insert /-
 -- TODO(Jeremy): get this automatically
 @[simp]
 theorem sSup_insert {a : α} {s : Set α} : sSup (insert a s) = a ⊔ sSup s :=
   ((isLUB_sSup s).insert a).sSup_eq
 #align Sup_insert sSup_insert
+-/
 
+#print sInf_insert /-
 @[simp]
 theorem sInf_insert {a : α} {s : Set α} : sInf (insert a s) = a ⊓ sInf s :=
   ((isGLB_sInf s).insert a).sInf_eq
 #align Inf_insert sInf_insert
+-/
 
+#print sSup_le_sSup_of_subset_insert_bot /-
 theorem sSup_le_sSup_of_subset_insert_bot (h : s ⊆ insert ⊥ t) : sSup s ≤ sSup t :=
   le_trans (sSup_le_sSup h) (le_of_eq (trans sSup_insert bot_sup_eq))
 #align Sup_le_Sup_of_subset_insert_bot sSup_le_sSup_of_subset_insert_bot
+-/
 
+#print sInf_le_sInf_of_subset_insert_top /-
 theorem sInf_le_sInf_of_subset_insert_top (h : s ⊆ insert ⊤ t) : sInf t ≤ sInf s :=
   le_trans (le_of_eq (trans top_inf_eq.symm sInf_insert.symm)) (sInf_le_sInf h)
 #align Inf_le_Inf_of_subset_insert_top sInf_le_sInf_of_subset_insert_top
+-/
 
+#print sSup_diff_singleton_bot /-
 @[simp]
 theorem sSup_diff_singleton_bot (s : Set α) : sSup (s \ {⊥}) = sSup s :=
   (sSup_le_sSup (diff_subset _ _)).antisymm <|
     sSup_le_sSup_of_subset_insert_bot <| subset_insert_diff_singleton _ _
 #align Sup_diff_singleton_bot sSup_diff_singleton_bot
+-/
 
+#print sInf_diff_singleton_top /-
 @[simp]
 theorem sInf_diff_singleton_top (s : Set α) : sInf (s \ {⊤}) = sInf s :=
   @sSup_diff_singleton_bot αᵒᵈ _ s
 #align Inf_diff_singleton_top sInf_diff_singleton_top
+-/
 
+#print sSup_pair /-
 theorem sSup_pair {a b : α} : sSup {a, b} = a ⊔ b :=
   (@isLUB_pair α _ a b).sSup_eq
 #align Sup_pair sSup_pair
+-/
 
+#print sInf_pair /-
 theorem sInf_pair {a b : α} : sInf {a, b} = a ⊓ b :=
   (@isGLB_pair α _ a b).sInf_eq
 #align Inf_pair sInf_pair
+-/
 
+#print sSup_eq_bot /-
 @[simp]
 theorem sSup_eq_bot : sSup s = ⊥ ↔ ∀ a ∈ s, a = ⊥ :=
   ⟨fun h a ha => bot_unique <| h ▸ le_sSup ha, fun h =>
     bot_unique <| sSup_le fun a ha => le_bot_iff.2 <| h a ha⟩
 #align Sup_eq_bot sSup_eq_bot
+-/
 
+#print sInf_eq_top /-
 @[simp]
 theorem sInf_eq_top : sInf s = ⊤ ↔ ∀ a ∈ s, a = ⊤ :=
   @sSup_eq_bot αᵒᵈ _ _
 #align Inf_eq_top sInf_eq_top
+-/
 
+#print eq_singleton_bot_of_sSup_eq_bot_of_nonempty /-
 theorem eq_singleton_bot_of_sSup_eq_bot_of_nonempty {s : Set α} (h_sup : sSup s = ⊥)
     (hne : s.Nonempty) : s = {⊥} := by rw [Set.eq_singleton_iff_nonempty_unique_mem];
   rw [sSup_eq_bot] at h_sup ; exact ⟨hne, h_sup⟩
 #align eq_singleton_bot_of_Sup_eq_bot_of_nonempty eq_singleton_bot_of_sSup_eq_bot_of_nonempty
+-/
 
+#print eq_singleton_top_of_sInf_eq_top_of_nonempty /-
 theorem eq_singleton_top_of_sInf_eq_top_of_nonempty : sInf s = ⊤ → s.Nonempty → s = {⊤} :=
   @eq_singleton_bot_of_sSup_eq_bot_of_nonempty αᵒᵈ _ _
 #align eq_singleton_top_of_Inf_eq_top_of_nonempty eq_singleton_top_of_sInf_eq_top_of_nonempty
+-/
 
+#print sSup_eq_of_forall_le_of_forall_lt_exists_gt /-
 /-- Introduction rule to prove that `b` is the supremum of `s`: it suffices to check that `b`
 is larger than all elements of `s`, and that this is not the case of any `w < b`.
 See `cSup_eq_of_forall_le_of_forall_lt_exists_gt` for a version in conditionally complete
@@ -561,7 +654,9 @@ theorem sSup_eq_of_forall_le_of_forall_lt_exists_gt (h₁ : ∀ a ∈ s, a ≤ b
     let ⟨a, ha, ha'⟩ := h₂ _ h
     ((le_sSup ha).trans_lt ha').False
 #align Sup_eq_of_forall_le_of_forall_lt_exists_gt sSup_eq_of_forall_le_of_forall_lt_exists_gt
+-/
 
+#print sInf_eq_of_forall_ge_of_forall_gt_exists_lt /-
 /-- Introduction rule to prove that `b` is the infimum of `s`: it suffices to check that `b`
 is smaller than all elements of `s`, and that this is not the case of any `w > b`.
 See `cInf_eq_of_forall_ge_of_forall_gt_exists_lt` for a version in conditionally complete
@@ -570,6 +665,7 @@ theorem sInf_eq_of_forall_ge_of_forall_gt_exists_lt :
     (∀ a ∈ s, b ≤ a) → (∀ w, b < w → ∃ a ∈ s, a < w) → sInf s = b :=
   @sSup_eq_of_forall_le_of_forall_lt_exists_gt αᵒᵈ _ _ _
 #align Inf_eq_of_forall_ge_of_forall_gt_exists_lt sInf_eq_of_forall_ge_of_forall_gt_exists_lt
+-/
 
 end
 
@@ -577,14 +673,19 @@ section CompleteLinearOrder
 
 variable [CompleteLinearOrder α] {s t : Set α} {a b : α}
 
+#print lt_sSup_iff /-
 theorem lt_sSup_iff : b < sSup s ↔ ∃ a ∈ s, b < a :=
   lt_isLUB_iff <| isLUB_sSup s
 #align lt_Sup_iff lt_sSup_iff
+-/
 
+#print sInf_lt_iff /-
 theorem sInf_lt_iff : sInf s < b ↔ ∃ a ∈ s, a < b :=
   isGLB_lt_iff <| isGLB_sInf s
 #align Inf_lt_iff sInf_lt_iff
+-/
 
+#print sSup_eq_top /-
 theorem sSup_eq_top : sSup s = ⊤ ↔ ∀ b < ⊤, ∃ a ∈ s, b < a :=
   ⟨fun h b hb => lt_sSup_iff.1 <| hb.trans_eq h.symm, fun h =>
     top_unique <|
@@ -592,18 +693,25 @@ theorem sSup_eq_top : sSup s = ⊤ ↔ ∀ b < ⊤, ∃ a ∈ s, b < a :=
         let ⟨a, ha, h⟩ := h _ h'
         (h.trans_le <| le_sSup ha).False⟩
 #align Sup_eq_top sSup_eq_top
+-/
 
+#print sInf_eq_bot /-
 theorem sInf_eq_bot : sInf s = ⊥ ↔ ∀ b > ⊥, ∃ a ∈ s, a < b :=
   @sSup_eq_top αᵒᵈ _ _
 #align Inf_eq_bot sInf_eq_bot
+-/
 
+#print lt_iSup_iff /-
 theorem lt_iSup_iff {f : ι → α} : a < iSup f ↔ ∃ i, a < f i :=
   lt_sSup_iff.trans exists_range_iff
 #align lt_supr_iff lt_iSup_iff
+-/
 
+#print iInf_lt_iff /-
 theorem iInf_lt_iff {f : ι → α} : iInf f < a ↔ ∃ i, f i < a :=
   sInf_lt_iff.trans exists_range_iff
 #align infi_lt_iff iInf_lt_iff
+-/
 
 end CompleteLinearOrder
 
@@ -614,36 +722,48 @@ section SupSet
 
 variable [SupSet α] {f g : ι → α}
 
+#print sSup_range /-
 theorem sSup_range : sSup (range f) = iSup f :=
   rfl
 #align Sup_range sSup_range
+-/
 
 #print sSup_eq_iSup' /-
 theorem sSup_eq_iSup' (s : Set α) : sSup s = ⨆ a : s, a := by rw [iSup, Subtype.range_coe]
 #align Sup_eq_supr' sSup_eq_iSup'
 -/
 
+#print iSup_congr /-
 theorem iSup_congr (h : ∀ i, f i = g i) : (⨆ i, f i) = ⨆ i, g i :=
   congr_arg _ <| funext h
 #align supr_congr iSup_congr
+-/
 
+#print Function.Surjective.iSup_comp /-
 theorem Function.Surjective.iSup_comp {f : ι → ι'} (hf : Surjective f) (g : ι' → α) :
     (⨆ x, g (f x)) = ⨆ y, g y := by simp only [iSup, hf.range_comp]
 #align function.surjective.supr_comp Function.Surjective.iSup_comp
+-/
 
+#print Equiv.iSup_comp /-
 theorem Equiv.iSup_comp {g : ι' → α} (e : ι ≃ ι') : (⨆ x, g (e x)) = ⨆ y, g y :=
   e.Surjective.iSup_comp _
 #align equiv.supr_comp Equiv.iSup_comp
+-/
 
+#print Function.Surjective.iSup_congr /-
 protected theorem Function.Surjective.iSup_congr {g : ι' → α} (h : ι → ι') (h1 : Surjective h)
     (h2 : ∀ x, g (h x) = f x) : (⨆ x, f x) = ⨆ y, g y := by convert h1.supr_comp g;
   exact (funext h2).symm
 #align function.surjective.supr_congr Function.Surjective.iSup_congr
+-/
 
+#print Equiv.iSup_congr /-
 protected theorem Equiv.iSup_congr {g : ι' → α} (e : ι ≃ ι') (h : ∀ x, g (e x) = f x) :
     (⨆ x, f x) = ⨆ y, g y :=
   e.Surjective.iSup_congr _ h
 #align equiv.supr_congr Equiv.iSup_congr
+-/
 
 #print iSup_congr_Prop /-
 @[congr]
@@ -659,13 +779,17 @@ theorem iSup_plift_up (f : PLift ι → α) : (⨆ i, f (PLift.up i)) = ⨆ i, f
 #align supr_plift_up iSup_plift_up
 -/
 
+#print iSup_plift_down /-
 theorem iSup_plift_down (f : ι → α) : (⨆ i, f (PLift.down i)) = ⨆ i, f i :=
   PLift.down_surjective.iSup_congr _ fun _ => rfl
 #align supr_plift_down iSup_plift_down
+-/
 
+#print iSup_range' /-
 theorem iSup_range' (g : β → α) (f : ι → β) : (⨆ b : range f, g b) = ⨆ i, g (f i) := by
   rw [iSup, iSup, ← image_eq_range, ← range_comp]
 #align supr_range' iSup_range'
+-/
 
 #print sSup_image' /-
 theorem sSup_image' {s : Set β} {f : β → α} : sSup (f '' s) = ⨆ a : s, f a := by
@@ -679,9 +803,11 @@ section InfSet
 
 variable [InfSet α] {f g : ι → α}
 
+#print sInf_range /-
 theorem sInf_range : sInf (range f) = iInf f :=
   rfl
 #align Inf_range sInf_range
+-/
 
 #print sInf_eq_iInf' /-
 theorem sInf_eq_iInf' (s : Set α) : sInf s = ⨅ a : s, a :=
@@ -689,28 +815,38 @@ theorem sInf_eq_iInf' (s : Set α) : sInf s = ⨅ a : s, a :=
 #align Inf_eq_infi' sInf_eq_iInf'
 -/
 
+#print iInf_congr /-
 theorem iInf_congr (h : ∀ i, f i = g i) : (⨅ i, f i) = ⨅ i, g i :=
   congr_arg _ <| funext h
 #align infi_congr iInf_congr
+-/
 
+#print Function.Surjective.iInf_comp /-
 theorem Function.Surjective.iInf_comp {f : ι → ι'} (hf : Surjective f) (g : ι' → α) :
     (⨅ x, g (f x)) = ⨅ y, g y :=
   @Function.Surjective.iSup_comp αᵒᵈ _ _ _ f hf g
 #align function.surjective.infi_comp Function.Surjective.iInf_comp
+-/
 
+#print Equiv.iInf_comp /-
 theorem Equiv.iInf_comp {g : ι' → α} (e : ι ≃ ι') : (⨅ x, g (e x)) = ⨅ y, g y :=
   @Equiv.iSup_comp αᵒᵈ _ _ _ _ e
 #align equiv.infi_comp Equiv.iInf_comp
+-/
 
+#print Function.Surjective.iInf_congr /-
 protected theorem Function.Surjective.iInf_congr {g : ι' → α} (h : ι → ι') (h1 : Surjective h)
     (h2 : ∀ x, g (h x) = f x) : (⨅ x, f x) = ⨅ y, g y :=
   @Function.Surjective.iSup_congr αᵒᵈ _ _ _ _ _ h h1 h2
 #align function.surjective.infi_congr Function.Surjective.iInf_congr
+-/
 
+#print Equiv.iInf_congr /-
 protected theorem Equiv.iInf_congr {g : ι' → α} (e : ι ≃ ι') (h : ∀ x, g (e x) = f x) :
     (⨅ x, f x) = ⨅ y, g y :=
   @Equiv.iSup_congr αᵒᵈ _ _ _ _ _ e h
 #align equiv.infi_congr Equiv.iInf_congr
+-/
 
 #print iInf_congr_Prop /-
 @[congr]
@@ -726,13 +862,17 @@ theorem iInf_plift_up (f : PLift ι → α) : (⨅ i, f (PLift.up i)) = ⨅ i, f
 #align infi_plift_up iInf_plift_up
 -/
 
+#print iInf_plift_down /-
 theorem iInf_plift_down (f : ι → α) : (⨅ i, f (PLift.down i)) = ⨅ i, f i :=
   PLift.down_surjective.iInf_congr _ fun _ => rfl
 #align infi_plift_down iInf_plift_down
+-/
 
+#print iInf_range' /-
 theorem iInf_range' (g : β → α) (f : ι → β) : (⨅ b : range f, g b) = ⨅ i, g (f i) :=
   @iSup_range' αᵒᵈ _ _ _ _ _
 #align infi_range' iInf_range'
+-/
 
 #print sInf_image' /-
 theorem sInf_image' {s : Set β} {f : β → α} : sInf (f '' s) = ⨅ a : s, f a :=
@@ -746,26 +886,35 @@ section
 
 variable [CompleteLattice α] {f g s t : ι → α} {a b : α}
 
+#print le_iSup /-
 -- TODO: this declaration gives error when starting smt state
 --@[ematch]
 theorem le_iSup (f : ι → α) (i : ι) : f i ≤ iSup f :=
   le_sSup ⟨i, rfl⟩
 #align le_supr le_iSup
+-/
 
+#print iInf_le /-
 theorem iInf_le (f : ι → α) (i : ι) : iInf f ≤ f i :=
   sInf_le ⟨i, rfl⟩
 #align infi_le iInf_le
+-/
 
+#print le_iSup' /-
 @[ematch]
 theorem le_iSup' (f : ι → α) (i : ι) : f i ≤ iSup f :=
   le_sSup ⟨i, rfl⟩
 #align le_supr' le_iSup'
+-/
 
+#print iInf_le' /-
 @[ematch]
 theorem iInf_le' (f : ι → α) (i : ι) : iInf f ≤ f i :=
   sInf_le ⟨i, rfl⟩
 #align infi_le' iInf_le'
+-/
 
+#print isLUB_iSup /-
 /- TODO: this version would be more powerful, but, alas, the pattern matcher
    doesn't accept it.
 @[ematch] lemma le_supr' (f : ι → α) (i : ι) : (: f i :) ≤ (: supr f :) :=
@@ -774,354 +923,496 @@ le_Sup ⟨i, rfl⟩
 theorem isLUB_iSup : IsLUB (range f) (⨆ j, f j) :=
   isLUB_sSup _
 #align is_lub_supr isLUB_iSup
+-/
 
+#print isGLB_iInf /-
 theorem isGLB_iInf : IsGLB (range f) (⨅ j, f j) :=
   isGLB_sInf _
 #align is_glb_infi isGLB_iInf
+-/
 
+#print IsLUB.iSup_eq /-
 theorem IsLUB.iSup_eq (h : IsLUB (range f) a) : (⨆ j, f j) = a :=
   h.sSup_eq
 #align is_lub.supr_eq IsLUB.iSup_eq
+-/
 
+#print IsGLB.iInf_eq /-
 theorem IsGLB.iInf_eq (h : IsGLB (range f) a) : (⨅ j, f j) = a :=
   h.sInf_eq
 #align is_glb.infi_eq IsGLB.iInf_eq
+-/
 
+#print le_iSup_of_le /-
 theorem le_iSup_of_le (i : ι) (h : a ≤ f i) : a ≤ iSup f :=
   h.trans <| le_iSup _ i
 #align le_supr_of_le le_iSup_of_le
+-/
 
+#print iInf_le_of_le /-
 theorem iInf_le_of_le (i : ι) (h : f i ≤ a) : iInf f ≤ a :=
   (iInf_le _ i).trans h
 #align infi_le_of_le iInf_le_of_le
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print le_iSup₂ /-
 theorem le_iSup₂ {f : ∀ i, κ i → α} (i : ι) (j : κ i) : f i j ≤ ⨆ (i) (j), f i j :=
   le_iSup_of_le i <| le_iSup (f i) j
 #align le_supr₂ le_iSup₂
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print iInf₂_le /-
 theorem iInf₂_le {f : ∀ i, κ i → α} (i : ι) (j : κ i) : (⨅ (i) (j), f i j) ≤ f i j :=
   iInf_le_of_le i <| iInf_le (f i) j
 #align infi₂_le iInf₂_le
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print le_iSup₂_of_le /-
 theorem le_iSup₂_of_le {f : ∀ i, κ i → α} (i : ι) (j : κ i) (h : a ≤ f i j) :
     a ≤ ⨆ (i) (j), f i j :=
   h.trans <| le_iSup₂ i j
 #align le_supr₂_of_le le_iSup₂_of_le
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print iInf₂_le_of_le /-
 theorem iInf₂_le_of_le {f : ∀ i, κ i → α} (i : ι) (j : κ i) (h : f i j ≤ a) :
     (⨅ (i) (j), f i j) ≤ a :=
   (iInf₂_le i j).trans h
 #align infi₂_le_of_le iInf₂_le_of_le
+-/
 
+#print iSup_le /-
 theorem iSup_le (h : ∀ i, f i ≤ a) : iSup f ≤ a :=
   sSup_le fun b ⟨i, Eq⟩ => Eq ▸ h i
 #align supr_le iSup_le
+-/
 
+#print le_iInf /-
 theorem le_iInf (h : ∀ i, a ≤ f i) : a ≤ iInf f :=
   le_sInf fun b ⟨i, Eq⟩ => Eq ▸ h i
 #align le_infi le_iInf
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print iSup₂_le /-
 theorem iSup₂_le {f : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ a) : (⨆ (i) (j), f i j) ≤ a :=
   iSup_le fun i => iSup_le <| h i
 #align supr₂_le iSup₂_le
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print le_iInf₂ /-
 theorem le_iInf₂ {f : ∀ i, κ i → α} (h : ∀ i j, a ≤ f i j) : a ≤ ⨅ (i) (j), f i j :=
   le_iInf fun i => le_iInf <| h i
 #align le_infi₂ le_iInf₂
+-/
 
+#print iSup₂_le_iSup /-
 theorem iSup₂_le_iSup (κ : ι → Sort _) (f : ι → α) : (⨆ (i) (j : κ i), f i) ≤ ⨆ i, f i :=
   iSup₂_le fun i j => le_iSup f i
 #align supr₂_le_supr iSup₂_le_iSup
+-/
 
+#print iInf_le_iInf₂ /-
 theorem iInf_le_iInf₂ (κ : ι → Sort _) (f : ι → α) : (⨅ i, f i) ≤ ⨅ (i) (j : κ i), f i :=
   le_iInf₂ fun i j => iInf_le f i
 #align infi_le_infi₂ iInf_le_iInf₂
+-/
 
+#print iSup_mono /-
 theorem iSup_mono (h : ∀ i, f i ≤ g i) : iSup f ≤ iSup g :=
   iSup_le fun i => le_iSup_of_le i <| h i
 #align supr_mono iSup_mono
+-/
 
+#print iInf_mono /-
 theorem iInf_mono (h : ∀ i, f i ≤ g i) : iInf f ≤ iInf g :=
   le_iInf fun i => iInf_le_of_le i <| h i
 #align infi_mono iInf_mono
+-/
 
 /- ./././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 iSup₂_mono /-
 theorem iSup₂_mono {f g : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ g i j) :
     (⨆ (i) (j), f i j) ≤ ⨆ (i) (j), g i j :=
   iSup_mono fun i => iSup_mono <| h i
 #align supr₂_mono iSup₂_mono
+-/
 
 /- ./././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 iInf₂_mono /-
 theorem iInf₂_mono {f g : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ g i j) :
     (⨅ (i) (j), f i j) ≤ ⨅ (i) (j), g i j :=
   iInf_mono fun i => iInf_mono <| h i
 #align infi₂_mono iInf₂_mono
+-/
 
+#print iSup_mono' /-
 theorem iSup_mono' {g : ι' → α} (h : ∀ i, ∃ i', f i ≤ g i') : iSup f ≤ iSup g :=
   iSup_le fun i => Exists.elim (h i) le_iSup_of_le
 #align supr_mono' iSup_mono'
+-/
 
+#print iInf_mono' /-
 theorem iInf_mono' {g : ι' → α} (h : ∀ i', ∃ i, f i ≤ g i') : iInf f ≤ iInf g :=
   le_iInf fun i' => Exists.elim (h i') iInf_le_of_le
 #align infi_mono' iInf_mono'
+-/
 
 /- ./././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 iSup₂_mono' /-
 theorem iSup₂_mono' {f : ∀ i, κ i → α} {g : ∀ i', κ' i' → α} (h : ∀ i j, ∃ i' j', f i j ≤ g i' j') :
     (⨆ (i) (j), f i j) ≤ ⨆ (i) (j), g i j :=
   iSup₂_le fun i j =>
     let ⟨i', j', h⟩ := h i j
     le_iSup₂_of_le i' j' h
 #align supr₂_mono' iSup₂_mono'
+-/
 
 /- ./././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 iInf₂_mono' /-
 theorem iInf₂_mono' {f : ∀ i, κ i → α} {g : ∀ i', κ' i' → α} (h : ∀ i j, ∃ i' j', f i' j' ≤ g i j) :
     (⨅ (i) (j), f i j) ≤ ⨅ (i) (j), g i j :=
   le_iInf₂ fun i j =>
     let ⟨i', j', h⟩ := h i j
     iInf₂_le_of_le i' j' h
 #align infi₂_mono' iInf₂_mono'
+-/
 
+#print iSup_const_mono /-
 theorem iSup_const_mono (h : ι → ι') : (⨆ i : ι, a) ≤ ⨆ j : ι', a :=
   iSup_le <| le_iSup _ ∘ h
 #align supr_const_mono iSup_const_mono
+-/
 
+#print iInf_const_mono /-
 theorem iInf_const_mono (h : ι' → ι) : (⨅ i : ι, a) ≤ ⨅ j : ι', a :=
   le_iInf <| iInf_le _ ∘ h
 #align infi_const_mono iInf_const_mono
+-/
 
+#print iSup_iInf_le_iInf_iSup /-
 theorem iSup_iInf_le_iInf_iSup (f : ι → ι' → α) : (⨆ i, ⨅ j, f i j) ≤ ⨅ j, ⨆ i, f i j :=
   iSup_le fun i => iInf_mono fun j => le_iSup _ i
 #align supr_infi_le_infi_supr iSup_iInf_le_iInf_iSup
+-/
 
+#print biSup_mono /-
 theorem biSup_mono {p q : ι → Prop} (hpq : ∀ i, p i → q i) :
     (⨆ (i) (h : p i), f i) ≤ ⨆ (i) (h : q i), f i :=
   iSup_mono fun i => iSup_const_mono (hpq i)
 #align bsupr_mono biSup_mono
+-/
 
+#print biInf_mono /-
 theorem biInf_mono {p q : ι → Prop} (hpq : ∀ i, p i → q i) :
     (⨅ (i) (h : q i), f i) ≤ ⨅ (i) (h : p i), f i :=
   iInf_mono fun i => iInf_const_mono (hpq i)
 #align binfi_mono biInf_mono
+-/
 
+#print iSup_le_iff /-
 @[simp]
 theorem iSup_le_iff : iSup f ≤ a ↔ ∀ i, f i ≤ a :=
   (isLUB_le_iff isLUB_iSup).trans forall_range_iff
 #align supr_le_iff iSup_le_iff
+-/
 
+#print le_iInf_iff /-
 @[simp]
 theorem le_iInf_iff : a ≤ iInf f ↔ ∀ i, a ≤ f i :=
   (le_isGLB_iff isGLB_iInf).trans forall_range_iff
 #align le_infi_iff le_iInf_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print iSup₂_le_iff /-
 @[simp]
 theorem iSup₂_le_iff {f : ∀ i, κ i → α} : (⨆ (i) (j), f i j) ≤ a ↔ ∀ i j, f i j ≤ a := by
   simp_rw [iSup_le_iff]
 #align supr₂_le_iff iSup₂_le_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print le_iInf₂_iff /-
 @[simp]
 theorem le_iInf₂_iff {f : ∀ i, κ i → α} : (a ≤ ⨅ (i) (j), f i j) ↔ ∀ i j, a ≤ f i j := by
   simp_rw [le_iInf_iff]
 #align le_infi₂_iff le_iInf₂_iff
+-/
 
+#print iSup_lt_iff /-
 theorem iSup_lt_iff : iSup f < a ↔ ∃ b, b < a ∧ ∀ i, f i ≤ b :=
   ⟨fun h => ⟨iSup f, h, le_iSup f⟩, fun ⟨b, h, hb⟩ => (iSup_le hb).trans_lt h⟩
 #align supr_lt_iff iSup_lt_iff
+-/
 
+#print lt_iInf_iff /-
 theorem lt_iInf_iff : a < iInf f ↔ ∃ b, a < b ∧ ∀ i, b ≤ f i :=
   ⟨fun h => ⟨iInf f, h, iInf_le f⟩, fun ⟨b, h, hb⟩ => h.trans_le <| le_iInf hb⟩
 #align lt_infi_iff lt_iInf_iff
+-/
 
+#print sSup_eq_iSup /-
 theorem sSup_eq_iSup {s : Set α} : sSup s = ⨆ a ∈ s, a :=
   le_antisymm (sSup_le le_iSup₂) (iSup₂_le fun b => le_sSup)
 #align Sup_eq_supr sSup_eq_iSup
+-/
 
+#print sInf_eq_iInf /-
 theorem sInf_eq_iInf {s : Set α} : sInf s = ⨅ a ∈ s, a :=
   @sSup_eq_iSup αᵒᵈ _ _
 #align Inf_eq_infi sInf_eq_iInf
+-/
 
+#print Monotone.le_map_iSup /-
 theorem Monotone.le_map_iSup [CompleteLattice β] {f : α → β} (hf : Monotone f) :
     (⨆ i, f (s i)) ≤ f (iSup s) :=
   iSup_le fun i => hf <| le_iSup _ _
 #align monotone.le_map_supr Monotone.le_map_iSup
+-/
 
+#print Antitone.le_map_iInf /-
 theorem Antitone.le_map_iInf [CompleteLattice β] {f : α → β} (hf : Antitone f) :
     (⨆ i, f (s i)) ≤ f (iInf s) :=
   hf.dual_left.le_map_iSup
 #align antitone.le_map_infi Antitone.le_map_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 Monotone.le_map_iSup₂ /-
 theorem Monotone.le_map_iSup₂ [CompleteLattice β] {f : α → β} (hf : Monotone f) (s : ∀ i, κ i → α) :
     (⨆ (i) (j), f (s i j)) ≤ f (⨆ (i) (j), s i j) :=
   iSup₂_le fun i j => hf <| le_iSup₂ _ _
 #align monotone.le_map_supr₂ Monotone.le_map_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 Antitone.le_map_iInf₂ /-
 theorem Antitone.le_map_iInf₂ [CompleteLattice β] {f : α → β} (hf : Antitone f) (s : ∀ i, κ i → α) :
     (⨆ (i) (j), f (s i j)) ≤ f (⨅ (i) (j), s i j) :=
   hf.dual_left.le_map_iSup₂ _
 #align antitone.le_map_infi₂ Antitone.le_map_iInf₂
+-/
 
+#print Monotone.le_map_sSup /-
 theorem Monotone.le_map_sSup [CompleteLattice β] {s : Set α} {f : α → β} (hf : Monotone f) :
     (⨆ a ∈ s, f a) ≤ f (sSup s) := by rw [sSup_eq_iSup] <;> exact hf.le_map_supr₂ _
 #align monotone.le_map_Sup Monotone.le_map_sSup
+-/
 
+#print Antitone.le_map_sInf /-
 theorem Antitone.le_map_sInf [CompleteLattice β] {s : Set α} {f : α → β} (hf : Antitone f) :
     (⨆ a ∈ s, f a) ≤ f (sInf s) :=
   hf.dual_left.le_map_sSup
 #align antitone.le_map_Inf Antitone.le_map_sInf
+-/
 
+#print OrderIso.map_iSup /-
 theorem OrderIso.map_iSup [CompleteLattice β] (f : α ≃o β) (x : ι → α) :
     f (⨆ i, x i) = ⨆ i, f (x i) :=
   eq_of_forall_ge_iff <| f.Surjective.forall.2 fun x => by simp only [f.le_iff_le, iSup_le_iff]
 #align order_iso.map_supr OrderIso.map_iSup
+-/
 
+#print OrderIso.map_iInf /-
 theorem OrderIso.map_iInf [CompleteLattice β] (f : α ≃o β) (x : ι → α) :
     f (⨅ i, x i) = ⨅ i, f (x i) :=
   OrderIso.map_iSup f.dual _
 #align order_iso.map_infi OrderIso.map_iInf
+-/
 
+#print OrderIso.map_sSup /-
 theorem OrderIso.map_sSup [CompleteLattice β] (f : α ≃o β) (s : Set α) :
     f (sSup s) = ⨆ a ∈ s, f a := by simp only [sSup_eq_iSup, OrderIso.map_iSup]
 #align order_iso.map_Sup OrderIso.map_sSup
+-/
 
+#print OrderIso.map_sInf /-
 theorem OrderIso.map_sInf [CompleteLattice β] (f : α ≃o β) (s : Set α) :
     f (sInf s) = ⨅ a ∈ s, f a :=
   OrderIso.map_sSup f.dual _
 #align order_iso.map_Inf OrderIso.map_sInf
+-/
 
+#print iSup_comp_le /-
 theorem iSup_comp_le {ι' : Sort _} (f : ι' → α) (g : ι → ι') : (⨆ x, f (g x)) ≤ ⨆ y, f y :=
   iSup_mono' fun x => ⟨_, le_rfl⟩
 #align supr_comp_le iSup_comp_le
+-/
 
+#print le_iInf_comp /-
 theorem le_iInf_comp {ι' : Sort _} (f : ι' → α) (g : ι → ι') : (⨅ y, f y) ≤ ⨅ x, f (g x) :=
   iInf_mono' fun x => ⟨_, le_rfl⟩
 #align le_infi_comp le_iInf_comp
+-/
 
+#print Monotone.iSup_comp_eq /-
 theorem Monotone.iSup_comp_eq [Preorder β] {f : β → α} (hf : Monotone f) {s : ι → β}
     (hs : ∀ x, ∃ i, x ≤ s i) : (⨆ x, f (s x)) = ⨆ y, f y :=
   le_antisymm (iSup_comp_le _ _) (iSup_mono' fun x => (hs x).imp fun i hi => hf hi)
 #align monotone.supr_comp_eq Monotone.iSup_comp_eq
+-/
 
+#print Monotone.iInf_comp_eq /-
 theorem Monotone.iInf_comp_eq [Preorder β] {f : β → α} (hf : Monotone f) {s : ι → β}
     (hs : ∀ x, ∃ i, s i ≤ x) : (⨅ x, f (s x)) = ⨅ y, f y :=
   le_antisymm (iInf_mono' fun x => (hs x).imp fun i hi => hf hi) (le_iInf_comp _ _)
 #align monotone.infi_comp_eq Monotone.iInf_comp_eq
+-/
 
+#print Antitone.map_iSup_le /-
 theorem Antitone.map_iSup_le [CompleteLattice β] {f : α → β} (hf : Antitone f) :
     f (iSup s) ≤ ⨅ i, f (s i) :=
   le_iInf fun i => hf <| le_iSup _ _
 #align antitone.map_supr_le Antitone.map_iSup_le
+-/
 
+#print Monotone.map_iInf_le /-
 theorem Monotone.map_iInf_le [CompleteLattice β] {f : α → β} (hf : Monotone f) :
     f (iInf s) ≤ ⨅ i, f (s i) :=
   hf.dual_left.map_iSup_le
 #align monotone.map_infi_le Monotone.map_iInf_le
+-/
 
 /- ./././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 Antitone.map_iSup₂_le /-
 theorem Antitone.map_iSup₂_le [CompleteLattice β] {f : α → β} (hf : Antitone f) (s : ∀ i, κ i → α) :
     f (⨆ (i) (j), s i j) ≤ ⨅ (i) (j), f (s i j) :=
   hf.dual.le_map_iInf₂ _
 #align antitone.map_supr₂_le Antitone.map_iSup₂_le
+-/
 
 /- ./././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 Monotone.map_iInf₂_le /-
 theorem Monotone.map_iInf₂_le [CompleteLattice β] {f : α → β} (hf : Monotone f) (s : ∀ i, κ i → α) :
     f (⨅ (i) (j), s i j) ≤ ⨅ (i) (j), f (s i j) :=
   hf.dual.le_map_iSup₂ _
 #align monotone.map_infi₂_le Monotone.map_iInf₂_le
+-/
 
+#print Antitone.map_sSup_le /-
 theorem Antitone.map_sSup_le [CompleteLattice β] {s : Set α} {f : α → β} (hf : Antitone f) :
     f (sSup s) ≤ ⨅ a ∈ s, f a := by rw [sSup_eq_iSup]; exact hf.map_supr₂_le _
 #align antitone.map_Sup_le Antitone.map_sSup_le
+-/
 
+#print Monotone.map_sInf_le /-
 theorem Monotone.map_sInf_le [CompleteLattice β] {s : Set α} {f : α → β} (hf : Monotone f) :
     f (sInf s) ≤ ⨅ a ∈ s, f a :=
   hf.dual_left.map_sSup_le
 #align monotone.map_Inf_le Monotone.map_sInf_le
+-/
 
+#print iSup_const_le /-
 theorem iSup_const_le : (⨆ i : ι, a) ≤ a :=
   iSup_le fun _ => le_rfl
 #align supr_const_le iSup_const_le
+-/
 
+#print le_iInf_const /-
 theorem le_iInf_const : a ≤ ⨅ i : ι, a :=
   le_iInf fun _ => le_rfl
 #align le_infi_const le_iInf_const
+-/
 
+#print iSup_const /-
 -- We generalize this to conditionally complete lattices in `csupr_const` and `cinfi_const`.
 theorem iSup_const [Nonempty ι] : (⨆ b : ι, a) = a := by rw [iSup, range_const, sSup_singleton]
 #align supr_const iSup_const
+-/
 
+#print iInf_const /-
 theorem iInf_const [Nonempty ι] : (⨅ b : ι, a) = a :=
   @iSup_const αᵒᵈ _ _ a _
 #align infi_const iInf_const
+-/
 
+#print iSup_bot /-
 @[simp]
 theorem iSup_bot : (⨆ i : ι, ⊥ : α) = ⊥ :=
   bot_unique iSup_const_le
 #align supr_bot iSup_bot
+-/
 
+#print iInf_top /-
 @[simp]
 theorem iInf_top : (⨅ i : ι, ⊤ : α) = ⊤ :=
   top_unique le_iInf_const
 #align infi_top iInf_top
+-/
 
+#print iSup_eq_bot /-
 @[simp]
 theorem iSup_eq_bot : iSup s = ⊥ ↔ ∀ i, s i = ⊥ :=
   sSup_eq_bot.trans forall_range_iff
 #align supr_eq_bot iSup_eq_bot
+-/
 
+#print iInf_eq_top /-
 @[simp]
 theorem iInf_eq_top : iInf s = ⊤ ↔ ∀ i, s i = ⊤ :=
   sInf_eq_top.trans forall_range_iff
 #align infi_eq_top iInf_eq_top
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print iSup₂_eq_bot /-
 @[simp]
 theorem iSup₂_eq_bot {f : ∀ i, κ i → α} : (⨆ (i) (j), f i j) = ⊥ ↔ ∀ i j, f i j = ⊥ := by
   simp_rw [iSup_eq_bot]
 #align supr₂_eq_bot iSup₂_eq_bot
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print iInf₂_eq_top /-
 @[simp]
 theorem iInf₂_eq_top {f : ∀ i, κ i → α} : (⨅ (i) (j), f i j) = ⊤ ↔ ∀ i j, f i j = ⊤ := by
   simp_rw [iInf_eq_top]
 #align infi₂_eq_top iInf₂_eq_top
+-/
 
+#print iSup_pos /-
 @[simp]
 theorem iSup_pos {p : Prop} {f : p → α} (hp : p) : (⨆ h : p, f h) = f hp :=
   le_antisymm (iSup_le fun h => le_rfl) (le_iSup _ _)
 #align supr_pos iSup_pos
+-/
 
+#print iInf_pos /-
 @[simp]
 theorem iInf_pos {p : Prop} {f : p → α} (hp : p) : (⨅ h : p, f h) = f hp :=
   le_antisymm (iInf_le _ _) (le_iInf fun h => le_rfl)
 #align infi_pos iInf_pos
+-/
 
+#print iSup_neg /-
 @[simp]
 theorem iSup_neg {p : Prop} {f : p → α} (hp : ¬p) : (⨆ h : p, f h) = ⊥ :=
   le_antisymm (iSup_le fun h => (hp h).elim) bot_le
 #align supr_neg iSup_neg
+-/
 
+#print iInf_neg /-
 @[simp]
 theorem iInf_neg {p : Prop} {f : p → α} (hp : ¬p) : (⨅ h : p, f h) = ⊤ :=
   le_antisymm le_top <| le_iInf fun h => (hp h).elim
 #align infi_neg iInf_neg
+-/
 
+#print iSup_eq_of_forall_le_of_forall_lt_exists_gt /-
 /-- Introduction rule to prove that `b` is the supremum of `f`: it suffices to check that `b`
 is larger than `f i` for all `i`, and that this is not the case of any `w<b`.
 See `csupr_eq_of_forall_le_of_forall_lt_exists_gt` for a version in conditionally complete
@@ -1131,7 +1422,9 @@ theorem iSup_eq_of_forall_le_of_forall_lt_exists_gt {f : ι → α} (h₁ : ∀
   sSup_eq_of_forall_le_of_forall_lt_exists_gt (forall_range_iff.mpr h₁) fun w hw =>
     exists_range_iff.mpr <| h₂ w hw
 #align supr_eq_of_forall_le_of_forall_lt_exists_gt iSup_eq_of_forall_le_of_forall_lt_exists_gt
+-/
 
+#print iInf_eq_of_forall_ge_of_forall_gt_exists_lt /-
 /-- Introduction rule to prove that `b` is the infimum of `f`: it suffices to check that `b`
 is smaller than `f i` for all `i`, and that this is not the case of any `w>b`.
 See `cinfi_eq_of_forall_ge_of_forall_gt_exists_lt` for a version in conditionally complete
@@ -1140,53 +1433,71 @@ theorem iInf_eq_of_forall_ge_of_forall_gt_exists_lt :
     (∀ i, b ≤ f i) → (∀ w, b < w → ∃ i, f i < w) → (⨅ i, f i) = b :=
   @iSup_eq_of_forall_le_of_forall_lt_exists_gt αᵒᵈ _ _ _ _
 #align infi_eq_of_forall_ge_of_forall_gt_exists_lt iInf_eq_of_forall_ge_of_forall_gt_exists_lt
+-/
 
+#print iSup_eq_dif /-
 theorem iSup_eq_dif {p : Prop} [Decidable p] (a : p → α) :
     (⨆ h : p, a h) = if h : p then a h else ⊥ := by by_cases p <;> simp [h]
 #align supr_eq_dif iSup_eq_dif
+-/
 
+#print iSup_eq_if /-
 theorem iSup_eq_if {p : Prop} [Decidable p] (a : α) : (⨆ h : p, a) = if p then a else ⊥ :=
   iSup_eq_dif fun _ => a
 #align supr_eq_if iSup_eq_if
+-/
 
+#print iInf_eq_dif /-
 theorem iInf_eq_dif {p : Prop} [Decidable p] (a : p → α) :
     (⨅ h : p, a h) = if h : p then a h else ⊤ :=
   @iSup_eq_dif αᵒᵈ _ _ _ _
 #align infi_eq_dif iInf_eq_dif
+-/
 
+#print iInf_eq_if /-
 theorem iInf_eq_if {p : Prop} [Decidable p] (a : α) : (⨅ h : p, a) = if p then a else ⊤ :=
   iInf_eq_dif fun _ => a
 #align infi_eq_if iInf_eq_if
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (j i) -/
+#print iSup_comm /-
 theorem iSup_comm {f : ι → ι' → α} : (⨆ (i) (j), f i j) = ⨆ (j) (i), f i j :=
   le_antisymm (iSup_le fun i => iSup_mono fun j => le_iSup _ i)
     (iSup_le fun j => iSup_mono fun i => le_iSup _ _)
 #align supr_comm iSup_comm
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (j i) -/
+#print iInf_comm /-
 theorem iInf_comm {f : ι → ι' → α} : (⨅ (i) (j), f i j) = ⨅ (j) (i), f i j :=
   @iSup_comm αᵒᵈ _ _ _ _
 #align infi_comm iInf_comm
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i₁ j₁ i₂ j₂) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i₂ j₂ i₁ j₁) -/
+#print iSup₂_comm /-
 theorem iSup₂_comm {ι₁ ι₂ : Sort _} {κ₁ : ι₁ → Sort _} {κ₂ : ι₂ → Sort _}
     (f : ∀ i₁, κ₁ i₁ → ∀ i₂, κ₂ i₂ → α) :
     (⨆ (i₁) (j₁) (i₂) (j₂), f i₁ j₁ i₂ j₂) = ⨆ (i₂) (j₂) (i₁) (j₁), f i₁ j₁ i₂ j₂ := by
   simp only [@iSup_comm _ (κ₁ _), @iSup_comm _ ι₁]
 #align supr₂_comm iSup₂_comm
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i₁ j₁ i₂ j₂) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i₂ j₂ i₁ j₁) -/
+#print iInf₂_comm /-
 theorem iInf₂_comm {ι₁ ι₂ : Sort _} {κ₁ : ι₁ → Sort _} {κ₂ : ι₂ → Sort _}
     (f : ∀ i₁, κ₁ i₁ → ∀ i₂, κ₂ i₂ → α) :
     (⨅ (i₁) (j₁) (i₂) (j₂), f i₁ j₁ i₂ j₂) = ⨅ (i₂) (j₂) (i₁) (j₁), f i₁ j₁ i₂ j₂ := by
   simp only [@iInf_comm _ (κ₁ _), @iInf_comm _ ι₁]
 #align infi₂_comm iInf₂_comm
+-/
 
+#print iSup_iSup_eq_left /-
 /- TODO: this is strange. In the proof below, we get exactly the desired
    among the equalities, but close does not get it.
 begin
@@ -1202,70 +1513,98 @@ end
 theorem iSup_iSup_eq_left {b : β} {f : ∀ x : β, x = b → α} : (⨆ x, ⨆ h : x = b, f x h) = f b rfl :=
   (@le_iSup₂ _ _ _ _ f b rfl).antisymm' (iSup_le fun c => iSup_le <| by rintro rfl; rfl)
 #align supr_supr_eq_left iSup_iSup_eq_left
+-/
 
+#print iInf_iInf_eq_left /-
 @[simp]
 theorem iInf_iInf_eq_left {b : β} {f : ∀ x : β, x = b → α} : (⨅ x, ⨅ h : x = b, f x h) = f b rfl :=
   @iSup_iSup_eq_left αᵒᵈ _ _ _ _
 #align infi_infi_eq_left iInf_iInf_eq_left
+-/
 
+#print iSup_iSup_eq_right /-
 @[simp]
 theorem iSup_iSup_eq_right {b : β} {f : ∀ x : β, b = x → α} : (⨆ x, ⨆ h : b = x, f x h) = f b rfl :=
   (le_iSup₂ b rfl).antisymm' (iSup₂_le fun c => by rintro rfl; rfl)
 #align supr_supr_eq_right iSup_iSup_eq_right
+-/
 
+#print iInf_iInf_eq_right /-
 @[simp]
 theorem iInf_iInf_eq_right {b : β} {f : ∀ x : β, b = x → α} : (⨅ x, ⨅ h : b = x, f x h) = f b rfl :=
   @iSup_iSup_eq_right αᵒᵈ _ _ _ _
 #align infi_infi_eq_right iInf_iInf_eq_right
+-/
 
 attribute [ematch] le_refl
 
+#print iSup_subtype /-
 theorem iSup_subtype {p : ι → Prop} {f : Subtype p → α} : iSup f = ⨆ (i) (h : p i), f ⟨i, h⟩ :=
   le_antisymm (iSup_le fun ⟨i, h⟩ => le_iSup₂ i h) (iSup₂_le fun i h => le_iSup _ _)
 #align supr_subtype iSup_subtype
+-/
 
+#print iInf_subtype /-
 theorem iInf_subtype : ∀ {p : ι → Prop} {f : Subtype p → α}, iInf f = ⨅ (i) (h : p i), f ⟨i, h⟩ :=
   @iSup_subtype αᵒᵈ _ _
 #align infi_subtype iInf_subtype
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i h) -/
+#print iSup_subtype' /-
 theorem iSup_subtype' {p : ι → Prop} {f : ∀ i, p i → α} :
     (⨆ (i) (h), f i h) = ⨆ x : Subtype p, f x x.property :=
   (@iSup_subtype _ _ _ p fun x => f x.val x.property).symm
 #align supr_subtype' iSup_subtype'
+-/
 
+#print iInf_subtype' /-
 theorem iInf_subtype' {p : ι → Prop} {f : ∀ i, p i → α} :
     (⨅ (i) (h : p i), f i h) = ⨅ x : Subtype p, f x x.property :=
   (@iInf_subtype _ _ _ p fun x => f x.val x.property).symm
 #align infi_subtype' iInf_subtype'
+-/
 
+#print iSup_subtype'' /-
 theorem iSup_subtype'' {ι} (s : Set ι) (f : ι → α) : (⨆ i : s, f i) = ⨆ (t : ι) (H : t ∈ s), f t :=
   iSup_subtype
 #align supr_subtype'' iSup_subtype''
+-/
 
+#print iInf_subtype'' /-
 theorem iInf_subtype'' {ι} (s : Set ι) (f : ι → α) : (⨅ i : s, f i) = ⨅ (t : ι) (H : t ∈ s), f t :=
   iInf_subtype
 #align infi_subtype'' iInf_subtype''
+-/
 
+#print biSup_const /-
 theorem biSup_const {ι : Sort _} {a : α} {s : Set ι} (hs : s.Nonempty) : (⨆ i ∈ s, a) = a :=
   by
   haveI : Nonempty s := set.nonempty_coe_sort.mpr hs
   rw [← iSup_subtype'', iSup_const]
 #align bsupr_const biSup_const
+-/
 
+#print biInf_const /-
 theorem biInf_const {ι : Sort _} {a : α} {s : Set ι} (hs : s.Nonempty) : (⨅ i ∈ s, a) = a :=
   @biSup_const αᵒᵈ _ ι _ s hs
 #align binfi_const biInf_const
+-/
 
+#print iSup_sup_eq /-
 theorem iSup_sup_eq : (⨆ x, f x ⊔ g x) = (⨆ x, f x) ⊔ ⨆ x, g x :=
   le_antisymm (iSup_le fun i => sup_le_sup (le_iSup _ _) <| le_iSup _ _)
     (sup_le (iSup_mono fun i => le_sup_left) <| iSup_mono fun i => le_sup_right)
 #align supr_sup_eq iSup_sup_eq
+-/
 
+#print iInf_inf_eq /-
 theorem iInf_inf_eq : (⨅ x, f x ⊓ g x) = (⨅ x, f x) ⊓ ⨅ x, g x :=
   @iSup_sup_eq αᵒᵈ _ _ _ _
 #align infi_inf_eq iInf_inf_eq
+-/
 
+#print iSup_sup /-
 /- TODO: here is another example where more flexible pattern matching
    might help.
 
@@ -1277,19 +1616,27 @@ end
 theorem iSup_sup [Nonempty ι] {f : ι → α} {a : α} : (⨆ x, f x) ⊔ a = ⨆ x, f x ⊔ a := by
   rw [iSup_sup_eq, iSup_const]
 #align supr_sup iSup_sup
+-/
 
+#print iInf_inf /-
 theorem iInf_inf [Nonempty ι] {f : ι → α} {a : α} : (⨅ x, f x) ⊓ a = ⨅ x, f x ⊓ a := by
   rw [iInf_inf_eq, iInf_const]
 #align infi_inf iInf_inf
+-/
 
+#print sup_iSup /-
 theorem sup_iSup [Nonempty ι] {f : ι → α} {a : α} : (a ⊔ ⨆ x, f x) = ⨆ x, a ⊔ f x := by
   rw [iSup_sup_eq, iSup_const]
 #align sup_supr sup_iSup
+-/
 
+#print inf_iInf /-
 theorem inf_iInf [Nonempty ι] {f : ι → α} {a : α} : (a ⊓ ⨅ x, f x) = ⨅ x, a ⊓ f x := by
   rw [iInf_inf_eq, iInf_const]
 #align inf_infi inf_iInf
+-/
 
+#print biSup_sup /-
 theorem biSup_sup {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
     (⨆ (i) (h : p i), f i h) ⊔ a = ⨆ (i) (h : p i), f i h ⊔ a := by
   haveI : Nonempty { i // p i } :=
@@ -1297,77 +1644,105 @@ theorem biSup_sup {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i,
       ⟨⟨i, hi⟩⟩ <;>
     rw [iSup_subtype', iSup_subtype', iSup_sup]
 #align bsupr_sup biSup_sup
+-/
 
+#print sup_biSup /-
 theorem sup_biSup {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
     (a ⊔ ⨆ (i) (h : p i), f i h) = ⨆ (i) (h : p i), a ⊔ f i h := by
   simpa only [sup_comm] using biSup_sup h
 #align sup_bsupr sup_biSup
+-/
 
+#print biInf_inf /-
 theorem biInf_inf {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
     (⨅ (i) (h : p i), f i h) ⊓ a = ⨅ (i) (h : p i), f i h ⊓ a :=
   @biSup_sup αᵒᵈ ι _ p f _ h
 #align binfi_inf biInf_inf
+-/
 
+#print inf_biInf /-
 theorem inf_biInf {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
     (a ⊓ ⨅ (i) (h : p i), f i h) = ⨅ (i) (h : p i), a ⊓ f i h :=
   @sup_biSup αᵒᵈ ι _ p f _ h
 #align inf_binfi inf_biInf
+-/
 
 /-! ### `supr` and `infi` under `Prop` -/
 
 
+#print iSup_false /-
 @[simp]
 theorem iSup_false {s : False → α} : iSup s = ⊥ :=
   le_antisymm (iSup_le fun i => False.elim i) bot_le
 #align supr_false iSup_false
+-/
 
+#print iInf_false /-
 @[simp]
 theorem iInf_false {s : False → α} : iInf s = ⊤ :=
   le_antisymm le_top (le_iInf fun i => False.elim i)
 #align infi_false iInf_false
+-/
 
+#print iSup_true /-
 theorem iSup_true {s : True → α} : iSup s = s trivial :=
   iSup_pos trivial
 #align supr_true iSup_true
+-/
 
+#print iInf_true /-
 theorem iInf_true {s : True → α} : iInf s = s trivial :=
   iInf_pos trivial
 #align infi_true iInf_true
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i h) -/
+#print iSup_exists /-
 @[simp]
 theorem iSup_exists {p : ι → Prop} {f : Exists p → α} : (⨆ x, f x) = ⨆ (i) (h), f ⟨i, h⟩ :=
   le_antisymm (iSup_le fun ⟨i, h⟩ => le_iSup₂ i h) (iSup₂_le fun i h => le_iSup _ _)
 #align supr_exists iSup_exists
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i h) -/
+#print iInf_exists /-
 @[simp]
 theorem iInf_exists {p : ι → Prop} {f : Exists p → α} : (⨅ x, f x) = ⨅ (i) (h), f ⟨i, h⟩ :=
   @iSup_exists αᵒᵈ _ _ _ _
 #align infi_exists iInf_exists
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (h₁ h₂) -/
+#print iSup_and /-
 theorem iSup_and {p q : Prop} {s : p ∧ q → α} : iSup s = ⨆ (h₁) (h₂), s ⟨h₁, h₂⟩ :=
   le_antisymm (iSup_le fun ⟨i, h⟩ => le_iSup₂ i h) (iSup₂_le fun i h => le_iSup _ _)
 #align supr_and iSup_and
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (h₁ h₂) -/
+#print iInf_and /-
 theorem iInf_and {p q : Prop} {s : p ∧ q → α} : iInf s = ⨅ (h₁) (h₂), s ⟨h₁, h₂⟩ :=
   @iSup_and αᵒᵈ _ _ _ _
 #align infi_and iInf_and
+-/
 
+#print iSup_and' /-
 /-- The symmetric case of `supr_and`, useful for rewriting into a supremum over a conjunction -/
 theorem iSup_and' {p q : Prop} {s : p → q → α} :
     (⨆ (h₁ : p) (h₂ : q), s h₁ h₂) = ⨆ h : p ∧ q, s h.1 h.2 :=
   Eq.symm iSup_and
 #align supr_and' iSup_and'
+-/
 
+#print iInf_and' /-
 /-- The symmetric case of `infi_and`, useful for rewriting into a infimum over a conjunction -/
 theorem iInf_and' {p q : Prop} {s : p → q → α} :
     (⨅ (h₁ : p) (h₂ : q), s h₁ h₂) = ⨅ h : p ∧ q, s h.1 h.2 :=
   Eq.symm iInf_and
 #align infi_and' iInf_and'
+-/
 
+#print iSup_or /-
 theorem iSup_or {p q : Prop} {s : p ∨ q → α} :
     (⨆ x, s x) = (⨆ i, s (Or.inl i)) ⊔ ⨆ j, s (Or.inr j) :=
   le_antisymm
@@ -1377,16 +1752,20 @@ theorem iSup_or {p q : Prop} {s : p ∨ q → α} :
       | Or.inr j => le_sup_of_le_right <| le_iSup _ j)
     (sup_le (iSup_comp_le _ _) (iSup_comp_le _ _))
 #align supr_or iSup_or
+-/
 
+#print iInf_or /-
 theorem iInf_or {p q : Prop} {s : p ∨ q → α} :
     (⨅ x, s x) = (⨅ i, s (Or.inl i)) ⊓ ⨅ j, s (Or.inr j) :=
   @iSup_or αᵒᵈ _ _ _ _
 #align infi_or iInf_or
+-/
 
 section
 
 variable (p : ι → Prop) [DecidablePred p]
 
+#print iSup_dite /-
 theorem iSup_dite (f : ∀ i, p i → α) (g : ∀ i, ¬p i → α) :
     (⨆ i, if h : p i then f i h else g i h) = (⨆ (i) (h : p i), f i h) ⊔ ⨆ (i) (h : ¬p i), g i h :=
   by
@@ -1394,237 +1773,341 @@ theorem iSup_dite (f : ∀ i, p i → α) (g : ∀ i, ¬p i → α) :
   congr 1 with i
   split_ifs with h <;> simp [h]
 #align supr_dite iSup_dite
+-/
 
+#print iInf_dite /-
 theorem iInf_dite (f : ∀ i, p i → α) (g : ∀ i, ¬p i → α) :
     (⨅ i, if h : p i then f i h else g i h) = (⨅ (i) (h : p i), f i h) ⊓ ⨅ (i) (h : ¬p i), g i h :=
   iSup_dite p (show ∀ i, p i → αᵒᵈ from f) g
 #align infi_dite iInf_dite
+-/
 
+#print iSup_ite /-
 theorem iSup_ite (f g : ι → α) :
     (⨆ i, if p i then f i else g i) = (⨆ (i) (h : p i), f i) ⊔ ⨆ (i) (h : ¬p i), g i :=
   iSup_dite _ _ _
 #align supr_ite iSup_ite
+-/
 
+#print iInf_ite /-
 theorem iInf_ite (f g : ι → α) :
     (⨅ i, if p i then f i else g i) = (⨅ (i) (h : p i), f i) ⊓ ⨅ (i) (h : ¬p i), g i :=
   iInf_dite _ _ _
 #align infi_ite iInf_ite
+-/
 
 end
 
+#print iSup_range /-
 theorem iSup_range {g : β → α} {f : ι → β} : (⨆ b ∈ range f, g b) = ⨆ i, g (f i) := by
   rw [← iSup_subtype'', iSup_range']
 #align supr_range iSup_range
+-/
 
+#print iInf_range /-
 theorem iInf_range : ∀ {g : β → α} {f : ι → β}, (⨅ b ∈ range f, g b) = ⨅ i, g (f i) :=
   @iSup_range αᵒᵈ _ _ _
 #align infi_range iInf_range
+-/
 
+#print sSup_image /-
 theorem sSup_image {s : Set β} {f : β → α} : sSup (f '' s) = ⨆ a ∈ s, f a := by
   rw [← iSup_subtype'', sSup_image']
 #align Sup_image sSup_image
+-/
 
+#print sInf_image /-
 theorem sInf_image {s : Set β} {f : β → α} : sInf (f '' s) = ⨅ a ∈ s, f a :=
   @sSup_image αᵒᵈ _ _ _ _
 #align Inf_image sInf_image
+-/
 
+#print iSup_emptyset /-
 /-
 ### supr and infi under set constructions
 -/
 theorem iSup_emptyset {f : β → α} : (⨆ x ∈ (∅ : Set β), f x) = ⊥ := by simp
 #align supr_emptyset iSup_emptyset
+-/
 
+#print iInf_emptyset /-
 theorem iInf_emptyset {f : β → α} : (⨅ x ∈ (∅ : Set β), f x) = ⊤ := by simp
 #align infi_emptyset iInf_emptyset
+-/
 
+#print iSup_univ /-
 theorem iSup_univ {f : β → α} : (⨆ x ∈ (univ : Set β), f x) = ⨆ x, f x := by simp
 #align supr_univ iSup_univ
+-/
 
+#print iInf_univ /-
 theorem iInf_univ {f : β → α} : (⨅ x ∈ (univ : Set β), f x) = ⨅ x, f x := by simp
 #align infi_univ iInf_univ
+-/
 
+#print iSup_union /-
 theorem iSup_union {f : β → α} {s t : Set β} : (⨆ x ∈ s ∪ t, f x) = (⨆ x ∈ s, f x) ⊔ ⨆ x ∈ t, f x :=
   by simp_rw [mem_union, iSup_or, iSup_sup_eq]
 #align supr_union iSup_union
+-/
 
+#print iInf_union /-
 theorem iInf_union {f : β → α} {s t : Set β} : (⨅ x ∈ s ∪ t, f x) = (⨅ x ∈ s, f x) ⊓ ⨅ x ∈ t, f x :=
   @iSup_union αᵒᵈ _ _ _ _ _
 #align infi_union iInf_union
+-/
 
+#print iSup_split /-
 theorem iSup_split (f : β → α) (p : β → Prop) :
     (⨆ i, f i) = (⨆ (i) (h : p i), f i) ⊔ ⨆ (i) (h : ¬p i), f i := by
   simpa [Classical.em] using @iSup_union _ _ _ f {i | p i} {i | ¬p i}
 #align supr_split iSup_split
+-/
 
+#print iInf_split /-
 theorem iInf_split :
     ∀ (f : β → α) (p : β → Prop), (⨅ i, f i) = (⨅ (i) (h : p i), f i) ⊓ ⨅ (i) (h : ¬p i), f i :=
   @iSup_split αᵒᵈ _ _
 #align infi_split iInf_split
+-/
 
+#print iSup_split_single /-
 theorem iSup_split_single (f : β → α) (i₀ : β) : (⨆ i, f i) = f i₀ ⊔ ⨆ (i) (h : i ≠ i₀), f i := by
   convert iSup_split _ _; simp
 #align supr_split_single iSup_split_single
+-/
 
+#print iInf_split_single /-
 theorem iInf_split_single (f : β → α) (i₀ : β) : (⨅ i, f i) = f i₀ ⊓ ⨅ (i) (h : i ≠ i₀), f i :=
   @iSup_split_single αᵒᵈ _ _ _ _
 #align infi_split_single iInf_split_single
+-/
 
+#print iSup_le_iSup_of_subset /-
 theorem iSup_le_iSup_of_subset {f : β → α} {s t : Set β} : s ⊆ t → (⨆ x ∈ s, f x) ≤ ⨆ x ∈ t, f x :=
   biSup_mono
 #align supr_le_supr_of_subset iSup_le_iSup_of_subset
+-/
 
+#print iInf_le_iInf_of_subset /-
 theorem iInf_le_iInf_of_subset {f : β → α} {s t : Set β} : s ⊆ t → (⨅ x ∈ t, f x) ≤ ⨅ x ∈ s, f x :=
   biInf_mono
 #align infi_le_infi_of_subset iInf_le_iInf_of_subset
+-/
 
+#print iSup_insert /-
 theorem iSup_insert {f : β → α} {s : Set β} {b : β} :
     (⨆ x ∈ insert b s, f x) = f b ⊔ ⨆ x ∈ s, f x :=
   Eq.trans iSup_union <| congr_arg (fun x => x ⊔ ⨆ x ∈ s, f x) iSup_iSup_eq_left
 #align supr_insert iSup_insert
+-/
 
+#print iInf_insert /-
 theorem iInf_insert {f : β → α} {s : Set β} {b : β} :
     (⨅ x ∈ insert b s, f x) = f b ⊓ ⨅ x ∈ s, f x :=
   Eq.trans iInf_union <| congr_arg (fun x => x ⊓ ⨅ x ∈ s, f x) iInf_iInf_eq_left
 #align infi_insert iInf_insert
+-/
 
+#print iSup_singleton /-
 theorem iSup_singleton {f : β → α} {b : β} : (⨆ x ∈ (singleton b : Set β), f x) = f b := by simp
 #align supr_singleton iSup_singleton
+-/
 
+#print iInf_singleton /-
 theorem iInf_singleton {f : β → α} {b : β} : (⨅ x ∈ (singleton b : Set β), f x) = f b := by simp
 #align infi_singleton iInf_singleton
+-/
 
+#print iSup_pair /-
 theorem iSup_pair {f : β → α} {a b : β} : (⨆ x ∈ ({a, b} : Set β), f x) = f a ⊔ f b := by
   rw [iSup_insert, iSup_singleton]
 #align supr_pair iSup_pair
+-/
 
+#print iInf_pair /-
 theorem iInf_pair {f : β → α} {a b : β} : (⨅ x ∈ ({a, b} : Set β), f x) = f a ⊓ f b := by
   rw [iInf_insert, iInf_singleton]
 #align infi_pair iInf_pair
+-/
 
+#print iSup_image /-
 theorem iSup_image {γ} {f : β → γ} {g : γ → α} {t : Set β} :
     (⨆ c ∈ f '' t, g c) = ⨆ b ∈ t, g (f b) := by rw [← sSup_image, ← sSup_image, ← image_comp]
 #align supr_image iSup_image
+-/
 
+#print iInf_image /-
 theorem iInf_image :
     ∀ {γ} {f : β → γ} {g : γ → α} {t : Set β}, (⨅ c ∈ f '' t, g c) = ⨅ b ∈ t, g (f b) :=
   @iSup_image αᵒᵈ _ _
 #align infi_image iInf_image
+-/
 
+#print iSup_extend_bot /-
 theorem iSup_extend_bot {e : ι → β} (he : Injective e) (f : ι → α) :
     (⨆ j, extend e f ⊥ j) = ⨆ i, f i :=
   by
   rw [iSup_split _ fun j => ∃ i, e i = j]
   simp (config := { contextual := true }) [he.extend_apply, extend_apply', @iSup_comm _ β ι]
 #align supr_extend_bot iSup_extend_bot
+-/
 
+#print iInf_extend_top /-
 theorem iInf_extend_top {e : ι → β} (he : Injective e) (f : ι → α) :
     (⨅ j, extend e f ⊤ j) = iInf f :=
   @iSup_extend_bot αᵒᵈ _ _ _ _ he _
 #align infi_extend_top iInf_extend_top
+-/
 
 /-!
 ### `supr` and `infi` under `Type`
 -/
 
 
+#print iSup_of_empty' /-
 theorem iSup_of_empty' {α ι} [SupSet α] [IsEmpty ι] (f : ι → α) : iSup f = sSup (∅ : Set α) :=
   congr_arg sSup (range_eq_empty f)
 #align supr_of_empty' iSup_of_empty'
+-/
 
+#print iInf_of_empty' /-
 theorem iInf_of_empty' {α ι} [InfSet α] [IsEmpty ι] (f : ι → α) : iInf f = sInf (∅ : Set α) :=
   congr_arg sInf (range_eq_empty f)
 #align infi_of_empty' iInf_of_empty'
+-/
 
+#print iSup_of_empty /-
 theorem iSup_of_empty [IsEmpty ι] (f : ι → α) : iSup f = ⊥ :=
   (iSup_of_empty' f).trans sSup_empty
 #align supr_of_empty iSup_of_empty
+-/
 
+#print iInf_of_empty /-
 theorem iInf_of_empty [IsEmpty ι] (f : ι → α) : iInf f = ⊤ :=
   @iSup_of_empty αᵒᵈ _ _ _ f
 #align infi_of_empty iInf_of_empty
+-/
 
+#print iSup_bool_eq /-
 theorem iSup_bool_eq {f : Bool → α} : (⨆ b : Bool, f b) = f true ⊔ f false := by
   rw [iSup, Bool.range_eq, sSup_pair, sup_comm]
 #align supr_bool_eq iSup_bool_eq
+-/
 
+#print iInf_bool_eq /-
 theorem iInf_bool_eq {f : Bool → α} : (⨅ b : Bool, f b) = f true ⊓ f false :=
   @iSup_bool_eq αᵒᵈ _ _
 #align infi_bool_eq iInf_bool_eq
+-/
 
+#print sup_eq_iSup /-
 theorem sup_eq_iSup (x y : α) : x ⊔ y = ⨆ b : Bool, cond b x y := by
   rw [iSup_bool_eq, Bool.cond_true, Bool.cond_false]
 #align sup_eq_supr sup_eq_iSup
+-/
 
+#print inf_eq_iInf /-
 theorem inf_eq_iInf (x y : α) : x ⊓ y = ⨅ b : Bool, cond b x y :=
   @sup_eq_iSup αᵒᵈ _ _ _
 #align inf_eq_infi inf_eq_iInf
+-/
 
+#print isGLB_biInf /-
 theorem isGLB_biInf {s : Set β} {f : β → α} : IsGLB (f '' s) (⨅ x ∈ s, f x) := by
   simpa only [range_comp, Subtype.range_coe, iInf_subtype'] using @isGLB_iInf α s _ (f ∘ coe)
 #align is_glb_binfi isGLB_biInf
+-/
 
+#print isLUB_biSup /-
 theorem isLUB_biSup {s : Set β} {f : β → α} : IsLUB (f '' s) (⨆ x ∈ s, f x) := by
   simpa only [range_comp, Subtype.range_coe, iSup_subtype'] using @isLUB_iSup α s _ (f ∘ coe)
 #align is_lub_bsupr isLUB_biSup
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print iSup_sigma /-
 theorem iSup_sigma {p : β → Type _} {f : Sigma p → α} : (⨆ x, f x) = ⨆ (i) (j), f ⟨i, j⟩ :=
   eq_of_forall_ge_iff fun c => by simp only [iSup_le_iff, Sigma.forall]
 #align supr_sigma iSup_sigma
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print iInf_sigma /-
 theorem iInf_sigma {p : β → Type _} {f : Sigma p → α} : (⨅ x, f x) = ⨅ (i) (j), f ⟨i, j⟩ :=
   @iSup_sigma αᵒᵈ _ _ _ _
 #align infi_sigma iInf_sigma
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print iSup_prod /-
 theorem iSup_prod {f : β × γ → α} : (⨆ x, f x) = ⨆ (i) (j), f (i, j) :=
   eq_of_forall_ge_iff fun c => by simp only [iSup_le_iff, Prod.forall]
 #align supr_prod iSup_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
+#print iInf_prod /-
 theorem iInf_prod {f : β × γ → α} : (⨅ x, f x) = ⨅ (i) (j), f (i, j) :=
   @iSup_prod αᵒᵈ _ _ _ _
 #align infi_prod iInf_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print biSup_prod /-
 theorem biSup_prod {f : β × γ → α} {s : Set β} {t : Set γ} :
     (⨆ x ∈ s ×ˢ t, f x) = ⨆ (a ∈ s) (b ∈ t), f (a, b) := by simp_rw [iSup_prod, mem_prod, iSup_and];
   exact iSup_congr fun _ => iSup_comm
 #align bsupr_prod biSup_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print biInf_prod /-
 theorem biInf_prod {f : β × γ → α} {s : Set β} {t : Set γ} :
     (⨅ x ∈ s ×ˢ t, f x) = ⨅ (a ∈ s) (b ∈ t), f (a, b) :=
   @biSup_prod αᵒᵈ _ _ _ _ _ _
 #align binfi_prod biInf_prod
+-/
 
+#print iSup_sum /-
 theorem iSup_sum {f : Sum β γ → α} : (⨆ x, f x) = (⨆ i, f (Sum.inl i)) ⊔ ⨆ j, f (Sum.inr j) :=
   eq_of_forall_ge_iff fun c => by simp only [sup_le_iff, iSup_le_iff, Sum.forall]
 #align supr_sum iSup_sum
+-/
 
+#print iInf_sum /-
 theorem iInf_sum {f : Sum β γ → α} : (⨅ x, f x) = (⨅ i, f (Sum.inl i)) ⊓ ⨅ j, f (Sum.inr j) :=
   @iSup_sum αᵒᵈ _ _ _ _
 #align infi_sum iInf_sum
+-/
 
+#print iSup_option /-
 theorem iSup_option (f : Option β → α) : (⨆ o, f o) = f none ⊔ ⨆ b, f (Option.some b) :=
   eq_of_forall_ge_iff fun c => by simp only [iSup_le_iff, sup_le_iff, Option.forall]
 #align supr_option iSup_option
+-/
 
+#print iInf_option /-
 theorem iInf_option (f : Option β → α) : (⨅ o, f o) = f none ⊓ ⨅ b, f (Option.some b) :=
   @iSup_option αᵒᵈ _ _ _
 #align infi_option iInf_option
+-/
 
+#print iSup_option_elim /-
 /-- A version of `supr_option` useful for rewriting right-to-left. -/
 theorem iSup_option_elim (a : α) (f : β → α) : (⨆ o : Option β, o.elim a f) = a ⊔ ⨆ b, f b := by
   simp [iSup_option]
 #align supr_option_elim iSup_option_elim
+-/
 
+#print iInf_option_elim /-
 /-- A version of `infi_option` useful for rewriting right-to-left. -/
 theorem iInf_option_elim (a : α) (f : β → α) : (⨅ o : Option β, o.elim a f) = a ⊓ ⨅ b, f b :=
   @iSup_option_elim αᵒᵈ _ _ _ _
 #align infi_option_elim iInf_option_elim
+-/
 
+#print iSup_ne_bot_subtype /-
 /-- When taking the supremum of `f : ι → α`, the elements of `ι` on which `f` gives `⊥` can be
 dropped, without changing the result. -/
 theorem iSup_ne_bot_subtype (f : ι → α) : (⨆ i : { i // f i ≠ ⊥ }, f i) = ⨆ i, f i :=
@@ -1638,45 +2121,61 @@ theorem iSup_ne_bot_subtype (f : ι → α) : (⨆ i : { i // f i ≠ ⊥ }, f i
     exact ⟨⟨i₀, hi₀⟩, bot_le⟩
   · exact ⟨⟨i, hi⟩, rfl.le⟩
 #align supr_ne_bot_subtype iSup_ne_bot_subtype
+-/
 
+#print iInf_ne_top_subtype /-
 /-- When taking the infimum of `f : ι → α`, the elements of `ι` on which `f` gives `⊤` can be
 dropped, without changing the result. -/
 theorem iInf_ne_top_subtype (f : ι → α) : (⨅ i : { i // f i ≠ ⊤ }, f i) = ⨅ i, f i :=
   @iSup_ne_bot_subtype αᵒᵈ ι _ f
 #align infi_ne_top_subtype iInf_ne_top_subtype
+-/
 
+#print sSup_image2 /-
 theorem sSup_image2 {f : β → γ → α} {s : Set β} {t : Set γ} :
     sSup (image2 f s t) = ⨆ (a ∈ s) (b ∈ t), f a b := by rw [← image_prod, sSup_image, biSup_prod]
 #align Sup_image2 sSup_image2
+-/
 
+#print sInf_image2 /-
 theorem sInf_image2 {f : β → γ → α} {s : Set β} {t : Set γ} :
     sInf (image2 f s t) = ⨅ (a ∈ s) (b ∈ t), f a b := by rw [← image_prod, sInf_image, biInf_prod]
 #align Inf_image2 sInf_image2
+-/
 
 /-!
 ### `supr` and `infi` under `ℕ`
 -/
 
 
+#print iSup_ge_eq_iSup_nat_add /-
 theorem iSup_ge_eq_iSup_nat_add (u : ℕ → α) (n : ℕ) : (⨆ i ≥ n, u i) = ⨆ i, u (i + n) :=
   by
   apply le_antisymm <;> simp only [iSup_le_iff]
   · exact fun i hi => le_sSup ⟨i - n, by dsimp only; rw [Nat.sub_add_cancel hi]⟩
   · exact fun i => le_sSup ⟨i + n, iSup_pos (Nat.le_add_left _ _)⟩
 #align supr_ge_eq_supr_nat_add iSup_ge_eq_iSup_nat_add
+-/
 
+#print iInf_ge_eq_iInf_nat_add /-
 theorem iInf_ge_eq_iInf_nat_add (u : ℕ → α) (n : ℕ) : (⨅ i ≥ n, u i) = ⨅ i, u (i + n) :=
   @iSup_ge_eq_iSup_nat_add αᵒᵈ _ _ _
 #align infi_ge_eq_infi_nat_add iInf_ge_eq_iInf_nat_add
+-/
 
+#print Monotone.iSup_nat_add /-
 theorem Monotone.iSup_nat_add {f : ℕ → α} (hf : Monotone f) (k : ℕ) : (⨆ n, f (n + k)) = ⨆ n, f n :=
   le_antisymm (iSup_le fun i => le_iSup _ (i + k)) <| iSup_mono fun i => hf <| Nat.le_add_right i k
 #align monotone.supr_nat_add Monotone.iSup_nat_add
+-/
 
+#print Antitone.iInf_nat_add /-
 theorem Antitone.iInf_nat_add {f : ℕ → α} (hf : Antitone f) (k : ℕ) : (⨅ n, f (n + k)) = ⨅ n, f n :=
   hf.dual_right.iSup_nat_add k
 #align antitone.infi_nat_add Antitone.iInf_nat_add
+-/
 
+#print iSup_iInf_ge_nat_add /-
 @[simp]
 theorem iSup_iInf_ge_nat_add (f : ℕ → α) (k : ℕ) : (⨆ n, ⨅ i ≥ n, f (i + k)) = ⨆ n, ⨅ i ≥ n, f i :=
   by
@@ -1684,31 +2183,42 @@ theorem iSup_iInf_ge_nat_add (f : ℕ → α) (k : ℕ) : (⨆ n, ⨅ i ≥ n, f
   rw [← Monotone.iSup_nat_add hf k]
   · simp_rw [iInf_ge_eq_iInf_nat_add, ← Nat.add_assoc]
 #align supr_infi_ge_nat_add iSup_iInf_ge_nat_add
+-/
 
+#print iInf_iSup_ge_nat_add /-
 @[simp]
 theorem iInf_iSup_ge_nat_add :
     ∀ (f : ℕ → α) (k : ℕ), (⨅ n, ⨆ i ≥ n, f (i + k)) = ⨅ n, ⨆ i ≥ n, f i :=
   @iSup_iInf_ge_nat_add αᵒᵈ _
 #align infi_supr_ge_nat_add iInf_iSup_ge_nat_add
+-/
 
+#print sup_iSup_nat_succ /-
 theorem sup_iSup_nat_succ (u : ℕ → α) : (u 0 ⊔ ⨆ i, u (i + 1)) = ⨆ i, u i :=
   calc
     (u 0 ⊔ ⨆ i, u (i + 1)) = ⨆ x ∈ {0} ∪ range Nat.succ, u x := by
       rw [iSup_union, iSup_singleton, iSup_range]
     _ = ⨆ i, u i := by rw [Nat.zero_union_range_succ, iSup_univ]
 #align sup_supr_nat_succ sup_iSup_nat_succ
+-/
 
+#print inf_iInf_nat_succ /-
 theorem inf_iInf_nat_succ (u : ℕ → α) : (u 0 ⊓ ⨅ i, u (i + 1)) = ⨅ i, u i :=
   @sup_iSup_nat_succ αᵒᵈ _ u
 #align inf_infi_nat_succ inf_iInf_nat_succ
+-/
 
+#print iInf_nat_gt_zero_eq /-
 theorem iInf_nat_gt_zero_eq (f : ℕ → α) : (⨅ i > 0, f i) = ⨅ i, f (i + 1) := by
   rw [← iInf_range, Nat.range_succ]; simp only [mem_set_of]
 #align infi_nat_gt_zero_eq iInf_nat_gt_zero_eq
+-/
 
+#print iSup_nat_gt_zero_eq /-
 theorem iSup_nat_gt_zero_eq (f : ℕ → α) : (⨆ i > 0, f i) = ⨆ i, f (i + 1) :=
   @iInf_nat_gt_zero_eq αᵒᵈ _ f
 #align supr_nat_gt_zero_eq iSup_nat_gt_zero_eq
+-/
 
 end
 
@@ -1716,13 +2226,17 @@ section CompleteLinearOrder
 
 variable [CompleteLinearOrder α]
 
+#print iSup_eq_top /-
 theorem iSup_eq_top (f : ι → α) : iSup f = ⊤ ↔ ∀ b < ⊤, ∃ i, b < f i := by
   simp only [← sSup_range, sSup_eq_top, Set.exists_range_iff]
 #align supr_eq_top iSup_eq_top
+-/
 
+#print iInf_eq_bot /-
 theorem iInf_eq_bot (f : ι → α) : iInf f = ⊥ ↔ ∀ b > ⊥, ∃ i, f i < b := by
   simp only [← sInf_range, sInf_eq_bot, Set.exists_range_iff]
 #align infi_eq_bot iInf_eq_bot
+-/
 
 end CompleteLinearOrder
 
@@ -1750,26 +2264,34 @@ noncomputable instance Prop.completeLinearOrder : CompleteLinearOrder Prop :=
 #align Prop.complete_linear_order Prop.completeLinearOrder
 -/
 
+#print sSup_Prop_eq /-
 @[simp]
 theorem sSup_Prop_eq {s : Set Prop} : sSup s = ∃ p ∈ s, p :=
   rfl
 #align Sup_Prop_eq sSup_Prop_eq
+-/
 
+#print sInf_Prop_eq /-
 @[simp]
 theorem sInf_Prop_eq {s : Set Prop} : sInf s = ∀ p ∈ s, p :=
   rfl
 #align Inf_Prop_eq sInf_Prop_eq
+-/
 
+#print iSup_Prop_eq /-
 @[simp]
 theorem iSup_Prop_eq {p : ι → Prop} : (⨆ i, p i) = ∃ i, p i :=
   le_antisymm (fun ⟨q, ⟨i, (Eq : p i = q)⟩, hq⟩ => ⟨i, Eq.symm ▸ hq⟩) fun ⟨i, hi⟩ =>
     ⟨p i, ⟨i, rfl⟩, hi⟩
 #align supr_Prop_eq iSup_Prop_eq
+-/
 
+#print iInf_Prop_eq /-
 @[simp]
 theorem iInf_Prop_eq {p : ι → Prop} : (⨅ i, p i) = ∀ i, p i :=
   le_antisymm (fun h i => h _ ⟨i, rfl⟩) fun h p ⟨i, Eq⟩ => Eq ▸ h i
 #align infi_Prop_eq iInf_Prop_eq
+-/
 
 #print Pi.supSet /-
 instance Pi.supSet {α : Type _} {β : α → Type _} [∀ i, SupSet (β i)] : SupSet (∀ i, β i) :=
@@ -1796,56 +2318,76 @@ instance Pi.completeLattice {α : Type _} {β : α → Type _} [∀ i, CompleteL
 #align pi.complete_lattice Pi.completeLattice
 -/
 
+#print sSup_apply /-
 theorem sSup_apply {α : Type _} {β : α → Type _} [∀ i, SupSet (β i)] {s : Set (∀ a, β a)} {a : α} :
     (sSup s) a = ⨆ f : s, (f : ∀ a, β a) a :=
   rfl
 #align Sup_apply sSup_apply
+-/
 
+#print sInf_apply /-
 theorem sInf_apply {α : Type _} {β : α → Type _} [∀ i, InfSet (β i)] {s : Set (∀ a, β a)} {a : α} :
     sInf s a = ⨅ f : s, (f : ∀ a, β a) a :=
   rfl
 #align Inf_apply sInf_apply
+-/
 
+#print iSup_apply /-
 @[simp]
 theorem iSup_apply {α : Type _} {β : α → Type _} {ι : Sort _} [∀ i, SupSet (β i)] {f : ι → ∀ a, β a}
     {a : α} : (⨆ i, f i) a = ⨆ i, f i a := by
   rw [iSup, sSup_apply, iSup, iSup, ← image_eq_range (fun f : ∀ i, β i => f a) (range f), ←
     range_comp]
 #align supr_apply iSup_apply
+-/
 
+#print iInf_apply /-
 @[simp]
 theorem iInf_apply {α : Type _} {β : α → Type _} {ι : Sort _} [∀ i, InfSet (β i)] {f : ι → ∀ a, β a}
     {a : α} : (⨅ i, f i) a = ⨅ i, f i a :=
   @iSup_apply α (fun i => (β i)ᵒᵈ) _ _ _ _
 #align infi_apply iInf_apply
+-/
 
+#print unary_relation_sSup_iff /-
 theorem unary_relation_sSup_iff {α : Type _} (s : Set (α → Prop)) {a : α} :
     sSup s a ↔ ∃ r : α → Prop, r ∈ s ∧ r a := by unfold Sup; simp [← eq_iff_iff]
 #align unary_relation_Sup_iff unary_relation_sSup_iff
+-/
 
+#print unary_relation_sInf_iff /-
 theorem unary_relation_sInf_iff {α : Type _} (s : Set (α → Prop)) {a : α} :
     sInf s a ↔ ∀ r : α → Prop, r ∈ s → r a := by unfold Inf; simp [← eq_iff_iff]
 #align unary_relation_Inf_iff unary_relation_sInf_iff
+-/
 
+#print binary_relation_sSup_iff /-
 theorem binary_relation_sSup_iff {α β : Type _} (s : Set (α → β → Prop)) {a : α} {b : β} :
     sSup s a b ↔ ∃ r : α → β → Prop, r ∈ s ∧ r a b := by unfold Sup; simp [← eq_iff_iff]
 #align binary_relation_Sup_iff binary_relation_sSup_iff
+-/
 
+#print binary_relation_sInf_iff /-
 theorem binary_relation_sInf_iff {α β : Type _} (s : Set (α → β → Prop)) {a : α} {b : β} :
     sInf s a b ↔ ∀ r : α → β → Prop, r ∈ s → r a b := by unfold Inf; simp [← eq_iff_iff]
 #align binary_relation_Inf_iff binary_relation_sInf_iff
+-/
 
 section CompleteLattice
 
 variable [Preorder α] [CompleteLattice β]
 
+#print monotone_sSup_of_monotone /-
 theorem monotone_sSup_of_monotone {s : Set (α → β)} (m_s : ∀ f ∈ s, Monotone f) :
     Monotone (sSup s) := fun x y h => iSup_mono fun f => m_s f f.2 h
 #align monotone_Sup_of_monotone monotone_sSup_of_monotone
+-/
 
+#print monotone_sInf_of_monotone /-
 theorem monotone_sInf_of_monotone {s : Set (α → β)} (m_s : ∀ f ∈ s, Monotone f) :
     Monotone (sInf s) := fun x y h => iInf_mono fun f => m_s f f.2 h
 #align monotone_Inf_of_monotone monotone_sInf_of_monotone
+-/
 
 end CompleteLattice
 
@@ -1861,65 +2403,93 @@ instance [InfSet α] [InfSet β] : InfSet (α × β) :=
 
 variable {α β}
 
+#print Prod.fst_sInf /-
 theorem fst_sInf [InfSet α] [InfSet β] (s : Set (α × β)) : (sInf s).fst = sInf (Prod.fst '' s) :=
   rfl
 #align prod.fst_Inf Prod.fst_sInf
+-/
 
+#print Prod.snd_sInf /-
 theorem snd_sInf [InfSet α] [InfSet β] (s : Set (α × β)) : (sInf s).snd = sInf (Prod.snd '' s) :=
   rfl
 #align prod.snd_Inf Prod.snd_sInf
+-/
 
+#print Prod.swap_sInf /-
 theorem swap_sInf [InfSet α] [InfSet β] (s : Set (α × β)) : (sInf s).symm = sInf (Prod.swap '' s) :=
   ext (congr_arg sInf <| image_comp Prod.fst swap s : _)
     (congr_arg sInf <| image_comp Prod.snd swap s : _)
 #align prod.swap_Inf Prod.swap_sInf
+-/
 
+#print Prod.fst_sSup /-
 theorem fst_sSup [SupSet α] [SupSet β] (s : Set (α × β)) : (sSup s).fst = sSup (Prod.fst '' s) :=
   rfl
 #align prod.fst_Sup Prod.fst_sSup
+-/
 
+#print Prod.snd_sSup /-
 theorem snd_sSup [SupSet α] [SupSet β] (s : Set (α × β)) : (sSup s).snd = sSup (Prod.snd '' s) :=
   rfl
 #align prod.snd_Sup Prod.snd_sSup
+-/
 
+#print Prod.swap_sSup /-
 theorem swap_sSup [SupSet α] [SupSet β] (s : Set (α × β)) : (sSup s).symm = sSup (Prod.swap '' s) :=
   ext (congr_arg sSup <| image_comp Prod.fst swap s : _)
     (congr_arg sSup <| image_comp Prod.snd swap s : _)
 #align prod.swap_Sup Prod.swap_sSup
+-/
 
+#print Prod.fst_iInf /-
 theorem fst_iInf [InfSet α] [InfSet β] (f : ι → α × β) : (iInf f).fst = ⨅ i, (f i).fst :=
   congr_arg sInf (range_comp _ _).symm
 #align prod.fst_infi Prod.fst_iInf
+-/
 
+#print Prod.snd_iInf /-
 theorem snd_iInf [InfSet α] [InfSet β] (f : ι → α × β) : (iInf f).snd = ⨅ i, (f i).snd :=
   congr_arg sInf (range_comp _ _).symm
 #align prod.snd_infi Prod.snd_iInf
+-/
 
+#print Prod.swap_iInf /-
 theorem swap_iInf [InfSet α] [InfSet β] (f : ι → α × β) : (iInf f).symm = ⨅ i, (f i).symm := by
   simp_rw [iInf, swap_Inf, range_comp]
 #align prod.swap_infi Prod.swap_iInf
+-/
 
+#print Prod.iInf_mk /-
 theorem iInf_mk [InfSet α] [InfSet β] (f : ι → α) (g : ι → β) :
     (⨅ i, (f i, g i)) = (⨅ i, f i, ⨅ i, g i) :=
   congr_arg₂ Prod.mk (fst_iInf _) (snd_iInf _)
 #align prod.infi_mk Prod.iInf_mk
+-/
 
+#print Prod.fst_iSup /-
 theorem fst_iSup [SupSet α] [SupSet β] (f : ι → α × β) : (iSup f).fst = ⨆ i, (f i).fst :=
   congr_arg sSup (range_comp _ _).symm
 #align prod.fst_supr Prod.fst_iSup
+-/
 
+#print Prod.snd_iSup /-
 theorem snd_iSup [SupSet α] [SupSet β] (f : ι → α × β) : (iSup f).snd = ⨆ i, (f i).snd :=
   congr_arg sSup (range_comp _ _).symm
 #align prod.snd_supr Prod.snd_iSup
+-/
 
+#print Prod.swap_iSup /-
 theorem swap_iSup [SupSet α] [SupSet β] (f : ι → α × β) : (iSup f).symm = ⨆ i, (f i).symm := by
   simp_rw [iSup, swap_Sup, range_comp]
 #align prod.swap_supr Prod.swap_iSup
+-/
 
+#print Prod.iSup_mk /-
 theorem iSup_mk [SupSet α] [SupSet β] (f : ι → α) (g : ι → β) :
     (⨆ i, (f i, g i)) = (⨆ i, f i, ⨆ i, g i) :=
   congr_arg₂ Prod.mk (fst_iSup _) (snd_iSup _)
 #align prod.supr_mk Prod.iSup_mk
+-/
 
 variable (α β)
 
@@ -1939,61 +2509,82 @@ instance [CompleteLattice α] [CompleteLattice β] : CompleteLattice (α × β)
 end Prod
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print sInf_prod /-
 theorem sInf_prod [InfSet α] [InfSet β] {s : Set α} {t : Set β} (hs : s.Nonempty)
     (ht : t.Nonempty) : sInf (s ×ˢ t) = (sInf s, sInf t) :=
   congr_arg₂ Prod.mk (congr_arg sInf <| fst_image_prod _ ht) (congr_arg sInf <| snd_image_prod hs _)
 #align Inf_prod sInf_prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print sSup_prod /-
 theorem sSup_prod [SupSet α] [SupSet β] {s : Set α} {t : Set β} (hs : s.Nonempty)
     (ht : t.Nonempty) : sSup (s ×ˢ t) = (sSup s, sSup t) :=
   congr_arg₂ Prod.mk (congr_arg sSup <| fst_image_prod _ ht) (congr_arg sSup <| snd_image_prod hs _)
 #align Sup_prod sSup_prod
+-/
 
 section CompleteLattice
 
 variable [CompleteLattice α] {a : α} {s : Set α}
 
+#print sup_sInf_le_iInf_sup /-
 /-- This is a weaker version of `sup_Inf_eq` -/
 theorem sup_sInf_le_iInf_sup : a ⊔ sInf s ≤ ⨅ b ∈ s, a ⊔ b :=
   le_iInf₂ fun i h => sup_le_sup_left (sInf_le h) _
 #align sup_Inf_le_infi_sup sup_sInf_le_iInf_sup
+-/
 
+#print iSup_inf_le_inf_sSup /-
 /-- This is a weaker version of `inf_Sup_eq` -/
 theorem iSup_inf_le_inf_sSup : (⨆ b ∈ s, a ⊓ b) ≤ a ⊓ sSup s :=
   @sup_sInf_le_iInf_sup αᵒᵈ _ _ _
 #align supr_inf_le_inf_Sup iSup_inf_le_inf_sSup
+-/
 
+#print sInf_sup_le_iInf_sup /-
 /-- This is a weaker version of `Inf_sup_eq` -/
 theorem sInf_sup_le_iInf_sup : sInf s ⊔ a ≤ ⨅ b ∈ s, b ⊔ a :=
   le_iInf₂ fun i h => sup_le_sup_right (sInf_le h) _
 #align Inf_sup_le_infi_sup sInf_sup_le_iInf_sup
+-/
 
+#print iSup_inf_le_sSup_inf /-
 /-- This is a weaker version of `Sup_inf_eq` -/
 theorem iSup_inf_le_sSup_inf : (⨆ b ∈ s, b ⊓ a) ≤ sSup s ⊓ a :=
   @sInf_sup_le_iInf_sup αᵒᵈ _ _ _
 #align supr_inf_le_Sup_inf iSup_inf_le_sSup_inf
+-/
 
+#print le_iSup_inf_iSup /-
 theorem le_iSup_inf_iSup (f g : ι → α) : (⨆ i, f i ⊓ g i) ≤ (⨆ i, f i) ⊓ ⨆ i, g i :=
   le_inf (iSup_mono fun i => inf_le_left) (iSup_mono fun i => inf_le_right)
 #align le_supr_inf_supr le_iSup_inf_iSup
+-/
 
+#print iInf_sup_iInf_le /-
 theorem iInf_sup_iInf_le (f g : ι → α) : ((⨅ i, f i) ⊔ ⨅ i, g i) ≤ ⨅ i, f i ⊔ g i :=
   @le_iSup_inf_iSup αᵒᵈ ι _ f g
 #align infi_sup_infi_le iInf_sup_iInf_le
+-/
 
+#print disjoint_sSup_left /-
 theorem disjoint_sSup_left {a : Set α} {b : α} (d : Disjoint (sSup a) b) {i} (hi : i ∈ a) :
     Disjoint i b :=
   disjoint_iff_inf_le.mpr (iSup₂_le_iff.1 (iSup_inf_le_sSup_inf.trans d.le_bot) i hi : _)
 #align disjoint_Sup_left disjoint_sSup_left
+-/
 
+#print disjoint_sSup_right /-
 theorem disjoint_sSup_right {a : Set α} {b : α} (d : Disjoint b (sSup a)) {i} (hi : i ∈ a) :
     Disjoint b i :=
   disjoint_iff_inf_le.mpr (iSup₂_le_iff.mp (iSup_inf_le_inf_sSup.trans d.le_bot) i hi : _)
 #align disjoint_Sup_right disjoint_sSup_right
+-/
 
 end CompleteLattice
 
+#print Function.Injective.completeLattice /-
 -- See note [reducible non-instances]
 /-- Pullback a `complete_lattice` along an injection. -/
 @[reducible]
@@ -2016,4 +2607,5 @@ protected def Function.Injective.completeLattice [Sup α] [Inf α] [SupSet α] [
     bot := ⊥
     bot_le := fun a => map_bot.le.trans bot_le }
 #align function.injective.complete_lattice Function.Injective.completeLattice
+-/
 

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

@@ -1696,7 +1696,6 @@ theorem sup_iSup_nat_succ (u : ℕ → α) : (u 0 ⊔ ⨆ i, u (i + 1)) = ⨆ i,
     (u 0 ⊔ ⨆ i, u (i + 1)) = ⨆ x ∈ {0} ∪ range Nat.succ, u x := by
       rw [iSup_union, iSup_singleton, iSup_range]
     _ = ⨆ i, u i := by rw [Nat.zero_union_range_succ, iSup_univ]
-    
 #align sup_supr_nat_succ sup_iSup_nat_succ
 
 theorem inf_iInf_nat_succ (u : ℕ → α) : (u 0 ⊓ ⨅ i, u (i + 1)) = ⨅ i, u i :=

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

@@ -244,7 +244,7 @@ theorem sInf_le_sInf_of_forall_exists_le (h : ∀ x ∈ s, ∃ y ∈ t, y ≤ x)
       simp only [le_sInf_iff]
       introv h₀ h₁
       rcases h _ h₁ with ⟨y, hy, hy'⟩
-      solve_by_elim [le_trans _ hy'] )
+      solve_by_elim [le_trans _ hy'])
 #align Inf_le_Inf_of_forall_exists_le sInf_le_sInf_of_forall_exists_le
 
 -- We will generalize this to conditionally complete lattices in `cInf_singleton`.
@@ -295,7 +295,7 @@ def completeLatticeOfInf (α : Type _) [H1 : PartialOrder α] [H2 : InfSet α]
     bot_le := fun x => (isGLB_sInf univ).1 trivial
     top := sInf ∅
     le_top := fun a => (isGLB_sInf ∅).2 <| by simp
-    sup := fun a b => sInf { x | a ≤ x ∧ b ≤ x }
+    sup := fun a b => sInf {x | a ≤ x ∧ b ≤ x}
     inf := fun a b => sInf {a, b}
     le_inf := fun a b c hab hac => by apply (isGLB_sInf _).2; simp [*]
     inf_le_right := fun a b => (isGLB_sInf _).1 <| mem_insert_of_mem _ <| mem_singleton _
@@ -350,7 +350,7 @@ def completeLatticeOfSup (α : Type _) [H1 : PartialOrder α] [H2 : SupSet α]
     sup_le := fun a b c hac hbc => (isLUB_sSup _).2 (by simp [*])
     le_sup_left := fun a b => (isLUB_sSup _).1 <| mem_insert _ _
     le_sup_right := fun a b => (isLUB_sSup _).1 <| mem_insert_of_mem _ <| mem_singleton _
-    inf := fun a b => sSup { x | x ≤ a ∧ x ≤ b }
+    inf := fun a b => sSup {x | x ≤ a ∧ x ≤ b}
     le_inf := fun a b c hab hac => (isLUB_sSup _).1 <| by simp [*]
     inf_le_left := fun a b => (isLUB_sSup _).2 fun x => And.left
     inf_le_right := fun a b => (isLUB_sSup _).2 fun x => And.right
@@ -375,10 +375,10 @@ def completeLatticeOfCompleteSemilatticeSup (α : Type _) [CompleteSemilatticeSu
 -/
 
 #print CompleteLinearOrder /-
-/- ./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure -/
 /-- A complete linear order is a linear order whose lattice structure is complete. -/
 class CompleteLinearOrder (α : Type _) extends CompleteLattice α,
-    "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure"
+    "./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure"
 #align complete_linear_order CompleteLinearOrder
 -/
 
@@ -1453,7 +1453,7 @@ theorem iInf_union {f : β → α} {s t : Set β} : (⨅ x ∈ s ∪ t, f x) = (
 
 theorem iSup_split (f : β → α) (p : β → Prop) :
     (⨆ i, f i) = (⨆ (i) (h : p i), f i) ⊔ ⨆ (i) (h : ¬p i), f i := by
-  simpa [Classical.em] using @iSup_union _ _ _ f { i | p i } { i | ¬p i }
+  simpa [Classical.em] using @iSup_union _ _ _ f {i | p i} {i | ¬p i}
 #align supr_split iSup_split
 
 theorem iInf_split :

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

@@ -258,7 +258,7 @@ end
 /-- A complete lattice is a bounded lattice which has suprema and infima for every subset. -/
 @[protect_proj]
 class CompleteLattice (α : Type _) extends Lattice α, CompleteSemilatticeSup α,
-  CompleteSemilatticeInf α, Top α, Bot α where
+    CompleteSemilatticeInf α, Top α, Bot α where
   le_top : ∀ x : α, x ≤ ⊤
   bot_le : ∀ x : α, ⊥ ≤ x
 #align complete_lattice CompleteLattice
@@ -378,7 +378,7 @@ def completeLatticeOfCompleteSemilatticeSup (α : Type _) [CompleteSemilatticeSu
 /- ./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure -/
 /-- A complete linear order is a linear order whose lattice structure is complete. -/
 class CompleteLinearOrder (α : Type _) extends CompleteLattice α,
-  "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure"
+    "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure"
 #align complete_linear_order CompleteLinearOrder
 -/
 
@@ -544,7 +544,7 @@ theorem sInf_eq_top : sInf s = ⊤ ↔ ∀ a ∈ s, a = ⊤ :=
 
 theorem eq_singleton_bot_of_sSup_eq_bot_of_nonempty {s : Set α} (h_sup : sSup s = ⊥)
     (hne : s.Nonempty) : s = {⊥} := by rw [Set.eq_singleton_iff_nonempty_unique_mem];
-  rw [sSup_eq_bot] at h_sup; exact ⟨hne, h_sup⟩
+  rw [sSup_eq_bot] at h_sup ; exact ⟨hne, h_sup⟩
 #align eq_singleton_bot_of_Sup_eq_bot_of_nonempty eq_singleton_bot_of_sSup_eq_bot_of_nonempty
 
 theorem eq_singleton_top_of_sInf_eq_top_of_nonempty : sInf s = ⊤ → s.Nonempty → s = {⊤} :=

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

@@ -264,11 +264,13 @@ class CompleteLattice (α : Type _) extends Lattice α, CompleteSemilatticeSup 
 #align complete_lattice CompleteLattice
 -/
 
+#print CompleteLattice.toBoundedOrder /-
 -- see Note [lower instance priority]
 instance (priority := 100) CompleteLattice.toBoundedOrder [h : CompleteLattice α] :
     BoundedOrder α :=
   { h with }
 #align complete_lattice.to_bounded_order CompleteLattice.toBoundedOrder
+-/
 
 #print completeLatticeOfInf /-
 /-- Create a `complete_lattice` from a `partial_order` and `Inf` function

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

@@ -132,104 +132,44 @@ section
 
 variable [CompleteSemilatticeSup α] {s t : Set α} {a b : α}
 
-/- warning: le_Sup -> le_sSup 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 le_Sup le_sSupₓ'. -/
 @[ematch]
 theorem le_sSup : a ∈ s → a ≤ sSup s :=
   CompleteSemilatticeSup.le_sup s a
 #align le_Sup le_sSup
 
-/- warning: Sup_le -> sSup_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align Sup_le sSup_leₓ'. -/
 theorem sSup_le : (∀ b ∈ s, b ≤ a) → sSup s ≤ a :=
   CompleteSemilatticeSup.sup_le s a
 #align Sup_le sSup_le
 
-/- warning: is_lub_Sup -> isLUB_sSup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_lub_Sup isLUB_sSupₓ'. -/
 theorem isLUB_sSup (s : Set α) : IsLUB s (sSup s) :=
   ⟨fun x => le_sSup, fun x => sSup_le⟩
 #align is_lub_Sup isLUB_sSup
 
-/- warning: is_lub.Sup_eq -> IsLUB.sSup_eq is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_lub.Sup_eq IsLUB.sSup_eqₓ'. -/
 theorem IsLUB.sSup_eq (h : IsLUB s a) : sSup s = a :=
   (isLUB_sSup s).unique h
 #align is_lub.Sup_eq IsLUB.sSup_eq
 
-/- warning: le_Sup_of_le -> le_sSup_of_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align le_Sup_of_le le_sSup_of_leₓ'. -/
 theorem le_sSup_of_le (hb : b ∈ s) (h : a ≤ b) : a ≤ sSup s :=
   le_trans h (le_sSup hb)
 #align le_Sup_of_le le_sSup_of_le
 
-/- warning: Sup_le_Sup -> sSup_le_sSup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align Sup_le_Sup sSup_le_sSupₓ'. -/
 theorem sSup_le_sSup (h : s ⊆ t) : sSup s ≤ sSup t :=
   (isLUB_sSup s).mono (isLUB_sSup t) h
 #align Sup_le_Sup sSup_le_sSup
 
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-Case conversion may be inaccurate. Consider using '#align Sup_le_iff sSup_le_iffₓ'. -/
 @[simp]
 theorem sSup_le_iff : sSup s ≤ a ↔ ∀ b ∈ s, b ≤ a :=
   isLUB_le_iff (isLUB_sSup s)
 #align Sup_le_iff sSup_le_iff
 
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-Case conversion may be inaccurate. Consider using '#align le_Sup_iff le_sSup_iffₓ'. -/
 theorem le_sSup_iff : a ≤ sSup s ↔ ∀ b ∈ upperBounds s, a ≤ b :=
   ⟨fun h b hb => le_trans h (sSup_le hb), fun hb => hb _ fun x => le_sSup⟩
 #align le_Sup_iff le_sSup_iff
 
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-Case conversion may be inaccurate. Consider using '#align le_supr_iff le_iSup_iffₓ'. -/
 theorem le_iSup_iff {s : ι → α} : a ≤ iSup s ↔ ∀ b, (∀ i, s i ≤ b) → a ≤ b := by
   simp [iSup, le_sSup_iff, upperBounds]
 #align le_supr_iff le_iSup_iff
 
-/- warning: Sup_le_Sup_of_forall_exists_le -> sSup_le_sSup_of_forall_exists_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align Sup_le_Sup_of_forall_exists_le sSup_le_sSup_of_forall_exists_leₓ'. -/
 theorem sSup_le_sSup_of_forall_exists_le (h : ∀ x ∈ s, ∃ y ∈ t, x ≤ y) : sSup s ≤ sSup t :=
   le_sSup_iff.2 fun b hb =>
     sSup_le fun a ha =>
@@ -237,12 +177,6 @@ theorem sSup_le_sSup_of_forall_exists_le (h : ∀ x ∈ s, ∃ y ∈ t, x ≤ y)
       hac.trans (hb hct)
 #align Sup_le_Sup_of_forall_exists_le sSup_le_sSup_of_forall_exists_le
 
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-Case conversion may be inaccurate. Consider using '#align Sup_singleton sSup_singletonₓ'. -/
 -- We will generalize this to conditionally complete lattices in `cSup_singleton`.
 theorem sSup_singleton {a : α} : sSup {a} = a :=
   isLUB_singleton.sSup_eq
@@ -266,104 +200,44 @@ section
 
 variable [CompleteSemilatticeInf α] {s t : Set α} {a b : α}
 
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-Case conversion may be inaccurate. Consider using '#align Inf_le sInf_leₓ'. -/
 @[ematch]
 theorem sInf_le : a ∈ s → sInf s ≤ a :=
   CompleteSemilatticeInf.inf_le s a
 #align Inf_le sInf_le
 
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-Case conversion may be inaccurate. Consider using '#align le_Inf le_sInfₓ'. -/
 theorem le_sInf : (∀ b ∈ s, a ≤ b) → a ≤ sInf s :=
   CompleteSemilatticeInf.le_inf s a
 #align le_Inf le_sInf
 
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-Case conversion may be inaccurate. Consider using '#align is_glb_Inf isGLB_sInfₓ'. -/
 theorem isGLB_sInf (s : Set α) : IsGLB s (sInf s) :=
   ⟨fun a => sInf_le, fun a => le_sInf⟩
 #align is_glb_Inf isGLB_sInf
 
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-Case conversion may be inaccurate. Consider using '#align is_glb.Inf_eq IsGLB.sInf_eqₓ'. -/
 theorem IsGLB.sInf_eq (h : IsGLB s a) : sInf s = a :=
   (isGLB_sInf s).unique h
 #align is_glb.Inf_eq IsGLB.sInf_eq
 
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-Case conversion may be inaccurate. Consider using '#align Inf_le_of_le sInf_le_of_leₓ'. -/
 theorem sInf_le_of_le (hb : b ∈ s) (h : b ≤ a) : sInf s ≤ a :=
   le_trans (sInf_le hb) h
 #align Inf_le_of_le sInf_le_of_le
 
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 theorem sInf_le_sInf (h : s ⊆ t) : sInf t ≤ sInf s :=
   (isGLB_sInf s).mono (isGLB_sInf t) h
 #align Inf_le_Inf sInf_le_sInf
 
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-Case conversion may be inaccurate. Consider using '#align le_Inf_iff le_sInf_iffₓ'. -/
 @[simp]
 theorem le_sInf_iff : a ≤ sInf s ↔ ∀ b ∈ s, a ≤ b :=
   le_isGLB_iff (isGLB_sInf s)
 #align le_Inf_iff le_sInf_iff
 
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-Case conversion may be inaccurate. Consider using '#align Inf_le_iff sInf_le_iffₓ'. -/
 theorem sInf_le_iff : sInf s ≤ a ↔ ∀ b ∈ lowerBounds s, b ≤ a :=
   ⟨fun h b hb => le_trans (le_sInf hb) h, fun hb => hb _ fun x => sInf_le⟩
 #align Inf_le_iff sInf_le_iff
 
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-Case conversion may be inaccurate. Consider using '#align infi_le_iff iInf_le_iffₓ'. -/
 theorem iInf_le_iff {s : ι → α} : iInf s ≤ a ↔ ∀ b, (∀ i, b ≤ s i) → b ≤ a := by
   simp [iInf, sInf_le_iff, lowerBounds]
 #align infi_le_iff iInf_le_iff
 
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-Case conversion may be inaccurate. Consider using '#align Inf_le_Inf_of_forall_exists_le sInf_le_sInf_of_forall_exists_leₓ'. -/
 theorem sInf_le_sInf_of_forall_exists_le (h : ∀ x ∈ s, ∃ y ∈ t, y ≤ x) : sInf t ≤ sInf s :=
   le_of_forall_le
     (by
@@ -373,12 +247,6 @@ theorem sInf_le_sInf_of_forall_exists_le (h : ∀ x ∈ s, ∃ y ∈ t, y ≤ x)
       solve_by_elim [le_trans _ hy'] )
 #align Inf_le_Inf_of_forall_exists_le sInf_le_sInf_of_forall_exists_le
 
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-Case conversion may be inaccurate. Consider using '#align Inf_singleton sInf_singletonₓ'. -/
 -- We will generalize this to conditionally complete lattices in `cInf_singleton`.
 theorem sInf_singleton {a : α} : sInf {a} = a :=
   isGLB_singleton.sInf_eq
@@ -396,12 +264,6 @@ class CompleteLattice (α : Type _) extends Lattice α, CompleteSemilatticeSup 
 #align complete_lattice CompleteLattice
 -/
 
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 -- see Note [lower instance priority]
 instance (priority := 100) CompleteLattice.toBoundedOrder [h : CompleteLattice α] :
     BoundedOrder α :=
@@ -569,280 +431,124 @@ theorem ofDual_sInf (s : Set αᵒᵈ) : ofDual (sInf s) = sSup (toDual ⁻¹' s
 #align of_dual_Inf ofDual_sInf
 -/
 
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 @[simp]
 theorem toDual_iSup (f : ι → α) : toDual (⨆ i, f i) = ⨅ i, toDual (f i) :=
   rfl
 #align to_dual_supr toDual_iSup
 
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 @[simp]
 theorem toDual_iInf (f : ι → α) : toDual (⨅ i, f i) = ⨆ i, toDual (f i) :=
   rfl
 #align to_dual_infi toDual_iInf
 
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 @[simp]
 theorem ofDual_iSup (f : ι → αᵒᵈ) : ofDual (⨆ i, f i) = ⨅ i, ofDual (f i) :=
   rfl
 #align of_dual_supr ofDual_iSup
 
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 @[simp]
 theorem ofDual_iInf (f : ι → αᵒᵈ) : ofDual (⨅ i, f i) = ⨆ i, ofDual (f i) :=
   rfl
 #align of_dual_infi ofDual_iInf
 
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 theorem sInf_le_sSup (hs : s.Nonempty) : sInf s ≤ sSup s :=
   isGLB_le_isLUB (isGLB_sInf s) (isLUB_sSup s) hs
 #align Inf_le_Sup sInf_le_sSup
 
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 theorem sSup_union {s t : Set α} : sSup (s ∪ t) = sSup s ⊔ sSup t :=
   ((isLUB_sSup s).union (isLUB_sSup t)).sSup_eq
 #align Sup_union sSup_union
 
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 theorem sInf_union {s t : Set α} : sInf (s ∪ t) = sInf s ⊓ sInf t :=
   ((isGLB_sInf s).union (isGLB_sInf t)).sInf_eq
 #align Inf_union sInf_union
 
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 theorem sSup_inter_le {s t : Set α} : sSup (s ∩ t) ≤ sSup s ⊓ sSup t :=
   sSup_le fun b hb => le_inf (le_sSup hb.1) (le_sSup hb.2)
 #align Sup_inter_le sSup_inter_le
 
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-Case conversion may be inaccurate. Consider using '#align le_Inf_inter le_sInf_interₓ'. -/
 theorem le_sInf_inter {s t : Set α} : sInf s ⊔ sInf t ≤ sInf (s ∩ t) :=
   @sSup_inter_le αᵒᵈ _ _ _
 #align le_Inf_inter le_sInf_inter
 
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 @[simp]
 theorem sSup_empty : sSup ∅ = (⊥ : α) :=
   (@isLUB_empty α _ _).sSup_eq
 #align Sup_empty sSup_empty
 
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 @[simp]
 theorem sInf_empty : sInf ∅ = (⊤ : α) :=
   (@isGLB_empty α _ _).sInf_eq
 #align Inf_empty sInf_empty
 
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 @[simp]
 theorem sSup_univ : sSup univ = (⊤ : α) :=
   (@isLUB_univ α _ _).sSup_eq
 #align Sup_univ sSup_univ
 
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 @[simp]
 theorem sInf_univ : sInf univ = (⊥ : α) :=
   (@isGLB_univ α _ _).sInf_eq
 #align Inf_univ sInf_univ
 
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 -- TODO(Jeremy): get this automatically
 @[simp]
 theorem sSup_insert {a : α} {s : Set α} : sSup (insert a s) = a ⊔ sSup s :=
   ((isLUB_sSup s).insert a).sSup_eq
 #align Sup_insert sSup_insert
 
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 @[simp]
 theorem sInf_insert {a : α} {s : Set α} : sInf (insert a s) = a ⊓ sInf s :=
   ((isGLB_sInf s).insert a).sInf_eq
 #align Inf_insert sInf_insert
 
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 theorem sSup_le_sSup_of_subset_insert_bot (h : s ⊆ insert ⊥ t) : sSup s ≤ sSup t :=
   le_trans (sSup_le_sSup h) (le_of_eq (trans sSup_insert bot_sup_eq))
 #align Sup_le_Sup_of_subset_insert_bot sSup_le_sSup_of_subset_insert_bot
 
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 theorem sInf_le_sInf_of_subset_insert_top (h : s ⊆ insert ⊤ t) : sInf t ≤ sInf s :=
   le_trans (le_of_eq (trans top_inf_eq.symm sInf_insert.symm)) (sInf_le_sInf h)
 #align Inf_le_Inf_of_subset_insert_top sInf_le_sInf_of_subset_insert_top
 
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 @[simp]
 theorem sSup_diff_singleton_bot (s : Set α) : sSup (s \ {⊥}) = sSup s :=
   (sSup_le_sSup (diff_subset _ _)).antisymm <|
     sSup_le_sSup_of_subset_insert_bot <| subset_insert_diff_singleton _ _
 #align Sup_diff_singleton_bot sSup_diff_singleton_bot
 
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 @[simp]
 theorem sInf_diff_singleton_top (s : Set α) : sInf (s \ {⊤}) = sInf s :=
   @sSup_diff_singleton_bot αᵒᵈ _ s
 #align Inf_diff_singleton_top sInf_diff_singleton_top
 
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-Case conversion may be inaccurate. Consider using '#align Sup_pair sSup_pairₓ'. -/
 theorem sSup_pair {a b : α} : sSup {a, b} = a ⊔ b :=
   (@isLUB_pair α _ a b).sSup_eq
 #align Sup_pair sSup_pair
 
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-Case conversion may be inaccurate. Consider using '#align Inf_pair sInf_pairₓ'. -/
 theorem sInf_pair {a b : α} : sInf {a, b} = a ⊓ b :=
   (@isGLB_pair α _ a b).sInf_eq
 #align Inf_pair sInf_pair
 
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 @[simp]
 theorem sSup_eq_bot : sSup s = ⊥ ↔ ∀ a ∈ s, a = ⊥ :=
   ⟨fun h a ha => bot_unique <| h ▸ le_sSup ha, fun h =>
     bot_unique <| sSup_le fun a ha => le_bot_iff.2 <| h a ha⟩
 #align Sup_eq_bot sSup_eq_bot
 
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 @[simp]
 theorem sInf_eq_top : sInf s = ⊤ ↔ ∀ a ∈ s, a = ⊤ :=
   @sSup_eq_bot αᵒᵈ _ _
 #align Inf_eq_top sInf_eq_top
 
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 theorem eq_singleton_bot_of_sSup_eq_bot_of_nonempty {s : Set α} (h_sup : sSup s = ⊥)
     (hne : s.Nonempty) : s = {⊥} := by rw [Set.eq_singleton_iff_nonempty_unique_mem];
   rw [sSup_eq_bot] at h_sup; exact ⟨hne, h_sup⟩
 #align eq_singleton_bot_of_Sup_eq_bot_of_nonempty eq_singleton_bot_of_sSup_eq_bot_of_nonempty
 
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 theorem eq_singleton_top_of_sInf_eq_top_of_nonempty : sInf s = ⊤ → s.Nonempty → s = {⊤} :=
   @eq_singleton_bot_of_sSup_eq_bot_of_nonempty αᵒᵈ _ _
 #align eq_singleton_top_of_Inf_eq_top_of_nonempty eq_singleton_top_of_sInf_eq_top_of_nonempty
 
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-Case conversion may be inaccurate. Consider using '#align Sup_eq_of_forall_le_of_forall_lt_exists_gt sSup_eq_of_forall_le_of_forall_lt_exists_gtₓ'. -/
 /-- Introduction rule to prove that `b` is the supremum of `s`: it suffices to check that `b`
 is larger than all elements of `s`, and that this is not the case of any `w < b`.
 See `cSup_eq_of_forall_le_of_forall_lt_exists_gt` for a version in conditionally complete
@@ -854,12 +560,6 @@ theorem sSup_eq_of_forall_le_of_forall_lt_exists_gt (h₁ : ∀ a ∈ s, a ≤ b
     ((le_sSup ha).trans_lt ha').False
 #align Sup_eq_of_forall_le_of_forall_lt_exists_gt sSup_eq_of_forall_le_of_forall_lt_exists_gt
 
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 /-- Introduction rule to prove that `b` is the infimum of `s`: it suffices to check that `b`
 is smaller than all elements of `s`, and that this is not the case of any `w > b`.
 See `cInf_eq_of_forall_ge_of_forall_gt_exists_lt` for a version in conditionally complete
@@ -875,32 +575,14 @@ section CompleteLinearOrder
 
 variable [CompleteLinearOrder α] {s t : Set α} {a b : α}
 
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-Case conversion may be inaccurate. Consider using '#align lt_Sup_iff lt_sSup_iffₓ'. -/
 theorem lt_sSup_iff : b < sSup s ↔ ∃ a ∈ s, b < a :=
   lt_isLUB_iff <| isLUB_sSup s
 #align lt_Sup_iff lt_sSup_iff
 
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-Case conversion may be inaccurate. Consider using '#align Inf_lt_iff sInf_lt_iffₓ'. -/
 theorem sInf_lt_iff : sInf s < b ↔ ∃ a ∈ s, a < b :=
   isGLB_lt_iff <| isGLB_sInf s
 #align Inf_lt_iff sInf_lt_iff
 
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-Case conversion may be inaccurate. Consider using '#align Sup_eq_top sSup_eq_topₓ'. -/
 theorem sSup_eq_top : sSup s = ⊤ ↔ ∀ b < ⊤, ∃ a ∈ s, b < a :=
   ⟨fun h b hb => lt_sSup_iff.1 <| hb.trans_eq h.symm, fun h =>
     top_unique <|
@@ -909,32 +591,14 @@ theorem sSup_eq_top : sSup s = ⊤ ↔ ∀ b < ⊤, ∃ a ∈ s, b < a :=
         (h.trans_le <| le_sSup ha).False⟩
 #align Sup_eq_top sSup_eq_top
 
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 theorem sInf_eq_bot : sInf s = ⊥ ↔ ∀ b > ⊥, ∃ a ∈ s, a < b :=
   @sSup_eq_top αᵒᵈ _ _
 #align Inf_eq_bot sInf_eq_bot
 
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 theorem lt_iSup_iff {f : ι → α} : a < iSup f ↔ ∃ i, a < f i :=
   lt_sSup_iff.trans exists_range_iff
 #align lt_supr_iff lt_iSup_iff
 
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 theorem iInf_lt_iff {f : ι → α} : iInf f < a ↔ ∃ i, f i < a :=
   sInf_lt_iff.trans exists_range_iff
 #align infi_lt_iff iInf_lt_iff
@@ -948,12 +612,6 @@ section SupSet
 
 variable [SupSet α] {f g : ι → α}
 
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 theorem sSup_range : sSup (range f) = iSup f :=
   rfl
 #align Sup_range sSup_range
@@ -963,53 +621,23 @@ theorem sSup_eq_iSup' (s : Set α) : sSup s = ⨆ a : s, a := by rw [iSup, Subty
 #align Sup_eq_supr' sSup_eq_iSup'
 -/
 
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 theorem iSup_congr (h : ∀ i, f i = g i) : (⨆ i, f i) = ⨆ i, g i :=
   congr_arg _ <| funext h
 #align supr_congr iSup_congr
 
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 theorem Function.Surjective.iSup_comp {f : ι → ι'} (hf : Surjective f) (g : ι' → α) :
     (⨆ x, g (f x)) = ⨆ y, g y := by simp only [iSup, hf.range_comp]
 #align function.surjective.supr_comp Function.Surjective.iSup_comp
 
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 theorem Equiv.iSup_comp {g : ι' → α} (e : ι ≃ ι') : (⨆ x, g (e x)) = ⨆ y, g y :=
   e.Surjective.iSup_comp _
 #align equiv.supr_comp Equiv.iSup_comp
 
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 protected theorem Function.Surjective.iSup_congr {g : ι' → α} (h : ι → ι') (h1 : Surjective h)
     (h2 : ∀ x, g (h x) = f x) : (⨆ x, f x) = ⨆ y, g y := by convert h1.supr_comp g;
   exact (funext h2).symm
 #align function.surjective.supr_congr Function.Surjective.iSup_congr
 
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 protected theorem Equiv.iSup_congr {g : ι' → α} (e : ι ≃ ι') (h : ∀ x, g (e x) = f x) :
     (⨆ x, f x) = ⨆ y, g y :=
   e.Surjective.iSup_congr _ h
@@ -1029,22 +657,10 @@ theorem iSup_plift_up (f : PLift ι → α) : (⨆ i, f (PLift.up i)) = ⨆ i, f
 #align supr_plift_up iSup_plift_up
 -/
 
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 theorem iSup_plift_down (f : ι → α) : (⨆ i, f (PLift.down i)) = ⨆ i, f i :=
   PLift.down_surjective.iSup_congr _ fun _ => rfl
 #align supr_plift_down iSup_plift_down
 
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 theorem iSup_range' (g : β → α) (f : ι → β) : (⨆ b : range f, g b) = ⨆ i, g (f i) := by
   rw [iSup, iSup, ← image_eq_range, ← range_comp]
 #align supr_range' iSup_range'
@@ -1061,12 +677,6 @@ section InfSet
 
 variable [InfSet α] {f g : ι → α}
 
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 theorem sInf_range : sInf (range f) = iInf f :=
   rfl
 #align Inf_range sInf_range
@@ -1077,54 +687,24 @@ theorem sInf_eq_iInf' (s : Set α) : sInf s = ⨅ a : s, a :=
 #align Inf_eq_infi' sInf_eq_iInf'
 -/
 
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 theorem iInf_congr (h : ∀ i, f i = g i) : (⨅ i, f i) = ⨅ i, g i :=
   congr_arg _ <| funext h
 #align infi_congr iInf_congr
 
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 theorem Function.Surjective.iInf_comp {f : ι → ι'} (hf : Surjective f) (g : ι' → α) :
     (⨅ x, g (f x)) = ⨅ y, g y :=
   @Function.Surjective.iSup_comp αᵒᵈ _ _ _ f hf g
 #align function.surjective.infi_comp Function.Surjective.iInf_comp
 
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 theorem Equiv.iInf_comp {g : ι' → α} (e : ι ≃ ι') : (⨅ x, g (e x)) = ⨅ y, g y :=
   @Equiv.iSup_comp αᵒᵈ _ _ _ _ e
 #align equiv.infi_comp Equiv.iInf_comp
 
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 protected theorem Function.Surjective.iInf_congr {g : ι' → α} (h : ι → ι') (h1 : Surjective h)
     (h2 : ∀ x, g (h x) = f x) : (⨅ x, f x) = ⨅ y, g y :=
   @Function.Surjective.iSup_congr αᵒᵈ _ _ _ _ _ h h1 h2
 #align function.surjective.infi_congr Function.Surjective.iInf_congr
 
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 protected theorem Equiv.iInf_congr {g : ι' → α} (e : ι ≃ ι') (h : ∀ x, g (e x) = f x) :
     (⨅ x, f x) = ⨅ y, g y :=
   @Equiv.iSup_congr αᵒᵈ _ _ _ _ _ e h
@@ -1144,22 +724,10 @@ theorem iInf_plift_up (f : PLift ι → α) : (⨅ i, f (PLift.up i)) = ⨅ i, f
 #align infi_plift_up iInf_plift_up
 -/
 
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 theorem iInf_plift_down (f : ι → α) : (⨅ i, f (PLift.down i)) = ⨅ i, f i :=
   PLift.down_surjective.iInf_congr _ fun _ => rfl
 #align infi_plift_down iInf_plift_down
 
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 theorem iInf_range' (g : β → α) (f : ι → β) : (⨅ b : range f, g b) = ⨅ i, g (f i) :=
   @iSup_range' αᵒᵈ _ _ _ _ _
 #align infi_range' iInf_range'
@@ -1176,56 +744,26 @@ section
 
 variable [CompleteLattice α] {f g s t : ι → α} {a b : α}
 
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 -- TODO: this declaration gives error when starting smt state
 --@[ematch]
 theorem le_iSup (f : ι → α) (i : ι) : f i ≤ iSup f :=
   le_sSup ⟨i, rfl⟩
 #align le_supr le_iSup
 
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 theorem iInf_le (f : ι → α) (i : ι) : iInf f ≤ f i :=
   sInf_le ⟨i, rfl⟩
 #align infi_le iInf_le
 
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 @[ematch]
 theorem le_iSup' (f : ι → α) (i : ι) : f i ≤ iSup f :=
   le_sSup ⟨i, rfl⟩
 #align le_supr' le_iSup'
 
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 @[ematch]
 theorem iInf_le' (f : ι → α) (i : ι) : iInf f ≤ f i :=
   sInf_le ⟨i, rfl⟩
 #align infi_le' iInf_le'
 
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 /- TODO: this version would be more powerful, but, alas, the pattern matcher
    doesn't accept it.
 @[ematch] lemma le_supr' (f : ι → α) (i : ι) : (: f i :) ≤ (: supr f :) :=
@@ -1235,190 +773,82 @@ theorem isLUB_iSup : IsLUB (range f) (⨆ j, f j) :=
   isLUB_sSup _
 #align is_lub_supr isLUB_iSup
 
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 theorem isGLB_iInf : IsGLB (range f) (⨅ j, f j) :=
   isGLB_sInf _
 #align is_glb_infi isGLB_iInf
 
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 theorem IsLUB.iSup_eq (h : IsLUB (range f) a) : (⨆ j, f j) = a :=
   h.sSup_eq
 #align is_lub.supr_eq IsLUB.iSup_eq
 
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-Case conversion may be inaccurate. Consider using '#align is_glb.infi_eq IsGLB.iInf_eqₓ'. -/
 theorem IsGLB.iInf_eq (h : IsGLB (range f) a) : (⨅ j, f j) = a :=
   h.sInf_eq
 #align is_glb.infi_eq IsGLB.iInf_eq
 
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-Case conversion may be inaccurate. Consider using '#align le_supr_of_le le_iSup_of_leₓ'. -/
 theorem le_iSup_of_le (i : ι) (h : a ≤ f i) : a ≤ iSup f :=
   h.trans <| le_iSup _ i
 #align le_supr_of_le le_iSup_of_le
 
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-Case conversion may be inaccurate. Consider using '#align infi_le_of_le iInf_le_of_leₓ'. -/
 theorem iInf_le_of_le (i : ι) (h : f i ≤ a) : iInf f ≤ a :=
   (iInf_le _ i).trans h
 #align infi_le_of_le iInf_le_of_le
 
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-Case conversion may be inaccurate. Consider using '#align le_supr₂ le_iSup₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem le_iSup₂ {f : ∀ i, κ i → α} (i : ι) (j : κ i) : f i j ≤ ⨆ (i) (j), f i j :=
   le_iSup_of_le i <| le_iSup (f i) j
 #align le_supr₂ le_iSup₂
 
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-Case conversion may be inaccurate. Consider using '#align infi₂_le iInf₂_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem iInf₂_le {f : ∀ i, κ i → α} (i : ι) (j : κ i) : (⨅ (i) (j), f i j) ≤ f i j :=
   iInf_le_of_le i <| iInf_le (f i) j
 #align infi₂_le iInf₂_le
 
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-Case conversion may be inaccurate. Consider using '#align le_supr₂_of_le le_iSup₂_of_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem le_iSup₂_of_le {f : ∀ i, κ i → α} (i : ι) (j : κ i) (h : a ≤ f i j) :
     a ≤ ⨆ (i) (j), f i j :=
   h.trans <| le_iSup₂ i j
 #align le_supr₂_of_le le_iSup₂_of_le
 
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-Case conversion may be inaccurate. Consider using '#align infi₂_le_of_le iInf₂_le_of_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem iInf₂_le_of_le {f : ∀ i, κ i → α} (i : ι) (j : κ i) (h : f i j ≤ a) :
     (⨅ (i) (j), f i j) ≤ a :=
   (iInf₂_le i j).trans h
 #align infi₂_le_of_le iInf₂_le_of_le
 
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-Case conversion may be inaccurate. Consider using '#align supr_le iSup_leₓ'. -/
 theorem iSup_le (h : ∀ i, f i ≤ a) : iSup f ≤ a :=
   sSup_le fun b ⟨i, Eq⟩ => Eq ▸ h i
 #align supr_le iSup_le
 
-/- warning: le_infi -> le_iInf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align le_infi le_iInfₓ'. -/
 theorem le_iInf (h : ∀ i, a ≤ f i) : a ≤ iInf f :=
   le_sInf fun b ⟨i, Eq⟩ => Eq ▸ h i
 #align le_infi le_iInf
 
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-Case conversion may be inaccurate. Consider using '#align supr₂_le iSup₂_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem iSup₂_le {f : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ a) : (⨆ (i) (j), f i j) ≤ a :=
   iSup_le fun i => iSup_le <| h i
 #align supr₂_le iSup₂_le
 
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-Case conversion may be inaccurate. Consider using '#align le_infi₂ le_iInf₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem le_iInf₂ {f : ∀ i, κ i → α} (h : ∀ i j, a ≤ f i j) : a ≤ ⨅ (i) (j), f i j :=
   le_iInf fun i => le_iInf <| h i
 #align le_infi₂ le_iInf₂
 
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 theorem iSup₂_le_iSup (κ : ι → Sort _) (f : ι → α) : (⨆ (i) (j : κ i), f i) ≤ ⨆ i, f i :=
   iSup₂_le fun i j => le_iSup f i
 #align supr₂_le_supr iSup₂_le_iSup
 
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-Case conversion may be inaccurate. Consider using '#align infi_le_infi₂ iInf_le_iInf₂ₓ'. -/
 theorem iInf_le_iInf₂ (κ : ι → Sort _) (f : ι → α) : (⨅ i, f i) ≤ ⨅ (i) (j : κ i), f i :=
   le_iInf₂ fun i j => iInf_le f i
 #align infi_le_infi₂ iInf_le_iInf₂
 
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-Case conversion may be inaccurate. Consider using '#align supr_mono iSup_monoₓ'. -/
 theorem iSup_mono (h : ∀ i, f i ≤ g i) : iSup f ≤ iSup g :=
   iSup_le fun i => le_iSup_of_le i <| h i
 #align supr_mono iSup_mono
 
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-Case conversion may be inaccurate. Consider using '#align infi_mono iInf_monoₓ'. -/
 theorem iInf_mono (h : ∀ i, f i ≤ g i) : iInf f ≤ iInf g :=
   le_iInf fun i => iInf_le_of_le i <| h i
 #align infi_mono iInf_mono
 
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-Case conversion may be inaccurate. Consider using '#align supr₂_mono iSup₂_monoₓ'. -/
 /- ./././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) -/
 theorem iSup₂_mono {f g : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ g i j) :
@@ -1426,12 +856,6 @@ theorem iSup₂_mono {f g : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ g i j) :
   iSup_mono fun i => iSup_mono <| h i
 #align supr₂_mono iSup₂_mono
 
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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) -/
 theorem iInf₂_mono {f g : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ g i j) :
@@ -1439,32 +863,14 @@ theorem iInf₂_mono {f g : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ g i j) :
   iInf_mono fun i => iInf_mono <| h i
 #align infi₂_mono iInf₂_mono
 
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-Case conversion may be inaccurate. Consider using '#align supr_mono' iSup_mono'ₓ'. -/
 theorem iSup_mono' {g : ι' → α} (h : ∀ i, ∃ i', f i ≤ g i') : iSup f ≤ iSup g :=
   iSup_le fun i => Exists.elim (h i) le_iSup_of_le
 #align supr_mono' iSup_mono'
 
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-Case conversion may be inaccurate. Consider using '#align infi_mono' iInf_mono'ₓ'. -/
 theorem iInf_mono' {g : ι' → α} (h : ∀ i', ∃ i, f i ≤ g i') : iInf f ≤ iInf g :=
   le_iInf fun i' => Exists.elim (h i') iInf_le_of_le
 #align infi_mono' iInf_mono'
 
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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) -/
 theorem iSup₂_mono' {f : ∀ i, κ i → α} {g : ∀ i', κ' i' → α} (h : ∀ i j, ∃ i' j', f i j ≤ g i' j') :
@@ -1474,12 +880,6 @@ theorem iSup₂_mono' {f : ∀ i, κ i → α} {g : ∀ i', κ' i' → α} (h :
     le_iSup₂_of_le i' j' h
 #align supr₂_mono' iSup₂_mono'
 
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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) -/
 theorem iInf₂_mono' {f : ∀ i, κ i → α} {g : ∀ i', κ' i' → α} (h : ∀ i j, ∃ i' j', f i' j' ≤ g i j) :
@@ -1489,172 +889,76 @@ theorem iInf₂_mono' {f : ∀ i, κ i → α} {g : ∀ i', κ' i' → α} (h :
     iInf₂_le_of_le i' j' h
 #align infi₂_mono' iInf₂_mono'
 
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 theorem iSup_const_mono (h : ι → ι') : (⨆ i : ι, a) ≤ ⨆ j : ι', a :=
   iSup_le <| le_iSup _ ∘ h
 #align supr_const_mono iSup_const_mono
 
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 theorem iInf_const_mono (h : ι' → ι) : (⨅ i : ι, a) ≤ ⨅ j : ι', a :=
   le_iInf <| iInf_le _ ∘ h
 #align infi_const_mono iInf_const_mono
 
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 theorem iSup_iInf_le_iInf_iSup (f : ι → ι' → α) : (⨆ i, ⨅ j, f i j) ≤ ⨅ j, ⨆ i, f i j :=
   iSup_le fun i => iInf_mono fun j => le_iSup _ i
 #align supr_infi_le_infi_supr iSup_iInf_le_iInf_iSup
 
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 theorem biSup_mono {p q : ι → Prop} (hpq : ∀ i, p i → q i) :
     (⨆ (i) (h : p i), f i) ≤ ⨆ (i) (h : q i), f i :=
   iSup_mono fun i => iSup_const_mono (hpq i)
 #align bsupr_mono biSup_mono
 
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 theorem biInf_mono {p q : ι → Prop} (hpq : ∀ i, p i → q i) :
     (⨅ (i) (h : q i), f i) ≤ ⨅ (i) (h : p i), f i :=
   iInf_mono fun i => iInf_const_mono (hpq i)
 #align binfi_mono biInf_mono
 
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 @[simp]
 theorem iSup_le_iff : iSup f ≤ a ↔ ∀ i, f i ≤ a :=
   (isLUB_le_iff isLUB_iSup).trans forall_range_iff
 #align supr_le_iff iSup_le_iff
 
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 @[simp]
 theorem le_iInf_iff : a ≤ iInf f ↔ ∀ i, a ≤ f i :=
   (le_isGLB_iff isGLB_iInf).trans forall_range_iff
 #align le_infi_iff le_iInf_iff
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
 theorem iSup₂_le_iff {f : ∀ i, κ i → α} : (⨆ (i) (j), f i j) ≤ a ↔ ∀ i j, f i j ≤ a := by
   simp_rw [iSup_le_iff]
 #align supr₂_le_iff iSup₂_le_iff
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
 theorem le_iInf₂_iff {f : ∀ i, κ i → α} : (a ≤ ⨅ (i) (j), f i j) ↔ ∀ i j, a ≤ f i j := by
   simp_rw [le_iInf_iff]
 #align le_infi₂_iff le_iInf₂_iff
 
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-Case conversion may be inaccurate. Consider using '#align supr_lt_iff iSup_lt_iffₓ'. -/
 theorem iSup_lt_iff : iSup f < a ↔ ∃ b, b < a ∧ ∀ i, f i ≤ b :=
   ⟨fun h => ⟨iSup f, h, le_iSup f⟩, fun ⟨b, h, hb⟩ => (iSup_le hb).trans_lt h⟩
 #align supr_lt_iff iSup_lt_iff
 
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 theorem lt_iInf_iff : a < iInf f ↔ ∃ b, a < b ∧ ∀ i, b ≤ f i :=
   ⟨fun h => ⟨iInf f, h, iInf_le f⟩, fun ⟨b, h, hb⟩ => h.trans_le <| le_iInf hb⟩
 #align lt_infi_iff lt_iInf_iff
 
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 theorem sSup_eq_iSup {s : Set α} : sSup s = ⨆ a ∈ s, a :=
   le_antisymm (sSup_le le_iSup₂) (iSup₂_le fun b => le_sSup)
 #align Sup_eq_supr sSup_eq_iSup
 
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-Case conversion may be inaccurate. Consider using '#align Inf_eq_infi sInf_eq_iInfₓ'. -/
 theorem sInf_eq_iInf {s : Set α} : sInf s = ⨅ a ∈ s, a :=
   @sSup_eq_iSup αᵒᵈ _ _
 #align Inf_eq_infi sInf_eq_iInf
 
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-Case conversion may be inaccurate. Consider using '#align monotone.le_map_supr Monotone.le_map_iSupₓ'. -/
 theorem Monotone.le_map_iSup [CompleteLattice β] {f : α → β} (hf : Monotone f) :
     (⨆ i, f (s i)) ≤ f (iSup s) :=
   iSup_le fun i => hf <| le_iSup _ _
 #align monotone.le_map_supr Monotone.le_map_iSup
 
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-Case conversion may be inaccurate. Consider using '#align antitone.le_map_infi Antitone.le_map_iInfₓ'. -/
 theorem Antitone.le_map_iInf [CompleteLattice β] {f : α → β} (hf : Antitone f) :
     (⨆ i, f (s i)) ≤ f (iInf s) :=
   hf.dual_left.le_map_iSup
 #align antitone.le_map_infi Antitone.le_map_iInf
 
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-Case conversion may be inaccurate. Consider using '#align monotone.le_map_supr₂ Monotone.le_map_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) -/
 theorem Monotone.le_map_iSup₂ [CompleteLattice β] {f : α → β} (hf : Monotone f) (s : ∀ i, κ i → α) :
@@ -1662,12 +966,6 @@ theorem Monotone.le_map_iSup₂ [CompleteLattice β] {f : α → β} (hf : Monot
   iSup₂_le fun i j => hf <| le_iSup₂ _ _
 #align monotone.le_map_supr₂ Monotone.le_map_iSup₂
 
-/- warning: antitone.le_map_infi₂ -> Antitone.le_map_iInf₂ is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align antitone.le_map_infi₂ Antitone.le_map_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) -/
 theorem Antitone.le_map_iInf₂ [CompleteLattice β] {f : α → β} (hf : Antitone f) (s : ∀ i, κ i → α) :
@@ -1675,128 +973,62 @@ theorem Antitone.le_map_iInf₂ [CompleteLattice β] {f : α → β} (hf : Antit
   hf.dual_left.le_map_iSup₂ _
 #align antitone.le_map_infi₂ Antitone.le_map_iInf₂
 
-/- warning: monotone.le_map_Sup -> Monotone.le_map_sSup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align monotone.le_map_Sup Monotone.le_map_sSupₓ'. -/
 theorem Monotone.le_map_sSup [CompleteLattice β] {s : Set α} {f : α → β} (hf : Monotone f) :
     (⨆ a ∈ s, f a) ≤ f (sSup s) := by rw [sSup_eq_iSup] <;> exact hf.le_map_supr₂ _
 #align monotone.le_map_Sup Monotone.le_map_sSup
 
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-Case conversion may be inaccurate. Consider using '#align antitone.le_map_Inf Antitone.le_map_sInfₓ'. -/
 theorem Antitone.le_map_sInf [CompleteLattice β] {s : Set α} {f : α → β} (hf : Antitone f) :
     (⨆ a ∈ s, f a) ≤ f (sInf s) :=
   hf.dual_left.le_map_sSup
 #align antitone.le_map_Inf Antitone.le_map_sInf
 
-/- warning: order_iso.map_supr -> OrderIso.map_iSup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align order_iso.map_supr OrderIso.map_iSupₓ'. -/
 theorem OrderIso.map_iSup [CompleteLattice β] (f : α ≃o β) (x : ι → α) :
     f (⨆ i, x i) = ⨆ i, f (x i) :=
   eq_of_forall_ge_iff <| f.Surjective.forall.2 fun x => by simp only [f.le_iff_le, iSup_le_iff]
 #align order_iso.map_supr OrderIso.map_iSup
 
-/- warning: order_iso.map_infi -> OrderIso.map_iInf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align order_iso.map_infi OrderIso.map_iInfₓ'. -/
 theorem OrderIso.map_iInf [CompleteLattice β] (f : α ≃o β) (x : ι → α) :
     f (⨅ i, x i) = ⨅ i, f (x i) :=
   OrderIso.map_iSup f.dual _
 #align order_iso.map_infi OrderIso.map_iInf
 
-/- warning: order_iso.map_Sup -> OrderIso.map_sSup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align order_iso.map_Sup OrderIso.map_sSupₓ'. -/
 theorem OrderIso.map_sSup [CompleteLattice β] (f : α ≃o β) (s : Set α) :
     f (sSup s) = ⨆ a ∈ s, f a := by simp only [sSup_eq_iSup, OrderIso.map_iSup]
 #align order_iso.map_Sup OrderIso.map_sSup
 
-/- warning: order_iso.map_Inf -> OrderIso.map_sInf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align order_iso.map_Inf OrderIso.map_sInfₓ'. -/
 theorem OrderIso.map_sInf [CompleteLattice β] (f : α ≃o β) (s : Set α) :
     f (sInf s) = ⨅ a ∈ s, f a :=
   OrderIso.map_sSup f.dual _
 #align order_iso.map_Inf OrderIso.map_sInf
 
-/- warning: supr_comp_le -> iSup_comp_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align supr_comp_le iSup_comp_leₓ'. -/
 theorem iSup_comp_le {ι' : Sort _} (f : ι' → α) (g : ι → ι') : (⨆ x, f (g x)) ≤ ⨆ y, f y :=
   iSup_mono' fun x => ⟨_, le_rfl⟩
 #align supr_comp_le iSup_comp_le
 
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-Case conversion may be inaccurate. Consider using '#align le_infi_comp le_iInf_compₓ'. -/
 theorem le_iInf_comp {ι' : Sort _} (f : ι' → α) (g : ι → ι') : (⨅ y, f y) ≤ ⨅ x, f (g x) :=
   iInf_mono' fun x => ⟨_, le_rfl⟩
 #align le_infi_comp le_iInf_comp
 
-/- warning: monotone.supr_comp_eq -> Monotone.iSup_comp_eq is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align monotone.supr_comp_eq Monotone.iSup_comp_eqₓ'. -/
 theorem Monotone.iSup_comp_eq [Preorder β] {f : β → α} (hf : Monotone f) {s : ι → β}
     (hs : ∀ x, ∃ i, x ≤ s i) : (⨆ x, f (s x)) = ⨆ y, f y :=
   le_antisymm (iSup_comp_le _ _) (iSup_mono' fun x => (hs x).imp fun i hi => hf hi)
 #align monotone.supr_comp_eq Monotone.iSup_comp_eq
 
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-Case conversion may be inaccurate. Consider using '#align monotone.infi_comp_eq Monotone.iInf_comp_eqₓ'. -/
 theorem Monotone.iInf_comp_eq [Preorder β] {f : β → α} (hf : Monotone f) {s : ι → β}
     (hs : ∀ x, ∃ i, s i ≤ x) : (⨅ x, f (s x)) = ⨅ y, f y :=
   le_antisymm (iInf_mono' fun x => (hs x).imp fun i hi => hf hi) (le_iInf_comp _ _)
 #align monotone.infi_comp_eq Monotone.iInf_comp_eq
 
-/- warning: antitone.map_supr_le -> Antitone.map_iSup_le is a dubious translation:
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 theorem Antitone.map_iSup_le [CompleteLattice β] {f : α → β} (hf : Antitone f) :
     f (iSup s) ≤ ⨅ i, f (s i) :=
   le_iInf fun i => hf <| le_iSup _ _
 #align antitone.map_supr_le Antitone.map_iSup_le
 
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-Case conversion may be inaccurate. Consider using '#align monotone.map_infi_le Monotone.map_iInf_leₓ'. -/
 theorem Monotone.map_iInf_le [CompleteLattice β] {f : α → β} (hf : Monotone f) :
     f (iInf s) ≤ ⨅ i, f (s i) :=
   hf.dual_left.map_iSup_le
 #align monotone.map_infi_le Monotone.map_iInf_le
 
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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) -/
 theorem Antitone.map_iSup₂_le [CompleteLattice β] {f : α → β} (hf : Antitone f) (s : ∀ i, κ i → α) :
@@ -1804,12 +1036,6 @@ theorem Antitone.map_iSup₂_le [CompleteLattice β] {f : α → β} (hf : Antit
   hf.dual.le_map_iInf₂ _
 #align antitone.map_supr₂_le Antitone.map_iSup₂_le
 
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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) -/
 theorem Monotone.map_iInf₂_le [CompleteLattice β] {f : α → β} (hf : Monotone f) (s : ∀ i, κ i → α) :
@@ -1817,185 +1043,83 @@ theorem Monotone.map_iInf₂_le [CompleteLattice β] {f : α → β} (hf : Monot
   hf.dual.le_map_iSup₂ _
 #align monotone.map_infi₂_le Monotone.map_iInf₂_le
 
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 theorem Antitone.map_sSup_le [CompleteLattice β] {s : Set α} {f : α → β} (hf : Antitone f) :
     f (sSup s) ≤ ⨅ a ∈ s, f a := by rw [sSup_eq_iSup]; exact hf.map_supr₂_le _
 #align antitone.map_Sup_le Antitone.map_sSup_le
 
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 theorem Monotone.map_sInf_le [CompleteLattice β] {s : Set α} {f : α → β} (hf : Monotone f) :
     f (sInf s) ≤ ⨅ a ∈ s, f a :=
   hf.dual_left.map_sSup_le
 #align monotone.map_Inf_le Monotone.map_sInf_le
 
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 theorem iSup_const_le : (⨆ i : ι, a) ≤ a :=
   iSup_le fun _ => le_rfl
 #align supr_const_le iSup_const_le
 
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 theorem le_iInf_const : a ≤ ⨅ i : ι, a :=
   le_iInf fun _ => le_rfl
 #align le_infi_const le_iInf_const
 
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 -- We generalize this to conditionally complete lattices in `csupr_const` and `cinfi_const`.
 theorem iSup_const [Nonempty ι] : (⨆ b : ι, a) = a := by rw [iSup, range_const, sSup_singleton]
 #align supr_const iSup_const
 
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 theorem iInf_const [Nonempty ι] : (⨅ b : ι, a) = a :=
   @iSup_const αᵒᵈ _ _ a _
 #align infi_const iInf_const
 
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 @[simp]
 theorem iSup_bot : (⨆ i : ι, ⊥ : α) = ⊥ :=
   bot_unique iSup_const_le
 #align supr_bot iSup_bot
 
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 @[simp]
 theorem iInf_top : (⨅ i : ι, ⊤ : α) = ⊤ :=
   top_unique le_iInf_const
 #align infi_top iInf_top
 
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 @[simp]
 theorem iSup_eq_bot : iSup s = ⊥ ↔ ∀ i, s i = ⊥ :=
   sSup_eq_bot.trans forall_range_iff
 #align supr_eq_bot iSup_eq_bot
 
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 @[simp]
 theorem iInf_eq_top : iInf s = ⊤ ↔ ∀ i, s i = ⊤ :=
   sInf_eq_top.trans forall_range_iff
 #align infi_eq_top iInf_eq_top
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
 theorem iSup₂_eq_bot {f : ∀ i, κ i → α} : (⨆ (i) (j), f i j) = ⊥ ↔ ∀ i j, f i j = ⊥ := by
   simp_rw [iSup_eq_bot]
 #align supr₂_eq_bot iSup₂_eq_bot
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
 theorem iInf₂_eq_top {f : ∀ i, κ i → α} : (⨅ (i) (j), f i j) = ⊤ ↔ ∀ i j, f i j = ⊤ := by
   simp_rw [iInf_eq_top]
 #align infi₂_eq_top iInf₂_eq_top
 
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 @[simp]
 theorem iSup_pos {p : Prop} {f : p → α} (hp : p) : (⨆ h : p, f h) = f hp :=
   le_antisymm (iSup_le fun h => le_rfl) (le_iSup _ _)
 #align supr_pos iSup_pos
 
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 @[simp]
 theorem iInf_pos {p : Prop} {f : p → α} (hp : p) : (⨅ h : p, f h) = f hp :=
   le_antisymm (iInf_le _ _) (le_iInf fun h => le_rfl)
 #align infi_pos iInf_pos
 
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 @[simp]
 theorem iSup_neg {p : Prop} {f : p → α} (hp : ¬p) : (⨆ h : p, f h) = ⊥ :=
   le_antisymm (iSup_le fun h => (hp h).elim) bot_le
 #align supr_neg iSup_neg
 
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 @[simp]
 theorem iInf_neg {p : Prop} {f : p → α} (hp : ¬p) : (⨅ h : p, f h) = ⊤ :=
   le_antisymm le_top <| le_iInf fun h => (hp h).elim
 #align infi_neg iInf_neg
 
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 /-- Introduction rule to prove that `b` is the supremum of `f`: it suffices to check that `b`
 is larger than `f i` for all `i`, and that this is not the case of any `w<b`.
 See `csupr_eq_of_forall_le_of_forall_lt_exists_gt` for a version in conditionally complete
@@ -2006,12 +1130,6 @@ theorem iSup_eq_of_forall_le_of_forall_lt_exists_gt {f : ι → α} (h₁ : ∀
     exists_range_iff.mpr <| h₂ w hw
 #align supr_eq_of_forall_le_of_forall_lt_exists_gt iSup_eq_of_forall_le_of_forall_lt_exists_gt
 
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 /-- Introduction rule to prove that `b` is the infimum of `f`: it suffices to check that `b`
 is smaller than `f i` for all `i`, and that this is not the case of any `w>b`.
 See `cinfi_eq_of_forall_ge_of_forall_gt_exists_lt` for a version in conditionally complete
@@ -2021,53 +1139,23 @@ theorem iInf_eq_of_forall_ge_of_forall_gt_exists_lt :
   @iSup_eq_of_forall_le_of_forall_lt_exists_gt αᵒᵈ _ _ _ _
 #align infi_eq_of_forall_ge_of_forall_gt_exists_lt iInf_eq_of_forall_ge_of_forall_gt_exists_lt
 
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 theorem iSup_eq_dif {p : Prop} [Decidable p] (a : p → α) :
     (⨆ h : p, a h) = if h : p then a h else ⊥ := by by_cases p <;> simp [h]
 #align supr_eq_dif iSup_eq_dif
 
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 theorem iSup_eq_if {p : Prop} [Decidable p] (a : α) : (⨆ h : p, a) = if p then a else ⊥ :=
   iSup_eq_dif fun _ => a
 #align supr_eq_if iSup_eq_if
 
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 theorem iInf_eq_dif {p : Prop} [Decidable p] (a : p → α) :
     (⨅ h : p, a h) = if h : p then a h else ⊤ :=
   @iSup_eq_dif αᵒᵈ _ _ _ _
 #align infi_eq_dif iInf_eq_dif
 
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 theorem iInf_eq_if {p : Prop} [Decidable p] (a : α) : (⨅ h : p, a) = if p then a else ⊤ :=
   iInf_eq_dif fun _ => a
 #align infi_eq_if iInf_eq_if
 
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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 (j i) -/
 theorem iSup_comm {f : ι → ι' → α} : (⨆ (i) (j), f i j) = ⨆ (j) (i), f i j :=
@@ -2075,24 +1163,12 @@ theorem iSup_comm {f : ι → ι' → α} : (⨆ (i) (j), f i j) = ⨆ (j) (i),
     (iSup_le fun j => iSup_mono fun i => le_iSup _ _)
 #align supr_comm iSup_comm
 
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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 (j i) -/
 theorem iInf_comm {f : ι → ι' → α} : (⨅ (i) (j), f i j) = ⨅ (j) (i), f i j :=
   @iSup_comm αᵒᵈ _ _ _ _
 #align infi_comm iInf_comm
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i₁ j₁ i₂ j₂) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i₂ j₂ i₁ j₁) -/
 theorem iSup₂_comm {ι₁ ι₂ : Sort _} {κ₁ : ι₁ → Sort _} {κ₂ : ι₂ → Sort _}
@@ -2101,12 +1177,6 @@ theorem iSup₂_comm {ι₁ ι₂ : Sort _} {κ₁ : ι₁ → Sort _} {κ₂ :
   simp only [@iSup_comm _ (κ₁ _), @iSup_comm _ ι₁]
 #align supr₂_comm iSup₂_comm
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i₁ j₁ i₂ j₂) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i₂ j₂ i₁ j₁) -/
 theorem iInf₂_comm {ι₁ ι₂ : Sort _} {κ₁ : ι₁ → Sort _} {κ₂ : ι₂ → Sort _}
@@ -2115,12 +1185,6 @@ theorem iInf₂_comm {ι₁ ι₂ : Sort _} {κ₁ : ι₁ → Sort _} {κ₂ :
   simp only [@iInf_comm _ (κ₁ _), @iInf_comm _ ι₁]
 #align infi₂_comm iInf₂_comm
 
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 /- TODO: this is strange. In the proof below, we get exactly the desired
    among the equalities, but close does not get it.
 begin
@@ -2137,34 +1201,16 @@ theorem iSup_iSup_eq_left {b : β} {f : ∀ x : β, x = b → α} : (⨆ x, ⨆
   (@le_iSup₂ _ _ _ _ f b rfl).antisymm' (iSup_le fun c => iSup_le <| by rintro rfl; rfl)
 #align supr_supr_eq_left iSup_iSup_eq_left
 
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 @[simp]
 theorem iInf_iInf_eq_left {b : β} {f : ∀ x : β, x = b → α} : (⨅ x, ⨅ h : x = b, f x h) = f b rfl :=
   @iSup_iSup_eq_left αᵒᵈ _ _ _ _
 #align infi_infi_eq_left iInf_iInf_eq_left
 
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 @[simp]
 theorem iSup_iSup_eq_right {b : β} {f : ∀ x : β, b = x → α} : (⨆ x, ⨆ h : b = x, f x h) = f b rfl :=
   (le_iSup₂ b rfl).antisymm' (iSup₂_le fun c => by rintro rfl; rfl)
 #align supr_supr_eq_right iSup_iSup_eq_right
 
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 @[simp]
 theorem iInf_iInf_eq_right {b : β} {f : ∀ x : β, b = x → α} : (⨅ x, ⨅ h : b = x, f x h) = f b rfl :=
   @iSup_iSup_eq_right αᵒᵈ _ _ _ _
@@ -2172,118 +1218,52 @@ theorem iInf_iInf_eq_right {b : β} {f : ∀ x : β, b = x → α} : (⨅ x, ⨅
 
 attribute [ematch] le_refl
 
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 theorem iSup_subtype {p : ι → Prop} {f : Subtype p → α} : iSup f = ⨆ (i) (h : p i), f ⟨i, h⟩ :=
   le_antisymm (iSup_le fun ⟨i, h⟩ => le_iSup₂ i h) (iSup₂_le fun i h => le_iSup _ _)
 #align supr_subtype iSup_subtype
 
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 theorem iInf_subtype : ∀ {p : ι → Prop} {f : Subtype p → α}, iInf f = ⨅ (i) (h : p i), f ⟨i, h⟩ :=
   @iSup_subtype αᵒᵈ _ _
 #align infi_subtype iInf_subtype
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i h) -/
 theorem iSup_subtype' {p : ι → Prop} {f : ∀ i, p i → α} :
     (⨆ (i) (h), f i h) = ⨆ x : Subtype p, f x x.property :=
   (@iSup_subtype _ _ _ p fun x => f x.val x.property).symm
 #align supr_subtype' iSup_subtype'
 
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 theorem iInf_subtype' {p : ι → Prop} {f : ∀ i, p i → α} :
     (⨅ (i) (h : p i), f i h) = ⨅ x : Subtype p, f x x.property :=
   (@iInf_subtype _ _ _ p fun x => f x.val x.property).symm
 #align infi_subtype' iInf_subtype'
 
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 theorem iSup_subtype'' {ι} (s : Set ι) (f : ι → α) : (⨆ i : s, f i) = ⨆ (t : ι) (H : t ∈ s), f t :=
   iSup_subtype
 #align supr_subtype'' iSup_subtype''
 
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 theorem iInf_subtype'' {ι} (s : Set ι) (f : ι → α) : (⨅ i : s, f i) = ⨅ (t : ι) (H : t ∈ s), f t :=
   iInf_subtype
 #align infi_subtype'' iInf_subtype''
 
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 theorem biSup_const {ι : Sort _} {a : α} {s : Set ι} (hs : s.Nonempty) : (⨆ i ∈ s, a) = a :=
   by
   haveI : Nonempty s := set.nonempty_coe_sort.mpr hs
   rw [← iSup_subtype'', iSup_const]
 #align bsupr_const biSup_const
 
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 theorem biInf_const {ι : Sort _} {a : α} {s : Set ι} (hs : s.Nonempty) : (⨅ i ∈ s, a) = a :=
   @biSup_const αᵒᵈ _ ι _ s hs
 #align binfi_const biInf_const
 
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 theorem iSup_sup_eq : (⨆ x, f x ⊔ g x) = (⨆ x, f x) ⊔ ⨆ x, g x :=
   le_antisymm (iSup_le fun i => sup_le_sup (le_iSup _ _) <| le_iSup _ _)
     (sup_le (iSup_mono fun i => le_sup_left) <| iSup_mono fun i => le_sup_right)
 #align supr_sup_eq iSup_sup_eq
 
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 theorem iInf_inf_eq : (⨅ x, f x ⊓ g x) = (⨅ x, f x) ⊓ ⨅ x, g x :=
   @iSup_sup_eq αᵒᵈ _ _ _ _
 #align infi_inf_eq iInf_inf_eq
 
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-Case conversion may be inaccurate. Consider using '#align supr_sup iSup_supₓ'. -/
 /- TODO: here is another example where more flexible pattern matching
    might help.
 
@@ -2296,42 +1276,18 @@ theorem iSup_sup [Nonempty ι] {f : ι → α} {a : α} : (⨆ x, f x) ⊔ a = 
   rw [iSup_sup_eq, iSup_const]
 #align supr_sup iSup_sup
 
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 theorem iInf_inf [Nonempty ι] {f : ι → α} {a : α} : (⨅ x, f x) ⊓ a = ⨅ x, f x ⊓ a := by
   rw [iInf_inf_eq, iInf_const]
 #align infi_inf iInf_inf
 
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-Case conversion may be inaccurate. Consider using '#align sup_supr sup_iSupₓ'. -/
 theorem sup_iSup [Nonempty ι] {f : ι → α} {a : α} : (a ⊔ ⨆ x, f x) = ⨆ x, a ⊔ f x := by
   rw [iSup_sup_eq, iSup_const]
 #align sup_supr sup_iSup
 
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-Case conversion may be inaccurate. Consider using '#align inf_infi inf_iInfₓ'. -/
 theorem inf_iInf [Nonempty ι] {f : ι → α} {a : α} : (a ⊓ ⨅ x, f x) = ⨅ x, a ⊓ f x := by
   rw [iInf_inf_eq, iInf_const]
 #align inf_infi inf_iInf
 
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-Case conversion may be inaccurate. Consider using '#align bsupr_sup biSup_supₓ'. -/
 theorem biSup_sup {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
     (⨆ (i) (h : p i), f i h) ⊔ a = ⨆ (i) (h : p i), f i h ⊔ a := by
   haveI : Nonempty { i // p i } :=
@@ -2340,34 +1296,16 @@ theorem biSup_sup {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i,
     rw [iSup_subtype', iSup_subtype', iSup_sup]
 #align bsupr_sup biSup_sup
 
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-Case conversion may be inaccurate. Consider using '#align sup_bsupr sup_biSupₓ'. -/
 theorem sup_biSup {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
     (a ⊔ ⨆ (i) (h : p i), f i h) = ⨆ (i) (h : p i), a ⊔ f i h := by
   simpa only [sup_comm] using biSup_sup h
 #align sup_bsupr sup_biSup
 
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 theorem biInf_inf {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
     (⨅ (i) (h : p i), f i h) ⊓ a = ⨅ (i) (h : p i), f i h ⊓ a :=
   @biSup_sup αᵒᵈ ι _ p f _ h
 #align binfi_inf biInf_inf
 
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 theorem inf_biInf {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
     (a ⊓ ⨅ (i) (h : p i), f i h) = ⨅ (i) (h : p i), a ⊓ f i h :=
   @sup_biSup αᵒᵈ ι _ p f _ h
@@ -2376,124 +1314,58 @@ theorem inf_biInf {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i,
 /-! ### `supr` and `infi` under `Prop` -/
 
 
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 @[simp]
 theorem iSup_false {s : False → α} : iSup s = ⊥ :=
   le_antisymm (iSup_le fun i => False.elim i) bot_le
 #align supr_false iSup_false
 
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 @[simp]
 theorem iInf_false {s : False → α} : iInf s = ⊤ :=
   le_antisymm le_top (le_iInf fun i => False.elim i)
 #align infi_false iInf_false
 
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 theorem iSup_true {s : True → α} : iSup s = s trivial :=
   iSup_pos trivial
 #align supr_true iSup_true
 
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 theorem iInf_true {s : True → α} : iInf s = s trivial :=
   iInf_pos trivial
 #align infi_true iInf_true
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i h) -/
 @[simp]
 theorem iSup_exists {p : ι → Prop} {f : Exists p → α} : (⨆ x, f x) = ⨆ (i) (h), f ⟨i, h⟩ :=
   le_antisymm (iSup_le fun ⟨i, h⟩ => le_iSup₂ i h) (iSup₂_le fun i h => le_iSup _ _)
 #align supr_exists iSup_exists
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i h) -/
 @[simp]
 theorem iInf_exists {p : ι → Prop} {f : Exists p → α} : (⨅ x, f x) = ⨅ (i) (h), f ⟨i, h⟩ :=
   @iSup_exists αᵒᵈ _ _ _ _
 #align infi_exists iInf_exists
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (h₁ h₂) -/
 theorem iSup_and {p q : Prop} {s : p ∧ q → α} : iSup s = ⨆ (h₁) (h₂), s ⟨h₁, h₂⟩ :=
   le_antisymm (iSup_le fun ⟨i, h⟩ => le_iSup₂ i h) (iSup₂_le fun i h => le_iSup _ _)
 #align supr_and iSup_and
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (h₁ h₂) -/
 theorem iInf_and {p q : Prop} {s : p ∧ q → α} : iInf s = ⨅ (h₁) (h₂), s ⟨h₁, h₂⟩ :=
   @iSup_and αᵒᵈ _ _ _ _
 #align infi_and iInf_and
 
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 /-- The symmetric case of `supr_and`, useful for rewriting into a supremum over a conjunction -/
 theorem iSup_and' {p q : Prop} {s : p → q → α} :
     (⨆ (h₁ : p) (h₂ : q), s h₁ h₂) = ⨆ h : p ∧ q, s h.1 h.2 :=
   Eq.symm iSup_and
 #align supr_and' iSup_and'
 
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 /-- The symmetric case of `infi_and`, useful for rewriting into a infimum over a conjunction -/
 theorem iInf_and' {p q : Prop} {s : p → q → α} :
     (⨅ (h₁ : p) (h₂ : q), s h₁ h₂) = ⨅ h : p ∧ q, s h.1 h.2 :=
   Eq.symm iInf_and
 #align infi_and' iInf_and'
 
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 theorem iSup_or {p q : Prop} {s : p ∨ q → α} :
     (⨆ x, s x) = (⨆ i, s (Or.inl i)) ⊔ ⨆ j, s (Or.inr j) :=
   le_antisymm
@@ -2504,12 +1376,6 @@ theorem iSup_or {p q : Prop} {s : p ∨ q → α} :
     (sup_le (iSup_comp_le _ _) (iSup_comp_le _ _))
 #align supr_or iSup_or
 
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 theorem iInf_or {p q : Prop} {s : p ∨ q → α} :
     (⨅ x, s x) = (⨅ i, s (Or.inl i)) ⊓ ⨅ j, s (Or.inr j) :=
   @iSup_or αᵒᵈ _ _ _ _
@@ -2519,12 +1385,6 @@ section
 
 variable (p : ι → Prop) [DecidablePred p]
 
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 theorem iSup_dite (f : ∀ i, p i → α) (g : ∀ i, ¬p i → α) :
     (⨆ i, if h : p i then f i h else g i h) = (⨆ (i) (h : p i), f i h) ⊔ ⨆ (i) (h : ¬p i), g i h :=
   by
@@ -2533,34 +1393,16 @@ theorem iSup_dite (f : ∀ i, p i → α) (g : ∀ i, ¬p i → α) :
   split_ifs with h <;> simp [h]
 #align supr_dite iSup_dite
 
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 theorem iInf_dite (f : ∀ i, p i → α) (g : ∀ i, ¬p i → α) :
     (⨅ i, if h : p i then f i h else g i h) = (⨅ (i) (h : p i), f i h) ⊓ ⨅ (i) (h : ¬p i), g i h :=
   iSup_dite p (show ∀ i, p i → αᵒᵈ from f) g
 #align infi_dite iInf_dite
 
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 theorem iSup_ite (f g : ι → α) :
     (⨆ i, if p i then f i else g i) = (⨆ (i) (h : p i), f i) ⊔ ⨆ (i) (h : ¬p i), g i :=
   iSup_dite _ _ _
 #align supr_ite iSup_ite
 
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 theorem iInf_ite (f g : ι → α) :
     (⨅ i, if p i then f i else g i) = (⨅ (i) (h : p i), f i) ⊓ ⨅ (i) (h : ¬p i), g i :=
   iInf_dite _ _ _
@@ -2568,254 +1410,104 @@ theorem iInf_ite (f g : ι → α) :
 
 end
 
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 theorem iSup_range {g : β → α} {f : ι → β} : (⨆ b ∈ range f, g b) = ⨆ i, g (f i) := by
   rw [← iSup_subtype'', iSup_range']
 #align supr_range iSup_range
 
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 theorem iInf_range : ∀ {g : β → α} {f : ι → β}, (⨅ b ∈ range f, g b) = ⨅ i, g (f i) :=
   @iSup_range αᵒᵈ _ _ _
 #align infi_range iInf_range
 
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 theorem sSup_image {s : Set β} {f : β → α} : sSup (f '' s) = ⨆ a ∈ s, f a := by
   rw [← iSup_subtype'', sSup_image']
 #align Sup_image sSup_image
 
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 theorem sInf_image {s : Set β} {f : β → α} : sInf (f '' s) = ⨅ a ∈ s, f a :=
   @sSup_image αᵒᵈ _ _ _ _
 #align Inf_image sInf_image
 
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 /-
 ### supr and infi under set constructions
 -/
 theorem iSup_emptyset {f : β → α} : (⨆ x ∈ (∅ : Set β), f x) = ⊥ := by simp
 #align supr_emptyset iSup_emptyset
 
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 theorem iInf_emptyset {f : β → α} : (⨅ x ∈ (∅ : Set β), f x) = ⊤ := by simp
 #align infi_emptyset iInf_emptyset
 
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 theorem iSup_univ {f : β → α} : (⨆ x ∈ (univ : Set β), f x) = ⨆ x, f x := by simp
 #align supr_univ iSup_univ
 
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 theorem iInf_univ {f : β → α} : (⨅ x ∈ (univ : Set β), f x) = ⨅ x, f x := by simp
 #align infi_univ iInf_univ
 
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 theorem iSup_union {f : β → α} {s t : Set β} : (⨆ x ∈ s ∪ t, f x) = (⨆ x ∈ s, f x) ⊔ ⨆ x ∈ t, f x :=
   by simp_rw [mem_union, iSup_or, iSup_sup_eq]
 #align supr_union iSup_union
 
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 theorem iInf_union {f : β → α} {s t : Set β} : (⨅ x ∈ s ∪ t, f x) = (⨅ x ∈ s, f x) ⊓ ⨅ x ∈ t, f x :=
   @iSup_union αᵒᵈ _ _ _ _ _
 #align infi_union iInf_union
 
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 theorem iSup_split (f : β → α) (p : β → Prop) :
     (⨆ i, f i) = (⨆ (i) (h : p i), f i) ⊔ ⨆ (i) (h : ¬p i), f i := by
   simpa [Classical.em] using @iSup_union _ _ _ f { i | p i } { i | ¬p i }
 #align supr_split iSup_split
 
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 theorem iInf_split :
     ∀ (f : β → α) (p : β → Prop), (⨅ i, f i) = (⨅ (i) (h : p i), f i) ⊓ ⨅ (i) (h : ¬p i), f i :=
   @iSup_split αᵒᵈ _ _
 #align infi_split iInf_split
 
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 theorem iSup_split_single (f : β → α) (i₀ : β) : (⨆ i, f i) = f i₀ ⊔ ⨆ (i) (h : i ≠ i₀), f i := by
   convert iSup_split _ _; simp
 #align supr_split_single iSup_split_single
 
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 theorem iInf_split_single (f : β → α) (i₀ : β) : (⨅ i, f i) = f i₀ ⊓ ⨅ (i) (h : i ≠ i₀), f i :=
   @iSup_split_single αᵒᵈ _ _ _ _
 #align infi_split_single iInf_split_single
 
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 theorem iSup_le_iSup_of_subset {f : β → α} {s t : Set β} : s ⊆ t → (⨆ x ∈ s, f x) ≤ ⨆ x ∈ t, f x :=
   biSup_mono
 #align supr_le_supr_of_subset iSup_le_iSup_of_subset
 
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 theorem iInf_le_iInf_of_subset {f : β → α} {s t : Set β} : s ⊆ t → (⨅ x ∈ t, f x) ≤ ⨅ x ∈ s, f x :=
   biInf_mono
 #align infi_le_infi_of_subset iInf_le_iInf_of_subset
 
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 theorem iSup_insert {f : β → α} {s : Set β} {b : β} :
     (⨆ x ∈ insert b s, f x) = f b ⊔ ⨆ x ∈ s, f x :=
   Eq.trans iSup_union <| congr_arg (fun x => x ⊔ ⨆ x ∈ s, f x) iSup_iSup_eq_left
 #align supr_insert iSup_insert
 
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 theorem iInf_insert {f : β → α} {s : Set β} {b : β} :
     (⨅ x ∈ insert b s, f x) = f b ⊓ ⨅ x ∈ s, f x :=
   Eq.trans iInf_union <| congr_arg (fun x => x ⊓ ⨅ x ∈ s, f x) iInf_iInf_eq_left
 #align infi_insert iInf_insert
 
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 theorem iSup_singleton {f : β → α} {b : β} : (⨆ x ∈ (singleton b : Set β), f x) = f b := by simp
 #align supr_singleton iSup_singleton
 
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 theorem iInf_singleton {f : β → α} {b : β} : (⨅ x ∈ (singleton b : Set β), f x) = f b := by simp
 #align infi_singleton iInf_singleton
 
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 theorem iSup_pair {f : β → α} {a b : β} : (⨆ x ∈ ({a, b} : Set β), f x) = f a ⊔ f b := by
   rw [iSup_insert, iSup_singleton]
 #align supr_pair iSup_pair
 
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 theorem iInf_pair {f : β → α} {a b : β} : (⨅ x ∈ ({a, b} : Set β), f x) = f a ⊓ f b := by
   rw [iInf_insert, iInf_singleton]
 #align infi_pair iInf_pair
 
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 theorem iSup_image {γ} {f : β → γ} {g : γ → α} {t : Set β} :
     (⨆ c ∈ f '' t, g c) = ⨆ b ∈ t, g (f b) := by rw [← sSup_image, ← sSup_image, ← image_comp]
 #align supr_image iSup_image
 
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 theorem iInf_image :
     ∀ {γ} {f : β → γ} {g : γ → α} {t : Set β}, (⨅ c ∈ f '' t, g c) = ⨅ b ∈ t, g (f b) :=
   @iSup_image αᵒᵈ _ _
 #align infi_image iInf_image
 
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 theorem iSup_extend_bot {e : ι → β} (he : Injective e) (f : ι → α) :
     (⨆ j, extend e f ⊥ j) = ⨆ i, f i :=
   by
@@ -2823,12 +1515,6 @@ theorem iSup_extend_bot {e : ι → β} (he : Injective e) (f : ι → α) :
   simp (config := { contextual := true }) [he.extend_apply, extend_apply', @iSup_comm _ β ι]
 #align supr_extend_bot iSup_extend_bot
 
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 theorem iInf_extend_top {e : ι → β} (he : Injective e) (f : ι → α) :
     (⨅ j, extend e f ⊤ j) = iInf f :=
   @iSup_extend_bot αᵒᵈ _ _ _ _ he _
@@ -2839,242 +1525,104 @@ theorem iInf_extend_top {e : ι → β} (he : Injective e) (f : ι → α) :
 -/
 
 
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 theorem iSup_of_empty' {α ι} [SupSet α] [IsEmpty ι] (f : ι → α) : iSup f = sSup (∅ : Set α) :=
   congr_arg sSup (range_eq_empty f)
 #align supr_of_empty' iSup_of_empty'
 
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 theorem iInf_of_empty' {α ι} [InfSet α] [IsEmpty ι] (f : ι → α) : iInf f = sInf (∅ : Set α) :=
   congr_arg sInf (range_eq_empty f)
 #align infi_of_empty' iInf_of_empty'
 
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 theorem iSup_of_empty [IsEmpty ι] (f : ι → α) : iSup f = ⊥ :=
   (iSup_of_empty' f).trans sSup_empty
 #align supr_of_empty iSup_of_empty
 
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-Case conversion may be inaccurate. Consider using '#align infi_of_empty iInf_of_emptyₓ'. -/
 theorem iInf_of_empty [IsEmpty ι] (f : ι → α) : iInf f = ⊤ :=
   @iSup_of_empty αᵒᵈ _ _ _ f
 #align infi_of_empty iInf_of_empty
 
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-Case conversion may be inaccurate. Consider using '#align supr_bool_eq iSup_bool_eqₓ'. -/
 theorem iSup_bool_eq {f : Bool → α} : (⨆ b : Bool, f b) = f true ⊔ f false := by
   rw [iSup, Bool.range_eq, sSup_pair, sup_comm]
 #align supr_bool_eq iSup_bool_eq
 
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 theorem iInf_bool_eq {f : Bool → α} : (⨅ b : Bool, f b) = f true ⊓ f false :=
   @iSup_bool_eq αᵒᵈ _ _
 #align infi_bool_eq iInf_bool_eq
 
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 theorem sup_eq_iSup (x y : α) : x ⊔ y = ⨆ b : Bool, cond b x y := by
   rw [iSup_bool_eq, Bool.cond_true, Bool.cond_false]
 #align sup_eq_supr sup_eq_iSup
 
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 theorem inf_eq_iInf (x y : α) : x ⊓ y = ⨅ b : Bool, cond b x y :=
   @sup_eq_iSup αᵒᵈ _ _ _
 #align inf_eq_infi inf_eq_iInf
 
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 theorem isGLB_biInf {s : Set β} {f : β → α} : IsGLB (f '' s) (⨅ x ∈ s, f x) := by
   simpa only [range_comp, Subtype.range_coe, iInf_subtype'] using @isGLB_iInf α s _ (f ∘ coe)
 #align is_glb_binfi isGLB_biInf
 
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 theorem isLUB_biSup {s : Set β} {f : β → α} : IsLUB (f '' s) (⨆ x ∈ s, f x) := by
   simpa only [range_comp, Subtype.range_coe, iSup_subtype'] using @isLUB_iSup α s _ (f ∘ coe)
 #align is_lub_bsupr isLUB_biSup
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem iSup_sigma {p : β → Type _} {f : Sigma p → α} : (⨆ x, f x) = ⨆ (i) (j), f ⟨i, j⟩ :=
   eq_of_forall_ge_iff fun c => by simp only [iSup_le_iff, Sigma.forall]
 #align supr_sigma iSup_sigma
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem iInf_sigma {p : β → Type _} {f : Sigma p → α} : (⨅ x, f x) = ⨅ (i) (j), f ⟨i, j⟩ :=
   @iSup_sigma αᵒᵈ _ _ _ _
 #align infi_sigma iInf_sigma
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem iSup_prod {f : β × γ → α} : (⨆ x, f x) = ⨆ (i) (j), f (i, j) :=
   eq_of_forall_ge_iff fun c => by simp only [iSup_le_iff, Prod.forall]
 #align supr_prod iSup_prod
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 theorem iInf_prod {f : β × γ → α} : (⨅ x, f x) = ⨅ (i) (j), f (i, j) :=
   @iSup_prod αᵒᵈ _ _ _ _
 #align infi_prod iInf_prod
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem biSup_prod {f : β × γ → α} {s : Set β} {t : Set γ} :
     (⨆ x ∈ s ×ˢ t, f x) = ⨆ (a ∈ s) (b ∈ t), f (a, b) := by simp_rw [iSup_prod, mem_prod, iSup_and];
   exact iSup_congr fun _ => iSup_comm
 #align bsupr_prod biSup_prod
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem biInf_prod {f : β × γ → α} {s : Set β} {t : Set γ} :
     (⨅ x ∈ s ×ˢ t, f x) = ⨅ (a ∈ s) (b ∈ t), f (a, b) :=
   @biSup_prod αᵒᵈ _ _ _ _ _ _
 #align binfi_prod biInf_prod
 
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 theorem iSup_sum {f : Sum β γ → α} : (⨆ x, f x) = (⨆ i, f (Sum.inl i)) ⊔ ⨆ j, f (Sum.inr j) :=
   eq_of_forall_ge_iff fun c => by simp only [sup_le_iff, iSup_le_iff, Sum.forall]
 #align supr_sum iSup_sum
 
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 theorem iInf_sum {f : Sum β γ → α} : (⨅ x, f x) = (⨅ i, f (Sum.inl i)) ⊓ ⨅ j, f (Sum.inr j) :=
   @iSup_sum αᵒᵈ _ _ _ _
 #align infi_sum iInf_sum
 
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 theorem iSup_option (f : Option β → α) : (⨆ o, f o) = f none ⊔ ⨆ b, f (Option.some b) :=
   eq_of_forall_ge_iff fun c => by simp only [iSup_le_iff, sup_le_iff, Option.forall]
 #align supr_option iSup_option
 
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 theorem iInf_option (f : Option β → α) : (⨅ o, f o) = f none ⊓ ⨅ b, f (Option.some b) :=
   @iSup_option αᵒᵈ _ _ _
 #align infi_option iInf_option
 
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 /-- A version of `supr_option` useful for rewriting right-to-left. -/
 theorem iSup_option_elim (a : α) (f : β → α) : (⨆ o : Option β, o.elim a f) = a ⊔ ⨆ b, f b := by
   simp [iSup_option]
 #align supr_option_elim iSup_option_elim
 
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 /-- A version of `infi_option` useful for rewriting right-to-left. -/
 theorem iInf_option_elim (a : α) (f : β → α) : (⨅ o : Option β, o.elim a f) = a ⊓ ⨅ b, f b :=
   @iSup_option_elim αᵒᵈ _ _ _ _
 #align infi_option_elim iInf_option_elim
 
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 /-- When taking the supremum of `f : ι → α`, the elements of `ι` on which `f` gives `⊥` can be
 dropped, without changing the result. -/
 theorem iSup_ne_bot_subtype (f : ι → α) : (⨆ i : { i // f i ≠ ⊥ }, f i) = ⨆ i, f i :=
@@ -3089,34 +1637,16 @@ theorem iSup_ne_bot_subtype (f : ι → α) : (⨆ i : { i // f i ≠ ⊥ }, f i
   · exact ⟨⟨i, hi⟩, rfl.le⟩
 #align supr_ne_bot_subtype iSup_ne_bot_subtype
 
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 /-- When taking the infimum of `f : ι → α`, the elements of `ι` on which `f` gives `⊤` can be
 dropped, without changing the result. -/
 theorem iInf_ne_top_subtype (f : ι → α) : (⨅ i : { i // f i ≠ ⊤ }, f i) = ⨅ i, f i :=
   @iSup_ne_bot_subtype αᵒᵈ ι _ f
 #align infi_ne_top_subtype iInf_ne_top_subtype
 
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 theorem sSup_image2 {f : β → γ → α} {s : Set β} {t : Set γ} :
     sSup (image2 f s t) = ⨆ (a ∈ s) (b ∈ t), f a b := by rw [← image_prod, sSup_image, biSup_prod]
 #align Sup_image2 sSup_image2
 
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 theorem sInf_image2 {f : β → γ → α} {s : Set β} {t : Set γ} :
     sInf (image2 f s t) = ⨅ (a ∈ s) (b ∈ t), f a b := by rw [← image_prod, sInf_image, biInf_prod]
 #align Inf_image2 sInf_image2
@@ -3126,12 +1656,6 @@ theorem sInf_image2 {f : β → γ → α} {s : Set β} {t : Set γ} :
 -/
 
 
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 theorem iSup_ge_eq_iSup_nat_add (u : ℕ → α) (n : ℕ) : (⨆ i ≥ n, u i) = ⨆ i, u (i + n) :=
   by
   apply le_antisymm <;> simp only [iSup_le_iff]
@@ -3139,42 +1663,18 @@ theorem iSup_ge_eq_iSup_nat_add (u : ℕ → α) (n : ℕ) : (⨆ i ≥ n, u i)
   · exact fun i => le_sSup ⟨i + n, iSup_pos (Nat.le_add_left _ _)⟩
 #align supr_ge_eq_supr_nat_add iSup_ge_eq_iSup_nat_add
 
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 theorem iInf_ge_eq_iInf_nat_add (u : ℕ → α) (n : ℕ) : (⨅ i ≥ n, u i) = ⨅ i, u (i + n) :=
   @iSup_ge_eq_iSup_nat_add αᵒᵈ _ _ _
 #align infi_ge_eq_infi_nat_add iInf_ge_eq_iInf_nat_add
 
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 theorem Monotone.iSup_nat_add {f : ℕ → α} (hf : Monotone f) (k : ℕ) : (⨆ n, f (n + k)) = ⨆ n, f n :=
   le_antisymm (iSup_le fun i => le_iSup _ (i + k)) <| iSup_mono fun i => hf <| Nat.le_add_right i k
 #align monotone.supr_nat_add Monotone.iSup_nat_add
 
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 theorem Antitone.iInf_nat_add {f : ℕ → α} (hf : Antitone f) (k : ℕ) : (⨅ n, f (n + k)) = ⨅ n, f n :=
   hf.dual_right.iSup_nat_add k
 #align antitone.infi_nat_add Antitone.iInf_nat_add
 
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 @[simp]
 theorem iSup_iInf_ge_nat_add (f : ℕ → α) (k : ℕ) : (⨆ n, ⨅ i ≥ n, f (i + k)) = ⨆ n, ⨅ i ≥ n, f i :=
   by
@@ -3183,24 +1683,12 @@ theorem iSup_iInf_ge_nat_add (f : ℕ → α) (k : ℕ) : (⨆ n, ⨅ i ≥ n, f
   · simp_rw [iInf_ge_eq_iInf_nat_add, ← Nat.add_assoc]
 #align supr_infi_ge_nat_add iSup_iInf_ge_nat_add
 
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 @[simp]
 theorem iInf_iSup_ge_nat_add :
     ∀ (f : ℕ → α) (k : ℕ), (⨅ n, ⨆ i ≥ n, f (i + k)) = ⨅ n, ⨆ i ≥ n, f i :=
   @iSup_iInf_ge_nat_add αᵒᵈ _
 #align infi_supr_ge_nat_add iInf_iSup_ge_nat_add
 
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 theorem sup_iSup_nat_succ (u : ℕ → α) : (u 0 ⊔ ⨆ i, u (i + 1)) = ⨆ i, u i :=
   calc
     (u 0 ⊔ ⨆ i, u (i + 1)) = ⨆ x ∈ {0} ∪ range Nat.succ, u x := by
@@ -3209,32 +1697,14 @@ theorem sup_iSup_nat_succ (u : ℕ → α) : (u 0 ⊔ ⨆ i, u (i + 1)) = ⨆ i,
     
 #align sup_supr_nat_succ sup_iSup_nat_succ
 
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 theorem inf_iInf_nat_succ (u : ℕ → α) : (u 0 ⊓ ⨅ i, u (i + 1)) = ⨅ i, u i :=
   @sup_iSup_nat_succ αᵒᵈ _ u
 #align inf_infi_nat_succ inf_iInf_nat_succ
 
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 theorem iInf_nat_gt_zero_eq (f : ℕ → α) : (⨅ i > 0, f i) = ⨅ i, f (i + 1) := by
   rw [← iInf_range, Nat.range_succ]; simp only [mem_set_of]
 #align infi_nat_gt_zero_eq iInf_nat_gt_zero_eq
 
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 theorem iSup_nat_gt_zero_eq (f : ℕ → α) : (⨆ i > 0, f i) = ⨆ i, f (i + 1) :=
   @iInf_nat_gt_zero_eq αᵒᵈ _ f
 #align supr_nat_gt_zero_eq iSup_nat_gt_zero_eq
@@ -3245,22 +1715,10 @@ section CompleteLinearOrder
 
 variable [CompleteLinearOrder α]
 
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 theorem iSup_eq_top (f : ι → α) : iSup f = ⊤ ↔ ∀ b < ⊤, ∃ i, b < f i := by
   simp only [← sSup_range, sSup_eq_top, Set.exists_range_iff]
 #align supr_eq_top iSup_eq_top
 
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 theorem iInf_eq_bot (f : ι → α) : iInf f = ⊥ ↔ ∀ b > ⊥, ∃ i, f i < b := by
   simp only [← sInf_range, sInf_eq_bot, Set.exists_range_iff]
 #align infi_eq_bot iInf_eq_bot
@@ -3291,46 +1749,22 @@ noncomputable instance Prop.completeLinearOrder : CompleteLinearOrder Prop :=
 #align Prop.complete_linear_order Prop.completeLinearOrder
 -/
 
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 @[simp]
 theorem sSup_Prop_eq {s : Set Prop} : sSup s = ∃ p ∈ s, p :=
   rfl
 #align Sup_Prop_eq sSup_Prop_eq
 
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 @[simp]
 theorem sInf_Prop_eq {s : Set Prop} : sInf s = ∀ p ∈ s, p :=
   rfl
 #align Inf_Prop_eq sInf_Prop_eq
 
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 @[simp]
 theorem iSup_Prop_eq {p : ι → Prop} : (⨆ i, p i) = ∃ i, p i :=
   le_antisymm (fun ⟨q, ⟨i, (Eq : p i = q)⟩, hq⟩ => ⟨i, Eq.symm ▸ hq⟩) fun ⟨i, hi⟩ =>
     ⟨p i, ⟨i, rfl⟩, hi⟩
 #align supr_Prop_eq iSup_Prop_eq
 
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 @[simp]
 theorem iInf_Prop_eq {p : ι → Prop} : (⨅ i, p i) = ∀ i, p i :=
   le_antisymm (fun h i => h _ ⟨i, rfl⟩) fun h p ⟨i, Eq⟩ => Eq ▸ h i
@@ -3361,34 +1795,16 @@ instance Pi.completeLattice {α : Type _} {β : α → Type _} [∀ i, CompleteL
 #align pi.complete_lattice Pi.completeLattice
 -/
 
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 theorem sSup_apply {α : Type _} {β : α → Type _} [∀ i, SupSet (β i)] {s : Set (∀ a, β a)} {a : α} :
     (sSup s) a = ⨆ f : s, (f : ∀ a, β a) a :=
   rfl
 #align Sup_apply sSup_apply
 
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 theorem sInf_apply {α : Type _} {β : α → Type _} [∀ i, InfSet (β i)] {s : Set (∀ a, β a)} {a : α} :
     sInf s a = ⨅ f : s, (f : ∀ a, β a) a :=
   rfl
 #align Inf_apply sInf_apply
 
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 @[simp]
 theorem iSup_apply {α : Type _} {β : α → Type _} {ι : Sort _} [∀ i, SupSet (β i)] {f : ι → ∀ a, β a}
     {a : α} : (⨆ i, f i) a = ⨆ i, f i a := by
@@ -3396,54 +1812,24 @@ theorem iSup_apply {α : Type _} {β : α → Type _} {ι : Sort _} [∀ i, SupS
     range_comp]
 #align supr_apply iSup_apply
 
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 @[simp]
 theorem iInf_apply {α : Type _} {β : α → Type _} {ι : Sort _} [∀ i, InfSet (β i)] {f : ι → ∀ a, β a}
     {a : α} : (⨅ i, f i) a = ⨅ i, f i a :=
   @iSup_apply α (fun i => (β i)ᵒᵈ) _ _ _ _
 #align infi_apply iInf_apply
 
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 theorem unary_relation_sSup_iff {α : Type _} (s : Set (α → Prop)) {a : α} :
     sSup s a ↔ ∃ r : α → Prop, r ∈ s ∧ r a := by unfold Sup; simp [← eq_iff_iff]
 #align unary_relation_Sup_iff unary_relation_sSup_iff
 
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 theorem unary_relation_sInf_iff {α : Type _} (s : Set (α → Prop)) {a : α} :
     sInf s a ↔ ∀ r : α → Prop, r ∈ s → r a := by unfold Inf; simp [← eq_iff_iff]
 #align unary_relation_Inf_iff unary_relation_sInf_iff
 
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 theorem binary_relation_sSup_iff {α β : Type _} (s : Set (α → β → Prop)) {a : α} {b : β} :
     sSup s a b ↔ ∃ r : α → β → Prop, r ∈ s ∧ r a b := by unfold Sup; simp [← eq_iff_iff]
 #align binary_relation_Sup_iff binary_relation_sSup_iff
 
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 theorem binary_relation_sInf_iff {α β : Type _} (s : Set (α → β → Prop)) {a : α} {b : β} :
     sInf s a b ↔ ∀ r : α → β → Prop, r ∈ s → r a b := by unfold Inf; simp [← eq_iff_iff]
 #align binary_relation_Inf_iff binary_relation_sInf_iff
@@ -3452,22 +1838,10 @@ section CompleteLattice
 
 variable [Preorder α] [CompleteLattice β]
 
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 theorem monotone_sSup_of_monotone {s : Set (α → β)} (m_s : ∀ f ∈ s, Monotone f) :
     Monotone (sSup s) := fun x y h => iSup_mono fun f => m_s f f.2 h
 #align monotone_Sup_of_monotone monotone_sSup_of_monotone
 
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 theorem monotone_sInf_of_monotone {s : Set (α → β)} (m_s : ∀ f ∈ s, Monotone f) :
     Monotone (sInf s) := fun x y h => iInf_mono fun f => m_s f f.2 h
 #align monotone_Inf_of_monotone monotone_sInf_of_monotone
@@ -3486,145 +1860,61 @@ instance [InfSet α] [InfSet β] : InfSet (α × β) :=
 
 variable {α β}
 
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 theorem fst_sInf [InfSet α] [InfSet β] (s : Set (α × β)) : (sInf s).fst = sInf (Prod.fst '' s) :=
   rfl
 #align prod.fst_Inf Prod.fst_sInf
 
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 theorem snd_sInf [InfSet α] [InfSet β] (s : Set (α × β)) : (sInf s).snd = sInf (Prod.snd '' s) :=
   rfl
 #align prod.snd_Inf Prod.snd_sInf
 
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 theorem swap_sInf [InfSet α] [InfSet β] (s : Set (α × β)) : (sInf s).symm = sInf (Prod.swap '' s) :=
   ext (congr_arg sInf <| image_comp Prod.fst swap s : _)
     (congr_arg sInf <| image_comp Prod.snd swap s : _)
 #align prod.swap_Inf Prod.swap_sInf
 
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 theorem fst_sSup [SupSet α] [SupSet β] (s : Set (α × β)) : (sSup s).fst = sSup (Prod.fst '' s) :=
   rfl
 #align prod.fst_Sup Prod.fst_sSup
 
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 theorem snd_sSup [SupSet α] [SupSet β] (s : Set (α × β)) : (sSup s).snd = sSup (Prod.snd '' s) :=
   rfl
 #align prod.snd_Sup Prod.snd_sSup
 
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 theorem swap_sSup [SupSet α] [SupSet β] (s : Set (α × β)) : (sSup s).symm = sSup (Prod.swap '' s) :=
   ext (congr_arg sSup <| image_comp Prod.fst swap s : _)
     (congr_arg sSup <| image_comp Prod.snd swap s : _)
 #align prod.swap_Sup Prod.swap_sSup
 
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 theorem fst_iInf [InfSet α] [InfSet β] (f : ι → α × β) : (iInf f).fst = ⨅ i, (f i).fst :=
   congr_arg sInf (range_comp _ _).symm
 #align prod.fst_infi Prod.fst_iInf
 
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 theorem snd_iInf [InfSet α] [InfSet β] (f : ι → α × β) : (iInf f).snd = ⨅ i, (f i).snd :=
   congr_arg sInf (range_comp _ _).symm
 #align prod.snd_infi Prod.snd_iInf
 
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 theorem swap_iInf [InfSet α] [InfSet β] (f : ι → α × β) : (iInf f).symm = ⨅ i, (f i).symm := by
   simp_rw [iInf, swap_Inf, range_comp]
 #align prod.swap_infi Prod.swap_iInf
 
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 theorem iInf_mk [InfSet α] [InfSet β] (f : ι → α) (g : ι → β) :
     (⨅ i, (f i, g i)) = (⨅ i, f i, ⨅ i, g i) :=
   congr_arg₂ Prod.mk (fst_iInf _) (snd_iInf _)
 #align prod.infi_mk Prod.iInf_mk
 
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 theorem fst_iSup [SupSet α] [SupSet β] (f : ι → α × β) : (iSup f).fst = ⨆ i, (f i).fst :=
   congr_arg sSup (range_comp _ _).symm
 #align prod.fst_supr Prod.fst_iSup
 
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 theorem snd_iSup [SupSet α] [SupSet β] (f : ι → α × β) : (iSup f).snd = ⨆ i, (f i).snd :=
   congr_arg sSup (range_comp _ _).symm
 #align prod.snd_supr Prod.snd_iSup
 
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 theorem swap_iSup [SupSet α] [SupSet β] (f : ι → α × β) : (iSup f).symm = ⨆ i, (f i).symm := by
   simp_rw [iSup, swap_Sup, range_comp]
 #align prod.swap_supr Prod.swap_iSup
 
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 theorem iSup_mk [SupSet α] [SupSet β] (f : ι → α) (g : ι → β) :
     (⨆ i, (f i, g i)) = (⨆ i, f i, ⨆ i, g i) :=
   congr_arg₂ Prod.mk (fst_iSup _) (snd_iSup _)
@@ -3647,24 +1937,12 @@ instance [CompleteLattice α] [CompleteLattice β] : CompleteLattice (α × β)
 
 end Prod
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem sInf_prod [InfSet α] [InfSet β] {s : Set α} {t : Set β} (hs : s.Nonempty)
     (ht : t.Nonempty) : sInf (s ×ˢ t) = (sInf s, sInf t) :=
   congr_arg₂ Prod.mk (congr_arg sInf <| fst_image_prod _ ht) (congr_arg sInf <| snd_image_prod hs _)
 #align Inf_prod sInf_prod
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem sSup_prod [SupSet α] [SupSet β] {s : Set α} {t : Set β} (hs : s.Nonempty)
     (ht : t.Nonempty) : sSup (s ×ˢ t) = (sSup s, sSup t) :=
@@ -3675,87 +1953,39 @@ section CompleteLattice
 
 variable [CompleteLattice α] {a : α} {s : Set α}
 
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 /-- This is a weaker version of `sup_Inf_eq` -/
 theorem sup_sInf_le_iInf_sup : a ⊔ sInf s ≤ ⨅ b ∈ s, a ⊔ b :=
   le_iInf₂ fun i h => sup_le_sup_left (sInf_le h) _
 #align sup_Inf_le_infi_sup sup_sInf_le_iInf_sup
 
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 /-- This is a weaker version of `inf_Sup_eq` -/
 theorem iSup_inf_le_inf_sSup : (⨆ b ∈ s, a ⊓ b) ≤ a ⊓ sSup s :=
   @sup_sInf_le_iInf_sup αᵒᵈ _ _ _
 #align supr_inf_le_inf_Sup iSup_inf_le_inf_sSup
 
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 /-- This is a weaker version of `Inf_sup_eq` -/
 theorem sInf_sup_le_iInf_sup : sInf s ⊔ a ≤ ⨅ b ∈ s, b ⊔ a :=
   le_iInf₂ fun i h => sup_le_sup_right (sInf_le h) _
 #align Inf_sup_le_infi_sup sInf_sup_le_iInf_sup
 
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 /-- This is a weaker version of `Sup_inf_eq` -/
 theorem iSup_inf_le_sSup_inf : (⨆ b ∈ s, b ⊓ a) ≤ sSup s ⊓ a :=
   @sInf_sup_le_iInf_sup αᵒᵈ _ _ _
 #align supr_inf_le_Sup_inf iSup_inf_le_sSup_inf
 
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 theorem le_iSup_inf_iSup (f g : ι → α) : (⨆ i, f i ⊓ g i) ≤ (⨆ i, f i) ⊓ ⨆ i, g i :=
   le_inf (iSup_mono fun i => inf_le_left) (iSup_mono fun i => inf_le_right)
 #align le_supr_inf_supr le_iSup_inf_iSup
 
-/- warning: infi_sup_infi_le -> iInf_sup_iInf_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align infi_sup_infi_le iInf_sup_iInf_leₓ'. -/
 theorem iInf_sup_iInf_le (f g : ι → α) : ((⨅ i, f i) ⊔ ⨅ i, g i) ≤ ⨅ i, f i ⊔ g i :=
   @le_iSup_inf_iSup αᵒᵈ ι _ f g
 #align infi_sup_infi_le iInf_sup_iInf_le
 
-/- warning: disjoint_Sup_left -> disjoint_sSup_left is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align disjoint_Sup_left disjoint_sSup_leftₓ'. -/
 theorem disjoint_sSup_left {a : Set α} {b : α} (d : Disjoint (sSup a) b) {i} (hi : i ∈ a) :
     Disjoint i b :=
   disjoint_iff_inf_le.mpr (iSup₂_le_iff.1 (iSup_inf_le_sSup_inf.trans d.le_bot) i hi : _)
 #align disjoint_Sup_left disjoint_sSup_left
 
-/- warning: disjoint_Sup_right -> disjoint_sSup_right is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align disjoint_Sup_right disjoint_sSup_rightₓ'. -/
 theorem disjoint_sSup_right {a : Set α} {b : α} (d : Disjoint b (sSup a)) {i} (hi : i ∈ a) :
     Disjoint b i :=
   disjoint_iff_inf_le.mpr (iSup₂_le_iff.mp (iSup_inf_le_inf_sSup.trans d.le_bot) i hi : _)
@@ -3763,12 +1993,6 @@ theorem disjoint_sSup_right {a : Set α} {b : α} (d : Disjoint b (sSup a)) {i}
 
 end CompleteLattice
 
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-Case conversion may be inaccurate. Consider using '#align function.injective.complete_lattice Function.Injective.completeLatticeₓ'. -/
 -- See note [reducible non-instances]
 /-- Pullback a `complete_lattice` along an injection. -/
 @[reducible]

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

@@ -433,9 +433,7 @@ def completeLatticeOfInf (α : Type _) [H1 : PartialOrder α] [H2 : InfSet α]
     le_top := fun a => (isGLB_sInf ∅).2 <| by simp
     sup := fun a b => sInf { x | a ≤ x ∧ b ≤ x }
     inf := fun a b => sInf {a, b}
-    le_inf := fun a b c hab hac => by
-      apply (isGLB_sInf _).2
-      simp [*]
+    le_inf := fun a b c hab hac => by apply (isGLB_sInf _).2; simp [*]
     inf_le_right := fun a b => (isGLB_sInf _).1 <| mem_insert_of_mem _ <| mem_singleton _
     inf_le_left := fun a b => (isGLB_sInf _).1 <| mem_insert _ _
     sup_le := fun a b c hac hbc => (isGLB_sInf _).1 <| by simp [*]
@@ -825,11 +823,8 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (Set.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))))
 Case conversion may be inaccurate. Consider using '#align eq_singleton_bot_of_Sup_eq_bot_of_nonempty eq_singleton_bot_of_sSup_eq_bot_of_nonemptyₓ'. -/
 theorem eq_singleton_bot_of_sSup_eq_bot_of_nonempty {s : Set α} (h_sup : sSup s = ⊥)
-    (hne : s.Nonempty) : s = {⊥} :=
-  by
-  rw [Set.eq_singleton_iff_nonempty_unique_mem]
-  rw [sSup_eq_bot] at h_sup
-  exact ⟨hne, h_sup⟩
+    (hne : s.Nonempty) : s = {⊥} := by rw [Set.eq_singleton_iff_nonempty_unique_mem];
+  rw [sSup_eq_bot] at h_sup; exact ⟨hne, h_sup⟩
 #align eq_singleton_bot_of_Sup_eq_bot_of_nonempty eq_singleton_bot_of_sSup_eq_bot_of_nonempty
 
 /- warning: eq_singleton_top_of_Inf_eq_top_of_nonempty -> eq_singleton_top_of_sInf_eq_top_of_nonempty is a dubious translation:
@@ -1005,9 +1000,7 @@ but is expected to have type
   forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι' -> α} (h : ι -> ι'), (Function.Surjective.{u3, u2} ι ι' h) -> (forall (x : ι), Eq.{succ u1} α (g (h x)) (f x)) -> (Eq.{succ u1} α (iSup.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (iSup.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
 Case conversion may be inaccurate. Consider using '#align function.surjective.supr_congr Function.Surjective.iSup_congrₓ'. -/
 protected theorem Function.Surjective.iSup_congr {g : ι' → α} (h : ι → ι') (h1 : Surjective h)
-    (h2 : ∀ x, g (h x) = f x) : (⨆ x, f x) = ⨆ y, g y :=
-  by
-  convert h1.supr_comp g
+    (h2 : ∀ x, g (h x) = f x) : (⨆ x, f x) = ⨆ y, g y := by convert h1.supr_comp g;
   exact (funext h2).symm
 #align function.surjective.supr_congr Function.Surjective.iSup_congr
 
@@ -1025,11 +1018,8 @@ protected theorem Equiv.iSup_congr {g : ι' → α} (e : ι ≃ ι') (h : ∀ x,
 #print iSup_congr_Prop /-
 @[congr]
 theorem iSup_congr_Prop {p q : Prop} {f₁ : p → α} {f₂ : q → α} (pq : p ↔ q)
-    (f : ∀ x, f₁ (pq.mpr x) = f₂ x) : iSup f₁ = iSup f₂ :=
-  by
-  obtain rfl := propext pq
-  congr with x
-  apply f
+    (f : ∀ x, f₁ (pq.mpr x) = f₂ x) : iSup f₁ = iSup f₂ := by obtain rfl := propext pq;
+  congr with x; apply f
 #align supr_congr_Prop iSup_congr_Prop
 -/
 
@@ -1834,9 +1824,7 @@ but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)) (iInf.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_2) α (fun (a : α) => iInf.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_2) (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) => f a))))
 Case conversion may be inaccurate. Consider using '#align antitone.map_Sup_le Antitone.map_sSup_leₓ'. -/
 theorem Antitone.map_sSup_le [CompleteLattice β] {s : Set α} {f : α → β} (hf : Antitone f) :
-    f (sSup s) ≤ ⨅ a ∈ s, f a := by
-  rw [sSup_eq_iSup]
-  exact hf.map_supr₂_le _
+    f (sSup s) ≤ ⨅ a ∈ s, f a := by rw [sSup_eq_iSup]; exact hf.map_supr₂_le _
 #align antitone.map_Sup_le Antitone.map_sSup_le
 
 /- warning: monotone.map_Inf_le -> Monotone.map_sInf_le is a dubious translation:
@@ -2146,11 +2134,7 @@ end
 -/
 @[simp]
 theorem iSup_iSup_eq_left {b : β} {f : ∀ x : β, x = b → α} : (⨆ x, ⨆ h : x = b, f x h) = f b rfl :=
-  (@le_iSup₂ _ _ _ _ f b rfl).antisymm'
-    (iSup_le fun c =>
-      iSup_le <| by
-        rintro rfl
-        rfl)
+  (@le_iSup₂ _ _ _ _ f b rfl).antisymm' (iSup_le fun c => iSup_le <| by rintro rfl; rfl)
 #align supr_supr_eq_left iSup_iSup_eq_left
 
 /- warning: infi_infi_eq_left -> iInf_iInf_eq_left is a dubious translation:
@@ -2172,10 +2156,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align supr_supr_eq_right iSup_iSup_eq_rightₓ'. -/
 @[simp]
 theorem iSup_iSup_eq_right {b : β} {f : ∀ x : β, b = x → α} : (⨆ x, ⨆ h : b = x, f x h) = f b rfl :=
-  (le_iSup₂ b rfl).antisymm'
-    (iSup₂_le fun c => by
-      rintro rfl
-      rfl)
+  (le_iSup₂ b rfl).antisymm' (iSup₂_le fun c => by rintro rfl; rfl)
 #align supr_supr_eq_right iSup_iSup_eq_right
 
 /- warning: infi_infi_eq_right -> iInf_iInf_eq_right is a dubious translation:
@@ -2714,10 +2695,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (i₀ : β), Eq.{succ u2} α (iSup.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => f i)) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f i₀) (iSup.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Ne.{succ u1} β i i₀) (fun (h : Ne.{succ u1} β i i₀) => f i))))
 Case conversion may be inaccurate. Consider using '#align supr_split_single iSup_split_singleₓ'. -/
-theorem iSup_split_single (f : β → α) (i₀ : β) : (⨆ i, f i) = f i₀ ⊔ ⨆ (i) (h : i ≠ i₀), f i :=
-  by
-  convert iSup_split _ _
-  simp
+theorem iSup_split_single (f : β → α) (i₀ : β) : (⨆ i, f i) = f i₀ ⊔ ⨆ (i) (h : i ≠ i₀), f i := by
+  convert iSup_split _ _; simp
 #align supr_split_single iSup_split_single
 
 /- warning: infi_split_single -> iInf_split_single is a dubious translation:
@@ -3012,9 +2991,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align bsupr_prod biSup_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem biSup_prod {f : β × γ → α} {s : Set β} {t : Set γ} :
-    (⨆ x ∈ s ×ˢ t, f x) = ⨆ (a ∈ s) (b ∈ t), f (a, b) :=
-  by
-  simp_rw [iSup_prod, mem_prod, iSup_and]
+    (⨆ x ∈ s ×ˢ t, f x) = ⨆ (a ∈ s) (b ∈ t), f (a, b) := by simp_rw [iSup_prod, mem_prod, iSup_and];
   exact iSup_congr fun _ => iSup_comm
 #align bsupr_prod biSup_prod
 
@@ -3158,12 +3135,7 @@ Case conversion may be inaccurate. Consider using '#align supr_ge_eq_supr_nat_ad
 theorem iSup_ge_eq_iSup_nat_add (u : ℕ → α) (n : ℕ) : (⨆ i ≥ n, u i) = ⨆ i, u (i + n) :=
   by
   apply le_antisymm <;> simp only [iSup_le_iff]
-  ·
-    exact fun i hi =>
-      le_sSup
-        ⟨i - n, by
-          dsimp only
-          rw [Nat.sub_add_cancel hi]⟩
+  · exact fun i hi => le_sSup ⟨i - n, by dsimp only; rw [Nat.sub_add_cancel hi]⟩
   · exact fun i => le_sSup ⟨i + n, iSup_pos (Nat.le_add_left _ _)⟩
 #align supr_ge_eq_supr_nat_add iSup_ge_eq_iSup_nat_add
 
@@ -3253,10 +3225,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α), Eq.{succ u1} α (iInf.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (GT.gt.{0} Nat instLTNat i (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (fun (H : GT.gt.{0} Nat instLTNat i (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) => f i))) (iInf.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
 Case conversion may be inaccurate. Consider using '#align infi_nat_gt_zero_eq iInf_nat_gt_zero_eqₓ'. -/
-theorem iInf_nat_gt_zero_eq (f : ℕ → α) : (⨅ i > 0, f i) = ⨅ i, f (i + 1) :=
-  by
-  rw [← iInf_range, Nat.range_succ]
-  simp only [mem_set_of]
+theorem iInf_nat_gt_zero_eq (f : ℕ → α) : (⨅ i > 0, f i) = ⨅ i, f (i + 1) := by
+  rw [← iInf_range, Nat.range_succ]; simp only [mem_set_of]
 #align infi_nat_gt_zero_eq iInf_nat_gt_zero_eq
 
 /- warning: supr_nat_gt_zero_eq -> iSup_nat_gt_zero_eq is a dubious translation:
@@ -3445,10 +3415,7 @@ but is expected to have type
   forall {α : Type.{u1}} (s : Set.{u1} (α -> Prop)) {a : α}, Iff (SupSet.sSup.{u1} (α -> Prop) (Pi.supSet.{u1, 0} α (fun (ᾰ : α) => Prop) (fun (i : α) => CompleteLattice.toSupSet.{0} Prop Prop.completeLattice)) s a) (Exists.{succ u1} (α -> Prop) (fun (r : α -> Prop) => And (Membership.mem.{u1, u1} (α -> Prop) (Set.{u1} (α -> Prop)) (Set.instMembershipSet.{u1} (α -> Prop)) r s) (r a)))
 Case conversion may be inaccurate. Consider using '#align unary_relation_Sup_iff unary_relation_sSup_iffₓ'. -/
 theorem unary_relation_sSup_iff {α : Type _} (s : Set (α → Prop)) {a : α} :
-    sSup s a ↔ ∃ r : α → Prop, r ∈ s ∧ r a :=
-  by
-  unfold Sup
-  simp [← eq_iff_iff]
+    sSup s a ↔ ∃ r : α → Prop, r ∈ s ∧ r a := by unfold Sup; simp [← eq_iff_iff]
 #align unary_relation_Sup_iff unary_relation_sSup_iff
 
 /- warning: unary_relation_Inf_iff -> unary_relation_sInf_iff is a dubious translation:
@@ -3458,10 +3425,7 @@ but is expected to have type
   forall {α : Type.{u1}} (s : Set.{u1} (α -> Prop)) {a : α}, Iff (InfSet.sInf.{u1} (α -> Prop) (Pi.infSet.{u1, 0} α (fun (ᾰ : α) => Prop) (fun (i : α) => CompleteLattice.toInfSet.{0} Prop Prop.completeLattice)) s a) (forall (r : α -> Prop), (Membership.mem.{u1, u1} (α -> Prop) (Set.{u1} (α -> Prop)) (Set.instMembershipSet.{u1} (α -> Prop)) r s) -> (r a))
 Case conversion may be inaccurate. Consider using '#align unary_relation_Inf_iff unary_relation_sInf_iffₓ'. -/
 theorem unary_relation_sInf_iff {α : Type _} (s : Set (α → Prop)) {a : α} :
-    sInf s a ↔ ∀ r : α → Prop, r ∈ s → r a :=
-  by
-  unfold Inf
-  simp [← eq_iff_iff]
+    sInf s a ↔ ∀ r : α → Prop, r ∈ s → r a := by unfold Inf; simp [← eq_iff_iff]
 #align unary_relation_Inf_iff unary_relation_sInf_iff
 
 /- warning: binary_relation_Sup_iff -> binary_relation_sSup_iff is a dubious translation:
@@ -3471,10 +3435,7 @@ but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} (s : Set.{max u2 u1} (α -> β -> Prop)) {a : α} {b : β}, Iff (SupSet.sSup.{max u2 u1} (α -> β -> Prop) (Pi.supSet.{u2, u1} α (fun (ᾰ : α) => β -> Prop) (fun (i : α) => Pi.supSet.{u1, 0} β (fun (ᾰ : β) => Prop) (fun (i : β) => CompleteLattice.toSupSet.{0} Prop Prop.completeLattice))) s a b) (Exists.{max (succ u2) (succ u1)} (α -> β -> Prop) (fun (r : α -> β -> Prop) => And (Membership.mem.{max u2 u1, max u2 u1} (α -> β -> Prop) (Set.{max u2 u1} (α -> β -> Prop)) (Set.instMembershipSet.{max u2 u1} (α -> β -> Prop)) r s) (r a b)))
 Case conversion may be inaccurate. Consider using '#align binary_relation_Sup_iff binary_relation_sSup_iffₓ'. -/
 theorem binary_relation_sSup_iff {α β : Type _} (s : Set (α → β → Prop)) {a : α} {b : β} :
-    sSup s a b ↔ ∃ r : α → β → Prop, r ∈ s ∧ r a b :=
-  by
-  unfold Sup
-  simp [← eq_iff_iff]
+    sSup s a b ↔ ∃ r : α → β → Prop, r ∈ s ∧ r a b := by unfold Sup; simp [← eq_iff_iff]
 #align binary_relation_Sup_iff binary_relation_sSup_iff
 
 /- warning: binary_relation_Inf_iff -> binary_relation_sInf_iff is a dubious translation:
@@ -3484,10 +3445,7 @@ but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} (s : Set.{max u2 u1} (α -> β -> Prop)) {a : α} {b : β}, Iff (InfSet.sInf.{max u2 u1} (α -> β -> Prop) (Pi.infSet.{u2, u1} α (fun (ᾰ : α) => β -> Prop) (fun (i : α) => Pi.infSet.{u1, 0} β (fun (ᾰ : β) => Prop) (fun (i : β) => CompleteLattice.toInfSet.{0} Prop Prop.completeLattice))) s a b) (forall (r : α -> β -> Prop), (Membership.mem.{max u2 u1, max u2 u1} (α -> β -> Prop) (Set.{max u2 u1} (α -> β -> Prop)) (Set.instMembershipSet.{max u2 u1} (α -> β -> Prop)) r s) -> (r a b))
 Case conversion may be inaccurate. Consider using '#align binary_relation_Inf_iff binary_relation_sInf_iffₓ'. -/
 theorem binary_relation_sInf_iff {α β : Type _} (s : Set (α → β → Prop)) {a : α} {b : β} :
-    sInf s a b ↔ ∀ r : α → β → Prop, r ∈ s → r a b :=
-  by
-  unfold Inf
-  simp [← eq_iff_iff]
+    sInf s a b ↔ ∀ r : α → β → Prop, r ∈ s → r a b := by unfold Inf; simp [← eq_iff_iff]
 #align binary_relation_Inf_iff binary_relation_sInf_iff
 
 section CompleteLattice

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

@@ -1707,10 +1707,7 @@ theorem Antitone.le_map_sInf [CompleteLattice β] {s : Set α} {f : α → β} (
 #align antitone.le_map_Inf Antitone.le_map_sInf
 
 /- warning: order_iso.map_supr -> OrderIso.map_iSup is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (x : ι -> α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => x i))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (x i)))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : CompleteLattice.{u3} β] (f : OrderIso.{u2, u3} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))))) (x : ι -> α), Eq.{succ u3} β (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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) 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 Case conversion may be inaccurate. Consider using '#align order_iso.map_supr OrderIso.map_iSupₓ'. -/
 theorem OrderIso.map_iSup [CompleteLattice β] (f : α ≃o β) (x : ι → α) :
     f (⨆ i, x i) = ⨆ i, f (x i) :=
@@ -1718,10 +1715,7 @@ theorem OrderIso.map_iSup [CompleteLattice β] (f : α ≃o β) (x : ι → α)
 #align order_iso.map_supr OrderIso.map_iSup
 
 /- warning: order_iso.map_infi -> OrderIso.map_iInf is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align order_iso.map_infi OrderIso.map_iInfₓ'. -/
 theorem OrderIso.map_iInf [CompleteLattice β] (f : α ≃o β) (x : ι → α) :
     f (⨅ i, x i) = ⨅ i, f (x i) :=
@@ -1729,20 +1723,14 @@ theorem OrderIso.map_iInf [CompleteLattice β] (f : α ≃o β) (x : ι → α)
 #align order_iso.map_infi OrderIso.map_iInf
 
 /- warning: order_iso.map_Sup -> OrderIso.map_sSup is a dubious translation:
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f a)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align order_iso.map_Sup OrderIso.map_sSupₓ'. -/
 theorem OrderIso.map_sSup [CompleteLattice β] (f : α ≃o β) (s : Set α) :
     f (sSup s) = ⨆ a ∈ s, f a := by simp only [sSup_eq_iSup, OrderIso.map_iSup]
 #align order_iso.map_Sup OrderIso.map_sSup
 
 /- warning: order_iso.map_Inf -> OrderIso.map_sInf is a dubious translation:
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(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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f a)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align order_iso.map_Inf OrderIso.map_sInfₓ'. -/
 theorem OrderIso.map_sInf [CompleteLattice β] (f : α ≃o β) (s : Set α) :
     f (sInf s) = ⨅ a ∈ s, f a :=

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

@@ -575,7 +575,7 @@ theorem ofDual_sInf (s : Set αᵒᵈ) : ofDual (sInf s) = sSup (toDual ⁻¹' s
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α), Eq.{succ u1} (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i))) (iInf.{u1, u2} (OrderDual.{u1} α) (OrderDual.hasInf.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1))) ι (fun (i : ι) => coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) (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} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (f i)))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u2} α) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (f i)))
 Case conversion may be inaccurate. Consider using '#align to_dual_supr toDual_iSupₓ'. -/
 @[simp]
 theorem toDual_iSup (f : ι → α) : toDual (⨆ i, f i) = ⨅ i, toDual (f i) :=
@@ -586,7 +586,7 @@ theorem toDual_iSup (f : ι → α) : toDual (⨆ i, f i) = ⨅ i, toDual (f i)
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α), Eq.{succ u1} (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => f i))) (iSup.{u1, u2} (OrderDual.{u1} α) (OrderDual.hasSup.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) ι (fun (i : ι) => coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) (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} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u1} (OrderDual.{u2} α) (OrderDual.supSet.{u2} α (CompleteLattice.toInfSet.{u2} α _inst_1)) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (f i)))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u2} α) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u1} (OrderDual.{u2} α) (OrderDual.supSet.{u2} α (CompleteLattice.toInfSet.{u2} α _inst_1)) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (f i)))
 Case conversion may be inaccurate. Consider using '#align to_dual_infi toDual_iInfₓ'. -/
 @[simp]
 theorem toDual_iInf (f : ι → α) : toDual (⨅ i, f i) = ⨆ i, toDual (f i) :=
@@ -597,7 +597,7 @@ theorem toDual_iInf (f : ι → α) : toDual (⨅ i, f i) = ⨆ i, toDual (f i)
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> (OrderDual.{u1} α)), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α) (iSup.{u1, u2} (OrderDual.{u1} α) (OrderDual.hasSup.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) ι (fun (i : ι) => f i))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α) (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> (OrderDual.{u2} α)), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) (iSup.{u2, u1} (OrderDual.{u2} α) (OrderDual.supSet.{u2} α (CompleteLattice.toInfSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (iSup.{u2, u1} (OrderDual.{u2} α) (OrderDual.supSet.{u2} α (CompleteLattice.toInfSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (f i)))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> (OrderDual.{u2} α)), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u2} α) => α) (iSup.{u2, u1} (OrderDual.{u2} α) (OrderDual.supSet.{u2} α (CompleteLattice.toInfSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (iSup.{u2, u1} (OrderDual.{u2} α) (OrderDual.supSet.{u2} α (CompleteLattice.toInfSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (f i)))
 Case conversion may be inaccurate. Consider using '#align of_dual_supr ofDual_iSupₓ'. -/
 @[simp]
 theorem ofDual_iSup (f : ι → αᵒᵈ) : ofDual (⨆ i, f i) = ⨅ i, ofDual (f i) :=
@@ -608,7 +608,7 @@ theorem ofDual_iSup (f : ι → αᵒᵈ) : ofDual (⨆ i, f i) = ⨅ i, ofDual
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> (OrderDual.{u1} α)), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α) (iInf.{u1, u2} (OrderDual.{u1} α) (OrderDual.hasInf.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1))) ι (fun (i : ι) => f i))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α) (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> (OrderDual.{u2} α)), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) (iInf.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (iInf.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (f i)))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> (OrderDual.{u2} α)), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u2} α) => α) (iInf.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (iInf.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (f i)))
 Case conversion may be inaccurate. Consider using '#align of_dual_infi ofDual_iInfₓ'. -/
 @[simp]
 theorem ofDual_iInf (f : ι → αᵒᵈ) : ofDual (⨅ i, f i) = ⨆ i, ofDual (f i) :=
@@ -992,7 +992,7 @@ theorem Function.Surjective.iSup_comp {f : ι → ι'} (hf : Surjective f) (g :
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : SupSet.{u1} α] {g : ι' -> α} (e : Equiv.{u2, u3} ι ι'), Eq.{succ u1} α (iSup.{u1, u2} α _inst_1 ι (fun (x : ι) => g (coeFn.{max 1 (imax u2 u3) (imax u3 u2), imax u2 u3} (Equiv.{u2, u3} ι ι') (fun (_x : Equiv.{u2, u3} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{u2, u3} ι ι') e x))) (iSup.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), Eq.{succ u1} α (iSup.{u1, u3} α _inst_1 ι (fun (x : ι) => g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x))) (iSup.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y))
+  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), Eq.{succ u1} α (iSup.{u1, u3} α _inst_1 ι (fun (x : ι) => g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x))) (iSup.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y))
 Case conversion may be inaccurate. Consider using '#align equiv.supr_comp Equiv.iSup_compₓ'. -/
 theorem Equiv.iSup_comp {g : ι' → α} (e : ι ≃ ι') : (⨆ x, g (e x)) = ⨆ y, g y :=
   e.Surjective.iSup_comp _
@@ -1015,7 +1015,7 @@ protected theorem Function.Surjective.iSup_congr {g : ι' → α} (h : ι → ι
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u2, u3} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (coeFn.{max 1 (imax u2 u3) (imax u3 u2), imax u2 u3} (Equiv.{u2, u3} ι ι') (fun (_x : Equiv.{u2, u3} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{u2, u3} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (iSup.{u1, u2} α _inst_1 ι (fun (x : ι) => f x)) (iSup.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (iSup.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (iSup.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
+  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (iSup.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (iSup.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
 Case conversion may be inaccurate. Consider using '#align equiv.supr_congr Equiv.iSup_congrₓ'. -/
 protected theorem Equiv.iSup_congr {g : ι' → α} (e : ι ≃ ι') (h : ∀ x, g (e x) = f x) :
     (⨆ x, f x) = ⨆ y, g y :=
@@ -1112,7 +1112,7 @@ theorem Function.Surjective.iInf_comp {f : ι → ι'} (hf : Surjective f) (g :
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : InfSet.{u1} α] {g : ι' -> α} (e : Equiv.{u2, u3} ι ι'), Eq.{succ u1} α (iInf.{u1, u2} α _inst_1 ι (fun (x : ι) => g (coeFn.{max 1 (imax u2 u3) (imax u3 u2), imax u2 u3} (Equiv.{u2, u3} ι ι') (fun (_x : Equiv.{u2, u3} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{u2, u3} ι ι') e x))) (iInf.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), Eq.{succ u1} α (iInf.{u1, u3} α _inst_1 ι (fun (x : ι) => g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x))) (iInf.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y))
+  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), Eq.{succ u1} α (iInf.{u1, u3} α _inst_1 ι (fun (x : ι) => g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x))) (iInf.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y))
 Case conversion may be inaccurate. Consider using '#align equiv.infi_comp Equiv.iInf_compₓ'. -/
 theorem Equiv.iInf_comp {g : ι' → α} (e : ι ≃ ι') : (⨅ x, g (e x)) = ⨅ y, g y :=
   @Equiv.iSup_comp αᵒᵈ _ _ _ _ e
@@ -1133,7 +1133,7 @@ protected theorem Function.Surjective.iInf_congr {g : ι' → α} (h : ι → ι
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : InfSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u2, u3} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (coeFn.{max 1 (imax u2 u3) (imax u3 u2), imax u2 u3} (Equiv.{u2, u3} ι ι') (fun (_x : Equiv.{u2, u3} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{u2, u3} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (iInf.{u1, u2} α _inst_1 ι (fun (x : ι) => f x)) (iInf.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (iInf.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (iInf.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
+  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (iInf.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (iInf.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
 Case conversion may be inaccurate. Consider using '#align equiv.infi_congr Equiv.iInf_congrₓ'. -/
 protected theorem Equiv.iInf_congr {g : ι' → α} (e : ι ≃ ι') (h : ∀ x, g (e x) = f x) :
     (⨅ x, f x) = ⨅ y, g y :=
@@ -1710,7 +1710,7 @@ theorem Antitone.le_map_sInf [CompleteLattice β] {s : Set α} {f : α → β} (
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (x : ι -> α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => x i))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (x i)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : CompleteLattice.{u3} β] (f : OrderIso.{u2, u3} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))))) (x : ι -> α), Eq.{succ u3} β (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => x i))) (iSup.{u3, u1} β (CompleteLattice.toSupSet.{u3} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (x i)))
+  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : CompleteLattice.{u3} β] (f : OrderIso.{u2, u3} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))))) (x : ι -> α), Eq.{succ u3} β (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => x i))) (iSup.{u3, u1} β (CompleteLattice.toSupSet.{u3} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f (x i)))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_supr OrderIso.map_iSupₓ'. -/
 theorem OrderIso.map_iSup [CompleteLattice β] (f : α ≃o β) (x : ι → α) :
     f (⨆ i, x i) = ⨆ i, f (x i) :=
@@ -1721,7 +1721,7 @@ theorem OrderIso.map_iSup [CompleteLattice β] (f : α ≃o β) (x : ι → α)
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (x : ι -> α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => x i))) (iInf.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (x i)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : CompleteLattice.{u3} β] (f : OrderIso.{u2, u3} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))))) (x : ι -> α), Eq.{succ u3} β (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => x i))) (iInf.{u3, u1} β (CompleteLattice.toInfSet.{u3} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (x i)))
+  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : CompleteLattice.{u3} β] (f : OrderIso.{u2, u3} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))))) (x : ι -> α), Eq.{succ u3} β (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => x i))) (iInf.{u3, u1} β (CompleteLattice.toInfSet.{u3} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{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.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f (x i)))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_infi OrderIso.map_iInfₓ'. -/
 theorem OrderIso.map_iInf [CompleteLattice β] (f : α ≃o β) (x : ι → α) :
     f (⨅ i, x i) = ⨅ i, f (x i) :=
@@ -1732,7 +1732,7 @@ theorem OrderIso.map_iInf [CompleteLattice β] (f : α ≃o β) (x : ι → α)
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s)) (iSup.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) α (fun (a : α) => iSup.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (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) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f a)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)) (iSup.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_2) α (fun (a : α) => iSup.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_2) (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) => 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)) (iSup.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_2) α (fun (a : α) => iSup.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_2) (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) => 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} 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 order_iso.map_Sup OrderIso.map_sSupₓ'. -/
 theorem OrderIso.map_sSup [CompleteLattice β] (f : α ≃o β) (s : Set α) :
     f (sSup s) = ⨆ a ∈ s, f a := by simp only [sSup_eq_iSup, OrderIso.map_iSup]
@@ -1742,7 +1742,7 @@ theorem OrderIso.map_sSup [CompleteLattice β] (f : α ≃o β) (s : Set α) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)) (iInf.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) α (fun (a : α) => iInf.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (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) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f a)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)) (iInf.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_2) α (fun (a : α) => iInf.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_2) (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) => 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f a)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) f (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)) (iInf.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_2) α (fun (a : α) => iInf.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_2) (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) => 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} 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 order_iso.map_Inf OrderIso.map_sInfₓ'. -/
 theorem OrderIso.map_sInf [CompleteLattice β] (f : α ≃o β) (s : Set α) :
     f (sInf s) = ⨅ a ∈ s, f a :=

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

@@ -134,7 +134,7 @@ variable [CompleteSemilatticeSup α] {s t : Set α} {a b : α}
 
 /- warning: le_Sup -> le_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align le_Sup le_sSupₓ'. -/
@@ -145,7 +145,7 @@ theorem le_sSup : a ∈ s → a ≤ sSup s :=
 
 /- warning: Sup_le -> sSup_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) b a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) b a)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) b a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s) a)
 Case conversion may be inaccurate. Consider using '#align Sup_le sSup_leₓ'. -/
@@ -175,7 +175,7 @@ theorem IsLUB.sSup_eq (h : IsLUB s a) : sSup s = a :=
 
 /- warning: le_Sup_of_le -> le_sSup_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align le_Sup_of_le le_sSup_of_leₓ'. -/
@@ -185,7 +185,7 @@ theorem le_sSup_of_le (hb : b ∈ s) (h : a ≤ b) : a ≤ sSup s :=
 
 /- warning: Sup_le_Sup -> sSup_le_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) t))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align Sup_le_Sup sSup_le_sSupₓ'. -/
@@ -195,7 +195,7 @@ theorem sSup_le_sSup (h : s ⊆ t) : sSup s ≤ sSup t :=
 
 /- warning: Sup_le_iff -> sSup_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) a) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) b a))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) a) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) b a))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s) a) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) b a))
 Case conversion may be inaccurate. Consider using '#align Sup_le_iff sSup_le_iffₓ'. -/
@@ -206,7 +206,7 @@ theorem sSup_le_iff : sSup s ≤ a ↔ ∀ b ∈ s, b ≤ a :=
 
 /- warning: le_Sup_iff -> le_sSup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1)) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1)) s)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1)) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b))
 Case conversion may be inaccurate. Consider using '#align le_Sup_iff le_sSup_iffₓ'. -/
@@ -216,7 +216,7 @@ theorem le_sSup_iff : a ≤ sSup s ↔ ∀ b ∈ upperBounds s, a ≤ b :=
 
 /- warning: le_supr_iff -> le_iSup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {a : α} {s : ι -> α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) ι s)) (forall (b : α), (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (s i) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {a : α} {s : ι -> α}, Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) ι s)) (forall (b : α), (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (s i) b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteSemilatticeSup.{u2} α] {a : α} {s : ι -> α}, Iff (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeSup.toPartialOrder.{u2} α _inst_1))) a (iSup.{u2, u1} α (CompleteSemilatticeSup.toSupSet.{u2} α _inst_1) ι s)) (forall (b : α), (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeSup.toPartialOrder.{u2} α _inst_1))) (s i) b) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeSup.toPartialOrder.{u2} α _inst_1))) a b))
 Case conversion may be inaccurate. Consider using '#align le_supr_iff le_iSup_iffₓ'. -/
@@ -226,7 +226,7 @@ theorem le_iSup_iff {s : ι → α} : a ≤ iSup s ↔ ∀ b, (∀ i, s i ≤ b)
 
 /- warning: Sup_le_Sup_of_forall_exists_le -> sSup_le_sSup_of_forall_exists_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) x y)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) x y)))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) t))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) x y)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align Sup_le_Sup_of_forall_exists_le sSup_le_sSup_of_forall_exists_leₓ'. -/
@@ -268,7 +268,7 @@ variable [CompleteSemilatticeInf α] {s t : Set α} {a b : α}
 
 /- warning: Inf_le -> sInf_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s) a)
 Case conversion may be inaccurate. Consider using '#align Inf_le sInf_leₓ'. -/
@@ -279,7 +279,7 @@ theorem sInf_le : a ∈ s → sInf s ≤ a :=
 
 /- warning: le_Inf -> le_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a b)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align le_Inf le_sInfₓ'. -/
@@ -309,7 +309,7 @@ theorem IsGLB.sInf_eq (h : IsGLB s a) : sInf s = a :=
 
 /- warning: Inf_le_of_le -> sInf_le_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s) a)
 Case conversion may be inaccurate. Consider using '#align Inf_le_of_le sInf_le_of_leₓ'. -/
@@ -319,7 +319,7 @@ theorem sInf_le_of_le (hb : b ∈ s) (h : b ≤ a) : sInf s ≤ a :=
 
 /- warning: Inf_le_Inf -> sInf_le_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) t) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) t) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) t) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align Inf_le_Inf sInf_le_sInfₓ'. -/
@@ -329,7 +329,7 @@ theorem sInf_le_sInf (h : s ⊆ t) : sInf t ≤ sInf s :=
 
 /- warning: le_Inf_iff -> le_sInf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a b))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a b))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a b))
 Case conversion may be inaccurate. Consider using '#align le_Inf_iff le_sInf_iffₓ'. -/
@@ -340,7 +340,7 @@ theorem le_sInf_iff : a ≤ sInf s ↔ ∀ b ∈ s, a ≤ b :=
 
 /- warning: Inf_le_iff -> sInf_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s) a) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1)) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s) a) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1)) s)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s) a) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1)) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a))
 Case conversion may be inaccurate. Consider using '#align Inf_le_iff sInf_le_iffₓ'. -/
@@ -350,7 +350,7 @@ theorem sInf_le_iff : sInf s ≤ a ↔ ∀ b ∈ lowerBounds s, b ≤ a :=
 
 /- warning: infi_le_iff -> iInf_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {a : α} {s : ι -> α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) ι s) a) (forall (b : α), (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b (s i)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {a : α} {s : ι -> α}, Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) ι s) a) (forall (b : α), (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b (s i)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteSemilatticeInf.{u2} α] {a : α} {s : ι -> α}, Iff (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α _inst_1))) (iInf.{u2, u1} α (CompleteSemilatticeInf.toInfSet.{u2} α _inst_1) ι s) a) (forall (b : α), (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α _inst_1))) b (s i)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α _inst_1))) b a))
 Case conversion may be inaccurate. Consider using '#align infi_le_iff iInf_le_iffₓ'. -/
@@ -360,7 +360,7 @@ theorem iInf_le_iff {s : ι → α} : iInf s ≤ a ↔ ∀ b, (∀ i, b ≤ s i)
 
 /- warning: Inf_le_Inf_of_forall_exists_le -> sInf_le_sInf_of_forall_exists_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) y x)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) t) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) y x)))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) t) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) y x)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) t) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align Inf_le_Inf_of_forall_exists_le sInf_le_sInf_of_forall_exists_leₓ'. -/
@@ -396,13 +396,17 @@ class CompleteLattice (α : Type _) extends Lattice α, CompleteSemilatticeSup 
 #align complete_lattice CompleteLattice
 -/
 
-#print CompleteLattice.toBoundedOrder /-
+/- warning: complete_lattice.to_bounded_order -> CompleteLattice.toBoundedOrder is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [h : CompleteLattice.{u1} α], BoundedOrder.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α h))))
+but is expected to have type
+  forall {α : Type.{u1}} [h : CompleteLattice.{u1} α], BoundedOrder.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α h))))
+Case conversion may be inaccurate. Consider using '#align complete_lattice.to_bounded_order CompleteLattice.toBoundedOrderₓ'. -/
 -- see Note [lower instance priority]
 instance (priority := 100) CompleteLattice.toBoundedOrder [h : CompleteLattice α] :
     BoundedOrder α :=
   { h with }
 #align complete_lattice.to_bounded_order CompleteLattice.toBoundedOrder
--/
 
 #print completeLatticeOfInf /-
 /-- Create a `complete_lattice` from a `partial_order` and `Inf` function
@@ -613,7 +617,7 @@ theorem ofDual_iInf (f : ι → αᵒᵈ) : ofDual (⨅ i, f i) = ⨆ i, ofDual
 
 /- warning: Inf_le_Sup -> sInf_le_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (LE.le.{u1} α (Preorder.toLE.{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) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (LE.le.{u1} α (Preorder.toHasLe.{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) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (LE.le.{u1} α (Preorder.toLE.{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) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align Inf_le_Sup sInf_le_sSupₓ'. -/
@@ -643,7 +647,7 @@ theorem sInf_union {s t : Set α} : sInf (s ∪ t) = sInf s ⊓ sInf t :=
 
 /- warning: Sup_inter_le -> sSup_inter_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{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)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toHasLe.{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)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) t))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{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) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align Sup_inter_le sSup_inter_leₓ'. -/
@@ -653,7 +657,7 @@ theorem sSup_inter_le {s t : Set α} : sSup (s ∩ t) ≤ sSup s ⊓ sSup t :=
 
 /- warning: le_Inf_inter -> le_sInf_inter is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) t)) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) t)) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) t)) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t))
 Case conversion may be inaccurate. Consider using '#align le_Inf_inter le_sInf_interₓ'. -/
@@ -730,7 +734,7 @@ theorem sInf_insert {a : α} {s : Set α} : sInf (insert a s) = a ⊓ sInf s :=
 
 /- warning: Sup_le_Sup_of_subset_insert_bot -> sSup_le_sSup_of_subset_insert_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)) t)) -> (LE.le.{u1} α (Preorder.toLE.{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) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)) t)) -> (LE.le.{u1} α (Preorder.toHasLe.{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) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) t))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1)) t)) -> (LE.le.{u1} α (Preorder.toLE.{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) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align Sup_le_Sup_of_subset_insert_bot sSup_le_sSup_of_subset_insert_botₓ'. -/
@@ -740,7 +744,7 @@ theorem sSup_le_sSup_of_subset_insert_bot (h : s ⊆ insert ⊥ t) : sSup s ≤
 
 /- warning: Inf_le_Inf_of_subset_insert_top -> sInf_le_sInf_of_subset_insert_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)) t)) -> (LE.le.{u1} α (Preorder.toLE.{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)) t) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)) t)) -> (LE.le.{u1} α (Preorder.toHasLe.{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)) t) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1)) t)) -> (LE.le.{u1} α (Preorder.toLE.{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) t) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align Inf_le_Inf_of_subset_insert_top sInf_le_sInf_of_subset_insert_topₓ'. -/
@@ -840,7 +844,7 @@ theorem eq_singleton_top_of_sInf_eq_top_of_nonempty : sInf s = ⊤ → s.Nonempt
 
 /- warning: Sup_eq_of_forall_le_of_forall_lt_exists_gt -> sSup_eq_of_forall_le_of_forall_lt_exists_gt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w b) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w a)))) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) b)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w b) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w a)))) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) b)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w b) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w a)))) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) b)
 Case conversion may be inaccurate. Consider using '#align Sup_eq_of_forall_le_of_forall_lt_exists_gt sSup_eq_of_forall_le_of_forall_lt_exists_gtₓ'. -/
@@ -857,7 +861,7 @@ theorem sSup_eq_of_forall_le_of_forall_lt_exists_gt (h₁ : ∀ a ∈ s, a ≤ b
 
 /- warning: Inf_eq_of_forall_ge_of_forall_gt_exists_lt -> sInf_eq_of_forall_ge_of_forall_gt_exists_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b a)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b w) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a w)))) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) b)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b a)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b w) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a w)))) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) b)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b a)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b w) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a w)))) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) b)
 Case conversion may be inaccurate. Consider using '#align Inf_eq_of_forall_ge_of_forall_gt_exists_lt sInf_eq_of_forall_ge_of_forall_gt_exists_ltₓ'. -/
@@ -878,7 +882,7 @@ variable [CompleteLinearOrder α] {s t : Set α} {a b : α}
 
 /- warning: lt_Sup_iff -> lt_sSup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, Iff (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)) s)) (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b a)))
 Case conversion may be inaccurate. Consider using '#align lt_Sup_iff lt_sSup_iffₓ'. -/
@@ -888,7 +892,7 @@ theorem lt_sSup_iff : b < sSup s ↔ ∃ a ∈ s, b < a :=
 
 /- warning: Inf_lt_iff -> sInf_lt_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s) b) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, Iff (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s) b) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a b)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)) s) b) (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a b)))
 Case conversion may be inaccurate. Consider using '#align Inf_lt_iff sInf_lt_iffₓ'. -/
@@ -898,7 +902,7 @@ theorem sInf_lt_iff : sInf s < b ↔ ∃ a ∈ s, a < b :=
 
 /- warning: Sup_eq_top -> sSup_eq_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b a))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b a))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)) s) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Top.top.{u1} α (CompleteLattice.toTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b a))))
 Case conversion may be inaccurate. Consider using '#align Sup_eq_top sSup_eq_topₓ'. -/
@@ -912,7 +916,7 @@ theorem sSup_eq_top : sSup s = ⊤ ↔ ∀ b < ⊤, ∃ a ∈ s, b < a :=
 
 /- warning: Inf_eq_bot -> sInf_eq_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a b))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a b))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)) s) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a b))))
 Case conversion may be inaccurate. Consider using '#align Inf_eq_bot sInf_eq_botₓ'. -/
@@ -922,7 +926,7 @@ theorem sInf_eq_bot : sInf s = ⊥ ↔ ∀ b > ⊥, ∃ a ∈ s, a < b :=
 
 /- warning: lt_supr_iff -> lt_iSup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] {a : α} {f : ι -> α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι f)) (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] {a : α} {f : ι -> α}, Iff (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι f)) (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a (f i)))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLinearOrder.{u2} α] {a : α} {f : ι -> α}, Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) a (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)) ι f)) (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) a (f i)))
 Case conversion may be inaccurate. Consider using '#align lt_supr_iff lt_iSup_iffₓ'. -/
@@ -932,7 +936,7 @@ theorem lt_iSup_iff {f : ι → α} : a < iSup f ↔ ∃ i, a < f i :=
 
 /- warning: infi_lt_iff -> iInf_lt_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] {a : α} {f : ι -> α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι f) a) (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (f i) a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] {a : α} {f : ι -> α}, Iff (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι f) a) (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (f i) a))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLinearOrder.{u2} α] {a : α} {f : ι -> α}, Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)) ι f) a) (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) (f i) a))
 Case conversion may be inaccurate. Consider using '#align infi_lt_iff iInf_lt_iffₓ'. -/
@@ -1184,7 +1188,7 @@ variable [CompleteLattice α] {f g s t : ι → α} {a b : α}
 
 /- warning: le_supr -> le_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι f)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι f)
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι f)
 Case conversion may be inaccurate. Consider using '#align le_supr le_iSupₓ'. -/
@@ -1196,7 +1200,7 @@ theorem le_iSup (f : ι → α) (i : ι) : f i ≤ iSup f :=
 
 /- warning: infi_le -> iInf_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toLE.{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 f) (f i)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toHasLe.{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 f) (f i)
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (i : ι), LE.le.{u2} α (Preorder.toLE.{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 f) (f i)
 Case conversion may be inaccurate. Consider using '#align infi_le iInf_leₓ'. -/
@@ -1206,7 +1210,7 @@ theorem iInf_le (f : ι → α) (i : ι) : iInf f ≤ f i :=
 
 /- warning: le_supr' -> le_iSup' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι f)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι f)
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι f)
 Case conversion may be inaccurate. Consider using '#align le_supr' le_iSup'ₓ'. -/
@@ -1217,7 +1221,7 @@ theorem le_iSup' (f : ι → α) (i : ι) : f i ≤ iSup f :=
 
 /- warning: infi_le' -> iInf_le' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toLE.{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 f) (f i)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toHasLe.{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 f) (f i)
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (i : ι), LE.le.{u2} α (Preorder.toLE.{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 f) (f i)
 Case conversion may be inaccurate. Consider using '#align infi_le' iInf_le'ₓ'. -/
@@ -1273,7 +1277,7 @@ theorem IsGLB.iInf_eq (h : IsGLB (range f) a) : (⨅ j, f j) = a :=
 
 /- warning: le_supr_of_le -> le_iSup_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α} (i : ι), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι f))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α} (i : ι), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι f))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α} (i : ι), (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (f i)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι f))
 Case conversion may be inaccurate. Consider using '#align le_supr_of_le le_iSup_of_leₓ'. -/
@@ -1283,7 +1287,7 @@ theorem le_iSup_of_le (i : ι) (h : a ≤ f i) : a ≤ iSup f :=
 
 /- warning: infi_le_of_le -> iInf_le_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α} (i : ι), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) a) -> (LE.le.{u1} α (Preorder.toLE.{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 f) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α} (i : ι), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) a) -> (LE.le.{u1} α (Preorder.toHasLe.{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 f) a)
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α} (i : ι), (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) a) -> (LE.le.{u2} α (Preorder.toLE.{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 f) a)
 Case conversion may be inaccurate. Consider using '#align infi_le_of_le iInf_le_of_leₓ'. -/
@@ -1293,7 +1297,7 @@ theorem iInf_le_of_le (i : ι) (h : f i ≤ a) : iInf f ≤ a :=
 
 /- warning: le_supr₂ -> le_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} (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) (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)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) (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)))
 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} (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) (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)))
 Case conversion may be inaccurate. Consider using '#align le_supr₂ le_iSup₂ₓ'. -/
@@ -1304,7 +1308,7 @@ theorem le_iSup₂ {f : ∀ i, κ i → α} (i : ι) (j : κ i) : f i j ≤ ⨆
 
 /- warning: infi₂_le -> iInf₂_le 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} (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{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))) (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} (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toHasLe.{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))) (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} (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{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))) (f i j)
 Case conversion may be inaccurate. Consider using '#align infi₂_le iInf₂_leₓ'. -/
@@ -1315,7 +1319,7 @@ theorem iInf₂_le {f : ∀ i, κ i → α} (i : ι) (j : κ i) : (⨅ (i) (j),
 
 /- warning: le_supr₂_of_le -> le_iSup₂_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i j)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (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))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i j)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (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))))
 but is expected to have type
   forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (f i j)) -> (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (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))))
 Case conversion may be inaccurate. Consider using '#align le_supr₂_of_le le_iSup₂_of_leₓ'. -/
@@ -1327,7 +1331,7 @@ theorem le_iSup₂_of_le {f : ∀ i, κ i → α} (i : ι) (j : κ i) (h : a ≤
 
 /- warning: infi₂_le_of_le -> iInf₂_le_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) a) -> (LE.le.{u1} α (Preorder.toLE.{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))) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) a) -> (LE.le.{u1} α (Preorder.toHasLe.{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))) a)
 but is expected to have type
   forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) a) -> (LE.le.{u3} α (Preorder.toLE.{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))) a)
 Case conversion may be inaccurate. Consider using '#align infi₂_le_of_le iInf₂_le_of_leₓ'. -/
@@ -1339,7 +1343,7 @@ theorem iInf₂_le_of_le {f : ∀ i, κ i → α} (i : ι) (j : κ i) (h : f i j
 
 /- warning: supr_le -> iSup_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) a) -> (LE.le.{u1} α (Preorder.toLE.{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 f) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) a) -> (LE.le.{u1} α (Preorder.toHasLe.{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 f) a)
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) a) -> (LE.le.{u2} α (Preorder.toLE.{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 f) a)
 Case conversion may be inaccurate. Consider using '#align supr_le iSup_leₓ'. -/
@@ -1349,7 +1353,7 @@ theorem iSup_le (h : ∀ i, f i ≤ a) : iSup f ≤ a :=
 
 /- warning: le_infi -> le_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι f))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι f))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (f i)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι f))
 Case conversion may be inaccurate. Consider using '#align le_infi le_iInfₓ'. -/
@@ -1359,7 +1363,7 @@ theorem le_iInf (h : ∀ i, a ≤ f i) : a ≤ iInf f :=
 
 /- warning: supr₂_le -> iSup₂_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) a) -> (LE.le.{u1} α (Preorder.toLE.{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))) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) a) -> (LE.le.{u1} α (Preorder.toHasLe.{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))) a)
 but is expected to have type
   forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) a) -> (LE.le.{u3} α (Preorder.toLE.{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))) a)
 Case conversion may be inaccurate. Consider using '#align supr₂_le iSup₂_leₓ'. -/
@@ -1370,7 +1374,7 @@ theorem iSup₂_le {f : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ a) : (⨆ (i
 
 /- warning: le_infi₂ -> le_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] {a : α} {f : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i j)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (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))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i j)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (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))))
 but is expected to have type
   forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (f i j)) -> (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (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))))
 Case conversion may be inaccurate. Consider using '#align le_infi₂ le_iInf₂ₓ'. -/
@@ -1381,7 +1385,7 @@ theorem le_iInf₂ {f : ∀ i, κ i → α} (h : ∀ i j, a ≤ f i j) : a ≤ 
 
 /- warning: supr₂_le_supr -> iSup₂_le_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (κ : ι -> Sort.{u3}) (f : ι -> α), LE.le.{u1} α (Preorder.toLE.{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))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (κ : ι -> Sort.{u3}) (f : ι -> α), LE.le.{u1} α (Preorder.toHasLe.{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))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (κ : ι -> Sort.{u3}) (f : ι -> α), LE.le.{u2} α (Preorder.toLE.{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) => iSup.{u2, u3} α (CompleteLattice.toSupSet.{u2} α _inst_1) (κ i) (fun (j : κ i) => f i))) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))
 Case conversion may be inaccurate. Consider using '#align supr₂_le_supr iSup₂_le_iSupₓ'. -/
@@ -1391,7 +1395,7 @@ theorem iSup₂_le_iSup (κ : ι → Sort _) (f : ι → α) : (⨆ (i) (j : κ
 
 /- warning: infi_le_infi₂ -> iInf_le_iInf₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (κ : ι -> Sort.{u3}) (f : ι -> α), LE.le.{u1} α (Preorder.toLE.{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} 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)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (κ : ι -> Sort.{u3}) (f : ι -> α), LE.le.{u1} α (Preorder.toHasLe.{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} 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)))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (κ : ι -> Sort.{u3}) (f : ι -> α), LE.le.{u2} α (Preorder.toLE.{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} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => iInf.{u2, u3} α (CompleteLattice.toInfSet.{u2} α _inst_1) (κ i) (fun (j : κ i) => f i)))
 Case conversion may be inaccurate. Consider using '#align infi_le_infi₂ iInf_le_iInf₂ₓ'. -/
@@ -1401,7 +1405,7 @@ theorem iInf_le_iInf₂ (κ : ι → Sort _) (f : ι → α) : (⨅ i, f i) ≤
 
 /- warning: supr_mono -> iSup_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (g i)) -> (LE.le.{u1} α (Preorder.toLE.{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 f) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι g))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (g i)) -> (LE.le.{u1} α (Preorder.toHasLe.{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 f) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι g))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (g i)) -> (LE.le.{u2} α (Preorder.toLE.{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 f) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι g))
 Case conversion may be inaccurate. Consider using '#align supr_mono iSup_monoₓ'. -/
@@ -1411,7 +1415,7 @@ theorem iSup_mono (h : ∀ i, f i ≤ g i) : iSup f ≤ iSup g :=
 
 /- warning: infi_mono -> iInf_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (g i)) -> (LE.le.{u1} α (Preorder.toLE.{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 f) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι g))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (g i)) -> (LE.le.{u1} α (Preorder.toHasLe.{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 f) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι g))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (g i)) -> (LE.le.{u2} α (Preorder.toLE.{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 f) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι g))
 Case conversion may be inaccurate. Consider using '#align infi_mono iInf_monoₓ'. -/
@@ -1421,7 +1425,7 @@ theorem iInf_mono (h : ∀ i, f i ≤ g i) : iInf f ≤ iInf g :=
 
 /- warning: supr₂_mono -> iSup₂_mono 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} {g : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) (g i j)) -> (LE.le.{u1} α (Preorder.toLE.{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} 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) => g 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} {g : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) (g i j)) -> (LE.le.{u1} α (Preorder.toHasLe.{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} 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) => g 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} {g : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) (g i j)) -> (LE.le.{u3} α (Preorder.toLE.{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} 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) => g i j))))
 Case conversion may be inaccurate. Consider using '#align supr₂_mono iSup₂_monoₓ'. -/
@@ -1434,7 +1438,7 @@ theorem iSup₂_mono {f g : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ g i j) :
 
 /- warning: infi₂_mono -> iInf₂_mono 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} {g : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) (g i j)) -> (LE.le.{u1} α (Preorder.toLE.{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} 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) => g 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} {g : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) (g i j)) -> (LE.le.{u1} α (Preorder.toHasLe.{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} 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) => g 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} {g : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) (g i j)) -> (LE.le.{u3} α (Preorder.toLE.{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} 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) => g i j))))
 Case conversion may be inaccurate. Consider using '#align infi₂_mono iInf₂_monoₓ'. -/
@@ -1447,7 +1451,7 @@ theorem iInf₂_mono {f g : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ g i j) :
 
 /- warning: supr_mono' -> iSup_mono' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι' -> α}, (forall (i : ι), Exists.{u3} ι' (fun (i' : ι') => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (g i'))) -> (LE.le.{u1} α (Preorder.toLE.{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 f) (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' g))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι' -> α}, (forall (i : ι), Exists.{u3} ι' (fun (i' : ι') => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (g i'))) -> (LE.le.{u1} α (Preorder.toHasLe.{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 f) (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' g))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι' -> α}, (forall (i : ι), Exists.{u3} ι' (fun (i' : ι') => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (g i'))) -> (LE.le.{u2} α (Preorder.toLE.{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 f) (iSup.{u2, u3} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι' g))
 Case conversion may be inaccurate. Consider using '#align supr_mono' iSup_mono'ₓ'. -/
@@ -1457,7 +1461,7 @@ theorem iSup_mono' {g : ι' → α} (h : ∀ i, ∃ i', f i ≤ g i') : iSup f 
 
 /- warning: infi_mono' -> iInf_mono' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι' -> α}, (forall (i' : ι'), Exists.{u2} ι (fun (i : ι) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (g i'))) -> (LE.le.{u1} α (Preorder.toLE.{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 f) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' g))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι' -> α}, (forall (i' : ι'), Exists.{u2} ι (fun (i : ι) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (g i'))) -> (LE.le.{u1} α (Preorder.toHasLe.{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 f) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' g))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u3}} {ι' : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι' -> α}, (forall (i' : ι'), Exists.{u3} ι (fun (i : ι) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (g i'))) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (iInf.{u2, u3} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι f) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι' g))
 Case conversion may be inaccurate. Consider using '#align infi_mono' iInf_mono'ₓ'. -/
@@ -1467,7 +1471,7 @@ theorem iInf_mono' {g : ι' → α} (h : ∀ i', ∃ i, f i ≤ g i') : iInf f 
 
 /- warning: supr₂_mono' -> iSup₂_mono' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} {κ : ι -> Sort.{u4}} {κ' : ι' -> Sort.{u5}} [_inst_1 : CompleteLattice.{u1} α] {f : forall (i : ι), (κ i) -> α} {g : forall (i' : ι'), (κ' i') -> α}, (forall (i : ι) (j : κ i), Exists.{u3} ι' (fun (i' : ι') => Exists.{u5} (κ' i') (fun (j' : κ' i') => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) (g i' j')))) -> (LE.le.{u1} α (Preorder.toLE.{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, u4} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ i) (fun (j : κ i) => f i j))) (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' (fun (i : ι') => iSup.{u1, u5} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ' i) (fun (j : κ' i) => g i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} {κ : ι -> Sort.{u4}} {κ' : ι' -> Sort.{u5}} [_inst_1 : CompleteLattice.{u1} α] {f : forall (i : ι), (κ i) -> α} {g : forall (i' : ι'), (κ' i') -> α}, (forall (i : ι) (j : κ i), Exists.{u3} ι' (fun (i' : ι') => Exists.{u5} (κ' i') (fun (j' : κ' i') => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) (g i' j')))) -> (LE.le.{u1} α (Preorder.toHasLe.{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, u4} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ i) (fun (j : κ i) => f i j))) (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' (fun (i : ι') => iSup.{u1, u5} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ' i) (fun (j : κ' i) => g i j))))
 but is expected to have type
   forall {α : Type.{u3}} {ι : Sort.{u2}} {ι' : Sort.{u5}} {κ : ι -> Sort.{u1}} {κ' : ι' -> Sort.{u4}} [_inst_1 : CompleteLattice.{u3} α] {f : forall (i : ι), (κ i) -> α} {g : forall (i' : ι'), (κ' i') -> α}, (forall (i : ι) (j : κ i), Exists.{u5} ι' (fun (i' : ι') => Exists.{u4} (κ' i') (fun (j' : κ' i') => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) (g i' j')))) -> (LE.le.{u3} α (Preorder.toLE.{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, u5} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι' (fun (i : ι') => iSup.{u3, u4} α (CompleteLattice.toSupSet.{u3} α _inst_1) (κ' i) (fun (j : κ' i) => g i j))))
 Case conversion may be inaccurate. Consider using '#align supr₂_mono' iSup₂_mono'ₓ'. -/
@@ -1482,7 +1486,7 @@ theorem iSup₂_mono' {f : ∀ i, κ i → α} {g : ∀ i', κ' i' → α} (h :
 
 /- warning: infi₂_mono' -> iInf₂_mono' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} {κ : ι -> Sort.{u4}} {κ' : ι' -> Sort.{u5}} [_inst_1 : CompleteLattice.{u1} α] {f : forall (i : ι), (κ i) -> α} {g : forall (i' : ι'), (κ' i') -> α}, (forall (i : ι') (j : κ' i), Exists.{u2} ι (fun (i' : ι) => Exists.{u4} (κ i') (fun (j' : κ i') => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i' j') (g i j)))) -> (LE.le.{u1} α (Preorder.toLE.{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, u4} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ i) (fun (j : κ i) => f i j))) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (i : ι') => iInf.{u1, u5} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ' i) (fun (j : κ' i) => g i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} {κ : ι -> Sort.{u4}} {κ' : ι' -> Sort.{u5}} [_inst_1 : CompleteLattice.{u1} α] {f : forall (i : ι), (κ i) -> α} {g : forall (i' : ι'), (κ' i') -> α}, (forall (i : ι') (j : κ' i), Exists.{u2} ι (fun (i' : ι) => Exists.{u4} (κ i') (fun (j' : κ i') => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i' j') (g i j)))) -> (LE.le.{u1} α (Preorder.toHasLe.{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, u4} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ i) (fun (j : κ i) => f i j))) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (i : ι') => iInf.{u1, u5} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ' i) (fun (j : κ' i) => g i j))))
 but is expected to have type
   forall {α : Type.{u3}} {ι : Sort.{u5}} {ι' : Sort.{u2}} {κ : ι -> Sort.{u4}} {κ' : ι' -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {f : forall (i : ι), (κ i) -> α} {g : forall (i' : ι'), (κ' i') -> α}, (forall (i : ι') (j : κ' i), Exists.{u5} ι (fun (i' : ι) => Exists.{u4} (κ i') (fun (j' : κ i') => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i' j') (g i j)))) -> (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (iInf.{u3, u5} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => iInf.{u3, u4} α (CompleteLattice.toInfSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j))) (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) => g i j))))
 Case conversion may be inaccurate. Consider using '#align infi₂_mono' iInf₂_mono'ₓ'. -/
@@ -1497,7 +1501,7 @@ theorem iInf₂_mono' {f : ∀ i, κ i → α} {g : ∀ i', κ' i' → α} (h :
 
 /- warning: supr_const_mono -> iSup_const_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α}, (ι -> ι') -> (LE.le.{u1} α (Preorder.toLE.{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) => a)) (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' (fun (j : ι') => a)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α}, (ι -> ι') -> (LE.le.{u1} α (Preorder.toHasLe.{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) => a)) (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' (fun (j : ι') => a)))
 but is expected to have type
   forall {α : Type.{u3}} {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α}, (ι -> ι') -> (LE.le.{u3} α (Preorder.toLE.{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) => a)) (iSup.{u3, u1} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι' (fun (j : ι') => a)))
 Case conversion may be inaccurate. Consider using '#align supr_const_mono iSup_const_monoₓ'. -/
@@ -1507,7 +1511,7 @@ theorem iSup_const_mono (h : ι → ι') : (⨆ i : ι, a) ≤ ⨆ j : ι', a :=
 
 /- warning: infi_const_mono -> iInf_const_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α}, (ι' -> ι) -> (LE.le.{u1} α (Preorder.toLE.{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) => a)) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (j : ι') => a)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α}, (ι' -> ι) -> (LE.le.{u1} α (Preorder.toHasLe.{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) => a)) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (j : ι') => a)))
 but is expected to have type
   forall {α : Type.{u3}} {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α}, (ι' -> ι) -> (LE.le.{u3} α (Preorder.toLE.{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) => a)) (iInf.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι' (fun (j : ι') => a)))
 Case conversion may be inaccurate. Consider using '#align infi_const_mono iInf_const_monoₓ'. -/
@@ -1517,7 +1521,7 @@ theorem iInf_const_mono (h : ι' → ι) : (⨅ i : ι, a) ≤ ⨅ j : ι', a :=
 
 /- warning: supr_infi_le_infi_supr -> iSup_iInf_le_iInf_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> ι' -> α), LE.le.{u1} α (Preorder.toLE.{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) => iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (j : ι') => f i j))) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (j : ι') => iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i j)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> ι' -> α), LE.le.{u1} α (Preorder.toHasLe.{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) => iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (j : ι') => f i j))) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (j : ι') => iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i j)))
 but is expected to have type
   forall {α : Type.{u3}} {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] (f : ι -> ι' -> α), LE.le.{u3} α (Preorder.toLE.{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) => iInf.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι' (fun (j : ι') => f i j))) (iInf.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι' (fun (j : ι') => iSup.{u3, u2} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => f i j)))
 Case conversion may be inaccurate. Consider using '#align supr_infi_le_infi_supr iSup_iInf_le_iInf_iSupₓ'. -/
@@ -1527,7 +1531,7 @@ theorem iSup_iInf_le_iInf_iSup (f : ι → ι' → α) : (⨆ i, ⨅ j, f i j) 
 
 /- warning: bsupr_mono -> biSup_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {p : ι -> Prop} {q : ι -> Prop}, (forall (i : ι), (p i) -> (q i)) -> (LE.le.{u1} α (Preorder.toLE.{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, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (q i) (fun (h : q i) => f i))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {p : ι -> Prop} {q : ι -> Prop}, (forall (i : ι), (p i) -> (q i)) -> (LE.le.{u1} α (Preorder.toHasLe.{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, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (q i) (fun (h : q i) => f i))))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {p : ι -> Prop} {q : ι -> Prop}, (forall (i : ι), (p i) -> (q i)) -> (LE.le.{u2} α (Preorder.toLE.{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) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (q i) (fun (h : q i) => f i))))
 Case conversion may be inaccurate. Consider using '#align bsupr_mono biSup_monoₓ'. -/
@@ -1538,7 +1542,7 @@ theorem biSup_mono {p q : ι → Prop} (hpq : ∀ i, p i → q i) :
 
 /- warning: binfi_mono -> biInf_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {p : ι -> Prop} {q : ι -> Prop}, (forall (i : ι), (p i) -> (q i)) -> (LE.le.{u1} α (Preorder.toLE.{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, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (q i) (fun (h : q i) => f i))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {p : ι -> Prop} {q : ι -> Prop}, (forall (i : ι), (p i) -> (q i)) -> (LE.le.{u1} α (Preorder.toHasLe.{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, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (q i) (fun (h : q i) => f i))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {p : ι -> Prop} {q : ι -> Prop}, (forall (i : ι), (p i) -> (q i)) -> (LE.le.{u2} α (Preorder.toLE.{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) => iInf.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (q i) (fun (h : q i) => f i))) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => iInf.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))))
 Case conversion may be inaccurate. Consider using '#align binfi_mono biInf_monoₓ'. -/
@@ -1549,7 +1553,7 @@ theorem biInf_mono {p q : ι → Prop} (hpq : ∀ i, p i → q i) :
 
 /- warning: supr_le_iff -> iSup_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{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 f) a) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, Iff (LE.le.{u1} α (Preorder.toHasLe.{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 f) a) (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) a)
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, Iff (LE.le.{u2} α (Preorder.toLE.{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 f) a) (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) a)
 Case conversion may be inaccurate. Consider using '#align supr_le_iff iSup_le_iffₓ'. -/
@@ -1560,7 +1564,7 @@ theorem iSup_le_iff : iSup f ≤ a ↔ ∀ i, f i ≤ a :=
 
 /- warning: le_infi_iff -> le_iInf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, Iff (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι f)) (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (f i))
 Case conversion may be inaccurate. Consider using '#align le_infi_iff le_iInf_iffₓ'. -/
@@ -1571,7 +1575,7 @@ theorem le_iInf_iff : a ≤ iInf f ↔ ∀ i, a ≤ f i :=
 
 /- warning: supr₂_le_iff -> iSup₂_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α}, Iff (LE.le.{u1} α (Preorder.toLE.{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))) a) (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α}, Iff (LE.le.{u1} α (Preorder.toHasLe.{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))) a) (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) a)
 but is expected to have type
   forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α}, Iff (LE.le.{u3} α (Preorder.toLE.{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))) a) (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) a)
 Case conversion may be inaccurate. Consider using '#align supr₂_le_iff iSup₂_le_iffₓ'. -/
@@ -1583,7 +1587,7 @@ theorem iSup₂_le_iff {f : ∀ i, κ i → α} : (⨆ (i) (j), f i j) ≤ a ↔
 
 /- warning: le_infi₂_iff -> le_iInf₂_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (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)))) (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i j))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α}, Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (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)))) (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α}, Iff (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (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)))) (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (f i j))
 Case conversion may be inaccurate. Consider using '#align le_infi₂_iff le_iInf₂_iffₓ'. -/
@@ -1595,7 +1599,7 @@ theorem le_iInf₂_iff {f : ∀ i, κ i → α} : (a ≤ ⨅ (i) (j), f i j) ↔
 
 /- warning: supr_lt_iff -> iSup_lt_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{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 f) a) (Exists.{succ u1} α (fun (b : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b a) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) b)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, Iff (LT.lt.{u1} α (Preorder.toHasLt.{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 f) a) (Exists.{succ u1} α (fun (b : α) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b a) (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) b)))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, Iff (LT.lt.{u2} α (Preorder.toLT.{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 f) a) (Exists.{succ u2} α (fun (b : α) => And (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) b a) (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) b)))
 Case conversion may be inaccurate. Consider using '#align supr_lt_iff iSup_lt_iffₓ'. -/
@@ -1605,7 +1609,7 @@ theorem iSup_lt_iff : iSup f < a ↔ ∃ b, b < a ∧ ∀ i, f i ≤ b :=
 
 /- warning: lt_infi_iff -> lt_iInf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι f)) (Exists.{succ u1} α (fun (b : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b (f i))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, Iff (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι f)) (Exists.{succ u1} α (fun (b : α) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b) (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b (f i))))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι f)) (Exists.{succ u2} α (fun (b : α) => And (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a b) (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) b (f i))))
 Case conversion may be inaccurate. Consider using '#align lt_infi_iff lt_iInf_iffₓ'. -/
@@ -1635,7 +1639,7 @@ theorem sInf_eq_iInf {s : Set α} : sInf s = ⨅ a ∈ s, a :=
 
 /- warning: monotone.le_map_supr -> Monotone.le_map_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => f (s i))) (f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => f (s i))) (f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι s)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u3} β] {f : α -> β}, (Monotone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))) f) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) (iSup.{u3, u1} β (CompleteLattice.toSupSet.{u3} β _inst_2) ι (fun (i : ι) => f (s i))) (f (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι s)))
 Case conversion may be inaccurate. Consider using '#align monotone.le_map_supr Monotone.le_map_iSupₓ'. -/
@@ -1646,7 +1650,7 @@ theorem Monotone.le_map_iSup [CompleteLattice β] {f : α → β} (hf : Monotone
 
 /- warning: antitone.le_map_infi -> Antitone.le_map_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => f (s i))) (f (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => f (s i))) (f (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι s)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u3} β] {f : α -> β}, (Antitone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))) f) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) (iSup.{u3, u1} β (CompleteLattice.toSupSet.{u3} β _inst_2) ι (fun (i : ι) => f (s i))) (f (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι s)))
 Case conversion may be inaccurate. Consider using '#align antitone.le_map_infi Antitone.le_map_iInfₓ'. -/
@@ -1657,7 +1661,7 @@ theorem Antitone.le_map_iInf [CompleteLattice β] {f : α → β} (hf : Antitone
 
 /- warning: monotone.le_map_supr₂ -> Monotone.le_map_iSup₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => iSup.{u2, u4} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (κ i) (fun (j : κ i) => f (s i j)))) (f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, u4} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ i) (fun (j : κ i) => s i j)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => iSup.{u2, u4} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (κ i) (fun (j : κ i) => f (s i j)))) (f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, u4} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ i) (fun (j : κ i) => s i j)))))
 but is expected to have type
   forall {α : Type.{u3}} {β : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] [_inst_2 : CompleteLattice.{u4} β] {f : α -> β}, (Monotone.{u3, u4} α β (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u4} β (Preorder.toLE.{u4} β (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2)))) (iSup.{u4, u2} β (CompleteLattice.toSupSet.{u4} β _inst_2) ι (fun (i : ι) => iSup.{u4, u1} β (CompleteLattice.toSupSet.{u4} β _inst_2) (κ i) (fun (j : κ i) => f (s i j)))) (f (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) => s i j)))))
 Case conversion may be inaccurate. Consider using '#align monotone.le_map_supr₂ Monotone.le_map_iSup₂ₓ'. -/
@@ -1670,7 +1674,7 @@ theorem Monotone.le_map_iSup₂ [CompleteLattice β] {f : α → β} (hf : Monot
 
 /- warning: antitone.le_map_infi₂ -> Antitone.le_map_iInf₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => iSup.{u2, u4} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (κ i) (fun (j : κ i) => f (s i j)))) (f (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, u4} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ i) (fun (j : κ i) => s i j)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => iSup.{u2, u4} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (κ i) (fun (j : κ i) => f (s i j)))) (f (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, u4} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ i) (fun (j : κ i) => s i j)))))
 but is expected to have type
   forall {α : Type.{u3}} {β : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] [_inst_2 : CompleteLattice.{u4} β] {f : α -> β}, (Antitone.{u3, u4} α β (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u4} β (Preorder.toLE.{u4} β (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2)))) (iSup.{u4, u2} β (CompleteLattice.toSupSet.{u4} β _inst_2) ι (fun (i : ι) => iSup.{u4, u1} β (CompleteLattice.toSupSet.{u4} β _inst_2) (κ i) (fun (j : κ i) => f (s i j)))) (f (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) => s i j)))))
 Case conversion may be inaccurate. Consider using '#align antitone.le_map_infi₂ Antitone.le_map_iInf₂ₓ'. -/
@@ -1683,7 +1687,7 @@ theorem Antitone.le_map_iInf₂ [CompleteLattice β] {f : α → β} (hf : Antit
 
 /- warning: monotone.le_map_Sup -> Monotone.le_map_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) α (fun (a : α) => iSup.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (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) => f a))) (f (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) α (fun (a : α) => iSup.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (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) => f a))) (f (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s)))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_2) α (fun (a : α) => iSup.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_2) (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) => f a))) (f (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)))
 Case conversion may be inaccurate. Consider using '#align monotone.le_map_Sup Monotone.le_map_sSupₓ'. -/
@@ -1693,7 +1697,7 @@ theorem Monotone.le_map_sSup [CompleteLattice β] {s : Set α} {f : α → β} (
 
 /- warning: antitone.le_map_Inf -> Antitone.le_map_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) α (fun (a : α) => iSup.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (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) => f a))) (f (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) α (fun (a : α) => iSup.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (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) => f a))) (f (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_2) α (fun (a : α) => iSup.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_2) (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) => f a))) (f (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)))
 Case conversion may be inaccurate. Consider using '#align antitone.le_map_Inf Antitone.le_map_sInfₓ'. -/
@@ -1704,7 +1708,7 @@ theorem Antitone.le_map_sInf [CompleteLattice β] {s : Set α} {f : α → β} (
 
 /- warning: order_iso.map_supr -> OrderIso.map_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (x : ι -> α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => x i))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (x i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (x : ι -> α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => x i))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (x i)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : CompleteLattice.{u3} β] (f : OrderIso.{u2, u3} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))))) (x : ι -> α), Eq.{succ u3} β (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => x i))) (iSup.{u3, u1} β (CompleteLattice.toSupSet.{u3} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (x i)))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_supr OrderIso.map_iSupₓ'. -/
@@ -1715,7 +1719,7 @@ theorem OrderIso.map_iSup [CompleteLattice β] (f : α ≃o β) (x : ι → α)
 
 /- warning: order_iso.map_infi -> OrderIso.map_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (x : ι -> α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => x i))) (iInf.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (x i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (x : ι -> α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => x i))) (iInf.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (x i)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : CompleteLattice.{u3} β] (f : OrderIso.{u2, u3} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))))) (x : ι -> α), Eq.{succ u3} β (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => x i))) (iInf.{u3, u1} β (CompleteLattice.toInfSet.{u3} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (x i)))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_infi OrderIso.map_iInfₓ'. -/
@@ -1726,7 +1730,7 @@ theorem OrderIso.map_iInf [CompleteLattice β] (f : α ≃o β) (x : ι → α)
 
 /- warning: order_iso.map_Sup -> OrderIso.map_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s)) (iSup.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) α (fun (a : α) => iSup.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (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) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f a)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s)) (iSup.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) α (fun (a : α) => iSup.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (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) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f a)))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)) (iSup.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_2) α (fun (a : α) => iSup.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_2) (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) => 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} 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 order_iso.map_Sup OrderIso.map_sSupₓ'. -/
@@ -1736,7 +1740,7 @@ theorem OrderIso.map_sSup [CompleteLattice β] (f : α ≃o β) (s : Set α) :
 
 /- warning: order_iso.map_Inf -> OrderIso.map_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)) (iInf.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) α (fun (a : α) => iInf.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (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) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f a)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)) (iInf.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) α (fun (a : α) => iInf.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (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) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f a)))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)) (iInf.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_2) α (fun (a : α) => iInf.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_2) (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) => 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} 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 order_iso.map_Inf OrderIso.map_sInfₓ'. -/
@@ -1747,7 +1751,7 @@ theorem OrderIso.map_sInf [CompleteLattice β] (f : α ≃o β) (s : Set α) :
 
 /- warning: supr_comp_le -> iSup_comp_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {ι' : Sort.{u3}} (f : ι' -> α) (g : ι -> ι'), LE.le.{u1} α (Preorder.toLE.{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 (x : ι) => f (g x))) (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' (fun (y : ι') => f y))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {ι' : Sort.{u3}} (f : ι' -> α) (g : ι -> ι'), LE.le.{u1} α (Preorder.toHasLe.{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 (x : ι) => f (g x))) (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' (fun (y : ι') => f y))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {ι' : Sort.{u3}} (f : ι' -> α) (g : ι -> ι'), LE.le.{u2} α (Preorder.toLE.{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 (x : ι) => f (g x))) (iSup.{u2, u3} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι' (fun (y : ι') => f y))
 Case conversion may be inaccurate. Consider using '#align supr_comp_le iSup_comp_leₓ'. -/
@@ -1757,7 +1761,7 @@ theorem iSup_comp_le {ι' : Sort _} (f : ι' → α) (g : ι → ι') : (⨆ x,
 
 /- warning: le_infi_comp -> le_iInf_comp is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {ι' : Sort.{u3}} (f : ι' -> α) (g : ι -> ι'), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (y : ι') => f y)) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f (g x)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {ι' : Sort.{u3}} (f : ι' -> α) (g : ι -> ι'), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (y : ι') => f y)) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f (g x)))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {ι' : Sort.{u3}} (f : ι' -> α) (g : ι -> ι'), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (iInf.{u2, u3} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι' (fun (y : ι') => f y)) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => f (g x)))
 Case conversion may be inaccurate. Consider using '#align le_infi_comp le_iInf_compₓ'. -/
@@ -1767,7 +1771,7 @@ theorem le_iInf_comp {ι' : Sort _} (f : ι' → α) (g : ι → ι') : (⨅ y,
 
 /- warning: monotone.supr_comp_eq -> Monotone.iSup_comp_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Preorder.{u2} β] {f : β -> α}, (Monotone.{u2, u1} β α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f) -> (forall {s : ι -> β}, (forall (x : β), Exists.{u3} ι (fun (i : ι) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x (s i))) -> (Eq.{succ u1} α (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => f (s x))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (y : β) => f y))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Preorder.{u2} β] {f : β -> α}, (Monotone.{u2, u1} β α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f) -> (forall {s : ι -> β}, (forall (x : β), Exists.{u3} ι (fun (i : ι) => LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) x (s i))) -> (Eq.{succ u1} α (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => f (s x))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (y : β) => f y))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : Preorder.{u3} β] {f : β -> α}, (Monotone.{u3, u2} β α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) f) -> (forall {s : ι -> β}, (forall (x : β), Exists.{u1} ι (fun (i : ι) => LE.le.{u3} β (Preorder.toLE.{u3} β _inst_2) x (s i))) -> (Eq.{succ u2} α (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (x : ι) => f (s x))) (iSup.{u2, succ u3} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (y : β) => f y))))
 Case conversion may be inaccurate. Consider using '#align monotone.supr_comp_eq Monotone.iSup_comp_eqₓ'. -/
@@ -1778,7 +1782,7 @@ theorem Monotone.iSup_comp_eq [Preorder β] {f : β → α} (hf : Monotone f) {s
 
 /- warning: monotone.infi_comp_eq -> Monotone.iInf_comp_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Preorder.{u2} β] {f : β -> α}, (Monotone.{u2, u1} β α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f) -> (forall {s : ι -> β}, (forall (x : β), Exists.{u3} ι (fun (i : ι) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (s i) x)) -> (Eq.{succ u1} α (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f (s x))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (y : β) => f y))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Preorder.{u2} β] {f : β -> α}, (Monotone.{u2, u1} β α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f) -> (forall {s : ι -> β}, (forall (x : β), Exists.{u3} ι (fun (i : ι) => LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (s i) x)) -> (Eq.{succ u1} α (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f (s x))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (y : β) => f y))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : Preorder.{u3} β] {f : β -> α}, (Monotone.{u3, u2} β α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) f) -> (forall {s : ι -> β}, (forall (x : β), Exists.{u1} ι (fun (i : ι) => LE.le.{u3} β (Preorder.toLE.{u3} β _inst_2) (s i) x)) -> (Eq.{succ u2} α (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => f (s x))) (iInf.{u2, succ u3} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (y : β) => f y))))
 Case conversion may be inaccurate. Consider using '#align monotone.infi_comp_eq Monotone.iInf_comp_eqₓ'. -/
@@ -1789,7 +1793,7 @@ theorem Monotone.iInf_comp_eq [Preorder β] {f : β → α} (hf : Monotone f) {s
 
 /- warning: antitone.map_supr_le -> Antitone.map_iSup_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι s)) (iInf.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => f (s i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι s)) (iInf.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => f (s i))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u3} β] {f : α -> β}, (Antitone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))) f) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) (f (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι s)) (iInf.{u3, u1} β (CompleteLattice.toInfSet.{u3} β _inst_2) ι (fun (i : ι) => f (s i))))
 Case conversion may be inaccurate. Consider using '#align antitone.map_supr_le Antitone.map_iSup_leₓ'. -/
@@ -1800,7 +1804,7 @@ theorem Antitone.map_iSup_le [CompleteLattice β] {f : α → β} (hf : Antitone
 
 /- warning: monotone.map_infi_le -> Monotone.map_iInf_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι s)) (iInf.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => f (s i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι s)) (iInf.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => f (s i))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u3} β] {f : α -> β}, (Monotone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))) f) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) (f (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι s)) (iInf.{u3, u1} β (CompleteLattice.toInfSet.{u3} β _inst_2) ι (fun (i : ι) => f (s i))))
 Case conversion may be inaccurate. Consider using '#align monotone.map_infi_le Monotone.map_iInf_leₓ'. -/
@@ -1811,7 +1815,7 @@ theorem Monotone.map_iInf_le [CompleteLattice β] {f : α → β} (hf : Monotone
 
 /- warning: antitone.map_supr₂_le -> Antitone.map_iSup₂_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, u4} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ i) (fun (j : κ i) => s i j)))) (iInf.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => iInf.{u2, u4} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (κ i) (fun (j : κ i) => f (s i j)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, u4} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ i) (fun (j : κ i) => s i j)))) (iInf.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => iInf.{u2, u4} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (κ i) (fun (j : κ i) => f (s i j)))))
 but is expected to have type
   forall {α : Type.{u3}} {β : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] [_inst_2 : CompleteLattice.{u4} β] {f : α -> β}, (Antitone.{u3, u4} α β (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u4} β (Preorder.toLE.{u4} β (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2)))) (f (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) => s i j)))) (iInf.{u4, u2} β (CompleteLattice.toInfSet.{u4} β _inst_2) ι (fun (i : ι) => iInf.{u4, u1} β (CompleteLattice.toInfSet.{u4} β _inst_2) (κ i) (fun (j : κ i) => f (s i j)))))
 Case conversion may be inaccurate. Consider using '#align antitone.map_supr₂_le Antitone.map_iSup₂_leₓ'. -/
@@ -1824,7 +1828,7 @@ theorem Antitone.map_iSup₂_le [CompleteLattice β] {f : α → β} (hf : Antit
 
 /- warning: monotone.map_infi₂_le -> Monotone.map_iInf₂_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, u4} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ i) (fun (j : κ i) => s i j)))) (iInf.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => iInf.{u2, u4} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (κ i) (fun (j : κ i) => f (s i j)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, u4} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ i) (fun (j : κ i) => s i j)))) (iInf.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => iInf.{u2, u4} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (κ i) (fun (j : κ i) => f (s i j)))))
 but is expected to have type
   forall {α : Type.{u3}} {β : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] [_inst_2 : CompleteLattice.{u4} β] {f : α -> β}, (Monotone.{u3, u4} α β (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u4} β (Preorder.toLE.{u4} β (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2)))) (f (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) => s i j)))) (iInf.{u4, u2} β (CompleteLattice.toInfSet.{u4} β _inst_2) ι (fun (i : ι) => iInf.{u4, u1} β (CompleteLattice.toInfSet.{u4} β _inst_2) (κ i) (fun (j : κ i) => f (s i j)))))
 Case conversion may be inaccurate. Consider using '#align monotone.map_infi₂_le Monotone.map_iInf₂_leₓ'. -/
@@ -1837,7 +1841,7 @@ theorem Monotone.map_iInf₂_le [CompleteLattice β] {f : α → β} (hf : Monot
 
 /- warning: antitone.map_Sup_le -> Antitone.map_sSup_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s)) (iInf.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) α (fun (a : α) => iInf.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (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) => f a))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s)) (iInf.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) α (fun (a : α) => iInf.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (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) => f a))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)) (iInf.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_2) α (fun (a : α) => iInf.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_2) (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) => f a))))
 Case conversion may be inaccurate. Consider using '#align antitone.map_Sup_le Antitone.map_sSup_leₓ'. -/
@@ -1849,7 +1853,7 @@ theorem Antitone.map_sSup_le [CompleteLattice β] {s : Set α} {f : α → β} (
 
 /- warning: monotone.map_Inf_le -> Monotone.map_sInf_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)) (iInf.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) α (fun (a : α) => iInf.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (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) => f a))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)) (iInf.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) α (fun (a : α) => iInf.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (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) => f a))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)) (iInf.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_2) α (fun (a : α) => iInf.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_2) (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) => f a))))
 Case conversion may be inaccurate. Consider using '#align monotone.map_Inf_le Monotone.map_sInf_leₓ'. -/
@@ -1860,7 +1864,7 @@ theorem Monotone.map_sInf_le [CompleteLattice β] {s : Set α} {f : α → β} (
 
 /- warning: supr_const_le -> iSup_const_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {a : α}, LE.le.{u1} α (Preorder.toLE.{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) => a)) a
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {a : α}, LE.le.{u1} α (Preorder.toHasLe.{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) => a)) a
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {a : α}, LE.le.{u2} α (Preorder.toLE.{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) => a)) a
 Case conversion may be inaccurate. Consider using '#align supr_const_le iSup_const_leₓ'. -/
@@ -1870,7 +1874,7 @@ theorem iSup_const_le : (⨆ i : ι, a) ≤ a :=
 
 /- warning: le_infi_const -> le_iInf_const is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {a : α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {a : α}, LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => a))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {a : α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => a))
 Case conversion may be inaccurate. Consider using '#align le_infi_const le_iInf_constₓ'. -/
@@ -2012,7 +2016,7 @@ theorem iInf_neg {p : Prop} {f : p → α} (hp : ¬p) : (⨅ h : p, f h) = ⊤ :
 
 /- warning: supr_eq_of_forall_le_of_forall_lt_exists_gt -> iSup_eq_of_forall_le_of_forall_lt_exists_gt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : α} {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) b) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w b) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w (f i)))) -> (Eq.{succ u1} α (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i)) b)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : α} {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) b) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w b) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w (f i)))) -> (Eq.{succ u1} α (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i)) b)
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {b : α} {f : ι -> α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) b) -> (forall (w : α), (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) w b) -> (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) w (f i)))) -> (Eq.{succ u2} α (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i)) b)
 Case conversion may be inaccurate. Consider using '#align supr_eq_of_forall_le_of_forall_lt_exists_gt iSup_eq_of_forall_le_of_forall_lt_exists_gtₓ'. -/
@@ -2028,7 +2032,7 @@ theorem iSup_eq_of_forall_le_of_forall_lt_exists_gt {f : ι → α} (h₁ : ∀
 
 /- warning: infi_eq_of_forall_ge_of_forall_gt_exists_lt -> iInf_eq_of_forall_ge_of_forall_gt_exists_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {b : α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b (f i)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b w) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) w))) -> (Eq.{succ u1} α (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => f i)) b)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {b : α}, (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b (f i)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b w) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) w))) -> (Eq.{succ u1} α (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => f i)) b)
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {b : α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) b (f i)) -> (forall (w : α), (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) b w) -> (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) w))) -> (Eq.{succ u2} α (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i)) b)
 Case conversion may be inaccurate. Consider using '#align infi_eq_of_forall_ge_of_forall_gt_exists_lt iInf_eq_of_forall_ge_of_forall_gt_exists_ltₓ'. -/
@@ -2740,7 +2744,7 @@ theorem iInf_split_single (f : β → α) (i₀ : β) : (⨅ i, f i) = f i₀ 
 
 /- warning: supr_le_supr_of_subset -> iSup_le_iSup_of_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, (HasSubset.Subset.{u2} (Set.{u2} β) (Set.hasSubset.{u2} β) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) => f x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, (HasSubset.Subset.{u2} (Set.{u2} β) (Set.hasSubset.{u2} β) s t) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) => f x))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, (HasSubset.Subset.{u2} (Set.{u2} β) (Set.instHasSubsetSet.{u2} β) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))) (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) => f x))))
 Case conversion may be inaccurate. Consider using '#align supr_le_supr_of_subset iSup_le_iSup_of_subsetₓ'. -/
@@ -2750,7 +2754,7 @@ theorem iSup_le_iSup_of_subset {f : β → α} {s t : Set β} : s ⊆ t → (⨆
 
 /- warning: infi_le_infi_of_subset -> iInf_le_iInf_of_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, (HasSubset.Subset.{u2} (Set.{u2} β) (Set.hasSubset.{u2} β) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) => f x))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, (HasSubset.Subset.{u2} (Set.{u2} β) (Set.hasSubset.{u2} β) s t) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) => f x))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, (HasSubset.Subset.{u2} (Set.{u2} β) (Set.instHasSubsetSet.{u2} β) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) => f x))) (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))))
 Case conversion may be inaccurate. Consider using '#align infi_le_infi_of_subset iInf_le_iInf_of_subsetₓ'. -/
@@ -3285,7 +3289,7 @@ variable [CompleteLinearOrder α]
 
 /- warning: supr_eq_top -> iSup_eq_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] (f : ι -> α), Iff (Eq.{succ u1} α (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι f) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (f i))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] (f : ι -> α), Iff (Eq.{succ u1} α (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι f) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (f i))))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLinearOrder.{u2} α] (f : ι -> α), Iff (Eq.{succ u2} α (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)) ι f) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (forall (b : α), (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) b (Top.top.{u2} α (CompleteLattice.toTop.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) -> (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) b (f i))))
 Case conversion may be inaccurate. Consider using '#align supr_eq_top iSup_eq_topₓ'. -/
@@ -3295,7 +3299,7 @@ theorem iSup_eq_top (f : ι → α) : iSup f = ⊤ ↔ ∀ b < ⊤, ∃ i, b < f
 
 /- warning: infi_eq_bot -> iInf_eq_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] (f : ι -> α), Iff (Eq.{succ u1} α (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι f) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (f i) b)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] (f : ι -> α), Iff (Eq.{succ u1} α (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι f) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (f i) b)))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLinearOrder.{u2} α] (f : ι -> α), Iff (Eq.{succ u2} α (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)) ι f) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (forall (b : α), (GT.gt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) b (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) -> (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) (f i) b)))
 Case conversion may be inaccurate. Consider using '#align infi_eq_bot iInf_eq_botₓ'. -/
@@ -3727,7 +3731,7 @@ variable [CompleteLattice α] {a : α} {s : Set α}
 
 /- warning: sup_Inf_le_infi_sup -> sup_sInf_le_iInf_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)) (iInf.{u1, succ u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) α (fun (b : α) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)) (iInf.{u1, succ u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) α (fun (b : α) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)) (iInf.{u1, succ u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) α (fun (b : α) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)))
 Case conversion may be inaccurate. Consider using '#align sup_Inf_le_infi_sup sup_sInf_le_iInf_supₓ'. -/
@@ -3738,7 +3742,7 @@ theorem sup_sInf_le_iInf_sup : a ⊔ sInf s ≤ ⨅ b ∈ s, a ⊔ b :=
 
 /- warning: supr_inf_le_inf_Sup -> iSup_inf_le_inf_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iSup.{u1, succ u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) α (fun (b : α) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iSup.{u1, succ u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) α (fun (b : α) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iSup.{u1, succ u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) α (fun (b : α) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a b))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align supr_inf_le_inf_Sup iSup_inf_le_inf_sSupₓ'. -/
@@ -3749,7 +3753,7 @@ theorem iSup_inf_le_inf_sSup : (⨆ b ∈ s, a ⊓ b) ≤ a ⊓ sSup s :=
 
 /- warning: Inf_sup_le_infi_sup -> sInf_sup_le_iInf_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) a) (iInf.{u1, succ u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) α (fun (b : α) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) a) (iInf.{u1, succ u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) α (fun (b : α) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) a) (iInf.{u1, succ u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) α (fun (b : α) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a)))
 Case conversion may be inaccurate. Consider using '#align Inf_sup_le_infi_sup sInf_sup_le_iInf_supₓ'. -/
@@ -3760,7 +3764,7 @@ theorem sInf_sup_le_iInf_sup : sInf s ⊔ a ≤ ⨅ b ∈ s, b ⊔ a :=
 
 /- warning: supr_inf_le_Sup_inf -> iSup_inf_le_sSup_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iSup.{u1, succ u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) α (fun (b : α) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) a)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iSup.{u1, succ u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) α (fun (b : α) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iSup.{u1, succ u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) α (fun (b : α) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) b a))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) a)
 Case conversion may be inaccurate. Consider using '#align supr_inf_le_Sup_inf iSup_inf_le_sSup_infₓ'. -/
@@ -3771,7 +3775,7 @@ theorem iSup_inf_le_sSup_inf : (⨆ b ∈ s, b ⊓ a) ≤ sSup s ⊓ a :=
 
 /- warning: le_supr_inf_supr -> le_iSup_inf_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (g : ι -> α), LE.le.{u1} α (Preorder.toLE.{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) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i) (g i))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{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} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => g i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (g : ι -> α), LE.le.{u1} α (Preorder.toHasLe.{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) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i) (g i))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{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} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => g i)))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (g : ι -> α), LE.le.{u2} α (Preorder.toLE.{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) => Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f i) (g i))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i)) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => g i)))
 Case conversion may be inaccurate. Consider using '#align le_supr_inf_supr le_iSup_inf_iSupₓ'. -/
@@ -3781,7 +3785,7 @@ theorem le_iSup_inf_iSup (f g : ι → α) : (⨆ i, f i ⊓ g i) ≤ (⨆ i, f
 
 /- warning: infi_sup_infi_le -> iInf_sup_iInf_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (g : ι -> α), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{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} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => g i))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i) (g i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (g : ι -> α), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{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} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => g i))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i) (g i)))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (g : ι -> α), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i)) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => g i))) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f i) (g i)))
 Case conversion may be inaccurate. Consider using '#align infi_sup_infi_le iInf_sup_iInf_leₓ'. -/
@@ -3791,7 +3795,7 @@ theorem iInf_sup_iInf_le (f g : ι → α) : ((⨅ i, f i) ⊔ ⨅ i, g i) ≤ 
 
 /- warning: disjoint_Sup_left -> disjoint_sSup_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : Set.{u1} α} {b : α}, (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) a) b) -> (forall {i : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) i a) -> (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) i b))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : Set.{u1} α} {b : α}, (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) a) b) -> (forall {i : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) i a) -> (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) i b))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : Set.{u1} α} {b : α}, (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) a) b) -> (forall {i : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) i a) -> (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) i b))
 Case conversion may be inaccurate. Consider using '#align disjoint_Sup_left disjoint_sSup_leftₓ'. -/
@@ -3802,7 +3806,7 @@ theorem disjoint_sSup_left {a : Set α} {b : α} (d : Disjoint (sSup a) b) {i} (
 
 /- warning: disjoint_Sup_right -> disjoint_sSup_right is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : Set.{u1} α} {b : α}, (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) b (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) a)) -> (forall {i : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) i a) -> (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) b i))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : Set.{u1} α} {b : α}, (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) b (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) a)) -> (forall {i : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) i a) -> (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) b i))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : Set.{u1} α} {b : α}, (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) b (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) a)) -> (forall {i : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) i a) -> (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) b i))
 Case conversion may be inaccurate. Consider using '#align disjoint_Sup_right disjoint_sSup_rightₓ'. -/

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

@@ -57,64 +57,64 @@ variable {α β β₂ γ : Type _} {ι ι' : Sort _} {κ : ι → Sort _} {κ' :
 #print SupSet /-
 /-- class for the `Sup` operator -/
 class SupSet (α : Type _) where
-  supₛ : Set α → α
+  sSup : Set α → α
 #align has_Sup SupSet
 -/
 
 #print InfSet /-
 /-- class for the `Inf` operator -/
 class InfSet (α : Type _) where
-  infₛ : Set α → α
+  sInf : Set α → α
 #align has_Inf InfSet
 -/
 
-export SupSet (supₛ)
+export SupSet (sSup)
 
-export InfSet (infₛ)
+export InfSet (sInf)
 
 /-- Supremum of a set -/
-add_decl_doc SupSet.supₛ
+add_decl_doc SupSet.sSup
 
 /-- Infimum of a set -/
-add_decl_doc InfSet.infₛ
+add_decl_doc InfSet.sInf
 
-#print supᵢ /-
+#print iSup /-
 /-- Indexed supremum -/
-def supᵢ [SupSet α] {ι} (s : ι → α) : α :=
-  supₛ (range s)
-#align supr supᵢ
+def iSup [SupSet α] {ι} (s : ι → α) : α :=
+  sSup (range s)
+#align supr iSup
 -/
 
-#print infᵢ /-
+#print iInf /-
 /-- Indexed infimum -/
-def infᵢ [InfSet α] {ι} (s : ι → α) : α :=
-  infₛ (range s)
-#align infi infᵢ
+def iInf [InfSet α] {ι} (s : ι → α) : α :=
+  sInf (range s)
+#align infi iInf
 -/
 
 #print infSet_to_nonempty /-
 instance (priority := 50) infSet_to_nonempty (α) [InfSet α] : Nonempty α :=
-  ⟨infₛ ∅⟩
+  ⟨sInf ∅⟩
 #align has_Inf_to_nonempty infSet_to_nonempty
 -/
 
 #print supSet_to_nonempty /-
 instance (priority := 50) supSet_to_nonempty (α) [SupSet α] : Nonempty α :=
-  ⟨supₛ ∅⟩
+  ⟨sSup ∅⟩
 #align has_Sup_to_nonempty supSet_to_nonempty
 -/
 
 -- mathport name: «expr⨆ , »
-notation3"⨆ "(...)", "r:(scoped f => supᵢ f) => r
+notation3"⨆ "(...)", "r:(scoped f => iSup f) => r
 
 -- mathport name: «expr⨅ , »
-notation3"⨅ "(...)", "r:(scoped f => infᵢ f) => r
+notation3"⨅ "(...)", "r:(scoped f => iInf f) => r
 
 instance (α) [InfSet α] : SupSet αᵒᵈ :=
-  ⟨(infₛ : Set α → α)⟩
+  ⟨(sInf : Set α → α)⟩
 
 instance (α) [SupSet α] : InfSet αᵒᵈ :=
-  ⟨(supₛ : Set α → α)⟩
+  ⟨(sSup : Set α → α)⟩
 
 #print CompleteSemilatticeSup /-
 /-- Note that we rarely use `complete_semilattice_Sup`
@@ -132,121 +132,121 @@ section
 
 variable [CompleteSemilatticeSup α] {s t : Set α} {a b : α}
 
-/- warning: le_Sup -> le_supₛ is a dubious translation:
+/- warning: le_Sup -> le_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align le_Sup le_supₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align le_Sup le_sSupₓ'. -/
 @[ematch]
-theorem le_supₛ : a ∈ s → a ≤ supₛ s :=
+theorem le_sSup : a ∈ s → a ≤ sSup s :=
   CompleteSemilatticeSup.le_sup s a
-#align le_Sup le_supₛ
+#align le_Sup le_sSup
 
-/- warning: Sup_le -> supₛ_le is a dubious translation:
+/- warning: Sup_le -> sSup_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) b a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) b a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) b a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s) a)
-Case conversion may be inaccurate. Consider using '#align Sup_le supₛ_leₓ'. -/
-theorem supₛ_le : (∀ b ∈ s, b ≤ a) → supₛ s ≤ a :=
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) b a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s) a)
+Case conversion may be inaccurate. Consider using '#align Sup_le sSup_leₓ'. -/
+theorem sSup_le : (∀ b ∈ s, b ≤ a) → sSup s ≤ a :=
   CompleteSemilatticeSup.sup_le s a
-#align Sup_le supₛ_le
+#align Sup_le sSup_le
 
-/- warning: is_lub_Sup -> isLUB_supₛ is a dubious translation:
+/- warning: is_lub_Sup -> isLUB_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] (s : Set.{u1} α), IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1)) s (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s)
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] (s : Set.{u1} α), IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1)) s (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] (s : Set.{u1} α), IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1)) s (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s)
-Case conversion may be inaccurate. Consider using '#align is_lub_Sup isLUB_supₛₓ'. -/
-theorem isLUB_supₛ (s : Set α) : IsLUB s (supₛ s) :=
-  ⟨fun x => le_supₛ, fun x => supₛ_le⟩
-#align is_lub_Sup isLUB_supₛ
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] (s : Set.{u1} α), IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1)) s (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s)
+Case conversion may be inaccurate. Consider using '#align is_lub_Sup isLUB_sSupₓ'. -/
+theorem isLUB_sSup (s : Set α) : IsLUB s (sSup s) :=
+  ⟨fun x => le_sSup, fun x => sSup_le⟩
+#align is_lub_Sup isLUB_sSup
 
-/- warning: is_lub.Sup_eq -> IsLUB.supₛ_eq is a dubious translation:
+/- warning: is_lub.Sup_eq -> IsLUB.sSup_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1)) s a) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1)) s a) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1)) s a) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s) a)
-Case conversion may be inaccurate. Consider using '#align is_lub.Sup_eq IsLUB.supₛ_eqₓ'. -/
-theorem IsLUB.supₛ_eq (h : IsLUB s a) : supₛ s = a :=
-  (isLUB_supₛ s).unique h
-#align is_lub.Sup_eq IsLUB.supₛ_eq
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1)) s a) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s) a)
+Case conversion may be inaccurate. Consider using '#align is_lub.Sup_eq IsLUB.sSup_eqₓ'. -/
+theorem IsLUB.sSup_eq (h : IsLUB s a) : sSup s = a :=
+  (isLUB_sSup s).unique h
+#align is_lub.Sup_eq IsLUB.sSup_eq
 
-/- warning: le_Sup_of_le -> le_supₛ_of_le is a dubious translation:
+/- warning: le_Sup_of_le -> le_sSup_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align le_Sup_of_le le_supₛ_of_leₓ'. -/
-theorem le_supₛ_of_le (hb : b ∈ s) (h : a ≤ b) : a ≤ supₛ s :=
-  le_trans h (le_supₛ hb)
-#align le_Sup_of_le le_supₛ_of_le
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align le_Sup_of_le le_sSup_of_leₓ'. -/
+theorem le_sSup_of_le (hb : b ∈ s) (h : a ≤ b) : a ≤ sSup s :=
+  le_trans h (le_sSup hb)
+#align le_Sup_of_le le_sSup_of_le
 
-/- warning: Sup_le_Sup -> supₛ_le_supₛ is a dubious translation:
+/- warning: Sup_le_Sup -> sSup_le_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) t))
-Case conversion may be inaccurate. Consider using '#align Sup_le_Sup supₛ_le_supₛₓ'. -/
-theorem supₛ_le_supₛ (h : s ⊆ t) : supₛ s ≤ supₛ t :=
-  (isLUB_supₛ s).mono (isLUB_supₛ t) h
-#align Sup_le_Sup supₛ_le_supₛ
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) t))
+Case conversion may be inaccurate. Consider using '#align Sup_le_Sup sSup_le_sSupₓ'. -/
+theorem sSup_le_sSup (h : s ⊆ t) : sSup s ≤ sSup t :=
+  (isLUB_sSup s).mono (isLUB_sSup t) h
+#align Sup_le_Sup sSup_le_sSup
 
-/- warning: Sup_le_iff -> supₛ_le_iff is a dubious translation:
+/- warning: Sup_le_iff -> sSup_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) a) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) b a))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) a) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) b a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s) a) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) b a))
-Case conversion may be inaccurate. Consider using '#align Sup_le_iff supₛ_le_iffₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s) a) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) b a))
+Case conversion may be inaccurate. Consider using '#align Sup_le_iff sSup_le_iffₓ'. -/
 @[simp]
-theorem supₛ_le_iff : supₛ s ≤ a ↔ ∀ b ∈ s, b ≤ a :=
-  isLUB_le_iff (isLUB_supₛ s)
-#align Sup_le_iff supₛ_le_iff
+theorem sSup_le_iff : sSup s ≤ a ↔ ∀ b ∈ s, b ≤ a :=
+  isLUB_le_iff (isLUB_sSup s)
+#align Sup_le_iff sSup_le_iff
 
-/- warning: le_Sup_iff -> le_supₛ_iff is a dubious translation:
+/- warning: le_Sup_iff -> le_sSup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1)) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1)) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1)) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b))
-Case conversion may be inaccurate. Consider using '#align le_Sup_iff le_supₛ_iffₓ'. -/
-theorem le_supₛ_iff : a ≤ supₛ s ↔ ∀ b ∈ upperBounds s, a ≤ b :=
-  ⟨fun h b hb => le_trans h (supₛ_le hb), fun hb => hb _ fun x => le_supₛ⟩
-#align le_Sup_iff le_supₛ_iff
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1)) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b))
+Case conversion may be inaccurate. Consider using '#align le_Sup_iff le_sSup_iffₓ'. -/
+theorem le_sSup_iff : a ≤ sSup s ↔ ∀ b ∈ upperBounds s, a ≤ b :=
+  ⟨fun h b hb => le_trans h (sSup_le hb), fun hb => hb _ fun x => le_sSup⟩
+#align le_Sup_iff le_sSup_iff
 
-/- warning: le_supr_iff -> le_supᵢ_iff is a dubious translation:
+/- warning: le_supr_iff -> le_iSup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {a : α} {s : ι -> α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) ι s)) (forall (b : α), (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (s i) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {a : α} {s : ι -> α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) ι s)) (forall (b : α), (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (s i) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) a b))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteSemilatticeSup.{u2} α] {a : α} {s : ι -> α}, Iff (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeSup.toPartialOrder.{u2} α _inst_1))) a (supᵢ.{u2, u1} α (CompleteSemilatticeSup.toSupSet.{u2} α _inst_1) ι s)) (forall (b : α), (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeSup.toPartialOrder.{u2} α _inst_1))) (s i) b) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeSup.toPartialOrder.{u2} α _inst_1))) a b))
-Case conversion may be inaccurate. Consider using '#align le_supr_iff le_supᵢ_iffₓ'. -/
-theorem le_supᵢ_iff {s : ι → α} : a ≤ supᵢ s ↔ ∀ b, (∀ i, s i ≤ b) → a ≤ b := by
-  simp [supᵢ, le_supₛ_iff, upperBounds]
-#align le_supr_iff le_supᵢ_iff
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteSemilatticeSup.{u2} α] {a : α} {s : ι -> α}, Iff (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeSup.toPartialOrder.{u2} α _inst_1))) a (iSup.{u2, u1} α (CompleteSemilatticeSup.toSupSet.{u2} α _inst_1) ι s)) (forall (b : α), (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeSup.toPartialOrder.{u2} α _inst_1))) (s i) b) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeSup.toPartialOrder.{u2} α _inst_1))) a b))
+Case conversion may be inaccurate. Consider using '#align le_supr_iff le_iSup_iffₓ'. -/
+theorem le_iSup_iff {s : ι → α} : a ≤ iSup s ↔ ∀ b, (∀ i, s i ≤ b) → a ≤ b := by
+  simp [iSup, le_sSup_iff, upperBounds]
+#align le_supr_iff le_iSup_iff
 
-/- warning: Sup_le_Sup_of_forall_exists_le -> supₛ_le_supₛ_of_forall_exists_le is a dubious translation:
+/- warning: Sup_le_Sup_of_forall_exists_le -> sSup_le_sSup_of_forall_exists_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) x y)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) x y)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) x y)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) t))
-Case conversion may be inaccurate. Consider using '#align Sup_le_Sup_of_forall_exists_le supₛ_le_supₛ_of_forall_exists_leₓ'. -/
-theorem supₛ_le_supₛ_of_forall_exists_le (h : ∀ x ∈ s, ∃ y ∈ t, x ≤ y) : supₛ s ≤ supₛ t :=
-  le_supₛ_iff.2 fun b hb =>
-    supₛ_le fun a ha =>
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) x y)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeSup.toPartialOrder.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) t))
+Case conversion may be inaccurate. Consider using '#align Sup_le_Sup_of_forall_exists_le sSup_le_sSup_of_forall_exists_leₓ'. -/
+theorem sSup_le_sSup_of_forall_exists_le (h : ∀ x ∈ s, ∃ y ∈ t, x ≤ y) : sSup s ≤ sSup t :=
+  le_sSup_iff.2 fun b hb =>
+    sSup_le fun a ha =>
       let ⟨c, hct, hac⟩ := h a ha
       hac.trans (hb hct)
-#align Sup_le_Sup_of_forall_exists_le supₛ_le_supₛ_of_forall_exists_le
+#align Sup_le_Sup_of_forall_exists_le sSup_le_sSup_of_forall_exists_le
 
-/- warning: Sup_singleton -> supₛ_singleton is a dubious translation:
+/- warning: Sup_singleton -> sSup_singleton is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {a : α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)) a
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {a : α}, Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α _inst_1) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)) a
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {a : α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)) a
-Case conversion may be inaccurate. Consider using '#align Sup_singleton supₛ_singletonₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeSup.{u1} α] {a : α}, Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toSupSet.{u1} α _inst_1) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)) a
+Case conversion may be inaccurate. Consider using '#align Sup_singleton sSup_singletonₓ'. -/
 -- We will generalize this to conditionally complete lattices in `cSup_singleton`.
-theorem supₛ_singleton {a : α} : supₛ {a} = a :=
-  isLUB_singleton.supₛ_eq
-#align Sup_singleton supₛ_singleton
+theorem sSup_singleton {a : α} : sSup {a} = a :=
+  isLUB_singleton.sSup_eq
+#align Sup_singleton sSup_singleton
 
 end
 
@@ -266,123 +266,123 @@ section
 
 variable [CompleteSemilatticeInf α] {s t : Set α} {a b : α}
 
-/- warning: Inf_le -> infₛ_le is a dubious translation:
+/- warning: Inf_le -> sInf_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s) a)
-Case conversion may be inaccurate. Consider using '#align Inf_le infₛ_leₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s) a)
+Case conversion may be inaccurate. Consider using '#align Inf_le sInf_leₓ'. -/
 @[ematch]
-theorem infₛ_le : a ∈ s → infₛ s ≤ a :=
+theorem sInf_le : a ∈ s → sInf s ≤ a :=
   CompleteSemilatticeInf.inf_le s a
-#align Inf_le infₛ_le
+#align Inf_le sInf_le
 
-/- warning: le_Inf -> le_infₛ is a dubious translation:
+/- warning: le_Inf -> le_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align le_Inf le_infₛₓ'. -/
-theorem le_infₛ : (∀ b ∈ s, a ≤ b) → a ≤ infₛ s :=
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align le_Inf le_sInfₓ'. -/
+theorem le_sInf : (∀ b ∈ s, a ≤ b) → a ≤ sInf s :=
   CompleteSemilatticeInf.le_inf s a
-#align le_Inf le_infₛ
+#align le_Inf le_sInf
 
-/- warning: is_glb_Inf -> isGLB_infₛ is a dubious translation:
+/- warning: is_glb_Inf -> isGLB_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] (s : Set.{u1} α), IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1)) s (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s)
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] (s : Set.{u1} α), IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1)) s (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] (s : Set.{u1} α), IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1)) s (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s)
-Case conversion may be inaccurate. Consider using '#align is_glb_Inf isGLB_infₛₓ'. -/
-theorem isGLB_infₛ (s : Set α) : IsGLB s (infₛ s) :=
-  ⟨fun a => infₛ_le, fun a => le_infₛ⟩
-#align is_glb_Inf isGLB_infₛ
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] (s : Set.{u1} α), IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1)) s (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s)
+Case conversion may be inaccurate. Consider using '#align is_glb_Inf isGLB_sInfₓ'. -/
+theorem isGLB_sInf (s : Set α) : IsGLB s (sInf s) :=
+  ⟨fun a => sInf_le, fun a => le_sInf⟩
+#align is_glb_Inf isGLB_sInf
 
-/- warning: is_glb.Inf_eq -> IsGLB.infₛ_eq is a dubious translation:
+/- warning: is_glb.Inf_eq -> IsGLB.sInf_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1)) s a) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1)) s a) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1)) s a) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s) a)
-Case conversion may be inaccurate. Consider using '#align is_glb.Inf_eq IsGLB.infₛ_eqₓ'. -/
-theorem IsGLB.infₛ_eq (h : IsGLB s a) : infₛ s = a :=
-  (isGLB_infₛ s).unique h
-#align is_glb.Inf_eq IsGLB.infₛ_eq
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1)) s a) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s) a)
+Case conversion may be inaccurate. Consider using '#align is_glb.Inf_eq IsGLB.sInf_eqₓ'. -/
+theorem IsGLB.sInf_eq (h : IsGLB s a) : sInf s = a :=
+  (isGLB_sInf s).unique h
+#align is_glb.Inf_eq IsGLB.sInf_eq
 
-/- warning: Inf_le_of_le -> infₛ_le_of_le is a dubious translation:
+/- warning: Inf_le_of_le -> sInf_le_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s) a)
-Case conversion may be inaccurate. Consider using '#align Inf_le_of_le infₛ_le_of_leₓ'. -/
-theorem infₛ_le_of_le (hb : b ∈ s) (h : b ≤ a) : infₛ s ≤ a :=
-  le_trans (infₛ_le hb) h
-#align Inf_le_of_le infₛ_le_of_le
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s) a)
+Case conversion may be inaccurate. Consider using '#align Inf_le_of_le sInf_le_of_leₓ'. -/
+theorem sInf_le_of_le (hb : b ∈ s) (h : b ≤ a) : sInf s ≤ a :=
+  le_trans (sInf_le hb) h
+#align Inf_le_of_le sInf_le_of_le
 
-/- warning: Inf_le_Inf -> infₛ_le_infₛ is a dubious translation:
+/- warning: Inf_le_Inf -> sInf_le_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) t) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) t) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) t) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align Inf_le_Inf infₛ_le_infₛₓ'. -/
-theorem infₛ_le_infₛ (h : s ⊆ t) : infₛ t ≤ infₛ s :=
-  (isGLB_infₛ s).mono (isGLB_infₛ t) h
-#align Inf_le_Inf infₛ_le_infₛ
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) t) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align Inf_le_Inf sInf_le_sInfₓ'. -/
+theorem sInf_le_sInf (h : s ⊆ t) : sInf t ≤ sInf s :=
+  (isGLB_sInf s).mono (isGLB_sInf t) h
+#align Inf_le_Inf sInf_le_sInf
 
-/- warning: le_Inf_iff -> le_infₛ_iff is a dubious translation:
+/- warning: le_Inf_iff -> le_sInf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a b))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a b))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a b))
-Case conversion may be inaccurate. Consider using '#align le_Inf_iff le_infₛ_iffₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) a b))
+Case conversion may be inaccurate. Consider using '#align le_Inf_iff le_sInf_iffₓ'. -/
 @[simp]
-theorem le_infₛ_iff : a ≤ infₛ s ↔ ∀ b ∈ s, a ≤ b :=
-  le_isGLB_iff (isGLB_infₛ s)
-#align le_Inf_iff le_infₛ_iff
+theorem le_sInf_iff : a ≤ sInf s ↔ ∀ b ∈ s, a ≤ b :=
+  le_isGLB_iff (isGLB_sInf s)
+#align le_Inf_iff le_sInf_iff
 
-/- warning: Inf_le_iff -> infₛ_le_iff is a dubious translation:
+/- warning: Inf_le_iff -> sInf_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s) a) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1)) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s) a) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1)) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s) a) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1)) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a))
-Case conversion may be inaccurate. Consider using '#align Inf_le_iff infₛ_le_iffₓ'. -/
-theorem infₛ_le_iff : infₛ s ≤ a ↔ ∀ b ∈ lowerBounds s, b ≤ a :=
-  ⟨fun h b hb => le_trans (le_infₛ hb) h, fun hb => hb _ fun x => infₛ_le⟩
-#align Inf_le_iff infₛ_le_iff
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s) a) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1)) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a))
+Case conversion may be inaccurate. Consider using '#align Inf_le_iff sInf_le_iffₓ'. -/
+theorem sInf_le_iff : sInf s ≤ a ↔ ∀ b ∈ lowerBounds s, b ≤ a :=
+  ⟨fun h b hb => le_trans (le_sInf hb) h, fun hb => hb _ fun x => sInf_le⟩
+#align Inf_le_iff sInf_le_iff
 
-/- warning: infi_le_iff -> infᵢ_le_iff is a dubious translation:
+/- warning: infi_le_iff -> iInf_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {a : α} {s : ι -> α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) ι s) a) (forall (b : α), (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b (s i)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {a : α} {s : ι -> α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) ι s) a) (forall (b : α), (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b (s i)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) b a))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteSemilatticeInf.{u2} α] {a : α} {s : ι -> α}, Iff (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α _inst_1))) (infᵢ.{u2, u1} α (CompleteSemilatticeInf.toInfSet.{u2} α _inst_1) ι s) a) (forall (b : α), (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α _inst_1))) b (s i)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α _inst_1))) b a))
-Case conversion may be inaccurate. Consider using '#align infi_le_iff infᵢ_le_iffₓ'. -/
-theorem infᵢ_le_iff {s : ι → α} : infᵢ s ≤ a ↔ ∀ b, (∀ i, b ≤ s i) → b ≤ a := by
-  simp [infᵢ, infₛ_le_iff, lowerBounds]
-#align infi_le_iff infᵢ_le_iff
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteSemilatticeInf.{u2} α] {a : α} {s : ι -> α}, Iff (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α _inst_1))) (iInf.{u2, u1} α (CompleteSemilatticeInf.toInfSet.{u2} α _inst_1) ι s) a) (forall (b : α), (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α _inst_1))) b (s i)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α _inst_1))) b a))
+Case conversion may be inaccurate. Consider using '#align infi_le_iff iInf_le_iffₓ'. -/
+theorem iInf_le_iff {s : ι → α} : iInf s ≤ a ↔ ∀ b, (∀ i, b ≤ s i) → b ≤ a := by
+  simp [iInf, sInf_le_iff, lowerBounds]
+#align infi_le_iff iInf_le_iff
 
-/- warning: Inf_le_Inf_of_forall_exists_le -> infₛ_le_infₛ_of_forall_exists_le is a dubious translation:
+/- warning: Inf_le_Inf_of_forall_exists_le -> sInf_le_sInf_of_forall_exists_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) y x)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) t) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) y x)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) t) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) y x)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) t) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align Inf_le_Inf_of_forall_exists_le infₛ_le_infₛ_of_forall_exists_leₓ'. -/
-theorem infₛ_le_infₛ_of_forall_exists_le (h : ∀ x ∈ s, ∃ y ∈ t, y ≤ x) : infₛ t ≤ infₛ s :=
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) y x)))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) t) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align Inf_le_Inf_of_forall_exists_le sInf_le_sInf_of_forall_exists_leₓ'. -/
+theorem sInf_le_sInf_of_forall_exists_le (h : ∀ x ∈ s, ∃ y ∈ t, y ≤ x) : sInf t ≤ sInf s :=
   le_of_forall_le
     (by
-      simp only [le_infₛ_iff]
+      simp only [le_sInf_iff]
       introv h₀ h₁
       rcases h _ h₁ with ⟨y, hy, hy'⟩
       solve_by_elim [le_trans _ hy'] )
-#align Inf_le_Inf_of_forall_exists_le infₛ_le_infₛ_of_forall_exists_le
+#align Inf_le_Inf_of_forall_exists_le sInf_le_sInf_of_forall_exists_le
 
-/- warning: Inf_singleton -> infₛ_singleton is a dubious translation:
+/- warning: Inf_singleton -> sInf_singleton is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {a : α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)) a
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {a : α}, Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α _inst_1) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)) a
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {a : α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)) a
-Case conversion may be inaccurate. Consider using '#align Inf_singleton infₛ_singletonₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteSemilatticeInf.{u1} α] {a : α}, Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toInfSet.{u1} α _inst_1) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)) a
+Case conversion may be inaccurate. Consider using '#align Inf_singleton sInf_singletonₓ'. -/
 -- We will generalize this to conditionally complete lattices in `cInf_singleton`.
-theorem infₛ_singleton {a : α} : infₛ {a} = a :=
-  isGLB_singleton.infₛ_eq
-#align Inf_singleton infₛ_singleton
+theorem sInf_singleton {a : α} : sInf {a} = a :=
+  isGLB_singleton.sInf_eq
+#align Inf_singleton sInf_singleton
 
 end
 
@@ -421,27 +421,27 @@ instance : complete_lattice my_T :=
 ```
 -/
 def completeLatticeOfInf (α : Type _) [H1 : PartialOrder α] [H2 : InfSet α]
-    (is_glb_Inf : ∀ s : Set α, IsGLB s (infₛ s)) : CompleteLattice α :=
+    (is_glb_Inf : ∀ s : Set α, IsGLB s (sInf s)) : CompleteLattice α :=
   { H1, H2 with
-    bot := infₛ univ
-    bot_le := fun x => (isGLB_infₛ univ).1 trivial
-    top := infₛ ∅
-    le_top := fun a => (isGLB_infₛ ∅).2 <| by simp
-    sup := fun a b => infₛ { x | a ≤ x ∧ b ≤ x }
-    inf := fun a b => infₛ {a, b}
+    bot := sInf univ
+    bot_le := fun x => (isGLB_sInf univ).1 trivial
+    top := sInf ∅
+    le_top := fun a => (isGLB_sInf ∅).2 <| by simp
+    sup := fun a b => sInf { x | a ≤ x ∧ b ≤ x }
+    inf := fun a b => sInf {a, b}
     le_inf := fun a b c hab hac => by
-      apply (isGLB_infₛ _).2
+      apply (isGLB_sInf _).2
       simp [*]
-    inf_le_right := fun a b => (isGLB_infₛ _).1 <| mem_insert_of_mem _ <| mem_singleton _
-    inf_le_left := fun a b => (isGLB_infₛ _).1 <| mem_insert _ _
-    sup_le := fun a b c hac hbc => (isGLB_infₛ _).1 <| by simp [*]
-    le_sup_left := fun a b => (isGLB_infₛ _).2 fun x => And.left
-    le_sup_right := fun a b => (isGLB_infₛ _).2 fun x => And.right
-    le_inf := fun s a ha => (isGLB_infₛ s).2 ha
-    inf_le := fun s a ha => (isGLB_infₛ s).1 ha
-    supₛ := fun s => infₛ (upperBounds s)
-    le_sup := fun s a ha => (isGLB_infₛ (upperBounds s)).2 fun b hb => hb ha
-    sup_le := fun s a ha => (isGLB_infₛ (upperBounds s)).1 ha }
+    inf_le_right := fun a b => (isGLB_sInf _).1 <| mem_insert_of_mem _ <| mem_singleton _
+    inf_le_left := fun a b => (isGLB_sInf _).1 <| mem_insert _ _
+    sup_le := fun a b c hac hbc => (isGLB_sInf _).1 <| by simp [*]
+    le_sup_left := fun a b => (isGLB_sInf _).2 fun x => And.left
+    le_sup_right := fun a b => (isGLB_sInf _).2 fun x => And.right
+    le_inf := fun s a ha => (isGLB_sInf s).2 ha
+    inf_le := fun s a ha => (isGLB_sInf s).1 ha
+    sSup := fun s => sInf (upperBounds s)
+    le_sup := fun s a ha => (isGLB_sInf (upperBounds s)).2 fun b hb => hb ha
+    sup_le := fun s a ha => (isGLB_sInf (upperBounds s)).1 ha }
 #align complete_lattice_of_Inf completeLatticeOfInf
 -/
 
@@ -453,7 +453,7 @@ see the doc-string on `complete_lattice_of_Inf`.
 -/
 def completeLatticeOfCompleteSemilatticeInf (α : Type _) [CompleteSemilatticeInf α] :
     CompleteLattice α :=
-  completeLatticeOfInf α fun s => isGLB_infₛ s
+  completeLatticeOfInf α fun s => isGLB_sInf s
 #align complete_lattice_of_complete_semilattice_Inf completeLatticeOfCompleteSemilatticeInf
 -/
 
@@ -474,25 +474,25 @@ instance : complete_lattice my_T :=
 ```
 -/
 def completeLatticeOfSup (α : Type _) [H1 : PartialOrder α] [H2 : SupSet α]
-    (is_lub_Sup : ∀ s : Set α, IsLUB s (supₛ s)) : CompleteLattice α :=
+    (is_lub_Sup : ∀ s : Set α, IsLUB s (sSup s)) : CompleteLattice α :=
   { H1, H2 with
-    top := supₛ univ
-    le_top := fun x => (isLUB_supₛ univ).1 trivial
-    bot := supₛ ∅
-    bot_le := fun x => (isLUB_supₛ ∅).2 <| by simp
-    sup := fun a b => supₛ {a, b}
-    sup_le := fun a b c hac hbc => (isLUB_supₛ _).2 (by simp [*])
-    le_sup_left := fun a b => (isLUB_supₛ _).1 <| mem_insert _ _
-    le_sup_right := fun a b => (isLUB_supₛ _).1 <| mem_insert_of_mem _ <| mem_singleton _
-    inf := fun a b => supₛ { x | x ≤ a ∧ x ≤ b }
-    le_inf := fun a b c hab hac => (isLUB_supₛ _).1 <| by simp [*]
-    inf_le_left := fun a b => (isLUB_supₛ _).2 fun x => And.left
-    inf_le_right := fun a b => (isLUB_supₛ _).2 fun x => And.right
-    infₛ := fun s => supₛ (lowerBounds s)
-    sup_le := fun s a ha => (isLUB_supₛ s).2 ha
-    le_sup := fun s a ha => (isLUB_supₛ s).1 ha
-    inf_le := fun s a ha => (isLUB_supₛ (lowerBounds s)).2 fun b hb => hb ha
-    le_inf := fun s a ha => (isLUB_supₛ (lowerBounds s)).1 ha }
+    top := sSup univ
+    le_top := fun x => (isLUB_sSup univ).1 trivial
+    bot := sSup ∅
+    bot_le := fun x => (isLUB_sSup ∅).2 <| by simp
+    sup := fun a b => sSup {a, b}
+    sup_le := fun a b c hac hbc => (isLUB_sSup _).2 (by simp [*])
+    le_sup_left := fun a b => (isLUB_sSup _).1 <| mem_insert _ _
+    le_sup_right := fun a b => (isLUB_sSup _).1 <| mem_insert_of_mem _ <| mem_singleton _
+    inf := fun a b => sSup { x | x ≤ a ∧ x ≤ b }
+    le_inf := fun a b c hab hac => (isLUB_sSup _).1 <| by simp [*]
+    inf_le_left := fun a b => (isLUB_sSup _).2 fun x => And.left
+    inf_le_right := fun a b => (isLUB_sSup _).2 fun x => And.right
+    sInf := fun s => sSup (lowerBounds s)
+    sup_le := fun s a ha => (isLUB_sSup s).2 ha
+    le_sup := fun s a ha => (isLUB_sSup s).1 ha
+    inf_le := fun s a ha => (isLUB_sSup (lowerBounds s)).2 fun b hb => hb ha
+    le_inf := fun s a ha => (isLUB_sSup (lowerBounds s)).1 ha }
 #align complete_lattice_of_Sup completeLatticeOfSup
 -/
 
@@ -504,7 +504,7 @@ see the doc-string on `complete_lattice_of_Sup`.
 -/
 def completeLatticeOfCompleteSemilatticeSup (α : Type _) [CompleteSemilatticeSup α] :
     CompleteLattice α :=
-  completeLatticeOfSup α fun s => isLUB_supₛ s
+  completeLatticeOfSup α fun s => isLUB_sSup s
 #align complete_lattice_of_complete_semilattice_Sup completeLatticeOfCompleteSemilatticeSup
 -/
 
@@ -539,336 +539,336 @@ section
 
 variable [CompleteLattice α] {s t : Set α} {a b : α}
 
-#print toDual_supₛ /-
+#print toDual_sSup /-
 @[simp]
-theorem toDual_supₛ (s : Set α) : toDual (supₛ s) = infₛ (ofDual ⁻¹' s) :=
+theorem toDual_sSup (s : Set α) : toDual (sSup s) = sInf (ofDual ⁻¹' s) :=
   rfl
-#align to_dual_Sup toDual_supₛ
+#align to_dual_Sup toDual_sSup
 -/
 
-#print toDual_infₛ /-
+#print toDual_sInf /-
 @[simp]
-theorem toDual_infₛ (s : Set α) : toDual (infₛ s) = supₛ (ofDual ⁻¹' s) :=
+theorem toDual_sInf (s : Set α) : toDual (sInf s) = sSup (ofDual ⁻¹' s) :=
   rfl
-#align to_dual_Inf toDual_infₛ
+#align to_dual_Inf toDual_sInf
 -/
 
-#print ofDual_supₛ /-
+#print ofDual_sSup /-
 @[simp]
-theorem ofDual_supₛ (s : Set αᵒᵈ) : ofDual (supₛ s) = infₛ (toDual ⁻¹' s) :=
+theorem ofDual_sSup (s : Set αᵒᵈ) : ofDual (sSup s) = sInf (toDual ⁻¹' s) :=
   rfl
-#align of_dual_Sup ofDual_supₛ
+#align of_dual_Sup ofDual_sSup
 -/
 
-#print ofDual_infₛ /-
+#print ofDual_sInf /-
 @[simp]
-theorem ofDual_infₛ (s : Set αᵒᵈ) : ofDual (infₛ s) = supₛ (toDual ⁻¹' s) :=
+theorem ofDual_sInf (s : Set αᵒᵈ) : ofDual (sInf s) = sSup (toDual ⁻¹' s) :=
   rfl
-#align of_dual_Inf ofDual_infₛ
+#align of_dual_Inf ofDual_sInf
 -/
 
-/- warning: to_dual_supr -> toDual_supᵢ is a dubious translation:
+/- warning: to_dual_supr -> toDual_iSup is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α), Eq.{succ u1} (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i))) (iInf.{u1, u2} (OrderDual.{u1} α) (OrderDual.hasInf.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1))) ι (fun (i : ι) => coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) (f i)))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align to_dual_supr toDual_supᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (f i)))
+Case conversion may be inaccurate. Consider using '#align to_dual_supr toDual_iSupₓ'. -/
 @[simp]
-theorem toDual_supᵢ (f : ι → α) : toDual (⨆ i, f i) = ⨅ i, toDual (f i) :=
+theorem toDual_iSup (f : ι → α) : toDual (⨆ i, f i) = ⨅ i, toDual (f i) :=
   rfl
-#align to_dual_supr toDual_supᵢ
+#align to_dual_supr toDual_iSup
 
-/- warning: to_dual_infi -> toDual_infᵢ is a dubious translation:
+/- warning: to_dual_infi -> toDual_iInf is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α), Eq.{succ u1} (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => f i))) (iSup.{u1, u2} (OrderDual.{u1} α) (OrderDual.hasSup.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) ι (fun (i : ι) => coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) (f i)))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align to_dual_infi toDual_infᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u1} (OrderDual.{u2} α) (OrderDual.supSet.{u2} α (CompleteLattice.toInfSet.{u2} α _inst_1)) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (f i)))
+Case conversion may be inaccurate. Consider using '#align to_dual_infi toDual_iInfₓ'. -/
 @[simp]
-theorem toDual_infᵢ (f : ι → α) : toDual (⨅ i, f i) = ⨆ i, toDual (f i) :=
+theorem toDual_iInf (f : ι → α) : toDual (⨅ i, f i) = ⨆ i, toDual (f i) :=
   rfl
-#align to_dual_infi toDual_infᵢ
+#align to_dual_infi toDual_iInf
 
-/- warning: of_dual_supr -> ofDual_supᵢ is a dubious translation:
+/- warning: of_dual_supr -> ofDual_iSup is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> (OrderDual.{u1} α)), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α) (iSup.{u1, u2} (OrderDual.{u1} α) (OrderDual.hasSup.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) ι (fun (i : ι) => f i))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α) (f i)))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align of_dual_supr ofDual_supᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> (OrderDual.{u2} α)), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) (iSup.{u2, u1} (OrderDual.{u2} α) (OrderDual.supSet.{u2} α (CompleteLattice.toInfSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (iSup.{u2, u1} (OrderDual.{u2} α) (OrderDual.supSet.{u2} α (CompleteLattice.toInfSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (f i)))
+Case conversion may be inaccurate. Consider using '#align of_dual_supr ofDual_iSupₓ'. -/
 @[simp]
-theorem ofDual_supᵢ (f : ι → αᵒᵈ) : ofDual (⨆ i, f i) = ⨅ i, ofDual (f i) :=
+theorem ofDual_iSup (f : ι → αᵒᵈ) : ofDual (⨆ i, f i) = ⨅ i, ofDual (f i) :=
   rfl
-#align of_dual_supr ofDual_supᵢ
+#align of_dual_supr ofDual_iSup
 
-/- warning: of_dual_infi -> ofDual_infᵢ is a dubious translation:
+/- warning: of_dual_infi -> ofDual_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> (OrderDual.{u1} α)), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α) (infᵢ.{u1, u2} (OrderDual.{u1} α) (OrderDual.hasInf.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1))) ι (fun (i : ι) => f i))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α) (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> (OrderDual.{u1} α)), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α) (iInf.{u1, u2} (OrderDual.{u1} α) (OrderDual.hasInf.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1))) ι (fun (i : ι) => f i))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α) (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> (OrderDual.{u2} α)), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) (infᵢ.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (infᵢ.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (f i)))
-Case conversion may be inaccurate. Consider using '#align of_dual_infi ofDual_infᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> (OrderDual.{u2} α)), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) (iInf.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (iInf.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (f i)))
+Case conversion may be inaccurate. Consider using '#align of_dual_infi ofDual_iInfₓ'. -/
 @[simp]
-theorem ofDual_infᵢ (f : ι → αᵒᵈ) : ofDual (⨅ i, f i) = ⨆ i, ofDual (f i) :=
+theorem ofDual_iInf (f : ι → αᵒᵈ) : ofDual (⨅ i, f i) = ⨆ i, ofDual (f i) :=
   rfl
-#align of_dual_infi ofDual_infᵢ
+#align of_dual_infi ofDual_iInf
 
-/- warning: Inf_le_Sup -> infₛ_le_supₛ is a dubious translation:
+/- warning: Inf_le_Sup -> sInf_le_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (LE.le.{u1} α (Preorder.toLE.{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) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (LE.le.{u1} α (Preorder.toLE.{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) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (LE.le.{u1} α (Preorder.toLE.{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) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align Inf_le_Sup infₛ_le_supₛₓ'. -/
-theorem infₛ_le_supₛ (hs : s.Nonempty) : infₛ s ≤ supₛ s :=
-  isGLB_le_isLUB (isGLB_infₛ s) (isLUB_supₛ s) hs
-#align Inf_le_Sup infₛ_le_supₛ
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (LE.le.{u1} α (Preorder.toLE.{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) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align Inf_le_Sup sInf_le_sSupₓ'. -/
+theorem sInf_le_sSup (hs : s.Nonempty) : sInf s ≤ sSup s :=
+  isGLB_le_isLUB (isGLB_sInf s) (isLUB_sSup s) hs
+#align Inf_le_Sup sInf_le_sSup
 
-/- warning: Sup_union -> supₛ_union is a dubious translation:
+/- warning: Sup_union -> sSup_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) t))
-Case conversion may be inaccurate. Consider using '#align Sup_union supₛ_unionₓ'. -/
-theorem supₛ_union {s t : Set α} : supₛ (s ∪ t) = supₛ s ⊔ supₛ t :=
-  ((isLUB_supₛ s).union (isLUB_supₛ t)).supₛ_eq
-#align Sup_union supₛ_union
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) t))
+Case conversion may be inaccurate. Consider using '#align Sup_union sSup_unionₓ'. -/
+theorem sSup_union {s t : Set α} : sSup (s ∪ t) = sSup s ⊔ sSup t :=
+  ((isLUB_sSup s).union (isLUB_sSup t)).sSup_eq
+#align Sup_union sSup_union
 
-/- warning: Inf_union -> infₛ_union is a dubious translation:
+/- warning: Inf_union -> sInf_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) t))
-Case conversion may be inaccurate. Consider using '#align Inf_union infₛ_unionₓ'. -/
-theorem infₛ_union {s t : Set α} : infₛ (s ∪ t) = infₛ s ⊓ infₛ t :=
-  ((isGLB_infₛ s).union (isGLB_infₛ t)).infₛ_eq
-#align Inf_union infₛ_union
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) t))
+Case conversion may be inaccurate. Consider using '#align Inf_union sInf_unionₓ'. -/
+theorem sInf_union {s t : Set α} : sInf (s ∪ t) = sInf s ⊓ sInf t :=
+  ((isGLB_sInf s).union (isGLB_sInf t)).sInf_eq
+#align Inf_union sInf_union
 
-/- warning: Sup_inter_le -> supₛ_inter_le is a dubious translation:
+/- warning: Sup_inter_le -> sSup_inter_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{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)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{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)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{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) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) t))
-Case conversion may be inaccurate. Consider using '#align Sup_inter_le supₛ_inter_leₓ'. -/
-theorem supₛ_inter_le {s t : Set α} : supₛ (s ∩ t) ≤ supₛ s ⊓ supₛ t :=
-  supₛ_le fun b hb => le_inf (le_supₛ hb.1) (le_supₛ hb.2)
-#align Sup_inter_le supₛ_inter_le
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{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) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) t))
+Case conversion may be inaccurate. Consider using '#align Sup_inter_le sSup_inter_leₓ'. -/
+theorem sSup_inter_le {s t : Set α} : sSup (s ∩ t) ≤ sSup s ⊓ sSup t :=
+  sSup_le fun b hb => le_inf (le_sSup hb.1) (le_sSup hb.2)
+#align Sup_inter_le sSup_inter_le
 
-/- warning: le_Inf_inter -> le_infₛ_inter is a dubious translation:
+/- warning: le_Inf_inter -> le_sInf_inter is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) t)) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) t)) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) t)) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t))
-Case conversion may be inaccurate. Consider using '#align le_Inf_inter le_infₛ_interₓ'. -/
-theorem le_infₛ_inter {s t : Set α} : infₛ s ⊔ infₛ t ≤ infₛ (s ∩ t) :=
-  @supₛ_inter_le αᵒᵈ _ _ _
-#align le_Inf_inter le_infₛ_inter
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) t)) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t))
+Case conversion may be inaccurate. Consider using '#align le_Inf_inter le_sInf_interₓ'. -/
+theorem le_sInf_inter {s t : Set α} : sInf s ⊔ sInf t ≤ sInf (s ∩ t) :=
+  @sSup_inter_le αᵒᵈ _ _ _
+#align le_Inf_inter le_sInf_inter
 
-/- warning: Sup_empty -> supₛ_empty is a dubious translation:
+/- warning: Sup_empty -> sSup_empty is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align Sup_empty supₛ_emptyₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align Sup_empty sSup_emptyₓ'. -/
 @[simp]
-theorem supₛ_empty : supₛ ∅ = (⊥ : α) :=
-  (@isLUB_empty α _ _).supₛ_eq
-#align Sup_empty supₛ_empty
+theorem sSup_empty : sSup ∅ = (⊥ : α) :=
+  (@isLUB_empty α _ _).sSup_eq
+#align Sup_empty sSup_empty
 
-/- warning: Inf_empty -> infₛ_empty is a dubious translation:
+/- warning: Inf_empty -> sInf_empty is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align Inf_empty infₛ_emptyₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align Inf_empty sInf_emptyₓ'. -/
 @[simp]
-theorem infₛ_empty : infₛ ∅ = (⊤ : α) :=
-  (@isGLB_empty α _ _).infₛ_eq
-#align Inf_empty infₛ_empty
+theorem sInf_empty : sInf ∅ = (⊤ : α) :=
+  (@isGLB_empty α _ _).sInf_eq
+#align Inf_empty sInf_empty
 
-/- warning: Sup_univ -> supₛ_univ is a dubious translation:
+/- warning: Sup_univ -> sSup_univ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Set.univ.{u1} α)) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Set.univ.{u1} α)) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Set.univ.{u1} α)) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align Sup_univ supₛ_univₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Set.univ.{u1} α)) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align Sup_univ sSup_univₓ'. -/
 @[simp]
-theorem supₛ_univ : supₛ univ = (⊤ : α) :=
-  (@isLUB_univ α _ _).supₛ_eq
-#align Sup_univ supₛ_univ
+theorem sSup_univ : sSup univ = (⊤ : α) :=
+  (@isLUB_univ α _ _).sSup_eq
+#align Sup_univ sSup_univ
 
-/- warning: Inf_univ -> infₛ_univ is a dubious translation:
+/- warning: Inf_univ -> sInf_univ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Set.univ.{u1} α)) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Set.univ.{u1} α)) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Set.univ.{u1} α)) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align Inf_univ infₛ_univₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Set.univ.{u1} α)) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align Inf_univ sInf_univₓ'. -/
 @[simp]
-theorem infₛ_univ : infₛ univ = (⊥ : α) :=
-  (@isGLB_univ α _ _).infₛ_eq
-#align Inf_univ infₛ_univ
+theorem sInf_univ : sInf univ = (⊥ : α) :=
+  (@isGLB_univ α _ _).sInf_eq
+#align Inf_univ sInf_univ
 
-/- warning: Sup_insert -> supₛ_insert is a dubious translation:
+/- warning: Sup_insert -> sSup_insert is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align Sup_insert supₛ_insertₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align Sup_insert sSup_insertₓ'. -/
 -- TODO(Jeremy): get this automatically
 @[simp]
-theorem supₛ_insert {a : α} {s : Set α} : supₛ (insert a s) = a ⊔ supₛ s :=
-  ((isLUB_supₛ s).insert a).supₛ_eq
-#align Sup_insert supₛ_insert
+theorem sSup_insert {a : α} {s : Set α} : sSup (insert a s) = a ⊔ sSup s :=
+  ((isLUB_sSup s).insert a).sSup_eq
+#align Sup_insert sSup_insert
 
-/- warning: Inf_insert -> infₛ_insert is a dubious translation:
+/- warning: Inf_insert -> sInf_insert is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align Inf_insert infₛ_insertₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align Inf_insert sInf_insertₓ'. -/
 @[simp]
-theorem infₛ_insert {a : α} {s : Set α} : infₛ (insert a s) = a ⊓ infₛ s :=
-  ((isGLB_infₛ s).insert a).infₛ_eq
-#align Inf_insert infₛ_insert
+theorem sInf_insert {a : α} {s : Set α} : sInf (insert a s) = a ⊓ sInf s :=
+  ((isGLB_sInf s).insert a).sInf_eq
+#align Inf_insert sInf_insert
 
-/- warning: Sup_le_Sup_of_subset_insert_bot -> supₛ_le_supₛ_of_subset_insert_bot is a dubious translation:
+/- warning: Sup_le_Sup_of_subset_insert_bot -> sSup_le_sSup_of_subset_insert_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)) t)) -> (LE.le.{u1} α (Preorder.toLE.{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) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)) t)) -> (LE.le.{u1} α (Preorder.toLE.{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) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1)) t)) -> (LE.le.{u1} α (Preorder.toLE.{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) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) t))
-Case conversion may be inaccurate. Consider using '#align Sup_le_Sup_of_subset_insert_bot supₛ_le_supₛ_of_subset_insert_botₓ'. -/
-theorem supₛ_le_supₛ_of_subset_insert_bot (h : s ⊆ insert ⊥ t) : supₛ s ≤ supₛ t :=
-  le_trans (supₛ_le_supₛ h) (le_of_eq (trans supₛ_insert bot_sup_eq))
-#align Sup_le_Sup_of_subset_insert_bot supₛ_le_supₛ_of_subset_insert_bot
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1)) t)) -> (LE.le.{u1} α (Preorder.toLE.{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) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) t))
+Case conversion may be inaccurate. Consider using '#align Sup_le_Sup_of_subset_insert_bot sSup_le_sSup_of_subset_insert_botₓ'. -/
+theorem sSup_le_sSup_of_subset_insert_bot (h : s ⊆ insert ⊥ t) : sSup s ≤ sSup t :=
+  le_trans (sSup_le_sSup h) (le_of_eq (trans sSup_insert bot_sup_eq))
+#align Sup_le_Sup_of_subset_insert_bot sSup_le_sSup_of_subset_insert_bot
 
-/- warning: Inf_le_Inf_of_subset_insert_top -> infₛ_le_infₛ_of_subset_insert_top is a dubious translation:
+/- warning: Inf_le_Inf_of_subset_insert_top -> sInf_le_sInf_of_subset_insert_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)) t)) -> (LE.le.{u1} α (Preorder.toLE.{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)) t) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)) t)) -> (LE.le.{u1} α (Preorder.toLE.{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)) t) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1)) t)) -> (LE.le.{u1} α (Preorder.toLE.{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) t) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align Inf_le_Inf_of_subset_insert_top infₛ_le_infₛ_of_subset_insert_topₓ'. -/
-theorem infₛ_le_infₛ_of_subset_insert_top (h : s ⊆ insert ⊤ t) : infₛ t ≤ infₛ s :=
-  le_trans (le_of_eq (trans top_inf_eq.symm infₛ_insert.symm)) (infₛ_le_infₛ h)
-#align Inf_le_Inf_of_subset_insert_top infₛ_le_infₛ_of_subset_insert_top
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1)) t)) -> (LE.le.{u1} α (Preorder.toLE.{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) t) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align Inf_le_Inf_of_subset_insert_top sInf_le_sInf_of_subset_insert_topₓ'. -/
+theorem sInf_le_sInf_of_subset_insert_top (h : s ⊆ insert ⊤ t) : sInf t ≤ sInf s :=
+  le_trans (le_of_eq (trans top_inf_eq.symm sInf_insert.symm)) (sInf_le_sInf h)
+#align Inf_le_Inf_of_subset_insert_top sInf_le_sInf_of_subset_insert_top
 
-/- warning: Sup_diff_singleton_bot -> supₛ_diff_singleton_bot is a dubious translation:
+/- warning: Sup_diff_singleton_bot -> sSup_diff_singleton_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (s : Set.{u1} α), Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (s : Set.{u1} α), Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (s : Set.{u1} α), Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)
-Case conversion may be inaccurate. Consider using '#align Sup_diff_singleton_bot supₛ_diff_singleton_botₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (s : Set.{u1} α), Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)
+Case conversion may be inaccurate. Consider using '#align Sup_diff_singleton_bot sSup_diff_singleton_botₓ'. -/
 @[simp]
-theorem supₛ_diff_singleton_bot (s : Set α) : supₛ (s \ {⊥}) = supₛ s :=
-  (supₛ_le_supₛ (diff_subset _ _)).antisymm <|
-    supₛ_le_supₛ_of_subset_insert_bot <| subset_insert_diff_singleton _ _
-#align Sup_diff_singleton_bot supₛ_diff_singleton_bot
+theorem sSup_diff_singleton_bot (s : Set α) : sSup (s \ {⊥}) = sSup s :=
+  (sSup_le_sSup (diff_subset _ _)).antisymm <|
+    sSup_le_sSup_of_subset_insert_bot <| subset_insert_diff_singleton _ _
+#align Sup_diff_singleton_bot sSup_diff_singleton_bot
 
-/- warning: Inf_diff_singleton_top -> infₛ_diff_singleton_top is a dubious translation:
+/- warning: Inf_diff_singleton_top -> sInf_diff_singleton_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (s : Set.{u1} α), Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (s : Set.{u1} α), Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (s : Set.{u1} α), Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)
-Case conversion may be inaccurate. Consider using '#align Inf_diff_singleton_top infₛ_diff_singleton_topₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (s : Set.{u1} α), Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)
+Case conversion may be inaccurate. Consider using '#align Inf_diff_singleton_top sInf_diff_singleton_topₓ'. -/
 @[simp]
-theorem infₛ_diff_singleton_top (s : Set α) : infₛ (s \ {⊤}) = infₛ s :=
-  @supₛ_diff_singleton_bot αᵒᵈ _ s
-#align Inf_diff_singleton_top infₛ_diff_singleton_top
+theorem sInf_diff_singleton_top (s : Set α) : sInf (s \ {⊤}) = sInf s :=
+  @sSup_diff_singleton_bot αᵒᵈ _ s
+#align Inf_diff_singleton_top sInf_diff_singleton_top
 
-/- warning: Sup_pair -> supₛ_pair is a dubious translation:
+/- warning: Sup_pair -> sSup_pair is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {b : α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {b : α}, Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {b : α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)
-Case conversion may be inaccurate. Consider using '#align Sup_pair supₛ_pairₓ'. -/
-theorem supₛ_pair {a b : α} : supₛ {a, b} = a ⊔ b :=
-  (@isLUB_pair α _ a b).supₛ_eq
-#align Sup_pair supₛ_pair
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {b : α}, Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)
+Case conversion may be inaccurate. Consider using '#align Sup_pair sSup_pairₓ'. -/
+theorem sSup_pair {a b : α} : sSup {a, b} = a ⊔ b :=
+  (@isLUB_pair α _ a b).sSup_eq
+#align Sup_pair sSup_pair
 
-/- warning: Inf_pair -> infₛ_pair is a dubious translation:
+/- warning: Inf_pair -> sInf_pair is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {b : α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {b : α}, Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {b : α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a b)
-Case conversion may be inaccurate. Consider using '#align Inf_pair infₛ_pairₓ'. -/
-theorem infₛ_pair {a b : α} : infₛ {a, b} = a ⊓ b :=
-  (@isGLB_pair α _ a b).infₛ_eq
-#align Inf_pair infₛ_pair
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {b : α}, Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a b)
+Case conversion may be inaccurate. Consider using '#align Inf_pair sInf_pairₓ'. -/
+theorem sInf_pair {a b : α} : sInf {a, b} = a ⊓ b :=
+  (@isGLB_pair α _ a b).sInf_eq
+#align Inf_pair sInf_pair
 
-/- warning: Sup_eq_bot -> supₛ_eq_bot is a dubious translation:
+/- warning: Sup_eq_bot -> sSup_eq_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))) (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Eq.{succ u1} α a (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))) (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Eq.{succ u1} α a (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))) (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (Eq.{succ u1} α a (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align Sup_eq_bot supₛ_eq_botₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))) (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (Eq.{succ u1} α a (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))))
+Case conversion may be inaccurate. Consider using '#align Sup_eq_bot sSup_eq_botₓ'. -/
 @[simp]
-theorem supₛ_eq_bot : supₛ s = ⊥ ↔ ∀ a ∈ s, a = ⊥ :=
-  ⟨fun h a ha => bot_unique <| h ▸ le_supₛ ha, fun h =>
-    bot_unique <| supₛ_le fun a ha => le_bot_iff.2 <| h a ha⟩
-#align Sup_eq_bot supₛ_eq_bot
+theorem sSup_eq_bot : sSup s = ⊥ ↔ ∀ a ∈ s, a = ⊥ :=
+  ⟨fun h a ha => bot_unique <| h ▸ le_sSup ha, fun h =>
+    bot_unique <| sSup_le fun a ha => le_bot_iff.2 <| h a ha⟩
+#align Sup_eq_bot sSup_eq_bot
 
-/- warning: Inf_eq_top -> infₛ_eq_top is a dubious translation:
+/- warning: Inf_eq_top -> sInf_eq_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))) (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Eq.{succ u1} α a (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))) (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Eq.{succ u1} α a (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))) (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (Eq.{succ u1} α a (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align Inf_eq_top infₛ_eq_topₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))) (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (Eq.{succ u1} α a (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))))
+Case conversion may be inaccurate. Consider using '#align Inf_eq_top sInf_eq_topₓ'. -/
 @[simp]
-theorem infₛ_eq_top : infₛ s = ⊤ ↔ ∀ a ∈ s, a = ⊤ :=
-  @supₛ_eq_bot αᵒᵈ _ _
-#align Inf_eq_top infₛ_eq_top
+theorem sInf_eq_top : sInf s = ⊤ ↔ ∀ a ∈ s, a = ⊤ :=
+  @sSup_eq_bot αᵒᵈ _ _
+#align Inf_eq_top sInf_eq_top
 
-/- warning: eq_singleton_bot_of_Sup_eq_bot_of_nonempty -> eq_singleton_bot_of_supₛ_eq_bot_of_nonempty is a dubious translation:
+/- warning: eq_singleton_bot_of_Sup_eq_bot_of_nonempty -> eq_singleton_bot_of_sSup_eq_bot_of_nonempty is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, (Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (Set.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (Set.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, (Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (Set.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align eq_singleton_bot_of_Sup_eq_bot_of_nonempty eq_singleton_bot_of_supₛ_eq_bot_of_nonemptyₓ'. -/
-theorem eq_singleton_bot_of_supₛ_eq_bot_of_nonempty {s : Set α} (h_sup : supₛ s = ⊥)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (Set.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))))
+Case conversion may be inaccurate. Consider using '#align eq_singleton_bot_of_Sup_eq_bot_of_nonempty eq_singleton_bot_of_sSup_eq_bot_of_nonemptyₓ'. -/
+theorem eq_singleton_bot_of_sSup_eq_bot_of_nonempty {s : Set α} (h_sup : sSup s = ⊥)
     (hne : s.Nonempty) : s = {⊥} :=
   by
   rw [Set.eq_singleton_iff_nonempty_unique_mem]
-  rw [supₛ_eq_bot] at h_sup
+  rw [sSup_eq_bot] at h_sup
   exact ⟨hne, h_sup⟩
-#align eq_singleton_bot_of_Sup_eq_bot_of_nonempty eq_singleton_bot_of_supₛ_eq_bot_of_nonempty
+#align eq_singleton_bot_of_Sup_eq_bot_of_nonempty eq_singleton_bot_of_sSup_eq_bot_of_nonempty
 
-/- warning: eq_singleton_top_of_Inf_eq_top_of_nonempty -> eq_singleton_top_of_infₛ_eq_top_of_nonempty is a dubious translation:
+/- warning: eq_singleton_top_of_Inf_eq_top_of_nonempty -> eq_singleton_top_of_sInf_eq_top_of_nonempty is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, (Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (Set.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, (Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (Set.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, (Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (Set.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))))
-Case conversion may be inaccurate. Consider using '#align eq_singleton_top_of_Inf_eq_top_of_nonempty eq_singleton_top_of_infₛ_eq_top_of_nonemptyₓ'. -/
-theorem eq_singleton_top_of_infₛ_eq_top_of_nonempty : infₛ s = ⊤ → s.Nonempty → s = {⊤} :=
-  @eq_singleton_bot_of_supₛ_eq_bot_of_nonempty αᵒᵈ _ _
-#align eq_singleton_top_of_Inf_eq_top_of_nonempty eq_singleton_top_of_infₛ_eq_top_of_nonempty
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, (Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (Set.{u1} α) s (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))))
+Case conversion may be inaccurate. Consider using '#align eq_singleton_top_of_Inf_eq_top_of_nonempty eq_singleton_top_of_sInf_eq_top_of_nonemptyₓ'. -/
+theorem eq_singleton_top_of_sInf_eq_top_of_nonempty : sInf s = ⊤ → s.Nonempty → s = {⊤} :=
+  @eq_singleton_bot_of_sSup_eq_bot_of_nonempty αᵒᵈ _ _
+#align eq_singleton_top_of_Inf_eq_top_of_nonempty eq_singleton_top_of_sInf_eq_top_of_nonempty
 
-/- warning: Sup_eq_of_forall_le_of_forall_lt_exists_gt -> supₛ_eq_of_forall_le_of_forall_lt_exists_gt is a dubious translation:
+/- warning: Sup_eq_of_forall_le_of_forall_lt_exists_gt -> sSup_eq_of_forall_le_of_forall_lt_exists_gt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w b) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w a)))) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) b)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w b) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w a)))) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w b) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w a)))) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) b)
-Case conversion may be inaccurate. Consider using '#align Sup_eq_of_forall_le_of_forall_lt_exists_gt supₛ_eq_of_forall_le_of_forall_lt_exists_gtₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w b) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w a)))) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) b)
+Case conversion may be inaccurate. Consider using '#align Sup_eq_of_forall_le_of_forall_lt_exists_gt sSup_eq_of_forall_le_of_forall_lt_exists_gtₓ'. -/
 /-- Introduction rule to prove that `b` is the supremum of `s`: it suffices to check that `b`
 is larger than all elements of `s`, and that this is not the case of any `w < b`.
 See `cSup_eq_of_forall_le_of_forall_lt_exists_gt` for a version in conditionally complete
 lattices. -/
-theorem supₛ_eq_of_forall_le_of_forall_lt_exists_gt (h₁ : ∀ a ∈ s, a ≤ b)
-    (h₂ : ∀ w, w < b → ∃ a ∈ s, w < a) : supₛ s = b :=
-  (supₛ_le h₁).eq_of_not_lt fun h =>
+theorem sSup_eq_of_forall_le_of_forall_lt_exists_gt (h₁ : ∀ a ∈ s, a ≤ b)
+    (h₂ : ∀ w, w < b → ∃ a ∈ s, w < a) : sSup s = b :=
+  (sSup_le h₁).eq_of_not_lt fun h =>
     let ⟨a, ha, ha'⟩ := h₂ _ h
-    ((le_supₛ ha).trans_lt ha').False
-#align Sup_eq_of_forall_le_of_forall_lt_exists_gt supₛ_eq_of_forall_le_of_forall_lt_exists_gt
+    ((le_sSup ha).trans_lt ha').False
+#align Sup_eq_of_forall_le_of_forall_lt_exists_gt sSup_eq_of_forall_le_of_forall_lt_exists_gt
 
-/- warning: Inf_eq_of_forall_ge_of_forall_gt_exists_lt -> infₛ_eq_of_forall_ge_of_forall_gt_exists_lt is a dubious translation:
+/- warning: Inf_eq_of_forall_ge_of_forall_gt_exists_lt -> sInf_eq_of_forall_ge_of_forall_gt_exists_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b a)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b w) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a w)))) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) b)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b a)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b w) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a w)))) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b a)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b w) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a w)))) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) b)
-Case conversion may be inaccurate. Consider using '#align Inf_eq_of_forall_ge_of_forall_gt_exists_lt infₛ_eq_of_forall_ge_of_forall_gt_exists_ltₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b a)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b w) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a w)))) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) b)
+Case conversion may be inaccurate. Consider using '#align Inf_eq_of_forall_ge_of_forall_gt_exists_lt sInf_eq_of_forall_ge_of_forall_gt_exists_ltₓ'. -/
 /-- Introduction rule to prove that `b` is the infimum of `s`: it suffices to check that `b`
 is smaller than all elements of `s`, and that this is not the case of any `w > b`.
 See `cInf_eq_of_forall_ge_of_forall_gt_exists_lt` for a version in conditionally complete
 lattices. -/
-theorem infₛ_eq_of_forall_ge_of_forall_gt_exists_lt :
-    (∀ a ∈ s, b ≤ a) → (∀ w, b < w → ∃ a ∈ s, a < w) → infₛ s = b :=
-  @supₛ_eq_of_forall_le_of_forall_lt_exists_gt αᵒᵈ _ _ _
-#align Inf_eq_of_forall_ge_of_forall_gt_exists_lt infₛ_eq_of_forall_ge_of_forall_gt_exists_lt
+theorem sInf_eq_of_forall_ge_of_forall_gt_exists_lt :
+    (∀ a ∈ s, b ≤ a) → (∀ w, b < w → ∃ a ∈ s, a < w) → sInf s = b :=
+  @sSup_eq_of_forall_le_of_forall_lt_exists_gt αᵒᵈ _ _ _
+#align Inf_eq_of_forall_ge_of_forall_gt_exists_lt sInf_eq_of_forall_ge_of_forall_gt_exists_lt
 
 end
 
@@ -876,69 +876,69 @@ section CompleteLinearOrder
 
 variable [CompleteLinearOrder α] {s t : Set α} {a b : α}
 
-/- warning: lt_Sup_iff -> lt_supₛ_iff is a dubious translation:
+/- warning: lt_Sup_iff -> lt_sSup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)) s)) (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b a)))
-Case conversion may be inaccurate. Consider using '#align lt_Sup_iff lt_supₛ_iffₓ'. -/
-theorem lt_supₛ_iff : b < supₛ s ↔ ∃ a ∈ s, b < a :=
-  lt_isLUB_iff <| isLUB_supₛ s
-#align lt_Sup_iff lt_supₛ_iff
+  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)) s)) (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b a)))
+Case conversion may be inaccurate. Consider using '#align lt_Sup_iff lt_sSup_iffₓ'. -/
+theorem lt_sSup_iff : b < sSup s ↔ ∃ a ∈ s, b < a :=
+  lt_isLUB_iff <| isLUB_sSup s
+#align lt_Sup_iff lt_sSup_iff
 
-/- warning: Inf_lt_iff -> infₛ_lt_iff is a dubious translation:
+/- warning: Inf_lt_iff -> sInf_lt_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s) b) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s) b) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a b)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)) s) b) (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a b)))
-Case conversion may be inaccurate. Consider using '#align Inf_lt_iff infₛ_lt_iffₓ'. -/
-theorem infₛ_lt_iff : infₛ s < b ↔ ∃ a ∈ s, a < b :=
-  isGLB_lt_iff <| isGLB_infₛ s
-#align Inf_lt_iff infₛ_lt_iff
+  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)) s) b) (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a b)))
+Case conversion may be inaccurate. Consider using '#align Inf_lt_iff sInf_lt_iffₓ'. -/
+theorem sInf_lt_iff : sInf s < b ↔ ∃ a ∈ s, a < b :=
+  isGLB_lt_iff <| isGLB_sInf s
+#align Inf_lt_iff sInf_lt_iff
 
-/- warning: Sup_eq_top -> supₛ_eq_top is a dubious translation:
+/- warning: Sup_eq_top -> sSup_eq_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b a))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b a))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)) s) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Top.top.{u1} α (CompleteLattice.toTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b a))))
-Case conversion may be inaccurate. Consider using '#align Sup_eq_top supₛ_eq_topₓ'. -/
-theorem supₛ_eq_top : supₛ s = ⊤ ↔ ∀ b < ⊤, ∃ a ∈ s, b < a :=
-  ⟨fun h b hb => lt_supₛ_iff.1 <| hb.trans_eq h.symm, fun h =>
+  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)) s) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Top.top.{u1} α (CompleteLattice.toTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b a))))
+Case conversion may be inaccurate. Consider using '#align Sup_eq_top sSup_eq_topₓ'. -/
+theorem sSup_eq_top : sSup s = ⊤ ↔ ∀ b < ⊤, ∃ a ∈ s, b < a :=
+  ⟨fun h b hb => lt_sSup_iff.1 <| hb.trans_eq h.symm, fun h =>
     top_unique <|
       le_of_not_gt fun h' =>
         let ⟨a, ha, h⟩ := h _ h'
-        (h.trans_le <| le_supₛ ha).False⟩
-#align Sup_eq_top supₛ_eq_top
+        (h.trans_le <| le_sSup ha).False⟩
+#align Sup_eq_top sSup_eq_top
 
-/- warning: Inf_eq_bot -> infₛ_eq_bot is a dubious translation:
+/- warning: Inf_eq_bot -> sInf_eq_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a b))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a b))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)) s) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a b))))
-Case conversion may be inaccurate. Consider using '#align Inf_eq_bot infₛ_eq_botₓ'. -/
-theorem infₛ_eq_bot : infₛ s = ⊥ ↔ ∀ b > ⊥, ∃ a ∈ s, a < b :=
-  @supₛ_eq_top αᵒᵈ _ _
-#align Inf_eq_bot infₛ_eq_bot
+  forall {α : Type.{u1}} [_inst_1 : CompleteLinearOrder.{u1} α] {s : Set.{u1} α}, Iff (Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)) s) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a b))))
+Case conversion may be inaccurate. Consider using '#align Inf_eq_bot sInf_eq_botₓ'. -/
+theorem sInf_eq_bot : sInf s = ⊥ ↔ ∀ b > ⊥, ∃ a ∈ s, a < b :=
+  @sSup_eq_top αᵒᵈ _ _
+#align Inf_eq_bot sInf_eq_bot
 
-/- warning: lt_supr_iff -> lt_supᵢ_iff is a dubious translation:
+/- warning: lt_supr_iff -> lt_iSup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] {a : α} {f : ι -> α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι f)) (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] {a : α} {f : ι -> α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι f)) (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) a (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLinearOrder.{u2} α] {a : α} {f : ι -> α}, Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) a (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)) ι f)) (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) a (f i)))
-Case conversion may be inaccurate. Consider using '#align lt_supr_iff lt_supᵢ_iffₓ'. -/
-theorem lt_supᵢ_iff {f : ι → α} : a < supᵢ f ↔ ∃ i, a < f i :=
-  lt_supₛ_iff.trans exists_range_iff
-#align lt_supr_iff lt_supᵢ_iff
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLinearOrder.{u2} α] {a : α} {f : ι -> α}, Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) a (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)) ι f)) (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) a (f i)))
+Case conversion may be inaccurate. Consider using '#align lt_supr_iff lt_iSup_iffₓ'. -/
+theorem lt_iSup_iff {f : ι → α} : a < iSup f ↔ ∃ i, a < f i :=
+  lt_sSup_iff.trans exists_range_iff
+#align lt_supr_iff lt_iSup_iff
 
-/- warning: infi_lt_iff -> infᵢ_lt_iff is a dubious translation:
+/- warning: infi_lt_iff -> iInf_lt_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] {a : α} {f : ι -> α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι f) a) (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (f i) a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] {a : α} {f : ι -> α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι f) a) (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (f i) a))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLinearOrder.{u2} α] {a : α} {f : ι -> α}, Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)) ι f) a) (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) (f i) a))
-Case conversion may be inaccurate. Consider using '#align infi_lt_iff infᵢ_lt_iffₓ'. -/
-theorem infᵢ_lt_iff {f : ι → α} : infᵢ f < a ↔ ∃ i, f i < a :=
-  infₛ_lt_iff.trans exists_range_iff
-#align infi_lt_iff infᵢ_lt_iff
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLinearOrder.{u2} α] {a : α} {f : ι -> α}, Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)) ι f) a) (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) (f i) a))
+Case conversion may be inaccurate. Consider using '#align infi_lt_iff iInf_lt_iffₓ'. -/
+theorem iInf_lt_iff {f : ι → α} : iInf f < a ↔ ∃ i, f i < a :=
+  sInf_lt_iff.trans exists_range_iff
+#align infi_lt_iff iInf_lt_iff
 
 end CompleteLinearOrder
 
@@ -949,116 +949,116 @@ section SupSet
 
 variable [SupSet α] {f g : ι → α}
 
-/- warning: Sup_range -> supₛ_range is a dubious translation:
+/- warning: Sup_range -> sSup_range is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {f : ι -> α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α _inst_1 (Set.range.{u1, u2} α ι f)) (supᵢ.{u1, u2} α _inst_1 ι f)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {f : ι -> α}, Eq.{succ u1} α (SupSet.sSup.{u1} α _inst_1 (Set.range.{u1, u2} α ι f)) (iSup.{u1, u2} α _inst_1 ι f)
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : SupSet.{u2} α] {f : ι -> α}, Eq.{succ u2} α (SupSet.supₛ.{u2} α _inst_1 (Set.range.{u2, u1} α ι f)) (supᵢ.{u2, u1} α _inst_1 ι f)
-Case conversion may be inaccurate. Consider using '#align Sup_range supₛ_rangeₓ'. -/
-theorem supₛ_range : supₛ (range f) = supᵢ f :=
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : SupSet.{u2} α] {f : ι -> α}, Eq.{succ u2} α (SupSet.sSup.{u2} α _inst_1 (Set.range.{u2, u1} α ι f)) (iSup.{u2, u1} α _inst_1 ι f)
+Case conversion may be inaccurate. Consider using '#align Sup_range sSup_rangeₓ'. -/
+theorem sSup_range : sSup (range f) = iSup f :=
   rfl
-#align Sup_range supₛ_range
+#align Sup_range sSup_range
 
-#print supₛ_eq_supᵢ' /-
-theorem supₛ_eq_supᵢ' (s : Set α) : supₛ s = ⨆ a : s, a := by rw [supᵢ, Subtype.range_coe]
-#align Sup_eq_supr' supₛ_eq_supᵢ'
+#print sSup_eq_iSup' /-
+theorem sSup_eq_iSup' (s : Set α) : sSup s = ⨆ a : s, a := by rw [iSup, Subtype.range_coe]
+#align Sup_eq_supr' sSup_eq_iSup'
 -/
 
-/- warning: supr_congr -> supᵢ_congr is a dubious translation:
+/- warning: supr_congr -> iSup_congr is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), Eq.{succ u1} α (f i) (g i)) -> (Eq.{succ u1} α (supᵢ.{u1, u2} α _inst_1 ι (fun (i : ι) => f i)) (supᵢ.{u1, u2} α _inst_1 ι (fun (i : ι) => g i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), Eq.{succ u1} α (f i) (g i)) -> (Eq.{succ u1} α (iSup.{u1, u2} α _inst_1 ι (fun (i : ι) => f i)) (iSup.{u1, u2} α _inst_1 ι (fun (i : ι) => g i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : SupSet.{u2} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), Eq.{succ u2} α (f i) (g i)) -> (Eq.{succ u2} α (supᵢ.{u2, u1} α _inst_1 ι (fun (i : ι) => f i)) (supᵢ.{u2, u1} α _inst_1 ι (fun (i : ι) => g i)))
-Case conversion may be inaccurate. Consider using '#align supr_congr supᵢ_congrₓ'. -/
-theorem supᵢ_congr (h : ∀ i, f i = g i) : (⨆ i, f i) = ⨆ i, g i :=
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : SupSet.{u2} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), Eq.{succ u2} α (f i) (g i)) -> (Eq.{succ u2} α (iSup.{u2, u1} α _inst_1 ι (fun (i : ι) => f i)) (iSup.{u2, u1} α _inst_1 ι (fun (i : ι) => g i)))
+Case conversion may be inaccurate. Consider using '#align supr_congr iSup_congrₓ'. -/
+theorem iSup_congr (h : ∀ i, f i = g i) : (⨆ i, f i) = ⨆ i, g i :=
   congr_arg _ <| funext h
-#align supr_congr supᵢ_congr
+#align supr_congr iSup_congr
 
-/- warning: function.surjective.supr_comp -> Function.Surjective.supᵢ_comp is a dubious translation:
+/- warning: function.surjective.supr_comp -> Function.Surjective.iSup_comp is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : SupSet.{u1} α] {f : ι -> ι'}, (Function.Surjective.{u2, u3} ι ι' f) -> (forall (g : ι' -> α), Eq.{succ u1} α (supᵢ.{u1, u2} α _inst_1 ι (fun (x : ι) => g (f x))) (supᵢ.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : SupSet.{u1} α] {f : ι -> ι'}, (Function.Surjective.{u2, u3} ι ι' f) -> (forall (g : ι' -> α), Eq.{succ u1} α (iSup.{u1, u2} α _inst_1 ι (fun (x : ι) => g (f x))) (iSup.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {f : ι -> ι'}, (Function.Surjective.{u3, u2} ι ι' f) -> (forall (g : ι' -> α), Eq.{succ u1} α (supᵢ.{u1, u3} α _inst_1 ι (fun (x : ι) => g (f x))) (supᵢ.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
-Case conversion may be inaccurate. Consider using '#align function.surjective.supr_comp Function.Surjective.supᵢ_compₓ'. -/
-theorem Function.Surjective.supᵢ_comp {f : ι → ι'} (hf : Surjective f) (g : ι' → α) :
-    (⨆ x, g (f x)) = ⨆ y, g y := by simp only [supᵢ, hf.range_comp]
-#align function.surjective.supr_comp Function.Surjective.supᵢ_comp
+  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {f : ι -> ι'}, (Function.Surjective.{u3, u2} ι ι' f) -> (forall (g : ι' -> α), Eq.{succ u1} α (iSup.{u1, u3} α _inst_1 ι (fun (x : ι) => g (f x))) (iSup.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
+Case conversion may be inaccurate. Consider using '#align function.surjective.supr_comp Function.Surjective.iSup_compₓ'. -/
+theorem Function.Surjective.iSup_comp {f : ι → ι'} (hf : Surjective f) (g : ι' → α) :
+    (⨆ x, g (f x)) = ⨆ y, g y := by simp only [iSup, hf.range_comp]
+#align function.surjective.supr_comp Function.Surjective.iSup_comp
 
-/- warning: equiv.supr_comp -> Equiv.supᵢ_comp is a dubious translation:
+/- warning: equiv.supr_comp -> Equiv.iSup_comp is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : SupSet.{u1} α] {g : ι' -> α} (e : Equiv.{u2, u3} ι ι'), Eq.{succ u1} α (supᵢ.{u1, u2} α _inst_1 ι (fun (x : ι) => g (coeFn.{max 1 (imax u2 u3) (imax u3 u2), imax u2 u3} (Equiv.{u2, u3} ι ι') (fun (_x : Equiv.{u2, u3} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{u2, u3} ι ι') e x))) (supᵢ.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : SupSet.{u1} α] {g : ι' -> α} (e : Equiv.{u2, u3} ι ι'), Eq.{succ u1} α (iSup.{u1, u2} α _inst_1 ι (fun (x : ι) => g (coeFn.{max 1 (imax u2 u3) (imax u3 u2), imax u2 u3} (Equiv.{u2, u3} ι ι') (fun (_x : Equiv.{u2, u3} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{u2, u3} ι ι') e x))) (iSup.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), Eq.{succ u1} α (supᵢ.{u1, u3} α _inst_1 ι (fun (x : ι) => g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x))) (supᵢ.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y))
-Case conversion may be inaccurate. Consider using '#align equiv.supr_comp Equiv.supᵢ_compₓ'. -/
-theorem Equiv.supᵢ_comp {g : ι' → α} (e : ι ≃ ι') : (⨆ x, g (e x)) = ⨆ y, g y :=
-  e.Surjective.supᵢ_comp _
-#align equiv.supr_comp Equiv.supᵢ_comp
+  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), Eq.{succ u1} α (iSup.{u1, u3} α _inst_1 ι (fun (x : ι) => g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x))) (iSup.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y))
+Case conversion may be inaccurate. Consider using '#align equiv.supr_comp Equiv.iSup_compₓ'. -/
+theorem Equiv.iSup_comp {g : ι' → α} (e : ι ≃ ι') : (⨆ x, g (e x)) = ⨆ y, g y :=
+  e.Surjective.iSup_comp _
+#align equiv.supr_comp Equiv.iSup_comp
 
-/- warning: function.surjective.supr_congr -> Function.Surjective.supᵢ_congr is a dubious translation:
+/- warning: function.surjective.supr_congr -> Function.Surjective.iSup_congr is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι' -> α} (h : ι -> ι'), (Function.Surjective.{u2, u3} ι ι' h) -> (forall (x : ι), Eq.{succ u1} α (g (h x)) (f x)) -> (Eq.{succ u1} α (supᵢ.{u1, u2} α _inst_1 ι (fun (x : ι) => f x)) (supᵢ.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι' -> α} (h : ι -> ι'), (Function.Surjective.{u2, u3} ι ι' h) -> (forall (x : ι), Eq.{succ u1} α (g (h x)) (f x)) -> (Eq.{succ u1} α (iSup.{u1, u2} α _inst_1 ι (fun (x : ι) => f x)) (iSup.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι' -> α} (h : ι -> ι'), (Function.Surjective.{u3, u2} ι ι' h) -> (forall (x : ι), Eq.{succ u1} α (g (h x)) (f x)) -> (Eq.{succ u1} α (supᵢ.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (supᵢ.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
-Case conversion may be inaccurate. Consider using '#align function.surjective.supr_congr Function.Surjective.supᵢ_congrₓ'. -/
-protected theorem Function.Surjective.supᵢ_congr {g : ι' → α} (h : ι → ι') (h1 : Surjective h)
+  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι' -> α} (h : ι -> ι'), (Function.Surjective.{u3, u2} ι ι' h) -> (forall (x : ι), Eq.{succ u1} α (g (h x)) (f x)) -> (Eq.{succ u1} α (iSup.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (iSup.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
+Case conversion may be inaccurate. Consider using '#align function.surjective.supr_congr Function.Surjective.iSup_congrₓ'. -/
+protected theorem Function.Surjective.iSup_congr {g : ι' → α} (h : ι → ι') (h1 : Surjective h)
     (h2 : ∀ x, g (h x) = f x) : (⨆ x, f x) = ⨆ y, g y :=
   by
   convert h1.supr_comp g
   exact (funext h2).symm
-#align function.surjective.supr_congr Function.Surjective.supᵢ_congr
+#align function.surjective.supr_congr Function.Surjective.iSup_congr
 
-/- warning: equiv.supr_congr -> Equiv.supᵢ_congr is a dubious translation:
+/- warning: equiv.supr_congr -> Equiv.iSup_congr is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u2, u3} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (coeFn.{max 1 (imax u2 u3) (imax u3 u2), imax u2 u3} (Equiv.{u2, u3} ι ι') (fun (_x : Equiv.{u2, u3} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{u2, u3} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (supᵢ.{u1, u2} α _inst_1 ι (fun (x : ι) => f x)) (supᵢ.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u2, u3} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (coeFn.{max 1 (imax u2 u3) (imax u3 u2), imax u2 u3} (Equiv.{u2, u3} ι ι') (fun (_x : Equiv.{u2, u3} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{u2, u3} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (iSup.{u1, u2} α _inst_1 ι (fun (x : ι) => f x)) (iSup.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (supᵢ.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (supᵢ.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
-Case conversion may be inaccurate. Consider using '#align equiv.supr_congr Equiv.supᵢ_congrₓ'. -/
-protected theorem Equiv.supᵢ_congr {g : ι' → α} (e : ι ≃ ι') (h : ∀ x, g (e x) = f x) :
+  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (iSup.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (iSup.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
+Case conversion may be inaccurate. Consider using '#align equiv.supr_congr Equiv.iSup_congrₓ'. -/
+protected theorem Equiv.iSup_congr {g : ι' → α} (e : ι ≃ ι') (h : ∀ x, g (e x) = f x) :
     (⨆ x, f x) = ⨆ y, g y :=
-  e.Surjective.supᵢ_congr _ h
-#align equiv.supr_congr Equiv.supᵢ_congr
+  e.Surjective.iSup_congr _ h
+#align equiv.supr_congr Equiv.iSup_congr
 
-#print supᵢ_congr_Prop /-
+#print iSup_congr_Prop /-
 @[congr]
-theorem supᵢ_congr_Prop {p q : Prop} {f₁ : p → α} {f₂ : q → α} (pq : p ↔ q)
-    (f : ∀ x, f₁ (pq.mpr x) = f₂ x) : supᵢ f₁ = supᵢ f₂ :=
+theorem iSup_congr_Prop {p q : Prop} {f₁ : p → α} {f₂ : q → α} (pq : p ↔ q)
+    (f : ∀ x, f₁ (pq.mpr x) = f₂ x) : iSup f₁ = iSup f₂ :=
   by
   obtain rfl := propext pq
   congr with x
   apply f
-#align supr_congr_Prop supᵢ_congr_Prop
+#align supr_congr_Prop iSup_congr_Prop
 -/
 
-#print supᵢ_plift_up /-
-theorem supᵢ_plift_up (f : PLift ι → α) : (⨆ i, f (PLift.up i)) = ⨆ i, f i :=
-  PLift.up_surjective.supᵢ_congr _ fun _ => rfl
-#align supr_plift_up supᵢ_plift_up
+#print iSup_plift_up /-
+theorem iSup_plift_up (f : PLift ι → α) : (⨆ i, f (PLift.up i)) = ⨆ i, f i :=
+  PLift.up_surjective.iSup_congr _ fun _ => rfl
+#align supr_plift_up iSup_plift_up
 -/
 
-/- warning: supr_plift_down -> supᵢ_plift_down is a dubious translation:
+/- warning: supr_plift_down -> iSup_plift_down is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : SupSet.{u1} α] (f : ι -> α), Eq.{succ u1} α (supᵢ.{u1, succ u2} α _inst_1 (PLift.{u2} ι) (fun (i : PLift.{u2} ι) => f (PLift.down.{u2} ι i))) (supᵢ.{u1, u2} α _inst_1 ι (fun (i : ι) => f i))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : SupSet.{u1} α] (f : ι -> α), Eq.{succ u1} α (iSup.{u1, succ u2} α _inst_1 (PLift.{u2} ι) (fun (i : PLift.{u2} ι) => f (PLift.down.{u2} ι i))) (iSup.{u1, u2} α _inst_1 ι (fun (i : ι) => f i))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : SupSet.{u2} α] (f : ι -> α), Eq.{succ u2} α (supᵢ.{u2, succ u1} α _inst_1 (PLift.{u1} ι) (fun (i : PLift.{u1} ι) => f (PLift.down.{u1} ι i))) (supᵢ.{u2, u1} α _inst_1 ι (fun (i : ι) => f i))
-Case conversion may be inaccurate. Consider using '#align supr_plift_down supᵢ_plift_downₓ'. -/
-theorem supᵢ_plift_down (f : ι → α) : (⨆ i, f (PLift.down i)) = ⨆ i, f i :=
-  PLift.down_surjective.supᵢ_congr _ fun _ => rfl
-#align supr_plift_down supᵢ_plift_down
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : SupSet.{u2} α] (f : ι -> α), Eq.{succ u2} α (iSup.{u2, succ u1} α _inst_1 (PLift.{u1} ι) (fun (i : PLift.{u1} ι) => f (PLift.down.{u1} ι i))) (iSup.{u2, u1} α _inst_1 ι (fun (i : ι) => f i))
+Case conversion may be inaccurate. Consider using '#align supr_plift_down iSup_plift_downₓ'. -/
+theorem iSup_plift_down (f : ι → α) : (⨆ i, f (PLift.down i)) = ⨆ i, f i :=
+  PLift.down_surjective.iSup_congr _ fun _ => rfl
+#align supr_plift_down iSup_plift_down
 
-/- warning: supr_range' -> supᵢ_range' is a dubious translation:
+/- warning: supr_range' -> iSup_range' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SupSet.{u1} α] (g : β -> α) (f : ι -> β), Eq.{succ u1} α (supᵢ.{u1, succ u2} α _inst_1 (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) (fun (b : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) => g ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Set.range.{u2, u3} β ι f)))))) b))) (supᵢ.{u1, u3} α _inst_1 ι (fun (i : ι) => g (f i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SupSet.{u1} α] (g : β -> α) (f : ι -> β), Eq.{succ u1} α (iSup.{u1, succ u2} α _inst_1 (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) (fun (b : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) => g ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Set.range.{u2, u3} β ι f)))))) b))) (iSup.{u1, u3} α _inst_1 ι (fun (i : ι) => g (f i)))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align supr_range' supᵢ_range'ₓ'. -/
-theorem supᵢ_range' (g : β → α) (f : ι → β) : (⨆ b : range f, g b) = ⨆ i, g (f i) := by
-  rw [supᵢ, supᵢ, ← image_eq_range, ← range_comp]
-#align supr_range' supᵢ_range'
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : SupSet.{u3} α] (g : β -> α) (f : ι -> β), Eq.{succ u3} α (iSup.{u3, succ u2} α _inst_1 (Set.Elem.{u2} β (Set.range.{u2, u1} β ι f)) (fun (b : Set.Elem.{u2} β (Set.range.{u2, u1} β ι f)) => g (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Set.range.{u2, u1} β ι f)) b))) (iSup.{u3, u1} α _inst_1 ι (fun (i : ι) => g (f i)))
+Case conversion may be inaccurate. Consider using '#align supr_range' iSup_range'ₓ'. -/
+theorem iSup_range' (g : β → α) (f : ι → β) : (⨆ b : range f, g b) = ⨆ i, g (f i) := by
+  rw [iSup, iSup, ← image_eq_range, ← range_comp]
+#align supr_range' iSup_range'
 
-#print supₛ_image' /-
-theorem supₛ_image' {s : Set β} {f : β → α} : supₛ (f '' s) = ⨆ a : s, f a := by
-  rw [supᵢ, image_eq_range]
-#align Sup_image' supₛ_image'
+#print sSup_image' /-
+theorem sSup_image' {s : Set β} {f : β → α} : sSup (f '' s) = ⨆ a : s, f a := by
+  rw [iSup, image_eq_range]
+#align Sup_image' sSup_image'
 -/
 
 end SupSet
@@ -1067,113 +1067,113 @@ section InfSet
 
 variable [InfSet α] {f g : ι → α}
 
-/- warning: Inf_range -> infₛ_range is a dubious translation:
+/- warning: Inf_range -> sInf_range is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {f : ι -> α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α _inst_1 (Set.range.{u1, u2} α ι f)) (infᵢ.{u1, u2} α _inst_1 ι f)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {f : ι -> α}, Eq.{succ u1} α (InfSet.sInf.{u1} α _inst_1 (Set.range.{u1, u2} α ι f)) (iInf.{u1, u2} α _inst_1 ι f)
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : InfSet.{u2} α] {f : ι -> α}, Eq.{succ u2} α (InfSet.infₛ.{u2} α _inst_1 (Set.range.{u2, u1} α ι f)) (infᵢ.{u2, u1} α _inst_1 ι f)
-Case conversion may be inaccurate. Consider using '#align Inf_range infₛ_rangeₓ'. -/
-theorem infₛ_range : infₛ (range f) = infᵢ f :=
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : InfSet.{u2} α] {f : ι -> α}, Eq.{succ u2} α (InfSet.sInf.{u2} α _inst_1 (Set.range.{u2, u1} α ι f)) (iInf.{u2, u1} α _inst_1 ι f)
+Case conversion may be inaccurate. Consider using '#align Inf_range sInf_rangeₓ'. -/
+theorem sInf_range : sInf (range f) = iInf f :=
   rfl
-#align Inf_range infₛ_range
+#align Inf_range sInf_range
 
-#print infₛ_eq_infᵢ' /-
-theorem infₛ_eq_infᵢ' (s : Set α) : infₛ s = ⨅ a : s, a :=
-  @supₛ_eq_supᵢ' αᵒᵈ _ _
-#align Inf_eq_infi' infₛ_eq_infᵢ'
+#print sInf_eq_iInf' /-
+theorem sInf_eq_iInf' (s : Set α) : sInf s = ⨅ a : s, a :=
+  @sSup_eq_iSup' αᵒᵈ _ _
+#align Inf_eq_infi' sInf_eq_iInf'
 -/
 
-/- warning: infi_congr -> infᵢ_congr is a dubious translation:
+/- warning: infi_congr -> iInf_congr is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), Eq.{succ u1} α (f i) (g i)) -> (Eq.{succ u1} α (infᵢ.{u1, u2} α _inst_1 ι (fun (i : ι) => f i)) (infᵢ.{u1, u2} α _inst_1 ι (fun (i : ι) => g i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), Eq.{succ u1} α (f i) (g i)) -> (Eq.{succ u1} α (iInf.{u1, u2} α _inst_1 ι (fun (i : ι) => f i)) (iInf.{u1, u2} α _inst_1 ι (fun (i : ι) => g i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : InfSet.{u2} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), Eq.{succ u2} α (f i) (g i)) -> (Eq.{succ u2} α (infᵢ.{u2, u1} α _inst_1 ι (fun (i : ι) => f i)) (infᵢ.{u2, u1} α _inst_1 ι (fun (i : ι) => g i)))
-Case conversion may be inaccurate. Consider using '#align infi_congr infᵢ_congrₓ'. -/
-theorem infᵢ_congr (h : ∀ i, f i = g i) : (⨅ i, f i) = ⨅ i, g i :=
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : InfSet.{u2} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), Eq.{succ u2} α (f i) (g i)) -> (Eq.{succ u2} α (iInf.{u2, u1} α _inst_1 ι (fun (i : ι) => f i)) (iInf.{u2, u1} α _inst_1 ι (fun (i : ι) => g i)))
+Case conversion may be inaccurate. Consider using '#align infi_congr iInf_congrₓ'. -/
+theorem iInf_congr (h : ∀ i, f i = g i) : (⨅ i, f i) = ⨅ i, g i :=
   congr_arg _ <| funext h
-#align infi_congr infᵢ_congr
+#align infi_congr iInf_congr
 
-/- warning: function.surjective.infi_comp -> Function.Surjective.infᵢ_comp is a dubious translation:
+/- warning: function.surjective.infi_comp -> Function.Surjective.iInf_comp is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : InfSet.{u1} α] {f : ι -> ι'}, (Function.Surjective.{u2, u3} ι ι' f) -> (forall (g : ι' -> α), Eq.{succ u1} α (infᵢ.{u1, u2} α _inst_1 ι (fun (x : ι) => g (f x))) (infᵢ.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : InfSet.{u1} α] {f : ι -> ι'}, (Function.Surjective.{u2, u3} ι ι' f) -> (forall (g : ι' -> α), Eq.{succ u1} α (iInf.{u1, u2} α _inst_1 ι (fun (x : ι) => g (f x))) (iInf.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {f : ι -> ι'}, (Function.Surjective.{u3, u2} ι ι' f) -> (forall (g : ι' -> α), Eq.{succ u1} α (infᵢ.{u1, u3} α _inst_1 ι (fun (x : ι) => g (f x))) (infᵢ.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
-Case conversion may be inaccurate. Consider using '#align function.surjective.infi_comp Function.Surjective.infᵢ_compₓ'. -/
-theorem Function.Surjective.infᵢ_comp {f : ι → ι'} (hf : Surjective f) (g : ι' → α) :
+  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {f : ι -> ι'}, (Function.Surjective.{u3, u2} ι ι' f) -> (forall (g : ι' -> α), Eq.{succ u1} α (iInf.{u1, u3} α _inst_1 ι (fun (x : ι) => g (f x))) (iInf.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
+Case conversion may be inaccurate. Consider using '#align function.surjective.infi_comp Function.Surjective.iInf_compₓ'. -/
+theorem Function.Surjective.iInf_comp {f : ι → ι'} (hf : Surjective f) (g : ι' → α) :
     (⨅ x, g (f x)) = ⨅ y, g y :=
-  @Function.Surjective.supᵢ_comp αᵒᵈ _ _ _ f hf g
-#align function.surjective.infi_comp Function.Surjective.infᵢ_comp
+  @Function.Surjective.iSup_comp αᵒᵈ _ _ _ f hf g
+#align function.surjective.infi_comp Function.Surjective.iInf_comp
 
-/- warning: equiv.infi_comp -> Equiv.infᵢ_comp is a dubious translation:
+/- warning: equiv.infi_comp -> Equiv.iInf_comp is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : InfSet.{u1} α] {g : ι' -> α} (e : Equiv.{u2, u3} ι ι'), Eq.{succ u1} α (infᵢ.{u1, u2} α _inst_1 ι (fun (x : ι) => g (coeFn.{max 1 (imax u2 u3) (imax u3 u2), imax u2 u3} (Equiv.{u2, u3} ι ι') (fun (_x : Equiv.{u2, u3} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{u2, u3} ι ι') e x))) (infᵢ.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : InfSet.{u1} α] {g : ι' -> α} (e : Equiv.{u2, u3} ι ι'), Eq.{succ u1} α (iInf.{u1, u2} α _inst_1 ι (fun (x : ι) => g (coeFn.{max 1 (imax u2 u3) (imax u3 u2), imax u2 u3} (Equiv.{u2, u3} ι ι') (fun (_x : Equiv.{u2, u3} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{u2, u3} ι ι') e x))) (iInf.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), Eq.{succ u1} α (infᵢ.{u1, u3} α _inst_1 ι (fun (x : ι) => g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x))) (infᵢ.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y))
-Case conversion may be inaccurate. Consider using '#align equiv.infi_comp Equiv.infᵢ_compₓ'. -/
-theorem Equiv.infᵢ_comp {g : ι' → α} (e : ι ≃ ι') : (⨅ x, g (e x)) = ⨅ y, g y :=
-  @Equiv.supᵢ_comp αᵒᵈ _ _ _ _ e
-#align equiv.infi_comp Equiv.infᵢ_comp
+  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), Eq.{succ u1} α (iInf.{u1, u3} α _inst_1 ι (fun (x : ι) => g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x))) (iInf.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y))
+Case conversion may be inaccurate. Consider using '#align equiv.infi_comp Equiv.iInf_compₓ'. -/
+theorem Equiv.iInf_comp {g : ι' → α} (e : ι ≃ ι') : (⨅ x, g (e x)) = ⨅ y, g y :=
+  @Equiv.iSup_comp αᵒᵈ _ _ _ _ e
+#align equiv.infi_comp Equiv.iInf_comp
 
-/- warning: function.surjective.infi_congr -> Function.Surjective.infᵢ_congr is a dubious translation:
+/- warning: function.surjective.infi_congr -> Function.Surjective.iInf_congr is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : InfSet.{u1} α] {f : ι -> α} {g : ι' -> α} (h : ι -> ι'), (Function.Surjective.{u2, u3} ι ι' h) -> (forall (x : ι), Eq.{succ u1} α (g (h x)) (f x)) -> (Eq.{succ u1} α (infᵢ.{u1, u2} α _inst_1 ι (fun (x : ι) => f x)) (infᵢ.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : InfSet.{u1} α] {f : ι -> α} {g : ι' -> α} (h : ι -> ι'), (Function.Surjective.{u2, u3} ι ι' h) -> (forall (x : ι), Eq.{succ u1} α (g (h x)) (f x)) -> (Eq.{succ u1} α (iInf.{u1, u2} α _inst_1 ι (fun (x : ι) => f x)) (iInf.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {f : ι -> α} {g : ι' -> α} (h : ι -> ι'), (Function.Surjective.{u3, u2} ι ι' h) -> (forall (x : ι), Eq.{succ u1} α (g (h x)) (f x)) -> (Eq.{succ u1} α (infᵢ.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (infᵢ.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
-Case conversion may be inaccurate. Consider using '#align function.surjective.infi_congr Function.Surjective.infᵢ_congrₓ'. -/
-protected theorem Function.Surjective.infᵢ_congr {g : ι' → α} (h : ι → ι') (h1 : Surjective h)
+  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {f : ι -> α} {g : ι' -> α} (h : ι -> ι'), (Function.Surjective.{u3, u2} ι ι' h) -> (forall (x : ι), Eq.{succ u1} α (g (h x)) (f x)) -> (Eq.{succ u1} α (iInf.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (iInf.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
+Case conversion may be inaccurate. Consider using '#align function.surjective.infi_congr Function.Surjective.iInf_congrₓ'. -/
+protected theorem Function.Surjective.iInf_congr {g : ι' → α} (h : ι → ι') (h1 : Surjective h)
     (h2 : ∀ x, g (h x) = f x) : (⨅ x, f x) = ⨅ y, g y :=
-  @Function.Surjective.supᵢ_congr αᵒᵈ _ _ _ _ _ h h1 h2
-#align function.surjective.infi_congr Function.Surjective.infᵢ_congr
+  @Function.Surjective.iSup_congr αᵒᵈ _ _ _ _ _ h h1 h2
+#align function.surjective.infi_congr Function.Surjective.iInf_congr
 
-/- warning: equiv.infi_congr -> Equiv.infᵢ_congr is a dubious translation:
+/- warning: equiv.infi_congr -> Equiv.iInf_congr is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : InfSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u2, u3} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (coeFn.{max 1 (imax u2 u3) (imax u3 u2), imax u2 u3} (Equiv.{u2, u3} ι ι') (fun (_x : Equiv.{u2, u3} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{u2, u3} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (infᵢ.{u1, u2} α _inst_1 ι (fun (x : ι) => f x)) (infᵢ.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : InfSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u2, u3} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (coeFn.{max 1 (imax u2 u3) (imax u3 u2), imax u2 u3} (Equiv.{u2, u3} ι ι') (fun (_x : Equiv.{u2, u3} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{u2, u3} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (iInf.{u1, u2} α _inst_1 ι (fun (x : ι) => f x)) (iInf.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (infᵢ.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (infᵢ.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
-Case conversion may be inaccurate. Consider using '#align equiv.infi_congr Equiv.infᵢ_congrₓ'. -/
-protected theorem Equiv.infᵢ_congr {g : ι' → α} (e : ι ≃ ι') (h : ∀ x, g (e x) = f x) :
+  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (iInf.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (iInf.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
+Case conversion may be inaccurate. Consider using '#align equiv.infi_congr Equiv.iInf_congrₓ'. -/
+protected theorem Equiv.iInf_congr {g : ι' → α} (e : ι ≃ ι') (h : ∀ x, g (e x) = f x) :
     (⨅ x, f x) = ⨅ y, g y :=
-  @Equiv.supᵢ_congr αᵒᵈ _ _ _ _ _ e h
-#align equiv.infi_congr Equiv.infᵢ_congr
+  @Equiv.iSup_congr αᵒᵈ _ _ _ _ _ e h
+#align equiv.infi_congr Equiv.iInf_congr
 
-#print infᵢ_congr_Prop /-
+#print iInf_congr_Prop /-
 @[congr]
-theorem infᵢ_congr_Prop {p q : Prop} {f₁ : p → α} {f₂ : q → α} (pq : p ↔ q)
-    (f : ∀ x, f₁ (pq.mpr x) = f₂ x) : infᵢ f₁ = infᵢ f₂ :=
-  @supᵢ_congr_Prop αᵒᵈ _ p q f₁ f₂ pq f
-#align infi_congr_Prop infᵢ_congr_Prop
+theorem iInf_congr_Prop {p q : Prop} {f₁ : p → α} {f₂ : q → α} (pq : p ↔ q)
+    (f : ∀ x, f₁ (pq.mpr x) = f₂ x) : iInf f₁ = iInf f₂ :=
+  @iSup_congr_Prop αᵒᵈ _ p q f₁ f₂ pq f
+#align infi_congr_Prop iInf_congr_Prop
 -/
 
-#print infᵢ_plift_up /-
-theorem infᵢ_plift_up (f : PLift ι → α) : (⨅ i, f (PLift.up i)) = ⨅ i, f i :=
-  PLift.up_surjective.infᵢ_congr _ fun _ => rfl
-#align infi_plift_up infᵢ_plift_up
+#print iInf_plift_up /-
+theorem iInf_plift_up (f : PLift ι → α) : (⨅ i, f (PLift.up i)) = ⨅ i, f i :=
+  PLift.up_surjective.iInf_congr _ fun _ => rfl
+#align infi_plift_up iInf_plift_up
 -/
 
-/- warning: infi_plift_down -> infᵢ_plift_down is a dubious translation:
+/- warning: infi_plift_down -> iInf_plift_down is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : InfSet.{u1} α] (f : ι -> α), Eq.{succ u1} α (infᵢ.{u1, succ u2} α _inst_1 (PLift.{u2} ι) (fun (i : PLift.{u2} ι) => f (PLift.down.{u2} ι i))) (infᵢ.{u1, u2} α _inst_1 ι (fun (i : ι) => f i))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : InfSet.{u1} α] (f : ι -> α), Eq.{succ u1} α (iInf.{u1, succ u2} α _inst_1 (PLift.{u2} ι) (fun (i : PLift.{u2} ι) => f (PLift.down.{u2} ι i))) (iInf.{u1, u2} α _inst_1 ι (fun (i : ι) => f i))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : InfSet.{u2} α] (f : ι -> α), Eq.{succ u2} α (infᵢ.{u2, succ u1} α _inst_1 (PLift.{u1} ι) (fun (i : PLift.{u1} ι) => f (PLift.down.{u1} ι i))) (infᵢ.{u2, u1} α _inst_1 ι (fun (i : ι) => f i))
-Case conversion may be inaccurate. Consider using '#align infi_plift_down infᵢ_plift_downₓ'. -/
-theorem infᵢ_plift_down (f : ι → α) : (⨅ i, f (PLift.down i)) = ⨅ i, f i :=
-  PLift.down_surjective.infᵢ_congr _ fun _ => rfl
-#align infi_plift_down infᵢ_plift_down
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : InfSet.{u2} α] (f : ι -> α), Eq.{succ u2} α (iInf.{u2, succ u1} α _inst_1 (PLift.{u1} ι) (fun (i : PLift.{u1} ι) => f (PLift.down.{u1} ι i))) (iInf.{u2, u1} α _inst_1 ι (fun (i : ι) => f i))
+Case conversion may be inaccurate. Consider using '#align infi_plift_down iInf_plift_downₓ'. -/
+theorem iInf_plift_down (f : ι → α) : (⨅ i, f (PLift.down i)) = ⨅ i, f i :=
+  PLift.down_surjective.iInf_congr _ fun _ => rfl
+#align infi_plift_down iInf_plift_down
 
-/- warning: infi_range' -> infᵢ_range' is a dubious translation:
+/- warning: infi_range' -> iInf_range' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : InfSet.{u1} α] (g : β -> α) (f : ι -> β), Eq.{succ u1} α (infᵢ.{u1, succ u2} α _inst_1 (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) (fun (b : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) => g ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Set.range.{u2, u3} β ι f)))))) b))) (infᵢ.{u1, u3} α _inst_1 ι (fun (i : ι) => g (f i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : InfSet.{u1} α] (g : β -> α) (f : ι -> β), Eq.{succ u1} α (iInf.{u1, succ u2} α _inst_1 (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) (fun (b : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) => g ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (Set.range.{u2, u3} β ι f)) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Set.range.{u2, u3} β ι f)))))) b))) (iInf.{u1, u3} α _inst_1 ι (fun (i : ι) => g (f i)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : InfSet.{u3} α] (g : β -> α) (f : ι -> β), Eq.{succ u3} α (infᵢ.{u3, succ u2} α _inst_1 (Set.Elem.{u2} β (Set.range.{u2, u1} β ι f)) (fun (b : Set.Elem.{u2} β (Set.range.{u2, u1} β ι f)) => g (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Set.range.{u2, u1} β ι f)) b))) (infᵢ.{u3, u1} α _inst_1 ι (fun (i : ι) => g (f i)))
-Case conversion may be inaccurate. Consider using '#align infi_range' infᵢ_range'ₓ'. -/
-theorem infᵢ_range' (g : β → α) (f : ι → β) : (⨅ b : range f, g b) = ⨅ i, g (f i) :=
-  @supᵢ_range' αᵒᵈ _ _ _ _ _
-#align infi_range' infᵢ_range'
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : InfSet.{u3} α] (g : β -> α) (f : ι -> β), Eq.{succ u3} α (iInf.{u3, succ u2} α _inst_1 (Set.Elem.{u2} β (Set.range.{u2, u1} β ι f)) (fun (b : Set.Elem.{u2} β (Set.range.{u2, u1} β ι f)) => g (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Set.range.{u2, u1} β ι f)) b))) (iInf.{u3, u1} α _inst_1 ι (fun (i : ι) => g (f i)))
+Case conversion may be inaccurate. Consider using '#align infi_range' iInf_range'ₓ'. -/
+theorem iInf_range' (g : β → α) (f : ι → β) : (⨅ b : range f, g b) = ⨅ i, g (f i) :=
+  @iSup_range' αᵒᵈ _ _ _ _ _
+#align infi_range' iInf_range'
 
-#print infₛ_image' /-
-theorem infₛ_image' {s : Set β} {f : β → α} : infₛ (f '' s) = ⨅ a : s, f a :=
-  @supₛ_image' αᵒᵈ _ _ _ _
-#align Inf_image' infₛ_image'
+#print sInf_image' /-
+theorem sInf_image' {s : Set β} {f : β → α} : sInf (f '' s) = ⨅ a : s, f a :=
+  @sSup_image' αᵒᵈ _ _ _ _
+#align Inf_image' sInf_image'
 -/
 
 end InfSet
@@ -1182,965 +1182,965 @@ section
 
 variable [CompleteLattice α] {f g s t : ι → α} {a b : α}
 
-/- warning: le_supr -> le_supᵢ is a dubious translation:
+/- warning: le_supr -> le_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι f)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι f)
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι f)
-Case conversion may be inaccurate. Consider using '#align le_supr le_supᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι f)
+Case conversion may be inaccurate. Consider using '#align le_supr le_iSupₓ'. -/
 -- TODO: this declaration gives error when starting smt state
 --@[ematch]
-theorem le_supᵢ (f : ι → α) (i : ι) : f i ≤ supᵢ f :=
-  le_supₛ ⟨i, rfl⟩
-#align le_supr le_supᵢ
+theorem le_iSup (f : ι → α) (i : ι) : f i ≤ iSup f :=
+  le_sSup ⟨i, rfl⟩
+#align le_supr le_iSup
 
-/- warning: infi_le -> infᵢ_le is a dubious translation:
+/- warning: infi_le -> iInf_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toLE.{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 f) (f i)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toLE.{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 f) (f i)
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (i : ι), LE.le.{u2} α (Preorder.toLE.{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 f) (f i)
-Case conversion may be inaccurate. Consider using '#align infi_le infᵢ_leₓ'. -/
-theorem infᵢ_le (f : ι → α) (i : ι) : infᵢ f ≤ f i :=
-  infₛ_le ⟨i, rfl⟩
-#align infi_le infᵢ_le
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (i : ι), LE.le.{u2} α (Preorder.toLE.{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 f) (f i)
+Case conversion may be inaccurate. Consider using '#align infi_le iInf_leₓ'. -/
+theorem iInf_le (f : ι → α) (i : ι) : iInf f ≤ f i :=
+  sInf_le ⟨i, rfl⟩
+#align infi_le iInf_le
 
-/- warning: le_supr' -> le_supᵢ' is a dubious translation:
+/- warning: le_supr' -> le_iSup' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι f)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι f)
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι f)
-Case conversion may be inaccurate. Consider using '#align le_supr' le_supᵢ'ₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι f)
+Case conversion may be inaccurate. Consider using '#align le_supr' le_iSup'ₓ'. -/
 @[ematch]
-theorem le_supᵢ' (f : ι → α) (i : ι) : f i ≤ supᵢ f :=
-  le_supₛ ⟨i, rfl⟩
-#align le_supr' le_supᵢ'
+theorem le_iSup' (f : ι → α) (i : ι) : f i ≤ iSup f :=
+  le_sSup ⟨i, rfl⟩
+#align le_supr' le_iSup'
 
-/- warning: infi_le' -> infᵢ_le' is a dubious translation:
+/- warning: infi_le' -> iInf_le' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toLE.{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 f) (f i)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toLE.{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 f) (f i)
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (i : ι), LE.le.{u2} α (Preorder.toLE.{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 f) (f i)
-Case conversion may be inaccurate. Consider using '#align infi_le' infᵢ_le'ₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (i : ι), LE.le.{u2} α (Preorder.toLE.{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 f) (f i)
+Case conversion may be inaccurate. Consider using '#align infi_le' iInf_le'ₓ'. -/
 @[ematch]
-theorem infᵢ_le' (f : ι → α) (i : ι) : infᵢ f ≤ f i :=
-  infₛ_le ⟨i, rfl⟩
-#align infi_le' infᵢ_le'
+theorem iInf_le' (f : ι → α) (i : ι) : iInf f ≤ f i :=
+  sInf_le ⟨i, rfl⟩
+#align infi_le' iInf_le'
 
-/- warning: is_lub_supr -> isLUB_supᵢ is a dubious translation:
+/- warning: is_lub_supr -> isLUB_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α}, IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Set.range.{u1, u2} α ι f) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (j : ι) => f j))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α}, IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Set.range.{u1, u2} α ι f) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (j : ι) => f j))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α}, IsLUB.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (Set.range.{u2, u1} α ι f) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (j : ι) => f j))
-Case conversion may be inaccurate. Consider using '#align is_lub_supr isLUB_supᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α}, IsLUB.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (Set.range.{u2, u1} α ι f) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (j : ι) => f j))
+Case conversion may be inaccurate. Consider using '#align is_lub_supr isLUB_iSupₓ'. -/
 /- TODO: this version would be more powerful, but, alas, the pattern matcher
    doesn't accept it.
 @[ematch] lemma le_supr' (f : ι → α) (i : ι) : (: f i :) ≤ (: supr f :) :=
 le_Sup ⟨i, rfl⟩
 -/
-theorem isLUB_supᵢ : IsLUB (range f) (⨆ j, f j) :=
-  isLUB_supₛ _
-#align is_lub_supr isLUB_supᵢ
+theorem isLUB_iSup : IsLUB (range f) (⨆ j, f j) :=
+  isLUB_sSup _
+#align is_lub_supr isLUB_iSup
 
-/- warning: is_glb_infi -> isGLB_infᵢ is a dubious translation:
+/- warning: is_glb_infi -> isGLB_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α}, IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Set.range.{u1, u2} α ι f) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (j : ι) => f j))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α}, IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Set.range.{u1, u2} α ι f) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (j : ι) => f j))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α}, IsGLB.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (Set.range.{u2, u1} α ι f) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (j : ι) => f j))
-Case conversion may be inaccurate. Consider using '#align is_glb_infi isGLB_infᵢₓ'. -/
-theorem isGLB_infᵢ : IsGLB (range f) (⨅ j, f j) :=
-  isGLB_infₛ _
-#align is_glb_infi isGLB_infᵢ
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α}, IsGLB.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (Set.range.{u2, u1} α ι f) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (j : ι) => f j))
+Case conversion may be inaccurate. Consider using '#align is_glb_infi isGLB_iInfₓ'. -/
+theorem isGLB_iInf : IsGLB (range f) (⨅ j, f j) :=
+  isGLB_sInf _
+#align is_glb_infi isGLB_iInf
 
-/- warning: is_lub.supr_eq -> IsLUB.supᵢ_eq is a dubious translation:
+/- warning: is_lub.supr_eq -> IsLUB.iSup_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Set.range.{u1, u2} α ι f) a) -> (Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (j : ι) => f j)) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Set.range.{u1, u2} α ι f) a) -> (Eq.{succ u1} α (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (j : ι) => f j)) a)
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, (IsLUB.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (Set.range.{u2, u1} α ι f) a) -> (Eq.{succ u2} α (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (j : ι) => f j)) a)
-Case conversion may be inaccurate. Consider using '#align is_lub.supr_eq IsLUB.supᵢ_eqₓ'. -/
-theorem IsLUB.supᵢ_eq (h : IsLUB (range f) a) : (⨆ j, f j) = a :=
-  h.supₛ_eq
-#align is_lub.supr_eq IsLUB.supᵢ_eq
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, (IsLUB.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (Set.range.{u2, u1} α ι f) a) -> (Eq.{succ u2} α (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (j : ι) => f j)) a)
+Case conversion may be inaccurate. Consider using '#align is_lub.supr_eq IsLUB.iSup_eqₓ'. -/
+theorem IsLUB.iSup_eq (h : IsLUB (range f) a) : (⨆ j, f j) = a :=
+  h.sSup_eq
+#align is_lub.supr_eq IsLUB.iSup_eq
 
-/- warning: is_glb.infi_eq -> IsGLB.infᵢ_eq is a dubious translation:
+/- warning: is_glb.infi_eq -> IsGLB.iInf_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Set.range.{u1, u2} α ι f) a) -> (Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (j : ι) => f j)) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Set.range.{u1, u2} α ι f) a) -> (Eq.{succ u1} α (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (j : ι) => f j)) a)
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, (IsGLB.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (Set.range.{u2, u1} α ι f) a) -> (Eq.{succ u2} α (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (j : ι) => f j)) a)
-Case conversion may be inaccurate. Consider using '#align is_glb.infi_eq IsGLB.infᵢ_eqₓ'. -/
-theorem IsGLB.infᵢ_eq (h : IsGLB (range f) a) : (⨅ j, f j) = a :=
-  h.infₛ_eq
-#align is_glb.infi_eq IsGLB.infᵢ_eq
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, (IsGLB.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (Set.range.{u2, u1} α ι f) a) -> (Eq.{succ u2} α (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (j : ι) => f j)) a)
+Case conversion may be inaccurate. Consider using '#align is_glb.infi_eq IsGLB.iInf_eqₓ'. -/
+theorem IsGLB.iInf_eq (h : IsGLB (range f) a) : (⨅ j, f j) = a :=
+  h.sInf_eq
+#align is_glb.infi_eq IsGLB.iInf_eq
 
-/- warning: le_supr_of_le -> le_supᵢ_of_le is a dubious translation:
+/- warning: le_supr_of_le -> le_iSup_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α} (i : ι), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι f))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α} (i : ι), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι f))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α} (i : ι), (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (f i)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι f))
-Case conversion may be inaccurate. Consider using '#align le_supr_of_le le_supᵢ_of_leₓ'. -/
-theorem le_supᵢ_of_le (i : ι) (h : a ≤ f i) : a ≤ supᵢ f :=
-  h.trans <| le_supᵢ _ i
-#align le_supr_of_le le_supᵢ_of_le
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α} (i : ι), (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (f i)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι f))
+Case conversion may be inaccurate. Consider using '#align le_supr_of_le le_iSup_of_leₓ'. -/
+theorem le_iSup_of_le (i : ι) (h : a ≤ f i) : a ≤ iSup f :=
+  h.trans <| le_iSup _ i
+#align le_supr_of_le le_iSup_of_le
 
-/- warning: infi_le_of_le -> infᵢ_le_of_le is a dubious translation:
+/- warning: infi_le_of_le -> iInf_le_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α} (i : ι), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) a) -> (LE.le.{u1} α (Preorder.toLE.{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 f) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α} (i : ι), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) a) -> (LE.le.{u1} α (Preorder.toLE.{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 f) a)
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α} (i : ι), (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) a) -> (LE.le.{u2} α (Preorder.toLE.{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 f) a)
-Case conversion may be inaccurate. Consider using '#align infi_le_of_le infᵢ_le_of_leₓ'. -/
-theorem infᵢ_le_of_le (i : ι) (h : f i ≤ a) : infᵢ f ≤ a :=
-  (infᵢ_le _ i).trans h
-#align infi_le_of_le infᵢ_le_of_le
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α} (i : ι), (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) a) -> (LE.le.{u2} α (Preorder.toLE.{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 f) a)
+Case conversion may be inaccurate. Consider using '#align infi_le_of_le iInf_le_of_leₓ'. -/
+theorem iInf_le_of_le (i : ι) (h : f i ≤ a) : iInf f ≤ a :=
+  (iInf_le _ i).trans h
+#align infi_le_of_le iInf_le_of_le
 
-/- warning: le_supr₂ -> le_supᵢ₂ is a dubious translation:
+/- warning: le_supr₂ -> le_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} (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) (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)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) (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)))
 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} (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) (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)))
-Case conversion may be inaccurate. Consider using '#align le_supr₂ le_supᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) (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)))
+Case conversion may be inaccurate. Consider using '#align le_supr₂ le_iSup₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem le_supᵢ₂ {f : ∀ i, κ i → α} (i : ι) (j : κ i) : f i j ≤ ⨆ (i) (j), f i j :=
-  le_supᵢ_of_le i <| le_supᵢ (f i) j
-#align le_supr₂ le_supᵢ₂
+theorem le_iSup₂ {f : ∀ i, κ i → α} (i : ι) (j : κ i) : f i j ≤ ⨆ (i) (j), f i j :=
+  le_iSup_of_le i <| le_iSup (f i) j
+#align le_supr₂ le_iSup₂
 
-/- warning: infi₂_le -> infᵢ₂_le is a dubious translation:
+/- warning: infi₂_le -> iInf₂_le 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} (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{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))) (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} (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{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))) (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} (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{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))) (f i j)
-Case conversion may be inaccurate. Consider using '#align infi₂_le infᵢ₂_leₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{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))) (f i j)
+Case conversion may be inaccurate. Consider using '#align infi₂_le iInf₂_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem infᵢ₂_le {f : ∀ i, κ i → α} (i : ι) (j : κ i) : (⨅ (i) (j), f i j) ≤ f i j :=
-  infᵢ_le_of_le i <| infᵢ_le (f i) j
-#align infi₂_le infᵢ₂_le
+theorem iInf₂_le {f : ∀ i, κ i → α} (i : ι) (j : κ i) : (⨅ (i) (j), f i j) ≤ f i j :=
+  iInf_le_of_le i <| iInf_le (f i) j
+#align infi₂_le iInf₂_le
 
-/- warning: le_supr₂_of_le -> le_supᵢ₂_of_le is a dubious translation:
+/- warning: le_supr₂_of_le -> le_iSup₂_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i j)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (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))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i j)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (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))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (f i j)) -> (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (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))))
-Case conversion may be inaccurate. Consider using '#align le_supr₂_of_le le_supᵢ₂_of_leₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (f i j)) -> (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (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))))
+Case conversion may be inaccurate. Consider using '#align le_supr₂_of_le le_iSup₂_of_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem le_supᵢ₂_of_le {f : ∀ i, κ i → α} (i : ι) (j : κ i) (h : a ≤ f i j) :
+theorem le_iSup₂_of_le {f : ∀ i, κ i → α} (i : ι) (j : κ i) (h : a ≤ f i j) :
     a ≤ ⨆ (i) (j), f i j :=
-  h.trans <| le_supᵢ₂ i j
-#align le_supr₂_of_le le_supᵢ₂_of_le
+  h.trans <| le_iSup₂ i j
+#align le_supr₂_of_le le_iSup₂_of_le
 
-/- warning: infi₂_le_of_le -> infᵢ₂_le_of_le is a dubious translation:
+/- warning: infi₂_le_of_le -> iInf₂_le_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) a) -> (LE.le.{u1} α (Preorder.toLE.{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))) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) a) -> (LE.le.{u1} α (Preorder.toLE.{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))) a)
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) a) -> (LE.le.{u3} α (Preorder.toLE.{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))) a)
-Case conversion may be inaccurate. Consider using '#align infi₂_le_of_le infᵢ₂_le_of_leₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α} (i : ι) (j : κ i), (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) a) -> (LE.le.{u3} α (Preorder.toLE.{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))) a)
+Case conversion may be inaccurate. Consider using '#align infi₂_le_of_le iInf₂_le_of_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem infᵢ₂_le_of_le {f : ∀ i, κ i → α} (i : ι) (j : κ i) (h : f i j ≤ a) :
+theorem iInf₂_le_of_le {f : ∀ i, κ i → α} (i : ι) (j : κ i) (h : f i j ≤ a) :
     (⨅ (i) (j), f i j) ≤ a :=
-  (infᵢ₂_le i j).trans h
-#align infi₂_le_of_le infᵢ₂_le_of_le
+  (iInf₂_le i j).trans h
+#align infi₂_le_of_le iInf₂_le_of_le
 
-/- warning: supr_le -> supᵢ_le is a dubious translation:
+/- warning: supr_le -> iSup_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) a) -> (LE.le.{u1} α (Preorder.toLE.{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 f) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) a) -> (LE.le.{u1} α (Preorder.toLE.{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 f) a)
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) a) -> (LE.le.{u2} α (Preorder.toLE.{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 f) a)
-Case conversion may be inaccurate. Consider using '#align supr_le supᵢ_leₓ'. -/
-theorem supᵢ_le (h : ∀ i, f i ≤ a) : supᵢ f ≤ a :=
-  supₛ_le fun b ⟨i, Eq⟩ => Eq ▸ h i
-#align supr_le supᵢ_le
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) a) -> (LE.le.{u2} α (Preorder.toLE.{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 f) a)
+Case conversion may be inaccurate. Consider using '#align supr_le iSup_leₓ'. -/
+theorem iSup_le (h : ∀ i, f i ≤ a) : iSup f ≤ a :=
+  sSup_le fun b ⟨i, Eq⟩ => Eq ▸ h i
+#align supr_le iSup_le
 
-/- warning: le_infi -> le_infᵢ is a dubious translation:
+/- warning: le_infi -> le_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι f))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι f))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (f i)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι f))
-Case conversion may be inaccurate. Consider using '#align le_infi le_infᵢₓ'. -/
-theorem le_infᵢ (h : ∀ i, a ≤ f i) : a ≤ infᵢ f :=
-  le_infₛ fun b ⟨i, Eq⟩ => Eq ▸ h i
-#align le_infi le_infᵢ
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (f i)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι f))
+Case conversion may be inaccurate. Consider using '#align le_infi le_iInfₓ'. -/
+theorem le_iInf (h : ∀ i, a ≤ f i) : a ≤ iInf f :=
+  le_sInf fun b ⟨i, Eq⟩ => Eq ▸ h i
+#align le_infi le_iInf
 
-/- warning: supr₂_le -> supᵢ₂_le is a dubious translation:
+/- warning: supr₂_le -> iSup₂_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) a) -> (LE.le.{u1} α (Preorder.toLE.{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))) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) a) -> (LE.le.{u1} α (Preorder.toLE.{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))) a)
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) a) -> (LE.le.{u3} α (Preorder.toLE.{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))) a)
-Case conversion may be inaccurate. Consider using '#align supr₂_le supᵢ₂_leₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) a) -> (LE.le.{u3} α (Preorder.toLE.{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))) a)
+Case conversion may be inaccurate. Consider using '#align supr₂_le iSup₂_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem supᵢ₂_le {f : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ a) : (⨆ (i) (j), f i j) ≤ a :=
-  supᵢ_le fun i => supᵢ_le <| h i
-#align supr₂_le supᵢ₂_le
+theorem iSup₂_le {f : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ a) : (⨆ (i) (j), f i j) ≤ a :=
+  iSup_le fun i => iSup_le <| h i
+#align supr₂_le iSup₂_le
 
-/- warning: le_infi₂ -> le_infᵢ₂ is a dubious translation:
+/- warning: le_infi₂ -> le_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] {a : α} {f : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i j)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (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))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i j)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (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))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (f i j)) -> (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (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))))
-Case conversion may be inaccurate. Consider using '#align le_infi₂ le_infᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (f i j)) -> (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (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))))
+Case conversion may be inaccurate. Consider using '#align le_infi₂ le_iInf₂ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem le_infᵢ₂ {f : ∀ i, κ i → α} (h : ∀ i j, a ≤ f i j) : a ≤ ⨅ (i) (j), f i j :=
-  le_infᵢ fun i => le_infᵢ <| h i
-#align le_infi₂ le_infᵢ₂
+theorem le_iInf₂ {f : ∀ i, κ i → α} (h : ∀ i j, a ≤ f i j) : a ≤ ⨅ (i) (j), f i j :=
+  le_iInf fun i => le_iInf <| h i
+#align le_infi₂ le_iInf₂
 
-/- warning: supr₂_le_supr -> supᵢ₂_le_supᵢ is a dubious translation:
+/- warning: supr₂_le_supr -> iSup₂_le_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (κ : ι -> Sort.{u3}) (f : ι -> α), LE.le.{u1} α (Preorder.toLE.{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))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (κ : ι -> Sort.{u3}) (f : ι -> α), LE.le.{u1} α (Preorder.toLE.{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))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (κ : ι -> Sort.{u3}) (f : ι -> α), LE.le.{u2} α (Preorder.toLE.{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) => supᵢ.{u2, u3} α (CompleteLattice.toSupSet.{u2} α _inst_1) (κ i) (fun (j : κ i) => f i))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))
-Case conversion may be inaccurate. Consider using '#align supr₂_le_supr supᵢ₂_le_supᵢₓ'. -/
-theorem supᵢ₂_le_supᵢ (κ : ι → Sort _) (f : ι → α) : (⨆ (i) (j : κ i), f i) ≤ ⨆ i, f i :=
-  supᵢ₂_le fun i j => le_supᵢ f i
-#align supr₂_le_supr supᵢ₂_le_supᵢ
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (κ : ι -> Sort.{u3}) (f : ι -> α), LE.le.{u2} α (Preorder.toLE.{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) => iSup.{u2, u3} α (CompleteLattice.toSupSet.{u2} α _inst_1) (κ i) (fun (j : κ i) => f i))) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))
+Case conversion may be inaccurate. Consider using '#align supr₂_le_supr iSup₂_le_iSupₓ'. -/
+theorem iSup₂_le_iSup (κ : ι → Sort _) (f : ι → α) : (⨆ (i) (j : κ i), f i) ≤ ⨆ i, f i :=
+  iSup₂_le fun i j => le_iSup f i
+#align supr₂_le_supr iSup₂_le_iSup
 
-/- warning: infi_le_infi₂ -> infᵢ_le_infᵢ₂ is a dubious translation:
+/- warning: infi_le_infi₂ -> iInf_le_iInf₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (κ : ι -> Sort.{u3}) (f : ι -> α), LE.le.{u1} α (Preorder.toLE.{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} 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)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (κ : ι -> Sort.{u3}) (f : ι -> α), LE.le.{u1} α (Preorder.toLE.{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} 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)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (κ : ι -> Sort.{u3}) (f : ι -> α), LE.le.{u2} α (Preorder.toLE.{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} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => infᵢ.{u2, u3} α (CompleteLattice.toInfSet.{u2} α _inst_1) (κ i) (fun (j : κ i) => f i)))
-Case conversion may be inaccurate. Consider using '#align infi_le_infi₂ infᵢ_le_infᵢ₂ₓ'. -/
-theorem infᵢ_le_infᵢ₂ (κ : ι → Sort _) (f : ι → α) : (⨅ i, f i) ≤ ⨅ (i) (j : κ i), f i :=
-  le_infᵢ₂ fun i j => infᵢ_le f i
-#align infi_le_infi₂ infᵢ_le_infᵢ₂
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (κ : ι -> Sort.{u3}) (f : ι -> α), LE.le.{u2} α (Preorder.toLE.{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} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => iInf.{u2, u3} α (CompleteLattice.toInfSet.{u2} α _inst_1) (κ i) (fun (j : κ i) => f i)))
+Case conversion may be inaccurate. Consider using '#align infi_le_infi₂ iInf_le_iInf₂ₓ'. -/
+theorem iInf_le_iInf₂ (κ : ι → Sort _) (f : ι → α) : (⨅ i, f i) ≤ ⨅ (i) (j : κ i), f i :=
+  le_iInf₂ fun i j => iInf_le f i
+#align infi_le_infi₂ iInf_le_iInf₂
 
-/- warning: supr_mono -> supᵢ_mono is a dubious translation:
+/- warning: supr_mono -> iSup_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (g i)) -> (LE.le.{u1} α (Preorder.toLE.{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 f) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι g))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (g i)) -> (LE.le.{u1} α (Preorder.toLE.{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 f) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι g))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (g i)) -> (LE.le.{u2} α (Preorder.toLE.{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 f) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι g))
-Case conversion may be inaccurate. Consider using '#align supr_mono supᵢ_monoₓ'. -/
-theorem supᵢ_mono (h : ∀ i, f i ≤ g i) : supᵢ f ≤ supᵢ g :=
-  supᵢ_le fun i => le_supᵢ_of_le i <| h i
-#align supr_mono supᵢ_mono
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (g i)) -> (LE.le.{u2} α (Preorder.toLE.{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 f) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι g))
+Case conversion may be inaccurate. Consider using '#align supr_mono iSup_monoₓ'. -/
+theorem iSup_mono (h : ∀ i, f i ≤ g i) : iSup f ≤ iSup g :=
+  iSup_le fun i => le_iSup_of_le i <| h i
+#align supr_mono iSup_mono
 
-/- warning: infi_mono -> infᵢ_mono is a dubious translation:
+/- warning: infi_mono -> iInf_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (g i)) -> (LE.le.{u1} α (Preorder.toLE.{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 f) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι g))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (g i)) -> (LE.le.{u1} α (Preorder.toLE.{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 f) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι g))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (g i)) -> (LE.le.{u2} α (Preorder.toLE.{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 f) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι g))
-Case conversion may be inaccurate. Consider using '#align infi_mono infᵢ_monoₓ'. -/
-theorem infᵢ_mono (h : ∀ i, f i ≤ g i) : infᵢ f ≤ infᵢ g :=
-  le_infᵢ fun i => infᵢ_le_of_le i <| h i
-#align infi_mono infᵢ_mono
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (g i)) -> (LE.le.{u2} α (Preorder.toLE.{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 f) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι g))
+Case conversion may be inaccurate. Consider using '#align infi_mono iInf_monoₓ'. -/
+theorem iInf_mono (h : ∀ i, f i ≤ g i) : iInf f ≤ iInf g :=
+  le_iInf fun i => iInf_le_of_le i <| h i
+#align infi_mono iInf_mono
 
-/- warning: supr₂_mono -> supᵢ₂_mono is a dubious translation:
+/- warning: supr₂_mono -> iSup₂_mono 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} {g : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) (g i j)) -> (LE.le.{u1} α (Preorder.toLE.{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} 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) => g 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} {g : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) (g i j)) -> (LE.le.{u1} α (Preorder.toLE.{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} 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) => g 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} {g : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) (g i j)) -> (LE.le.{u3} α (Preorder.toLE.{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} 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) => g i j))))
-Case conversion may be inaccurate. Consider using '#align supr₂_mono supᵢ₂_monoₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {f : forall (i : ι), (κ i) -> α} {g : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) (g i j)) -> (LE.le.{u3} α (Preorder.toLE.{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} 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) => g i j))))
+Case conversion may be inaccurate. Consider using '#align supr₂_mono iSup₂_monoₓ'. -/
 /- ./././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) -/
-theorem supᵢ₂_mono {f g : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ g i j) :
+theorem iSup₂_mono {f g : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ g i j) :
     (⨆ (i) (j), f i j) ≤ ⨆ (i) (j), g i j :=
-  supᵢ_mono fun i => supᵢ_mono <| h i
-#align supr₂_mono supᵢ₂_mono
+  iSup_mono fun i => iSup_mono <| h i
+#align supr₂_mono iSup₂_mono
 
-/- warning: infi₂_mono -> infᵢ₂_mono is a dubious translation:
+/- warning: infi₂_mono -> iInf₂_mono 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} {g : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) (g i j)) -> (LE.le.{u1} α (Preorder.toLE.{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} 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) => g 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} {g : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) (g i j)) -> (LE.le.{u1} α (Preorder.toLE.{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} 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) => g 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} {g : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) (g i j)) -> (LE.le.{u3} α (Preorder.toLE.{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} 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) => g i j))))
-Case conversion may be inaccurate. Consider using '#align infi₂_mono infᵢ₂_monoₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {f : forall (i : ι), (κ i) -> α} {g : forall (i : ι), (κ i) -> α}, (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) (g i j)) -> (LE.le.{u3} α (Preorder.toLE.{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} 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) => g i j))))
+Case conversion may be inaccurate. Consider using '#align infi₂_mono iInf₂_monoₓ'. -/
 /- ./././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) -/
-theorem infᵢ₂_mono {f g : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ g i j) :
+theorem iInf₂_mono {f g : ∀ i, κ i → α} (h : ∀ i j, f i j ≤ g i j) :
     (⨅ (i) (j), f i j) ≤ ⨅ (i) (j), g i j :=
-  infᵢ_mono fun i => infᵢ_mono <| h i
-#align infi₂_mono infᵢ₂_mono
+  iInf_mono fun i => iInf_mono <| h i
+#align infi₂_mono iInf₂_mono
 
-/- warning: supr_mono' -> supᵢ_mono' is a dubious translation:
+/- warning: supr_mono' -> iSup_mono' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι' -> α}, (forall (i : ι), Exists.{u3} ι' (fun (i' : ι') => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (g i'))) -> (LE.le.{u1} α (Preorder.toLE.{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 f) (supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' g))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι' -> α}, (forall (i : ι), Exists.{u3} ι' (fun (i' : ι') => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (g i'))) -> (LE.le.{u1} α (Preorder.toLE.{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 f) (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' g))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι' -> α}, (forall (i : ι), Exists.{u3} ι' (fun (i' : ι') => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (g i'))) -> (LE.le.{u2} α (Preorder.toLE.{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 f) (supᵢ.{u2, u3} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι' g))
-Case conversion may be inaccurate. Consider using '#align supr_mono' supᵢ_mono'ₓ'. -/
-theorem supᵢ_mono' {g : ι' → α} (h : ∀ i, ∃ i', f i ≤ g i') : supᵢ f ≤ supᵢ g :=
-  supᵢ_le fun i => Exists.elim (h i) le_supᵢ_of_le
-#align supr_mono' supᵢ_mono'
+  forall {α : Type.{u2}} {ι : Sort.{u1}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι' -> α}, (forall (i : ι), Exists.{u3} ι' (fun (i' : ι') => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (g i'))) -> (LE.le.{u2} α (Preorder.toLE.{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 f) (iSup.{u2, u3} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι' g))
+Case conversion may be inaccurate. Consider using '#align supr_mono' iSup_mono'ₓ'. -/
+theorem iSup_mono' {g : ι' → α} (h : ∀ i, ∃ i', f i ≤ g i') : iSup f ≤ iSup g :=
+  iSup_le fun i => Exists.elim (h i) le_iSup_of_le
+#align supr_mono' iSup_mono'
 
-/- warning: infi_mono' -> infᵢ_mono' is a dubious translation:
+/- warning: infi_mono' -> iInf_mono' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι' -> α}, (forall (i' : ι'), Exists.{u2} ι (fun (i : ι) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (g i'))) -> (LE.le.{u1} α (Preorder.toLE.{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 f) (infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' g))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι' -> α}, (forall (i' : ι'), Exists.{u2} ι (fun (i : ι) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) (g i'))) -> (LE.le.{u1} α (Preorder.toLE.{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 f) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' g))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u3}} {ι' : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι' -> α}, (forall (i' : ι'), Exists.{u3} ι (fun (i : ι) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (g i'))) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (infᵢ.{u2, u3} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι f) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι' g))
-Case conversion may be inaccurate. Consider using '#align infi_mono' infᵢ_mono'ₓ'. -/
-theorem infᵢ_mono' {g : ι' → α} (h : ∀ i', ∃ i, f i ≤ g i') : infᵢ f ≤ infᵢ g :=
-  le_infᵢ fun i' => Exists.elim (h i') infᵢ_le_of_le
-#align infi_mono' infᵢ_mono'
+  forall {α : Type.{u2}} {ι : Sort.{u3}} {ι' : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι' -> α}, (forall (i' : ι'), Exists.{u3} ι (fun (i : ι) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) (g i'))) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (iInf.{u2, u3} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι f) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι' g))
+Case conversion may be inaccurate. Consider using '#align infi_mono' iInf_mono'ₓ'. -/
+theorem iInf_mono' {g : ι' → α} (h : ∀ i', ∃ i, f i ≤ g i') : iInf f ≤ iInf g :=
+  le_iInf fun i' => Exists.elim (h i') iInf_le_of_le
+#align infi_mono' iInf_mono'
 
-/- warning: supr₂_mono' -> supᵢ₂_mono' is a dubious translation:
+/- warning: supr₂_mono' -> iSup₂_mono' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} {κ : ι -> Sort.{u4}} {κ' : ι' -> Sort.{u5}} [_inst_1 : CompleteLattice.{u1} α] {f : forall (i : ι), (κ i) -> α} {g : forall (i' : ι'), (κ' i') -> α}, (forall (i : ι) (j : κ i), Exists.{u3} ι' (fun (i' : ι') => Exists.{u5} (κ' i') (fun (j' : κ' i') => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) (g i' j')))) -> (LE.le.{u1} α (Preorder.toLE.{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, u4} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ i) (fun (j : κ i) => f i j))) (supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' (fun (i : ι') => supᵢ.{u1, u5} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ' i) (fun (j : κ' i) => g i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} {κ : ι -> Sort.{u4}} {κ' : ι' -> Sort.{u5}} [_inst_1 : CompleteLattice.{u1} α] {f : forall (i : ι), (κ i) -> α} {g : forall (i' : ι'), (κ' i') -> α}, (forall (i : ι) (j : κ i), Exists.{u3} ι' (fun (i' : ι') => Exists.{u5} (κ' i') (fun (j' : κ' i') => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) (g i' j')))) -> (LE.le.{u1} α (Preorder.toLE.{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, u4} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ i) (fun (j : κ i) => f i j))) (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' (fun (i : ι') => iSup.{u1, u5} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ' i) (fun (j : κ' i) => g i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {ι' : Sort.{u5}} {κ : ι -> Sort.{u1}} {κ' : ι' -> Sort.{u4}} [_inst_1 : CompleteLattice.{u3} α] {f : forall (i : ι), (κ i) -> α} {g : forall (i' : ι'), (κ' i') -> α}, (forall (i : ι) (j : κ i), Exists.{u5} ι' (fun (i' : ι') => Exists.{u4} (κ' i') (fun (j' : κ' i') => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) (g i' j')))) -> (LE.le.{u3} α (Preorder.toLE.{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, u5} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι' (fun (i : ι') => supᵢ.{u3, u4} α (CompleteLattice.toSupSet.{u3} α _inst_1) (κ' i) (fun (j : κ' i) => g i j))))
-Case conversion may be inaccurate. Consider using '#align supr₂_mono' supᵢ₂_mono'ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {ι' : Sort.{u5}} {κ : ι -> Sort.{u1}} {κ' : ι' -> Sort.{u4}} [_inst_1 : CompleteLattice.{u3} α] {f : forall (i : ι), (κ i) -> α} {g : forall (i' : ι'), (κ' i') -> α}, (forall (i : ι) (j : κ i), Exists.{u5} ι' (fun (i' : ι') => Exists.{u4} (κ' i') (fun (j' : κ' i') => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) (g i' j')))) -> (LE.le.{u3} α (Preorder.toLE.{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, u5} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι' (fun (i : ι') => iSup.{u3, u4} α (CompleteLattice.toSupSet.{u3} α _inst_1) (κ' i) (fun (j : κ' i) => g i j))))
+Case conversion may be inaccurate. Consider using '#align supr₂_mono' iSup₂_mono'ₓ'. -/
 /- ./././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) -/
-theorem supᵢ₂_mono' {f : ∀ i, κ i → α} {g : ∀ i', κ' i' → α} (h : ∀ i j, ∃ i' j', f i j ≤ g i' j') :
+theorem iSup₂_mono' {f : ∀ i, κ i → α} {g : ∀ i', κ' i' → α} (h : ∀ i j, ∃ i' j', f i j ≤ g i' j') :
     (⨆ (i) (j), f i j) ≤ ⨆ (i) (j), g i j :=
-  supᵢ₂_le fun i j =>
+  iSup₂_le fun i j =>
     let ⟨i', j', h⟩ := h i j
-    le_supᵢ₂_of_le i' j' h
-#align supr₂_mono' supᵢ₂_mono'
+    le_iSup₂_of_le i' j' h
+#align supr₂_mono' iSup₂_mono'
 
-/- warning: infi₂_mono' -> infᵢ₂_mono' is a dubious translation:
+/- warning: infi₂_mono' -> iInf₂_mono' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} {κ : ι -> Sort.{u4}} {κ' : ι' -> Sort.{u5}} [_inst_1 : CompleteLattice.{u1} α] {f : forall (i : ι), (κ i) -> α} {g : forall (i' : ι'), (κ' i') -> α}, (forall (i : ι') (j : κ' i), Exists.{u2} ι (fun (i' : ι) => Exists.{u4} (κ i') (fun (j' : κ i') => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i' j') (g i j)))) -> (LE.le.{u1} α (Preorder.toLE.{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, u4} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ i) (fun (j : κ i) => f i j))) (infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (i : ι') => infᵢ.{u1, u5} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ' i) (fun (j : κ' i) => g i j))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} {κ : ι -> Sort.{u4}} {κ' : ι' -> Sort.{u5}} [_inst_1 : CompleteLattice.{u1} α] {f : forall (i : ι), (κ i) -> α} {g : forall (i' : ι'), (κ' i') -> α}, (forall (i : ι') (j : κ' i), Exists.{u2} ι (fun (i' : ι) => Exists.{u4} (κ i') (fun (j' : κ i') => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i' j') (g i j)))) -> (LE.le.{u1} α (Preorder.toLE.{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, u4} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ i) (fun (j : κ i) => f i j))) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (i : ι') => iInf.{u1, u5} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ' i) (fun (j : κ' i) => g i j))))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u5}} {ι' : Sort.{u2}} {κ : ι -> Sort.{u4}} {κ' : ι' -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {f : forall (i : ι), (κ i) -> α} {g : forall (i' : ι'), (κ' i') -> α}, (forall (i : ι') (j : κ' i), Exists.{u5} ι (fun (i' : ι) => Exists.{u4} (κ i') (fun (j' : κ i') => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i' j') (g i j)))) -> (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (infᵢ.{u3, u5} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => infᵢ.{u3, u4} α (CompleteLattice.toInfSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j))) (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) => g i j))))
-Case conversion may be inaccurate. Consider using '#align infi₂_mono' infᵢ₂_mono'ₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u5}} {ι' : Sort.{u2}} {κ : ι -> Sort.{u4}} {κ' : ι' -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {f : forall (i : ι), (κ i) -> α} {g : forall (i' : ι'), (κ' i') -> α}, (forall (i : ι') (j : κ' i), Exists.{u5} ι (fun (i' : ι) => Exists.{u4} (κ i') (fun (j' : κ i') => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i' j') (g i j)))) -> (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (iInf.{u3, u5} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => iInf.{u3, u4} α (CompleteLattice.toInfSet.{u3} α _inst_1) (κ i) (fun (j : κ i) => f i j))) (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) => g i j))))
+Case conversion may be inaccurate. Consider using '#align infi₂_mono' iInf₂_mono'ₓ'. -/
 /- ./././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) -/
-theorem infᵢ₂_mono' {f : ∀ i, κ i → α} {g : ∀ i', κ' i' → α} (h : ∀ i j, ∃ i' j', f i' j' ≤ g i j) :
+theorem iInf₂_mono' {f : ∀ i, κ i → α} {g : ∀ i', κ' i' → α} (h : ∀ i j, ∃ i' j', f i' j' ≤ g i j) :
     (⨅ (i) (j), f i j) ≤ ⨅ (i) (j), g i j :=
-  le_infᵢ₂ fun i j =>
+  le_iInf₂ fun i j =>
     let ⟨i', j', h⟩ := h i j
-    infᵢ₂_le_of_le i' j' h
-#align infi₂_mono' infᵢ₂_mono'
+    iInf₂_le_of_le i' j' h
+#align infi₂_mono' iInf₂_mono'
 
-/- warning: supr_const_mono -> supᵢ_const_mono is a dubious translation:
+/- warning: supr_const_mono -> iSup_const_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α}, (ι -> ι') -> (LE.le.{u1} α (Preorder.toLE.{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) => a)) (supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' (fun (j : ι') => a)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α}, (ι -> ι') -> (LE.le.{u1} α (Preorder.toLE.{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) => a)) (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' (fun (j : ι') => a)))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α}, (ι -> ι') -> (LE.le.{u3} α (Preorder.toLE.{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) => a)) (supᵢ.{u3, u1} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι' (fun (j : ι') => a)))
-Case conversion may be inaccurate. Consider using '#align supr_const_mono supᵢ_const_monoₓ'. -/
-theorem supᵢ_const_mono (h : ι → ι') : (⨆ i : ι, a) ≤ ⨆ j : ι', a :=
-  supᵢ_le <| le_supᵢ _ ∘ h
-#align supr_const_mono supᵢ_const_mono
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α}, (ι -> ι') -> (LE.le.{u3} α (Preorder.toLE.{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) => a)) (iSup.{u3, u1} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι' (fun (j : ι') => a)))
+Case conversion may be inaccurate. Consider using '#align supr_const_mono iSup_const_monoₓ'. -/
+theorem iSup_const_mono (h : ι → ι') : (⨆ i : ι, a) ≤ ⨆ j : ι', a :=
+  iSup_le <| le_iSup _ ∘ h
+#align supr_const_mono iSup_const_mono
 
-/- warning: infi_const_mono -> infᵢ_const_mono is a dubious translation:
+/- warning: infi_const_mono -> iInf_const_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α}, (ι' -> ι) -> (LE.le.{u1} α (Preorder.toLE.{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) => a)) (infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (j : ι') => a)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α}, (ι' -> ι) -> (LE.le.{u1} α (Preorder.toLE.{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) => a)) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (j : ι') => a)))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α}, (ι' -> ι) -> (LE.le.{u3} α (Preorder.toLE.{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) => a)) (infᵢ.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι' (fun (j : ι') => a)))
-Case conversion may be inaccurate. Consider using '#align infi_const_mono infᵢ_const_monoₓ'. -/
-theorem infᵢ_const_mono (h : ι' → ι) : (⨅ i : ι, a) ≤ ⨅ j : ι', a :=
-  le_infᵢ <| infᵢ_le _ ∘ h
-#align infi_const_mono infᵢ_const_mono
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α}, (ι' -> ι) -> (LE.le.{u3} α (Preorder.toLE.{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) => a)) (iInf.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι' (fun (j : ι') => a)))
+Case conversion may be inaccurate. Consider using '#align infi_const_mono iInf_const_monoₓ'. -/
+theorem iInf_const_mono (h : ι' → ι) : (⨅ i : ι, a) ≤ ⨅ j : ι', a :=
+  le_iInf <| iInf_le _ ∘ h
+#align infi_const_mono iInf_const_mono
 
-/- warning: supr_infi_le_infi_supr -> supᵢ_infᵢ_le_infᵢ_supᵢ is a dubious translation:
+/- warning: supr_infi_le_infi_supr -> iSup_iInf_le_iInf_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> ι' -> α), LE.le.{u1} α (Preorder.toLE.{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) => infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (j : ι') => f i j))) (infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (j : ι') => supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i j)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> ι' -> α), LE.le.{u1} α (Preorder.toLE.{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) => iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (j : ι') => f i j))) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (j : ι') => iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i j)))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] (f : ι -> ι' -> α), LE.le.{u3} α (Preorder.toLE.{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) => infᵢ.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι' (fun (j : ι') => f i j))) (infᵢ.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι' (fun (j : ι') => supᵢ.{u3, u2} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => f i j)))
-Case conversion may be inaccurate. Consider using '#align supr_infi_le_infi_supr supᵢ_infᵢ_le_infᵢ_supᵢₓ'. -/
-theorem supᵢ_infᵢ_le_infᵢ_supᵢ (f : ι → ι' → α) : (⨆ i, ⨅ j, f i j) ≤ ⨅ j, ⨆ i, f i j :=
-  supᵢ_le fun i => infᵢ_mono fun j => le_supᵢ _ i
-#align supr_infi_le_infi_supr supᵢ_infᵢ_le_infᵢ_supᵢ
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] (f : ι -> ι' -> α), LE.le.{u3} α (Preorder.toLE.{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) => iInf.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι' (fun (j : ι') => f i j))) (iInf.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι' (fun (j : ι') => iSup.{u3, u2} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => f i j)))
+Case conversion may be inaccurate. Consider using '#align supr_infi_le_infi_supr iSup_iInf_le_iInf_iSupₓ'. -/
+theorem iSup_iInf_le_iInf_iSup (f : ι → ι' → α) : (⨆ i, ⨅ j, f i j) ≤ ⨅ j, ⨆ i, f i j :=
+  iSup_le fun i => iInf_mono fun j => le_iSup _ i
+#align supr_infi_le_infi_supr iSup_iInf_le_iInf_iSup
 
-/- warning: bsupr_mono -> bsupᵢ_mono is a dubious translation:
+/- warning: bsupr_mono -> biSup_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {p : ι -> Prop} {q : ι -> Prop}, (forall (i : ι), (p i) -> (q i)) -> (LE.le.{u1} α (Preorder.toLE.{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, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (q i) (fun (h : q i) => f i))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {p : ι -> Prop} {q : ι -> Prop}, (forall (i : ι), (p i) -> (q i)) -> (LE.le.{u1} α (Preorder.toLE.{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, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (q i) (fun (h : q i) => f i))))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {p : ι -> Prop} {q : ι -> Prop}, (forall (i : ι), (p i) -> (q i)) -> (LE.le.{u2} α (Preorder.toLE.{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) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (q i) (fun (h : q i) => f i))))
-Case conversion may be inaccurate. Consider using '#align bsupr_mono bsupᵢ_monoₓ'. -/
-theorem bsupᵢ_mono {p q : ι → Prop} (hpq : ∀ i, p i → q i) :
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {p : ι -> Prop} {q : ι -> Prop}, (forall (i : ι), (p i) -> (q i)) -> (LE.le.{u2} α (Preorder.toLE.{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) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (q i) (fun (h : q i) => f i))))
+Case conversion may be inaccurate. Consider using '#align bsupr_mono biSup_monoₓ'. -/
+theorem biSup_mono {p q : ι → Prop} (hpq : ∀ i, p i → q i) :
     (⨆ (i) (h : p i), f i) ≤ ⨆ (i) (h : q i), f i :=
-  supᵢ_mono fun i => supᵢ_const_mono (hpq i)
-#align bsupr_mono bsupᵢ_mono
+  iSup_mono fun i => iSup_const_mono (hpq i)
+#align bsupr_mono biSup_mono
 
-/- warning: binfi_mono -> binfᵢ_mono is a dubious translation:
+/- warning: binfi_mono -> biInf_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {p : ι -> Prop} {q : ι -> Prop}, (forall (i : ι), (p i) -> (q i)) -> (LE.le.{u1} α (Preorder.toLE.{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, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (q i) (fun (h : q i) => f i))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {p : ι -> Prop} {q : ι -> Prop}, (forall (i : ι), (p i) -> (q i)) -> (LE.le.{u1} α (Preorder.toLE.{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, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (q i) (fun (h : q i) => f i))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {p : ι -> Prop} {q : ι -> Prop}, (forall (i : ι), (p i) -> (q i)) -> (LE.le.{u2} α (Preorder.toLE.{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) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (q i) (fun (h : q i) => f i))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))))
-Case conversion may be inaccurate. Consider using '#align binfi_mono binfᵢ_monoₓ'. -/
-theorem binfᵢ_mono {p q : ι → Prop} (hpq : ∀ i, p i → q i) :
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {p : ι -> Prop} {q : ι -> Prop}, (forall (i : ι), (p i) -> (q i)) -> (LE.le.{u2} α (Preorder.toLE.{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) => iInf.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (q i) (fun (h : q i) => f i))) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => iInf.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))))
+Case conversion may be inaccurate. Consider using '#align binfi_mono biInf_monoₓ'. -/
+theorem biInf_mono {p q : ι → Prop} (hpq : ∀ i, p i → q i) :
     (⨅ (i) (h : q i), f i) ≤ ⨅ (i) (h : p i), f i :=
-  infᵢ_mono fun i => infᵢ_const_mono (hpq i)
-#align binfi_mono binfᵢ_mono
+  iInf_mono fun i => iInf_const_mono (hpq i)
+#align binfi_mono biInf_mono
 
-/- warning: supr_le_iff -> supᵢ_le_iff is a dubious translation:
+/- warning: supr_le_iff -> iSup_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{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 f) a) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{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 f) a) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) a)
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, Iff (LE.le.{u2} α (Preorder.toLE.{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 f) a) (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) a)
-Case conversion may be inaccurate. Consider using '#align supr_le_iff supᵢ_le_iffₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, Iff (LE.le.{u2} α (Preorder.toLE.{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 f) a) (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) a)
+Case conversion may be inaccurate. Consider using '#align supr_le_iff iSup_le_iffₓ'. -/
 @[simp]
-theorem supᵢ_le_iff : supᵢ f ≤ a ↔ ∀ i, f i ≤ a :=
-  (isLUB_le_iff isLUB_supᵢ).trans forall_range_iff
-#align supr_le_iff supᵢ_le_iff
+theorem iSup_le_iff : iSup f ≤ a ↔ ∀ i, f i ≤ a :=
+  (isLUB_le_iff isLUB_iSup).trans forall_range_iff
+#align supr_le_iff iSup_le_iff
 
-/- warning: le_infi_iff -> le_infᵢ_iff is a dubious translation:
+/- warning: le_infi_iff -> le_iInf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, Iff (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι f)) (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (f i))
-Case conversion may be inaccurate. Consider using '#align le_infi_iff le_infᵢ_iffₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, Iff (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι f)) (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (f i))
+Case conversion may be inaccurate. Consider using '#align le_infi_iff le_iInf_iffₓ'. -/
 @[simp]
-theorem le_infᵢ_iff : a ≤ infᵢ f ↔ ∀ i, a ≤ f i :=
-  (le_isGLB_iff isGLB_infᵢ).trans forall_range_iff
-#align le_infi_iff le_infᵢ_iff
+theorem le_iInf_iff : a ≤ iInf f ↔ ∀ i, a ≤ f i :=
+  (le_isGLB_iff isGLB_iInf).trans forall_range_iff
+#align le_infi_iff le_iInf_iff
 
-/- warning: supr₂_le_iff -> supᵢ₂_le_iff is a dubious translation:
+/- warning: supr₂_le_iff -> iSup₂_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α}, Iff (LE.le.{u1} α (Preorder.toLE.{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))) a) (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α}, Iff (LE.le.{u1} α (Preorder.toLE.{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))) a) (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i j) a)
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α}, Iff (LE.le.{u3} α (Preorder.toLE.{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))) a) (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) a)
-Case conversion may be inaccurate. Consider using '#align supr₂_le_iff supᵢ₂_le_iffₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α}, Iff (LE.le.{u3} α (Preorder.toLE.{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))) a) (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) (f i j) a)
+Case conversion may be inaccurate. Consider using '#align supr₂_le_iff iSup₂_le_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
-theorem supᵢ₂_le_iff {f : ∀ i, κ i → α} : (⨆ (i) (j), f i j) ≤ a ↔ ∀ i j, f i j ≤ a := by
-  simp_rw [supᵢ_le_iff]
-#align supr₂_le_iff supᵢ₂_le_iff
+theorem iSup₂_le_iff {f : ∀ i, κ i → α} : (⨆ (i) (j), f i j) ≤ a ↔ ∀ i j, f i j ≤ a := by
+  simp_rw [iSup_le_iff]
+#align supr₂_le_iff iSup₂_le_iff
 
-/- warning: le_infi₂_iff -> le_infᵢ₂_iff is a dubious translation:
+/- warning: le_infi₂_iff -> le_iInf₂_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (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)))) (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (f i j))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {f : forall (i : ι), (κ i) -> α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (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)))) (forall (i : ι) (j : κ i), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α}, Iff (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (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)))) (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (f i j))
-Case conversion may be inaccurate. Consider using '#align le_infi₂_iff le_infᵢ₂_iffₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {a : α} {f : forall (i : ι), (κ i) -> α}, Iff (LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (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)))) (forall (i : ι) (j : κ i), LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1)))) a (f i j))
+Case conversion may be inaccurate. Consider using '#align le_infi₂_iff le_iInf₂_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
-theorem le_infᵢ₂_iff {f : ∀ i, κ i → α} : (a ≤ ⨅ (i) (j), f i j) ↔ ∀ i j, a ≤ f i j := by
-  simp_rw [le_infᵢ_iff]
-#align le_infi₂_iff le_infᵢ₂_iff
+theorem le_iInf₂_iff {f : ∀ i, κ i → α} : (a ≤ ⨅ (i) (j), f i j) ↔ ∀ i j, a ≤ f i j := by
+  simp_rw [le_iInf_iff]
+#align le_infi₂_iff le_iInf₂_iff
 
-/- warning: supr_lt_iff -> supᵢ_lt_iff is a dubious translation:
+/- warning: supr_lt_iff -> iSup_lt_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{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 f) a) (Exists.{succ u1} α (fun (b : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b a) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) b)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{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 f) a) (Exists.{succ u1} α (fun (b : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b a) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) b)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, Iff (LT.lt.{u2} α (Preorder.toLT.{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 f) a) (Exists.{succ u2} α (fun (b : α) => And (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) b a) (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) b)))
-Case conversion may be inaccurate. Consider using '#align supr_lt_iff supᵢ_lt_iffₓ'. -/
-theorem supᵢ_lt_iff : supᵢ f < a ↔ ∃ b, b < a ∧ ∀ i, f i ≤ b :=
-  ⟨fun h => ⟨supᵢ f, h, le_supᵢ f⟩, fun ⟨b, h, hb⟩ => (supᵢ_le hb).trans_lt h⟩
-#align supr_lt_iff supᵢ_lt_iff
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, Iff (LT.lt.{u2} α (Preorder.toLT.{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 f) a) (Exists.{succ u2} α (fun (b : α) => And (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) b a) (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) b)))
+Case conversion may be inaccurate. Consider using '#align supr_lt_iff iSup_lt_iffₓ'. -/
+theorem iSup_lt_iff : iSup f < a ↔ ∃ b, b < a ∧ ∀ i, f i ≤ b :=
+  ⟨fun h => ⟨iSup f, h, le_iSup f⟩, fun ⟨b, h, hb⟩ => (iSup_le hb).trans_lt h⟩
+#align supr_lt_iff iSup_lt_iff
 
-/- warning: lt_infi_iff -> lt_infᵢ_iff is a dubious translation:
+/- warning: lt_infi_iff -> lt_iInf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι f)) (Exists.{succ u1} α (fun (b : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b (f i))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {a : α}, Iff (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι f)) (Exists.{succ u1} α (fun (b : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a b) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b (f i))))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι f)) (Exists.{succ u2} α (fun (b : α) => And (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a b) (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) b (f i))))
-Case conversion may be inaccurate. Consider using '#align lt_infi_iff lt_infᵢ_iffₓ'. -/
-theorem lt_infᵢ_iff : a < infᵢ f ↔ ∃ b, a < b ∧ ∀ i, b ≤ f i :=
-  ⟨fun h => ⟨infᵢ f, h, infᵢ_le f⟩, fun ⟨b, h, hb⟩ => h.trans_le <| le_infᵢ hb⟩
-#align lt_infi_iff lt_infᵢ_iff
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {a : α}, Iff (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι f)) (Exists.{succ u2} α (fun (b : α) => And (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a b) (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) b (f i))))
+Case conversion may be inaccurate. Consider using '#align lt_infi_iff lt_iInf_iffₓ'. -/
+theorem lt_iInf_iff : a < iInf f ↔ ∃ b, a < b ∧ ∀ i, b ≤ f i :=
+  ⟨fun h => ⟨iInf f, h, iInf_le f⟩, fun ⟨b, h, hb⟩ => h.trans_le <| le_iInf hb⟩
+#align lt_infi_iff lt_iInf_iff
 
-/- warning: Sup_eq_supr -> supₛ_eq_supᵢ is a dubious translation:
+/- warning: Sup_eq_supr -> sSup_eq_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) (supᵢ.{u1, succ u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) α (fun (a : α) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{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) => a)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) (iSup.{u1, succ u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) α (fun (a : α) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{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) => a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) (supᵢ.{u1, succ u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) α (fun (a : α) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{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) => a)))
-Case conversion may be inaccurate. Consider using '#align Sup_eq_supr supₛ_eq_supᵢₓ'. -/
-theorem supₛ_eq_supᵢ {s : Set α} : supₛ s = ⨆ a ∈ s, a :=
-  le_antisymm (supₛ_le le_supᵢ₂) (supᵢ₂_le fun b => le_supₛ)
-#align Sup_eq_supr supₛ_eq_supᵢ
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) (iSup.{u1, succ u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) α (fun (a : α) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{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) => a)))
+Case conversion may be inaccurate. Consider using '#align Sup_eq_supr sSup_eq_iSupₓ'. -/
+theorem sSup_eq_iSup {s : Set α} : sSup s = ⨆ a ∈ s, a :=
+  le_antisymm (sSup_le le_iSup₂) (iSup₂_le fun b => le_sSup)
+#align Sup_eq_supr sSup_eq_iSup
 
-/- warning: Inf_eq_infi -> infₛ_eq_infᵢ is a dubious translation:
+/- warning: Inf_eq_infi -> sInf_eq_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) (infᵢ.{u1, succ u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) α (fun (a : α) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{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) => a)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) (iInf.{u1, succ u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) α (fun (a : α) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{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) => a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) (infᵢ.{u1, succ u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) α (fun (a : α) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{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) => a)))
-Case conversion may be inaccurate. Consider using '#align Inf_eq_infi infₛ_eq_infᵢₓ'. -/
-theorem infₛ_eq_infᵢ {s : Set α} : infₛ s = ⨅ a ∈ s, a :=
-  @supₛ_eq_supᵢ αᵒᵈ _ _
-#align Inf_eq_infi infₛ_eq_infᵢ
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α}, Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) (iInf.{u1, succ u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) α (fun (a : α) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{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) => a)))
+Case conversion may be inaccurate. Consider using '#align Inf_eq_infi sInf_eq_iInfₓ'. -/
+theorem sInf_eq_iInf {s : Set α} : sInf s = ⨅ a ∈ s, a :=
+  @sSup_eq_iSup αᵒᵈ _ _
+#align Inf_eq_infi sInf_eq_iInf
 
-/- warning: monotone.le_map_supr -> Monotone.le_map_supᵢ is a dubious translation:
+/- warning: monotone.le_map_supr -> Monotone.le_map_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (supᵢ.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => f (s i))) (f (supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => f (s i))) (f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι s)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u3} β] {f : α -> β}, (Monotone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))) f) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) (supᵢ.{u3, u1} β (CompleteLattice.toSupSet.{u3} β _inst_2) ι (fun (i : ι) => f (s i))) (f (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι s)))
-Case conversion may be inaccurate. Consider using '#align monotone.le_map_supr Monotone.le_map_supᵢₓ'. -/
-theorem Monotone.le_map_supᵢ [CompleteLattice β] {f : α → β} (hf : Monotone f) :
-    (⨆ i, f (s i)) ≤ f (supᵢ s) :=
-  supᵢ_le fun i => hf <| le_supᵢ _ _
-#align monotone.le_map_supr Monotone.le_map_supᵢ
+  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u3} β] {f : α -> β}, (Monotone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))) f) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) (iSup.{u3, u1} β (CompleteLattice.toSupSet.{u3} β _inst_2) ι (fun (i : ι) => f (s i))) (f (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι s)))
+Case conversion may be inaccurate. Consider using '#align monotone.le_map_supr Monotone.le_map_iSupₓ'. -/
+theorem Monotone.le_map_iSup [CompleteLattice β] {f : α → β} (hf : Monotone f) :
+    (⨆ i, f (s i)) ≤ f (iSup s) :=
+  iSup_le fun i => hf <| le_iSup _ _
+#align monotone.le_map_supr Monotone.le_map_iSup
 
-/- warning: antitone.le_map_infi -> Antitone.le_map_infᵢ is a dubious translation:
+/- warning: antitone.le_map_infi -> Antitone.le_map_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (supᵢ.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => f (s i))) (f (infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => f (s i))) (f (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι s)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u3} β] {f : α -> β}, (Antitone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))) f) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) (supᵢ.{u3, u1} β (CompleteLattice.toSupSet.{u3} β _inst_2) ι (fun (i : ι) => f (s i))) (f (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι s)))
-Case conversion may be inaccurate. Consider using '#align antitone.le_map_infi Antitone.le_map_infᵢₓ'. -/
-theorem Antitone.le_map_infᵢ [CompleteLattice β] {f : α → β} (hf : Antitone f) :
-    (⨆ i, f (s i)) ≤ f (infᵢ s) :=
-  hf.dual_left.le_map_supᵢ
-#align antitone.le_map_infi Antitone.le_map_infᵢ
+  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u3} β] {f : α -> β}, (Antitone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))) f) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) (iSup.{u3, u1} β (CompleteLattice.toSupSet.{u3} β _inst_2) ι (fun (i : ι) => f (s i))) (f (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι s)))
+Case conversion may be inaccurate. Consider using '#align antitone.le_map_infi Antitone.le_map_iInfₓ'. -/
+theorem Antitone.le_map_iInf [CompleteLattice β] {f : α → β} (hf : Antitone f) :
+    (⨆ i, f (s i)) ≤ f (iInf s) :=
+  hf.dual_left.le_map_iSup
+#align antitone.le_map_infi Antitone.le_map_iInf
 
-/- warning: monotone.le_map_supr₂ -> Monotone.le_map_supᵢ₂ is a dubious translation:
+/- warning: monotone.le_map_supr₂ -> Monotone.le_map_iSup₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (supᵢ.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => supᵢ.{u2, u4} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (κ i) (fun (j : κ i) => f (s i j)))) (f (supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, u4} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ i) (fun (j : κ i) => s i j)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => iSup.{u2, u4} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (κ i) (fun (j : κ i) => f (s i j)))) (f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, u4} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ i) (fun (j : κ i) => s i j)))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] [_inst_2 : CompleteLattice.{u4} β] {f : α -> β}, (Monotone.{u3, u4} α β (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u4} β (Preorder.toLE.{u4} β (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2)))) (supᵢ.{u4, u2} β (CompleteLattice.toSupSet.{u4} β _inst_2) ι (fun (i : ι) => supᵢ.{u4, u1} β (CompleteLattice.toSupSet.{u4} β _inst_2) (κ i) (fun (j : κ i) => f (s i j)))) (f (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) => s i j)))))
-Case conversion may be inaccurate. Consider using '#align monotone.le_map_supr₂ Monotone.le_map_supᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {β : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] [_inst_2 : CompleteLattice.{u4} β] {f : α -> β}, (Monotone.{u3, u4} α β (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u4} β (Preorder.toLE.{u4} β (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2)))) (iSup.{u4, u2} β (CompleteLattice.toSupSet.{u4} β _inst_2) ι (fun (i : ι) => iSup.{u4, u1} β (CompleteLattice.toSupSet.{u4} β _inst_2) (κ i) (fun (j : κ i) => f (s i j)))) (f (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) => s i j)))))
+Case conversion may be inaccurate. Consider using '#align monotone.le_map_supr₂ Monotone.le_map_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) -/
-theorem Monotone.le_map_supᵢ₂ [CompleteLattice β] {f : α → β} (hf : Monotone f) (s : ∀ i, κ i → α) :
+theorem Monotone.le_map_iSup₂ [CompleteLattice β] {f : α → β} (hf : Monotone f) (s : ∀ i, κ i → α) :
     (⨆ (i) (j), f (s i j)) ≤ f (⨆ (i) (j), s i j) :=
-  supᵢ₂_le fun i j => hf <| le_supᵢ₂ _ _
-#align monotone.le_map_supr₂ Monotone.le_map_supᵢ₂
+  iSup₂_le fun i j => hf <| le_iSup₂ _ _
+#align monotone.le_map_supr₂ Monotone.le_map_iSup₂
 
-/- warning: antitone.le_map_infi₂ -> Antitone.le_map_infᵢ₂ is a dubious translation:
+/- warning: antitone.le_map_infi₂ -> Antitone.le_map_iInf₂ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (supᵢ.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => supᵢ.{u2, u4} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (κ i) (fun (j : κ i) => f (s i j)))) (f (infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, u4} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ i) (fun (j : κ i) => s i j)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => iSup.{u2, u4} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (κ i) (fun (j : κ i) => f (s i j)))) (f (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, u4} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ i) (fun (j : κ i) => s i j)))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] [_inst_2 : CompleteLattice.{u4} β] {f : α -> β}, (Antitone.{u3, u4} α β (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u4} β (Preorder.toLE.{u4} β (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2)))) (supᵢ.{u4, u2} β (CompleteLattice.toSupSet.{u4} β _inst_2) ι (fun (i : ι) => supᵢ.{u4, u1} β (CompleteLattice.toSupSet.{u4} β _inst_2) (κ i) (fun (j : κ i) => f (s i j)))) (f (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) => s i j)))))
-Case conversion may be inaccurate. Consider using '#align antitone.le_map_infi₂ Antitone.le_map_infᵢ₂ₓ'. -/
+  forall {α : Type.{u3}} {β : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] [_inst_2 : CompleteLattice.{u4} β] {f : α -> β}, (Antitone.{u3, u4} α β (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u4} β (Preorder.toLE.{u4} β (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2)))) (iSup.{u4, u2} β (CompleteLattice.toSupSet.{u4} β _inst_2) ι (fun (i : ι) => iSup.{u4, u1} β (CompleteLattice.toSupSet.{u4} β _inst_2) (κ i) (fun (j : κ i) => f (s i j)))) (f (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) => s i j)))))
+Case conversion may be inaccurate. Consider using '#align antitone.le_map_infi₂ Antitone.le_map_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) -/
-theorem Antitone.le_map_infᵢ₂ [CompleteLattice β] {f : α → β} (hf : Antitone f) (s : ∀ i, κ i → α) :
+theorem Antitone.le_map_iInf₂ [CompleteLattice β] {f : α → β} (hf : Antitone f) (s : ∀ i, κ i → α) :
     (⨆ (i) (j), f (s i j)) ≤ f (⨅ (i) (j), s i j) :=
-  hf.dual_left.le_map_supᵢ₂ _
-#align antitone.le_map_infi₂ Antitone.le_map_infᵢ₂
+  hf.dual_left.le_map_iSup₂ _
+#align antitone.le_map_infi₂ Antitone.le_map_iInf₂
 
-/- warning: monotone.le_map_Sup -> Monotone.le_map_supₛ is a dubious translation:
+/- warning: monotone.le_map_Sup -> Monotone.le_map_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (supᵢ.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) α (fun (a : α) => supᵢ.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (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) => f a))) (f (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) α (fun (a : α) => iSup.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (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) => f a))) (f (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (supᵢ.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_2) α (fun (a : α) => supᵢ.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_2) (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) => f a))) (f (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)))
-Case conversion may be inaccurate. Consider using '#align monotone.le_map_Sup Monotone.le_map_supₛₓ'. -/
-theorem Monotone.le_map_supₛ [CompleteLattice β] {s : Set α} {f : α → β} (hf : Monotone f) :
-    (⨆ a ∈ s, f a) ≤ f (supₛ s) := by rw [supₛ_eq_supᵢ] <;> exact hf.le_map_supr₂ _
-#align monotone.le_map_Sup Monotone.le_map_supₛ
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_2) α (fun (a : α) => iSup.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_2) (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) => f a))) (f (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)))
+Case conversion may be inaccurate. Consider using '#align monotone.le_map_Sup Monotone.le_map_sSupₓ'. -/
+theorem Monotone.le_map_sSup [CompleteLattice β] {s : Set α} {f : α → β} (hf : Monotone f) :
+    (⨆ a ∈ s, f a) ≤ f (sSup s) := by rw [sSup_eq_iSup] <;> exact hf.le_map_supr₂ _
+#align monotone.le_map_Sup Monotone.le_map_sSup
 
-/- warning: antitone.le_map_Inf -> Antitone.le_map_infₛ is a dubious translation:
+/- warning: antitone.le_map_Inf -> Antitone.le_map_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (supᵢ.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) α (fun (a : α) => supᵢ.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (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) => f a))) (f (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) α (fun (a : α) => iSup.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (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) => f a))) (f (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (supᵢ.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_2) α (fun (a : α) => supᵢ.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_2) (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) => f a))) (f (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)))
-Case conversion may be inaccurate. Consider using '#align antitone.le_map_Inf Antitone.le_map_infₛₓ'. -/
-theorem Antitone.le_map_infₛ [CompleteLattice β] {s : Set α} {f : α → β} (hf : Antitone f) :
-    (⨆ a ∈ s, f a) ≤ f (infₛ s) :=
-  hf.dual_left.le_map_supₛ
-#align antitone.le_map_Inf Antitone.le_map_infₛ
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (iSup.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_2) α (fun (a : α) => iSup.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_2) (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) => f a))) (f (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)))
+Case conversion may be inaccurate. Consider using '#align antitone.le_map_Inf Antitone.le_map_sInfₓ'. -/
+theorem Antitone.le_map_sInf [CompleteLattice β] {s : Set α} {f : α → β} (hf : Antitone f) :
+    (⨆ a ∈ s, f a) ≤ f (sInf s) :=
+  hf.dual_left.le_map_sSup
+#align antitone.le_map_Inf Antitone.le_map_sInf
 
-/- warning: order_iso.map_supr -> OrderIso.map_supᵢ is a dubious translation:
+/- warning: order_iso.map_supr -> OrderIso.map_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (x : ι -> α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => x i))) (supᵢ.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (x i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (x : ι -> α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => x i))) (iSup.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (x i)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : CompleteLattice.{u3} β] (f : OrderIso.{u2, u3} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))))) (x : ι -> α), Eq.{succ u3} β (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => x i))) (supᵢ.{u3, u1} β (CompleteLattice.toSupSet.{u3} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (x i)))
-Case conversion may be inaccurate. Consider using '#align order_iso.map_supr OrderIso.map_supᵢₓ'. -/
-theorem OrderIso.map_supᵢ [CompleteLattice β] (f : α ≃o β) (x : ι → α) :
+  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : CompleteLattice.{u3} β] (f : OrderIso.{u2, u3} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))))) (x : ι -> α), Eq.{succ u3} β (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => x i))) (iSup.{u3, u1} β (CompleteLattice.toSupSet.{u3} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (x i)))
+Case conversion may be inaccurate. Consider using '#align order_iso.map_supr OrderIso.map_iSupₓ'. -/
+theorem OrderIso.map_iSup [CompleteLattice β] (f : α ≃o β) (x : ι → α) :
     f (⨆ i, x i) = ⨆ i, f (x i) :=
-  eq_of_forall_ge_iff <| f.Surjective.forall.2 fun x => by simp only [f.le_iff_le, supᵢ_le_iff]
-#align order_iso.map_supr OrderIso.map_supᵢ
+  eq_of_forall_ge_iff <| f.Surjective.forall.2 fun x => by simp only [f.le_iff_le, iSup_le_iff]
+#align order_iso.map_supr OrderIso.map_iSup
 
-/- warning: order_iso.map_infi -> OrderIso.map_infᵢ is a dubious translation:
+/- warning: order_iso.map_infi -> OrderIso.map_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (x : ι -> α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => x i))) (infᵢ.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (x i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (x : ι -> α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => x i))) (iInf.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (x i)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : CompleteLattice.{u3} β] (f : OrderIso.{u2, u3} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))))) (x : ι -> α), Eq.{succ u3} β (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => x i))) (infᵢ.{u3, u1} β (CompleteLattice.toInfSet.{u3} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (x i)))
-Case conversion may be inaccurate. Consider using '#align order_iso.map_infi OrderIso.map_infᵢₓ'. -/
-theorem OrderIso.map_infᵢ [CompleteLattice β] (f : α ≃o β) (x : ι → α) :
+  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : CompleteLattice.{u3} β] (f : OrderIso.{u2, u3} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))))) (x : ι -> α), Eq.{succ u3} β (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => x i))) (iInf.{u3, u1} β (CompleteLattice.toInfSet.{u3} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (x i)))
+Case conversion may be inaccurate. Consider using '#align order_iso.map_infi OrderIso.map_iInfₓ'. -/
+theorem OrderIso.map_iInf [CompleteLattice β] (f : α ≃o β) (x : ι → α) :
     f (⨅ i, x i) = ⨅ i, f (x i) :=
-  OrderIso.map_supᵢ f.dual _
-#align order_iso.map_infi OrderIso.map_infᵢ
+  OrderIso.map_iSup f.dual _
+#align order_iso.map_infi OrderIso.map_iInf
 
-/- warning: order_iso.map_Sup -> OrderIso.map_supₛ is a dubious translation:
+/- warning: order_iso.map_Sup -> OrderIso.map_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s)) (supᵢ.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) α (fun (a : α) => supᵢ.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (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) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f a)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s)) (iSup.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) α (fun (a : α) => iSup.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (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) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f a)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)) (supᵢ.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_2) α (fun (a : α) => supᵢ.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_2) (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) => 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} 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 order_iso.map_Sup OrderIso.map_supₛₓ'. -/
-theorem OrderIso.map_supₛ [CompleteLattice β] (f : α ≃o β) (s : Set α) :
-    f (supₛ s) = ⨆ a ∈ s, f a := by simp only [supₛ_eq_supᵢ, OrderIso.map_supᵢ]
-#align order_iso.map_Sup OrderIso.map_supₛ
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)) (iSup.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_2) α (fun (a : α) => iSup.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_2) (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) => 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} 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 order_iso.map_Sup OrderIso.map_sSupₓ'. -/
+theorem OrderIso.map_sSup [CompleteLattice β] (f : α ≃o β) (s : Set α) :
+    f (sSup s) = ⨆ a ∈ s, f a := by simp only [sSup_eq_iSup, OrderIso.map_iSup]
+#align order_iso.map_Sup OrderIso.map_sSup
 
-/- warning: order_iso.map_Inf -> OrderIso.map_infₛ is a dubious translation:
+/- warning: order_iso.map_Inf -> OrderIso.map_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)) (infᵢ.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) α (fun (a : α) => infᵢ.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (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) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f a)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)) (iInf.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) α (fun (a : α) => iInf.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (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) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f a)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)) (infᵢ.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_2) α (fun (a : α) => infᵢ.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_2) (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) => 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} 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 order_iso.map_Inf OrderIso.map_infₛₓ'. -/
-theorem OrderIso.map_infₛ [CompleteLattice β] (f : α ≃o β) (s : Set α) :
-    f (infₛ s) = ⨅ a ∈ s, f a :=
-  OrderIso.map_supₛ f.dual _
-#align order_iso.map_Inf OrderIso.map_infₛ
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)) (iInf.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_2) α (fun (a : α) => iInf.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_2) (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) => 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} 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 order_iso.map_Inf OrderIso.map_sInfₓ'. -/
+theorem OrderIso.map_sInf [CompleteLattice β] (f : α ≃o β) (s : Set α) :
+    f (sInf s) = ⨅ a ∈ s, f a :=
+  OrderIso.map_sSup f.dual _
+#align order_iso.map_Inf OrderIso.map_sInf
 
-/- warning: supr_comp_le -> supᵢ_comp_le is a dubious translation:
+/- warning: supr_comp_le -> iSup_comp_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {ι' : Sort.{u3}} (f : ι' -> α) (g : ι -> ι'), LE.le.{u1} α (Preorder.toLE.{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 (x : ι) => f (g x))) (supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' (fun (y : ι') => f y))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {ι' : Sort.{u3}} (f : ι' -> α) (g : ι -> ι'), LE.le.{u1} α (Preorder.toLE.{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 (x : ι) => f (g x))) (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' (fun (y : ι') => f y))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {ι' : Sort.{u3}} (f : ι' -> α) (g : ι -> ι'), LE.le.{u2} α (Preorder.toLE.{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 (x : ι) => f (g x))) (supᵢ.{u2, u3} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι' (fun (y : ι') => f y))
-Case conversion may be inaccurate. Consider using '#align supr_comp_le supᵢ_comp_leₓ'. -/
-theorem supᵢ_comp_le {ι' : Sort _} (f : ι' → α) (g : ι → ι') : (⨆ x, f (g x)) ≤ ⨆ y, f y :=
-  supᵢ_mono' fun x => ⟨_, le_rfl⟩
-#align supr_comp_le supᵢ_comp_le
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {ι' : Sort.{u3}} (f : ι' -> α) (g : ι -> ι'), LE.le.{u2} α (Preorder.toLE.{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 (x : ι) => f (g x))) (iSup.{u2, u3} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι' (fun (y : ι') => f y))
+Case conversion may be inaccurate. Consider using '#align supr_comp_le iSup_comp_leₓ'. -/
+theorem iSup_comp_le {ι' : Sort _} (f : ι' → α) (g : ι → ι') : (⨆ x, f (g x)) ≤ ⨆ y, f y :=
+  iSup_mono' fun x => ⟨_, le_rfl⟩
+#align supr_comp_le iSup_comp_le
 
-/- warning: le_infi_comp -> le_infᵢ_comp is a dubious translation:
+/- warning: le_infi_comp -> le_iInf_comp is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {ι' : Sort.{u3}} (f : ι' -> α) (g : ι -> ι'), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (y : ι') => f y)) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f (g x)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {ι' : Sort.{u3}} (f : ι' -> α) (g : ι -> ι'), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (y : ι') => f y)) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f (g x)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {ι' : Sort.{u3}} (f : ι' -> α) (g : ι -> ι'), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (infᵢ.{u2, u3} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι' (fun (y : ι') => f y)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => f (g x)))
-Case conversion may be inaccurate. Consider using '#align le_infi_comp le_infᵢ_compₓ'. -/
-theorem le_infᵢ_comp {ι' : Sort _} (f : ι' → α) (g : ι → ι') : (⨅ y, f y) ≤ ⨅ x, f (g x) :=
-  infᵢ_mono' fun x => ⟨_, le_rfl⟩
-#align le_infi_comp le_infᵢ_comp
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {ι' : Sort.{u3}} (f : ι' -> α) (g : ι -> ι'), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (iInf.{u2, u3} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι' (fun (y : ι') => f y)) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => f (g x)))
+Case conversion may be inaccurate. Consider using '#align le_infi_comp le_iInf_compₓ'. -/
+theorem le_iInf_comp {ι' : Sort _} (f : ι' → α) (g : ι → ι') : (⨅ y, f y) ≤ ⨅ x, f (g x) :=
+  iInf_mono' fun x => ⟨_, le_rfl⟩
+#align le_infi_comp le_iInf_comp
 
-/- warning: monotone.supr_comp_eq -> Monotone.supᵢ_comp_eq is a dubious translation:
+/- warning: monotone.supr_comp_eq -> Monotone.iSup_comp_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Preorder.{u2} β] {f : β -> α}, (Monotone.{u2, u1} β α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f) -> (forall {s : ι -> β}, (forall (x : β), Exists.{u3} ι (fun (i : ι) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x (s i))) -> (Eq.{succ u1} α (supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => f (s x))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (y : β) => f y))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Preorder.{u2} β] {f : β -> α}, (Monotone.{u2, u1} β α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f) -> (forall {s : ι -> β}, (forall (x : β), Exists.{u3} ι (fun (i : ι) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x (s i))) -> (Eq.{succ u1} α (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => f (s x))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (y : β) => f y))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : Preorder.{u3} β] {f : β -> α}, (Monotone.{u3, u2} β α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) f) -> (forall {s : ι -> β}, (forall (x : β), Exists.{u1} ι (fun (i : ι) => LE.le.{u3} β (Preorder.toLE.{u3} β _inst_2) x (s i))) -> (Eq.{succ u2} α (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (x : ι) => f (s x))) (supᵢ.{u2, succ u3} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (y : β) => f y))))
-Case conversion may be inaccurate. Consider using '#align monotone.supr_comp_eq Monotone.supᵢ_comp_eqₓ'. -/
-theorem Monotone.supᵢ_comp_eq [Preorder β] {f : β → α} (hf : Monotone f) {s : ι → β}
+  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : Preorder.{u3} β] {f : β -> α}, (Monotone.{u3, u2} β α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) f) -> (forall {s : ι -> β}, (forall (x : β), Exists.{u1} ι (fun (i : ι) => LE.le.{u3} β (Preorder.toLE.{u3} β _inst_2) x (s i))) -> (Eq.{succ u2} α (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (x : ι) => f (s x))) (iSup.{u2, succ u3} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (y : β) => f y))))
+Case conversion may be inaccurate. Consider using '#align monotone.supr_comp_eq Monotone.iSup_comp_eqₓ'. -/
+theorem Monotone.iSup_comp_eq [Preorder β] {f : β → α} (hf : Monotone f) {s : ι → β}
     (hs : ∀ x, ∃ i, x ≤ s i) : (⨆ x, f (s x)) = ⨆ y, f y :=
-  le_antisymm (supᵢ_comp_le _ _) (supᵢ_mono' fun x => (hs x).imp fun i hi => hf hi)
-#align monotone.supr_comp_eq Monotone.supᵢ_comp_eq
+  le_antisymm (iSup_comp_le _ _) (iSup_mono' fun x => (hs x).imp fun i hi => hf hi)
+#align monotone.supr_comp_eq Monotone.iSup_comp_eq
 
-/- warning: monotone.infi_comp_eq -> Monotone.infᵢ_comp_eq is a dubious translation:
+/- warning: monotone.infi_comp_eq -> Monotone.iInf_comp_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Preorder.{u2} β] {f : β -> α}, (Monotone.{u2, u1} β α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f) -> (forall {s : ι -> β}, (forall (x : β), Exists.{u3} ι (fun (i : ι) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (s i) x)) -> (Eq.{succ u1} α (infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f (s x))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (y : β) => f y))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Preorder.{u2} β] {f : β -> α}, (Monotone.{u2, u1} β α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f) -> (forall {s : ι -> β}, (forall (x : β), Exists.{u3} ι (fun (i : ι) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (s i) x)) -> (Eq.{succ u1} α (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f (s x))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (y : β) => f y))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : Preorder.{u3} β] {f : β -> α}, (Monotone.{u3, u2} β α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) f) -> (forall {s : ι -> β}, (forall (x : β), Exists.{u1} ι (fun (i : ι) => LE.le.{u3} β (Preorder.toLE.{u3} β _inst_2) (s i) x)) -> (Eq.{succ u2} α (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => f (s x))) (infᵢ.{u2, succ u3} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (y : β) => f y))))
-Case conversion may be inaccurate. Consider using '#align monotone.infi_comp_eq Monotone.infᵢ_comp_eqₓ'. -/
-theorem Monotone.infᵢ_comp_eq [Preorder β] {f : β → α} (hf : Monotone f) {s : ι → β}
+  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : Preorder.{u3} β] {f : β -> α}, (Monotone.{u3, u2} β α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) f) -> (forall {s : ι -> β}, (forall (x : β), Exists.{u1} ι (fun (i : ι) => LE.le.{u3} β (Preorder.toLE.{u3} β _inst_2) (s i) x)) -> (Eq.{succ u2} α (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => f (s x))) (iInf.{u2, succ u3} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (y : β) => f y))))
+Case conversion may be inaccurate. Consider using '#align monotone.infi_comp_eq Monotone.iInf_comp_eqₓ'. -/
+theorem Monotone.iInf_comp_eq [Preorder β] {f : β → α} (hf : Monotone f) {s : ι → β}
     (hs : ∀ x, ∃ i, s i ≤ x) : (⨅ x, f (s x)) = ⨅ y, f y :=
-  le_antisymm (infᵢ_mono' fun x => (hs x).imp fun i hi => hf hi) (le_infᵢ_comp _ _)
-#align monotone.infi_comp_eq Monotone.infᵢ_comp_eq
+  le_antisymm (iInf_mono' fun x => (hs x).imp fun i hi => hf hi) (le_iInf_comp _ _)
+#align monotone.infi_comp_eq Monotone.iInf_comp_eq
 
-/- warning: antitone.map_supr_le -> Antitone.map_supᵢ_le is a dubious translation:
+/- warning: antitone.map_supr_le -> Antitone.map_iSup_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι s)) (infᵢ.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => f (s i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι s)) (iInf.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => f (s i))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u3} β] {f : α -> β}, (Antitone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))) f) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) (f (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι s)) (infᵢ.{u3, u1} β (CompleteLattice.toInfSet.{u3} β _inst_2) ι (fun (i : ι) => f (s i))))
-Case conversion may be inaccurate. Consider using '#align antitone.map_supr_le Antitone.map_supᵢ_leₓ'. -/
-theorem Antitone.map_supᵢ_le [CompleteLattice β] {f : α → β} (hf : Antitone f) :
-    f (supᵢ s) ≤ ⨅ i, f (s i) :=
-  le_infᵢ fun i => hf <| le_supᵢ _ _
-#align antitone.map_supr_le Antitone.map_supᵢ_le
+  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u3} β] {f : α -> β}, (Antitone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))) f) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) (f (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι s)) (iInf.{u3, u1} β (CompleteLattice.toInfSet.{u3} β _inst_2) ι (fun (i : ι) => f (s i))))
+Case conversion may be inaccurate. Consider using '#align antitone.map_supr_le Antitone.map_iSup_leₓ'. -/
+theorem Antitone.map_iSup_le [CompleteLattice β] {f : α → β} (hf : Antitone f) :
+    f (iSup s) ≤ ⨅ i, f (s i) :=
+  le_iInf fun i => hf <| le_iSup _ _
+#align antitone.map_supr_le Antitone.map_iSup_le
 
-/- warning: monotone.map_infi_le -> Monotone.map_infᵢ_le is a dubious translation:
+/- warning: monotone.map_infi_le -> Monotone.map_iInf_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι s)) (infᵢ.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => f (s i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι s)) (iInf.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => f (s i))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u3} β] {f : α -> β}, (Monotone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))) f) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) (f (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι s)) (infᵢ.{u3, u1} β (CompleteLattice.toInfSet.{u3} β _inst_2) ι (fun (i : ι) => f (s i))))
-Case conversion may be inaccurate. Consider using '#align monotone.map_infi_le Monotone.map_infᵢ_leₓ'. -/
-theorem Monotone.map_infᵢ_le [CompleteLattice β] {f : α → β} (hf : Monotone f) :
-    f (infᵢ s) ≤ ⨅ i, f (s i) :=
-  hf.dual_left.map_supᵢ_le
-#align monotone.map_infi_le Monotone.map_infᵢ_le
+  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {s : ι -> α} [_inst_2 : CompleteLattice.{u3} β] {f : α -> β}, (Monotone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))) f) -> (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) (f (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι s)) (iInf.{u3, u1} β (CompleteLattice.toInfSet.{u3} β _inst_2) ι (fun (i : ι) => f (s i))))
+Case conversion may be inaccurate. Consider using '#align monotone.map_infi_le Monotone.map_iInf_leₓ'. -/
+theorem Monotone.map_iInf_le [CompleteLattice β] {f : α → β} (hf : Monotone f) :
+    f (iInf s) ≤ ⨅ i, f (s i) :=
+  hf.dual_left.map_iSup_le
+#align monotone.map_infi_le Monotone.map_iInf_le
 
-/- warning: antitone.map_supr₂_le -> Antitone.map_supᵢ₂_le is a dubious translation:
+/- warning: antitone.map_supr₂_le -> Antitone.map_iSup₂_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, u4} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ i) (fun (j : κ i) => s i j)))) (infᵢ.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => infᵢ.{u2, u4} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (κ i) (fun (j : κ i) => f (s i j)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, u4} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ i) (fun (j : κ i) => s i j)))) (iInf.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => iInf.{u2, u4} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (κ i) (fun (j : κ i) => f (s i j)))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] [_inst_2 : CompleteLattice.{u4} β] {f : α -> β}, (Antitone.{u3, u4} α β (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u4} β (Preorder.toLE.{u4} β (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2)))) (f (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) => s i j)))) (infᵢ.{u4, u2} β (CompleteLattice.toInfSet.{u4} β _inst_2) ι (fun (i : ι) => infᵢ.{u4, u1} β (CompleteLattice.toInfSet.{u4} β _inst_2) (κ i) (fun (j : κ i) => f (s i j)))))
-Case conversion may be inaccurate. Consider using '#align antitone.map_supr₂_le Antitone.map_supᵢ₂_leₓ'. -/
+  forall {α : Type.{u3}} {β : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] [_inst_2 : CompleteLattice.{u4} β] {f : α -> β}, (Antitone.{u3, u4} α β (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u4} β (Preorder.toLE.{u4} β (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2)))) (f (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) => s i j)))) (iInf.{u4, u2} β (CompleteLattice.toInfSet.{u4} β _inst_2) ι (fun (i : ι) => iInf.{u4, u1} β (CompleteLattice.toInfSet.{u4} β _inst_2) (κ i) (fun (j : κ i) => f (s i j)))))
+Case conversion may be inaccurate. Consider using '#align antitone.map_supr₂_le Antitone.map_iSup₂_leₓ'. -/
 /- ./././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) -/
-theorem Antitone.map_supᵢ₂_le [CompleteLattice β] {f : α → β} (hf : Antitone f) (s : ∀ i, κ i → α) :
+theorem Antitone.map_iSup₂_le [CompleteLattice β] {f : α → β} (hf : Antitone f) (s : ∀ i, κ i → α) :
     f (⨆ (i) (j), s i j) ≤ ⨅ (i) (j), f (s i j) :=
-  hf.dual.le_map_infᵢ₂ _
-#align antitone.map_supr₂_le Antitone.map_supᵢ₂_le
+  hf.dual.le_map_iInf₂ _
+#align antitone.map_supr₂_le Antitone.map_iSup₂_le
 
-/- warning: monotone.map_infi₂_le -> Monotone.map_infᵢ₂_le is a dubious translation:
+/- warning: monotone.map_infi₂_le -> Monotone.map_iInf₂_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, u4} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ i) (fun (j : κ i) => s i j)))) (infᵢ.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => infᵢ.{u2, u4} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (κ i) (fun (j : κ i) => f (s i j)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} {κ : ι -> Sort.{u4}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, u4} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ i) (fun (j : κ i) => s i j)))) (iInf.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => iInf.{u2, u4} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (κ i) (fun (j : κ i) => f (s i j)))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] [_inst_2 : CompleteLattice.{u4} β] {f : α -> β}, (Monotone.{u3, u4} α β (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u4} β (Preorder.toLE.{u4} β (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2)))) (f (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) => s i j)))) (infᵢ.{u4, u2} β (CompleteLattice.toInfSet.{u4} β _inst_2) ι (fun (i : ι) => infᵢ.{u4, u1} β (CompleteLattice.toInfSet.{u4} β _inst_2) (κ i) (fun (j : κ i) => f (s i j)))))
-Case conversion may be inaccurate. Consider using '#align monotone.map_infi₂_le Monotone.map_infᵢ₂_leₓ'. -/
+  forall {α : Type.{u3}} {β : Type.{u4}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] [_inst_2 : CompleteLattice.{u4} β] {f : α -> β}, (Monotone.{u3, u4} α β (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_1))) (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2))) f) -> (forall (s : forall (i : ι), (κ i) -> α), LE.le.{u4} β (Preorder.toLE.{u4} β (PartialOrder.toPreorder.{u4} β (CompleteSemilatticeInf.toPartialOrder.{u4} β (CompleteLattice.toCompleteSemilatticeInf.{u4} β _inst_2)))) (f (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) => s i j)))) (iInf.{u4, u2} β (CompleteLattice.toInfSet.{u4} β _inst_2) ι (fun (i : ι) => iInf.{u4, u1} β (CompleteLattice.toInfSet.{u4} β _inst_2) (κ i) (fun (j : κ i) => f (s i j)))))
+Case conversion may be inaccurate. Consider using '#align monotone.map_infi₂_le Monotone.map_iInf₂_leₓ'. -/
 /- ./././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) -/
-theorem Monotone.map_infᵢ₂_le [CompleteLattice β] {f : α → β} (hf : Monotone f) (s : ∀ i, κ i → α) :
+theorem Monotone.map_iInf₂_le [CompleteLattice β] {f : α → β} (hf : Monotone f) (s : ∀ i, κ i → α) :
     f (⨅ (i) (j), s i j) ≤ ⨅ (i) (j), f (s i j) :=
-  hf.dual.le_map_supᵢ₂ _
-#align monotone.map_infi₂_le Monotone.map_infᵢ₂_le
+  hf.dual.le_map_iSup₂ _
+#align monotone.map_infi₂_le Monotone.map_iInf₂_le
 
-/- warning: antitone.map_Sup_le -> Antitone.map_supₛ_le is a dubious translation:
+/- warning: antitone.map_Sup_le -> Antitone.map_sSup_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s)) (infᵢ.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) α (fun (a : α) => infᵢ.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (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) => f a))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s)) (iInf.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) α (fun (a : α) => iInf.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (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) => f a))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)) (infᵢ.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_2) α (fun (a : α) => infᵢ.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_2) (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) => f a))))
-Case conversion may be inaccurate. Consider using '#align antitone.map_Sup_le Antitone.map_supₛ_leₓ'. -/
-theorem Antitone.map_supₛ_le [CompleteLattice β] {s : Set α} {f : α → β} (hf : Antitone f) :
-    f (supₛ s) ≤ ⨅ a ∈ s, f a := by
-  rw [supₛ_eq_supᵢ]
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)) (iInf.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_2) α (fun (a : α) => iInf.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_2) (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) => f a))))
+Case conversion may be inaccurate. Consider using '#align antitone.map_Sup_le Antitone.map_sSup_leₓ'. -/
+theorem Antitone.map_sSup_le [CompleteLattice β] {s : Set α} {f : α → β} (hf : Antitone f) :
+    f (sSup s) ≤ ⨅ a ∈ s, f a := by
+  rw [sSup_eq_iSup]
   exact hf.map_supr₂_le _
-#align antitone.map_Sup_le Antitone.map_supₛ_le
+#align antitone.map_Sup_le Antitone.map_sSup_le
 
-/- warning: monotone.map_Inf_le -> Monotone.map_infₛ_le is a dubious translation:
+/- warning: monotone.map_Inf_le -> Monotone.map_sInf_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)) (infᵢ.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) α (fun (a : α) => infᵢ.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (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) => f a))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)) (iInf.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) α (fun (a : α) => iInf.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (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) => f a))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)) (infᵢ.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_2) α (fun (a : α) => infᵢ.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_2) (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) => f a))))
-Case conversion may be inaccurate. Consider using '#align monotone.map_Inf_le Monotone.map_infₛ_leₓ'. -/
-theorem Monotone.map_infₛ_le [CompleteLattice β] {s : Set α} {f : α → β} (hf : Monotone f) :
-    f (infₛ s) ≤ ⨅ a ∈ s, f a :=
-  hf.dual_left.map_supₛ_le
-#align monotone.map_Inf_le Monotone.map_infₛ_le
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{u1} α} {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (f (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)) (iInf.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_2) α (fun (a : α) => iInf.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_2) (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) => f a))))
+Case conversion may be inaccurate. Consider using '#align monotone.map_Inf_le Monotone.map_sInf_leₓ'. -/
+theorem Monotone.map_sInf_le [CompleteLattice β] {s : Set α} {f : α → β} (hf : Monotone f) :
+    f (sInf s) ≤ ⨅ a ∈ s, f a :=
+  hf.dual_left.map_sSup_le
+#align monotone.map_Inf_le Monotone.map_sInf_le
 
-/- warning: supr_const_le -> supᵢ_const_le is a dubious translation:
+/- warning: supr_const_le -> iSup_const_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {a : α}, LE.le.{u1} α (Preorder.toLE.{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) => a)) a
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {a : α}, LE.le.{u1} α (Preorder.toLE.{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) => a)) a
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {a : α}, LE.le.{u2} α (Preorder.toLE.{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) => a)) a
-Case conversion may be inaccurate. Consider using '#align supr_const_le supᵢ_const_leₓ'. -/
-theorem supᵢ_const_le : (⨆ i : ι, a) ≤ a :=
-  supᵢ_le fun _ => le_rfl
-#align supr_const_le supᵢ_const_le
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {a : α}, LE.le.{u2} α (Preorder.toLE.{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) => a)) a
+Case conversion may be inaccurate. Consider using '#align supr_const_le iSup_const_leₓ'. -/
+theorem iSup_const_le : (⨆ i : ι, a) ≤ a :=
+  iSup_le fun _ => le_rfl
+#align supr_const_le iSup_const_le
 
-/- warning: le_infi_const -> le_infᵢ_const is a dubious translation:
+/- warning: le_infi_const -> le_iInf_const is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {a : α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {a : α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) a (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => a))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {a : α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => a))
-Case conversion may be inaccurate. Consider using '#align le_infi_const le_infᵢ_constₓ'. -/
-theorem le_infᵢ_const : a ≤ ⨅ i : ι, a :=
-  le_infᵢ fun _ => le_rfl
-#align le_infi_const le_infᵢ_const
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {a : α}, LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) a (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => a))
+Case conversion may be inaccurate. Consider using '#align le_infi_const le_iInf_constₓ'. -/
+theorem le_iInf_const : a ≤ ⨅ i : ι, a :=
+  le_iInf fun _ => le_rfl
+#align le_infi_const le_iInf_const
 
-/- warning: supr_const -> supᵢ_const is a dubious translation:
+/- warning: supr_const -> iSup_const is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι], Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (b : ι) => a)) a
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι], Eq.{succ u1} α (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (b : ι) => a)) a
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι], Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (b : ι) => a)) a
-Case conversion may be inaccurate. Consider using '#align supr_const supᵢ_constₓ'. -/
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι], Eq.{succ u1} α (iSup.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (b : ι) => a)) a
+Case conversion may be inaccurate. Consider using '#align supr_const iSup_constₓ'. -/
 -- We generalize this to conditionally complete lattices in `csupr_const` and `cinfi_const`.
-theorem supᵢ_const [Nonempty ι] : (⨆ b : ι, a) = a := by rw [supᵢ, range_const, supₛ_singleton]
-#align supr_const supᵢ_const
+theorem iSup_const [Nonempty ι] : (⨆ b : ι, a) = a := by rw [iSup, range_const, sSup_singleton]
+#align supr_const iSup_const
 
-/- warning: infi_const -> infᵢ_const is a dubious translation:
+/- warning: infi_const -> iInf_const is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι], Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (b : ι) => a)) a
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι], Eq.{succ u1} α (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (b : ι) => a)) a
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι], Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (b : ι) => a)) a
-Case conversion may be inaccurate. Consider using '#align infi_const infᵢ_constₓ'. -/
-theorem infᵢ_const [Nonempty ι] : (⨅ b : ι, a) = a :=
-  @supᵢ_const αᵒᵈ _ _ a _
-#align infi_const infᵢ_const
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι], Eq.{succ u1} α (iInf.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (b : ι) => a)) a
+Case conversion may be inaccurate. Consider using '#align infi_const iInf_constₓ'. -/
+theorem iInf_const [Nonempty ι] : (⨅ b : ι, a) = a :=
+  @iSup_const αᵒᵈ _ _ a _
+#align infi_const iInf_const
 
-/- warning: supr_bot -> supᵢ_bot is a dubious translation:
+/- warning: supr_bot -> iSup_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α], Eq.{succ u2} α (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α _inst_1))) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align supr_bot supᵢ_botₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α], Eq.{succ u2} α (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α _inst_1))) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align supr_bot iSup_botₓ'. -/
 @[simp]
-theorem supᵢ_bot : (⨆ i : ι, ⊥ : α) = ⊥ :=
-  bot_unique supᵢ_const_le
-#align supr_bot supᵢ_bot
+theorem iSup_bot : (⨆ i : ι, ⊥ : α) = ⊥ :=
+  bot_unique iSup_const_le
+#align supr_bot iSup_bot
 
-/- warning: infi_top -> infᵢ_top is a dubious translation:
+/- warning: infi_top -> iInf_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α], Eq.{succ u1} α (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α], Eq.{succ u2} α (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => Top.top.{u2} α (CompleteLattice.toTop.{u2} α _inst_1))) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align infi_top infᵢ_topₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α], Eq.{succ u2} α (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => Top.top.{u2} α (CompleteLattice.toTop.{u2} α _inst_1))) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align infi_top iInf_topₓ'. -/
 @[simp]
-theorem infᵢ_top : (⨅ i : ι, ⊤ : α) = ⊤ :=
-  top_unique le_infᵢ_const
-#align infi_top infᵢ_top
+theorem iInf_top : (⨅ i : ι, ⊤ : α) = ⊤ :=
+  top_unique le_iInf_const
+#align infi_top iInf_top
 
-/- warning: supr_eq_bot -> supᵢ_eq_bot is a dubious translation:
+/- warning: supr_eq_bot -> iSup_eq_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α}, Iff (Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι s) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))) (forall (i : ι), Eq.{succ u1} α (s i) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α}, Iff (Eq.{succ u1} α (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι s) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))) (forall (i : ι), Eq.{succ u1} α (s i) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {s : ι -> α}, Iff (Eq.{succ u2} α (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι s) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α _inst_1))) (forall (i : ι), Eq.{succ u2} α (s i) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α _inst_1)))
-Case conversion may be inaccurate. Consider using '#align supr_eq_bot supᵢ_eq_botₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {s : ι -> α}, Iff (Eq.{succ u2} α (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι s) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α _inst_1))) (forall (i : ι), Eq.{succ u2} α (s i) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align supr_eq_bot iSup_eq_botₓ'. -/
 @[simp]
-theorem supᵢ_eq_bot : supᵢ s = ⊥ ↔ ∀ i, s i = ⊥ :=
-  supₛ_eq_bot.trans forall_range_iff
-#align supr_eq_bot supᵢ_eq_bot
+theorem iSup_eq_bot : iSup s = ⊥ ↔ ∀ i, s i = ⊥ :=
+  sSup_eq_bot.trans forall_range_iff
+#align supr_eq_bot iSup_eq_bot
 
-/- warning: infi_eq_top -> infᵢ_eq_top is a dubious translation:
+/- warning: infi_eq_top -> iInf_eq_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α}, Iff (Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι s) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))) (forall (i : ι), Eq.{succ u1} α (s i) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : ι -> α}, Iff (Eq.{succ u1} α (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι s) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))) (forall (i : ι), Eq.{succ u1} α (s i) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {s : ι -> α}, Iff (Eq.{succ u2} α (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι s) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α _inst_1))) (forall (i : ι), Eq.{succ u2} α (s i) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α _inst_1)))
-Case conversion may be inaccurate. Consider using '#align infi_eq_top infᵢ_eq_topₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {s : ι -> α}, Iff (Eq.{succ u2} α (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι s) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α _inst_1))) (forall (i : ι), Eq.{succ u2} α (s i) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align infi_eq_top iInf_eq_topₓ'. -/
 @[simp]
-theorem infᵢ_eq_top : infᵢ s = ⊤ ↔ ∀ i, s i = ⊤ :=
-  infₛ_eq_top.trans forall_range_iff
-#align infi_eq_top infᵢ_eq_top
+theorem iInf_eq_top : iInf s = ⊤ ↔ ∀ i, s i = ⊤ :=
+  sInf_eq_top.trans forall_range_iff
+#align infi_eq_top iInf_eq_top
 
-/- warning: supr₂_eq_bot -> supᵢ₂_eq_bot is a dubious translation:
+/- warning: supr₂_eq_bot -> iSup₂_eq_bot 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}, Iff (Eq.{succ u1} α (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))) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))) (forall (i : ι) (j : κ i), Eq.{succ u1} α (f i j) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : forall (i : ι), (κ i) -> α}, Iff (Eq.{succ u1} α (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))) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))) (forall (i : ι) (j : κ i), Eq.{succ u1} α (f i j) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))
 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}, Iff (Eq.{succ u3} α (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))) (Bot.bot.{u3} α (CompleteLattice.toBot.{u3} α _inst_1))) (forall (i : ι) (j : κ i), Eq.{succ u3} α (f i j) (Bot.bot.{u3} α (CompleteLattice.toBot.{u3} α _inst_1)))
-Case conversion may be inaccurate. Consider using '#align supr₂_eq_bot supᵢ₂_eq_botₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {f : forall (i : ι), (κ i) -> α}, Iff (Eq.{succ u3} α (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))) (Bot.bot.{u3} α (CompleteLattice.toBot.{u3} α _inst_1))) (forall (i : ι) (j : κ i), Eq.{succ u3} α (f i j) (Bot.bot.{u3} α (CompleteLattice.toBot.{u3} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align supr₂_eq_bot iSup₂_eq_botₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
-theorem supᵢ₂_eq_bot {f : ∀ i, κ i → α} : (⨆ (i) (j), f i j) = ⊥ ↔ ∀ i j, f i j = ⊥ := by
-  simp_rw [supᵢ_eq_bot]
-#align supr₂_eq_bot supᵢ₂_eq_bot
+theorem iSup₂_eq_bot {f : ∀ i, κ i → α} : (⨆ (i) (j), f i j) = ⊥ ↔ ∀ i j, f i j = ⊥ := by
+  simp_rw [iSup_eq_bot]
+#align supr₂_eq_bot iSup₂_eq_bot
 
-/- warning: infi₂_eq_top -> infᵢ₂_eq_top is a dubious translation:
+/- warning: infi₂_eq_top -> iInf₂_eq_top 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}, Iff (Eq.{succ u1} α (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))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))) (forall (i : ι) (j : κ i), Eq.{succ u1} α (f i j) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {κ : ι -> Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : forall (i : ι), (κ i) -> α}, Iff (Eq.{succ u1} α (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))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))) (forall (i : ι) (j : κ i), Eq.{succ u1} α (f i j) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))
 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}, Iff (Eq.{succ u3} α (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))) (Top.top.{u3} α (CompleteLattice.toTop.{u3} α _inst_1))) (forall (i : ι) (j : κ i), Eq.{succ u3} α (f i j) (Top.top.{u3} α (CompleteLattice.toTop.{u3} α _inst_1)))
-Case conversion may be inaccurate. Consider using '#align infi₂_eq_top infᵢ₂_eq_topₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {κ : ι -> Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {f : forall (i : ι), (κ i) -> α}, Iff (Eq.{succ u3} α (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))) (Top.top.{u3} α (CompleteLattice.toTop.{u3} α _inst_1))) (forall (i : ι) (j : κ i), Eq.{succ u3} α (f i j) (Top.top.{u3} α (CompleteLattice.toTop.{u3} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align infi₂_eq_top iInf₂_eq_topₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 @[simp]
-theorem infᵢ₂_eq_top {f : ∀ i, κ i → α} : (⨅ (i) (j), f i j) = ⊤ ↔ ∀ i j, f i j = ⊤ := by
-  simp_rw [infᵢ_eq_top]
-#align infi₂_eq_top infᵢ₂_eq_top
+theorem iInf₂_eq_top {f : ∀ i, κ i → α} : (⨅ (i) (j), f i j) = ⊤ ↔ ∀ i j, f i j = ⊤ := by
+  simp_rw [iInf_eq_top]
+#align infi₂_eq_top iInf₂_eq_top
 
-/- warning: supr_pos -> supᵢ_pos is a dubious translation:
+/- warning: supr_pos -> iSup_pos is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {f : p -> α} (hp : p), Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) p (fun (h : p) => f h)) (f hp)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {f : p -> α} (hp : p), Eq.{succ u1} α (iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) p (fun (h : p) => f h)) (f hp)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {f : p -> α} (hp : p), Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) p (fun (h : p) => f h)) (f hp)
-Case conversion may be inaccurate. Consider using '#align supr_pos supᵢ_posₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {f : p -> α} (hp : p), Eq.{succ u1} α (iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) p (fun (h : p) => f h)) (f hp)
+Case conversion may be inaccurate. Consider using '#align supr_pos iSup_posₓ'. -/
 @[simp]
-theorem supᵢ_pos {p : Prop} {f : p → α} (hp : p) : (⨆ h : p, f h) = f hp :=
-  le_antisymm (supᵢ_le fun h => le_rfl) (le_supᵢ _ _)
-#align supr_pos supᵢ_pos
+theorem iSup_pos {p : Prop} {f : p → α} (hp : p) : (⨆ h : p, f h) = f hp :=
+  le_antisymm (iSup_le fun h => le_rfl) (le_iSup _ _)
+#align supr_pos iSup_pos
 
-/- warning: infi_pos -> infᵢ_pos is a dubious translation:
+/- warning: infi_pos -> iInf_pos is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {f : p -> α} (hp : p), Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) p (fun (h : p) => f h)) (f hp)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {f : p -> α} (hp : p), Eq.{succ u1} α (iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) p (fun (h : p) => f h)) (f hp)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {f : p -> α} (hp : p), Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) p (fun (h : p) => f h)) (f hp)
-Case conversion may be inaccurate. Consider using '#align infi_pos infᵢ_posₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {f : p -> α} (hp : p), Eq.{succ u1} α (iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) p (fun (h : p) => f h)) (f hp)
+Case conversion may be inaccurate. Consider using '#align infi_pos iInf_posₓ'. -/
 @[simp]
-theorem infᵢ_pos {p : Prop} {f : p → α} (hp : p) : (⨅ h : p, f h) = f hp :=
-  le_antisymm (infᵢ_le _ _) (le_infᵢ fun h => le_rfl)
-#align infi_pos infᵢ_pos
+theorem iInf_pos {p : Prop} {f : p → α} (hp : p) : (⨅ h : p, f h) = f hp :=
+  le_antisymm (iInf_le _ _) (le_iInf fun h => le_rfl)
+#align infi_pos iInf_pos
 
-/- warning: supr_neg -> supᵢ_neg is a dubious translation:
+/- warning: supr_neg -> iSup_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {f : p -> α}, (Not p) -> (Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) p (fun (h : p) => f h)) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {f : p -> α}, (Not p) -> (Eq.{succ u1} α (iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) p (fun (h : p) => f h)) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {f : p -> α}, (Not p) -> (Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) p (fun (h : p) => f h)) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1)))
-Case conversion may be inaccurate. Consider using '#align supr_neg supᵢ_negₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {f : p -> α}, (Not p) -> (Eq.{succ u1} α (iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) p (fun (h : p) => f h)) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align supr_neg iSup_negₓ'. -/
 @[simp]
-theorem supᵢ_neg {p : Prop} {f : p → α} (hp : ¬p) : (⨆ h : p, f h) = ⊥ :=
-  le_antisymm (supᵢ_le fun h => (hp h).elim) bot_le
-#align supr_neg supᵢ_neg
+theorem iSup_neg {p : Prop} {f : p → α} (hp : ¬p) : (⨆ h : p, f h) = ⊥ :=
+  le_antisymm (iSup_le fun h => (hp h).elim) bot_le
+#align supr_neg iSup_neg
 
-/- warning: infi_neg -> infᵢ_neg is a dubious translation:
+/- warning: infi_neg -> iInf_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {f : p -> α}, (Not p) -> (Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) p (fun (h : p) => f h)) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {f : p -> α}, (Not p) -> (Eq.{succ u1} α (iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) p (fun (h : p) => f h)) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {f : p -> α}, (Not p) -> (Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) p (fun (h : p) => f h)) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1)))
-Case conversion may be inaccurate. Consider using '#align infi_neg infᵢ_negₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {f : p -> α}, (Not p) -> (Eq.{succ u1} α (iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) p (fun (h : p) => f h)) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align infi_neg iInf_negₓ'. -/
 @[simp]
-theorem infᵢ_neg {p : Prop} {f : p → α} (hp : ¬p) : (⨅ h : p, f h) = ⊤ :=
-  le_antisymm le_top <| le_infᵢ fun h => (hp h).elim
-#align infi_neg infᵢ_neg
+theorem iInf_neg {p : Prop} {f : p → α} (hp : ¬p) : (⨅ h : p, f h) = ⊤ :=
+  le_antisymm le_top <| le_iInf fun h => (hp h).elim
+#align infi_neg iInf_neg
 
-/- warning: supr_eq_of_forall_le_of_forall_lt_exists_gt -> supᵢ_eq_of_forall_le_of_forall_lt_exists_gt is a dubious translation:
+/- warning: supr_eq_of_forall_le_of_forall_lt_exists_gt -> iSup_eq_of_forall_le_of_forall_lt_exists_gt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : α} {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) b) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w b) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w (f i)))) -> (Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i)) b)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : α} {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) b) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w b) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) w (f i)))) -> (Eq.{succ u1} α (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i)) b)
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {b : α} {f : ι -> α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) b) -> (forall (w : α), (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) w b) -> (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) w (f i)))) -> (Eq.{succ u2} α (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i)) b)
-Case conversion may be inaccurate. Consider using '#align supr_eq_of_forall_le_of_forall_lt_exists_gt supᵢ_eq_of_forall_le_of_forall_lt_exists_gtₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {b : α} {f : ι -> α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) b) -> (forall (w : α), (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) w b) -> (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) w (f i)))) -> (Eq.{succ u2} α (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i)) b)
+Case conversion may be inaccurate. Consider using '#align supr_eq_of_forall_le_of_forall_lt_exists_gt iSup_eq_of_forall_le_of_forall_lt_exists_gtₓ'. -/
 /-- Introduction rule to prove that `b` is the supremum of `f`: it suffices to check that `b`
 is larger than `f i` for all `i`, and that this is not the case of any `w<b`.
 See `csupr_eq_of_forall_le_of_forall_lt_exists_gt` for a version in conditionally complete
 lattices. -/
-theorem supᵢ_eq_of_forall_le_of_forall_lt_exists_gt {f : ι → α} (h₁ : ∀ i, f i ≤ b)
+theorem iSup_eq_of_forall_le_of_forall_lt_exists_gt {f : ι → α} (h₁ : ∀ i, f i ≤ b)
     (h₂ : ∀ w, w < b → ∃ i, w < f i) : (⨆ i : ι, f i) = b :=
-  supₛ_eq_of_forall_le_of_forall_lt_exists_gt (forall_range_iff.mpr h₁) fun w hw =>
+  sSup_eq_of_forall_le_of_forall_lt_exists_gt (forall_range_iff.mpr h₁) fun w hw =>
     exists_range_iff.mpr <| h₂ w hw
-#align supr_eq_of_forall_le_of_forall_lt_exists_gt supᵢ_eq_of_forall_le_of_forall_lt_exists_gt
+#align supr_eq_of_forall_le_of_forall_lt_exists_gt iSup_eq_of_forall_le_of_forall_lt_exists_gt
 
-/- warning: infi_eq_of_forall_ge_of_forall_gt_exists_lt -> infᵢ_eq_of_forall_ge_of_forall_gt_exists_lt is a dubious translation:
+/- warning: infi_eq_of_forall_ge_of_forall_gt_exists_lt -> iInf_eq_of_forall_ge_of_forall_gt_exists_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {b : α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b (f i)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b w) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) w))) -> (Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => f i)) b)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {b : α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b (f i)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) b w) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (f i) w))) -> (Eq.{succ u1} α (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => f i)) b)
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {b : α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) b (f i)) -> (forall (w : α), (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) b w) -> (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) w))) -> (Eq.{succ u2} α (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i)) b)
-Case conversion may be inaccurate. Consider using '#align infi_eq_of_forall_ge_of_forall_gt_exists_lt infᵢ_eq_of_forall_ge_of_forall_gt_exists_ltₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {b : α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) b (f i)) -> (forall (w : α), (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) b w) -> (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (f i) w))) -> (Eq.{succ u2} α (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i)) b)
+Case conversion may be inaccurate. Consider using '#align infi_eq_of_forall_ge_of_forall_gt_exists_lt iInf_eq_of_forall_ge_of_forall_gt_exists_ltₓ'. -/
 /-- Introduction rule to prove that `b` is the infimum of `f`: it suffices to check that `b`
 is smaller than `f i` for all `i`, and that this is not the case of any `w>b`.
 See `cinfi_eq_of_forall_ge_of_forall_gt_exists_lt` for a version in conditionally complete
 lattices. -/
-theorem infᵢ_eq_of_forall_ge_of_forall_gt_exists_lt :
+theorem iInf_eq_of_forall_ge_of_forall_gt_exists_lt :
     (∀ i, b ≤ f i) → (∀ w, b < w → ∃ i, f i < w) → (⨅ i, f i) = b :=
-  @supᵢ_eq_of_forall_le_of_forall_lt_exists_gt αᵒᵈ _ _ _ _
-#align infi_eq_of_forall_ge_of_forall_gt_exists_lt infᵢ_eq_of_forall_ge_of_forall_gt_exists_lt
+  @iSup_eq_of_forall_le_of_forall_lt_exists_gt αᵒᵈ _ _ _ _
+#align infi_eq_of_forall_ge_of_forall_gt_exists_lt iInf_eq_of_forall_ge_of_forall_gt_exists_lt
 
-/- warning: supr_eq_dif -> supᵢ_eq_dif is a dubious translation:
+/- warning: supr_eq_dif -> iSup_eq_dif is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} [_inst_2 : Decidable p] (a : p -> α), Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) p (fun (h : p) => a h)) (dite.{succ u1} α p _inst_2 (fun (h : p) => a h) (fun (h : Not p) => Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} [_inst_2 : Decidable p] (a : p -> α), Eq.{succ u1} α (iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) p (fun (h : p) => a h)) (dite.{succ u1} α p _inst_2 (fun (h : p) => a h) (fun (h : Not p) => Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} [_inst_2 : Decidable p] (a : p -> α), Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) p (fun (h : p) => a h)) (dite.{succ u1} α p _inst_2 (fun (h : p) => a h) (fun (h : Not p) => Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1)))
-Case conversion may be inaccurate. Consider using '#align supr_eq_dif supᵢ_eq_difₓ'. -/
-theorem supᵢ_eq_dif {p : Prop} [Decidable p] (a : p → α) :
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} [_inst_2 : Decidable p] (a : p -> α), Eq.{succ u1} α (iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) p (fun (h : p) => a h)) (dite.{succ u1} α p _inst_2 (fun (h : p) => a h) (fun (h : Not p) => Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align supr_eq_dif iSup_eq_difₓ'. -/
+theorem iSup_eq_dif {p : Prop} [Decidable p] (a : p → α) :
     (⨆ h : p, a h) = if h : p then a h else ⊥ := by by_cases p <;> simp [h]
-#align supr_eq_dif supᵢ_eq_dif
+#align supr_eq_dif iSup_eq_dif
 
-/- warning: supr_eq_if -> supᵢ_eq_if is a dubious translation:
+/- warning: supr_eq_if -> iSup_eq_if is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} [_inst_2 : Decidable p] (a : α), Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) p (fun (h : p) => a)) (ite.{succ u1} α p _inst_2 a (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} [_inst_2 : Decidable p] (a : α), Eq.{succ u1} α (iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) p (fun (h : p) => a)) (ite.{succ u1} α p _inst_2 a (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} [_inst_2 : Decidable p] (a : α), Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) p (fun (h : p) => a)) (ite.{succ u1} α p _inst_2 a (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1)))
-Case conversion may be inaccurate. Consider using '#align supr_eq_if supᵢ_eq_ifₓ'. -/
-theorem supᵢ_eq_if {p : Prop} [Decidable p] (a : α) : (⨆ h : p, a) = if p then a else ⊥ :=
-  supᵢ_eq_dif fun _ => a
-#align supr_eq_if supᵢ_eq_if
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} [_inst_2 : Decidable p] (a : α), Eq.{succ u1} α (iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) p (fun (h : p) => a)) (ite.{succ u1} α p _inst_2 a (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align supr_eq_if iSup_eq_ifₓ'. -/
+theorem iSup_eq_if {p : Prop} [Decidable p] (a : α) : (⨆ h : p, a) = if p then a else ⊥ :=
+  iSup_eq_dif fun _ => a
+#align supr_eq_if iSup_eq_if
 
-/- warning: infi_eq_dif -> infᵢ_eq_dif is a dubious translation:
+/- warning: infi_eq_dif -> iInf_eq_dif is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} [_inst_2 : Decidable p] (a : p -> α), Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) p (fun (h : p) => a h)) (dite.{succ u1} α p _inst_2 (fun (h : p) => a h) (fun (h : Not p) => Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} [_inst_2 : Decidable p] (a : p -> α), Eq.{succ u1} α (iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) p (fun (h : p) => a h)) (dite.{succ u1} α p _inst_2 (fun (h : p) => a h) (fun (h : Not p) => Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} [_inst_2 : Decidable p] (a : p -> α), Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) p (fun (h : p) => a h)) (dite.{succ u1} α p _inst_2 (fun (h : p) => a h) (fun (h : Not p) => Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1)))
-Case conversion may be inaccurate. Consider using '#align infi_eq_dif infᵢ_eq_difₓ'. -/
-theorem infᵢ_eq_dif {p : Prop} [Decidable p] (a : p → α) :
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} [_inst_2 : Decidable p] (a : p -> α), Eq.{succ u1} α (iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) p (fun (h : p) => a h)) (dite.{succ u1} α p _inst_2 (fun (h : p) => a h) (fun (h : Not p) => Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align infi_eq_dif iInf_eq_difₓ'. -/
+theorem iInf_eq_dif {p : Prop} [Decidable p] (a : p → α) :
     (⨅ h : p, a h) = if h : p then a h else ⊤ :=
-  @supᵢ_eq_dif αᵒᵈ _ _ _ _
-#align infi_eq_dif infᵢ_eq_dif
+  @iSup_eq_dif αᵒᵈ _ _ _ _
+#align infi_eq_dif iInf_eq_dif
 
-/- warning: infi_eq_if -> infᵢ_eq_if is a dubious translation:
+/- warning: infi_eq_if -> iInf_eq_if is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} [_inst_2 : Decidable p] (a : α), Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) p (fun (h : p) => a)) (ite.{succ u1} α p _inst_2 a (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} [_inst_2 : Decidable p] (a : α), Eq.{succ u1} α (iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) p (fun (h : p) => a)) (ite.{succ u1} α p _inst_2 a (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} [_inst_2 : Decidable p] (a : α), Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) p (fun (h : p) => a)) (ite.{succ u1} α p _inst_2 a (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1)))
-Case conversion may be inaccurate. Consider using '#align infi_eq_if infᵢ_eq_ifₓ'. -/
-theorem infᵢ_eq_if {p : Prop} [Decidable p] (a : α) : (⨅ h : p, a) = if p then a else ⊤ :=
-  infᵢ_eq_dif fun _ => a
-#align infi_eq_if infᵢ_eq_if
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} [_inst_2 : Decidable p] (a : α), Eq.{succ u1} α (iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) p (fun (h : p) => a)) (ite.{succ u1} α p _inst_2 a (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align infi_eq_if iInf_eq_ifₓ'. -/
+theorem iInf_eq_if {p : Prop} [Decidable p] (a : α) : (⨅ h : p, a) = if p then a else ⊤ :=
+  iInf_eq_dif fun _ => a
+#align infi_eq_if iInf_eq_if
 
-/- warning: supr_comm -> supᵢ_comm is a dubious translation:
+/- warning: supr_comm -> iSup_comm is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> ι' -> α}, Eq.{succ u1} α (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)) ι' (fun (j : ι') => f i j))) (supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' (fun (j : ι') => supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i j)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> ι' -> α}, Eq.{succ u1} α (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)) ι' (fun (j : ι') => f i j))) (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι' (fun (j : ι') => iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i j)))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {f : ι -> ι' -> α}, Eq.{succ u3} α (supᵢ.{u3, u2} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => supᵢ.{u3, u1} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι' (fun (j : ι') => f i j))) (supᵢ.{u3, u1} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι' (fun (j : ι') => supᵢ.{u3, u2} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => f i j)))
-Case conversion may be inaccurate. Consider using '#align supr_comm supᵢ_commₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {f : ι -> ι' -> α}, Eq.{succ u3} α (iSup.{u3, u2} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => iSup.{u3, u1} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι' (fun (j : ι') => f i j))) (iSup.{u3, u1} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι' (fun (j : ι') => iSup.{u3, u2} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => f i j)))
+Case conversion may be inaccurate. Consider using '#align supr_comm iSup_commₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (j i) -/
-theorem supᵢ_comm {f : ι → ι' → α} : (⨆ (i) (j), f i j) = ⨆ (j) (i), f i j :=
-  le_antisymm (supᵢ_le fun i => supᵢ_mono fun j => le_supᵢ _ i)
-    (supᵢ_le fun j => supᵢ_mono fun i => le_supᵢ _ _)
-#align supr_comm supᵢ_comm
+theorem iSup_comm {f : ι → ι' → α} : (⨆ (i) (j), f i j) = ⨆ (j) (i), f i j :=
+  le_antisymm (iSup_le fun i => iSup_mono fun j => le_iSup _ i)
+    (iSup_le fun j => iSup_mono fun i => le_iSup _ _)
+#align supr_comm iSup_comm
 
-/- warning: infi_comm -> infᵢ_comm is a dubious translation:
+/- warning: infi_comm -> iInf_comm is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> ι' -> α}, Eq.{succ u1} α (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)) ι' (fun (j : ι') => f i j))) (infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (j : ι') => infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => f i j)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> ι' -> α}, Eq.{succ u1} α (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)) ι' (fun (j : ι') => f i j))) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι' (fun (j : ι') => iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => f i j)))
 but is expected to have type
-  forall {α : Type.{u3}} {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {f : ι -> ι' -> α}, Eq.{succ u3} α (infᵢ.{u3, u2} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => infᵢ.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι' (fun (j : ι') => f i j))) (infᵢ.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι' (fun (j : ι') => infᵢ.{u3, u2} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => f i j)))
-Case conversion may be inaccurate. Consider using '#align infi_comm infᵢ_commₓ'. -/
+  forall {α : Type.{u3}} {ι : Sort.{u2}} {ι' : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {f : ι -> ι' -> α}, Eq.{succ u3} α (iInf.{u3, u2} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => iInf.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι' (fun (j : ι') => f i j))) (iInf.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι' (fun (j : ι') => iInf.{u3, u2} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => f i j)))
+Case conversion may be inaccurate. Consider using '#align infi_comm iInf_commₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (j i) -/
-theorem infᵢ_comm {f : ι → ι' → α} : (⨅ (i) (j), f i j) = ⨅ (j) (i), f i j :=
-  @supᵢ_comm αᵒᵈ _ _ _ _
-#align infi_comm infᵢ_comm
+theorem iInf_comm {f : ι → ι' → α} : (⨅ (i) (j), f i j) = ⨅ (j) (i), f i j :=
+  @iSup_comm αᵒᵈ _ _ _ _
+#align infi_comm iInf_comm
 
-/- warning: supr₂_comm -> supᵢ₂_comm is a dubious translation:
+/- warning: supr₂_comm -> iSup₂_comm is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι₁ : Sort.{u2}} {ι₂ : Sort.{u3}} {κ₁ : ι₁ -> Sort.{u4}} {κ₂ : ι₂ -> Sort.{u5}} (f : forall (i₁ : ι₁), (κ₁ i₁) -> (forall (i₂ : ι₂), (κ₂ i₂) -> α)), Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι₁ (fun (i₁ : ι₁) => supᵢ.{u1, u4} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ₁ i₁) (fun (j₁ : κ₁ i₁) => supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι₂ (fun (i₂ : ι₂) => supᵢ.{u1, u5} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ₂ i₂) (fun (j₂ : κ₂ i₂) => f i₁ j₁ i₂ j₂))))) (supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι₂ (fun (i₂ : ι₂) => supᵢ.{u1, u5} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ₂ i₂) (fun (j₂ : κ₂ i₂) => supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι₁ (fun (i₁ : ι₁) => supᵢ.{u1, u4} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ₁ i₁) (fun (j₁ : κ₁ i₁) => f i₁ j₁ i₂ j₂)))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι₁ : Sort.{u2}} {ι₂ : Sort.{u3}} {κ₁ : ι₁ -> Sort.{u4}} {κ₂ : ι₂ -> Sort.{u5}} (f : forall (i₁ : ι₁), (κ₁ i₁) -> (forall (i₂ : ι₂), (κ₂ i₂) -> α)), Eq.{succ u1} α (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι₁ (fun (i₁ : ι₁) => iSup.{u1, u4} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ₁ i₁) (fun (j₁ : κ₁ i₁) => iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι₂ (fun (i₂ : ι₂) => iSup.{u1, u5} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ₂ i₂) (fun (j₂ : κ₂ i₂) => f i₁ j₁ i₂ j₂))))) (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι₂ (fun (i₂ : ι₂) => iSup.{u1, u5} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ₂ i₂) (fun (j₂ : κ₂ i₂) => iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι₁ (fun (i₁ : ι₁) => iSup.{u1, u4} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (κ₁ i₁) (fun (j₁ : κ₁ i₁) => f i₁ j₁ i₂ j₂)))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι₁ : Sort.{u5}} {ι₂ : Sort.{u4}} {κ₁ : ι₁ -> Sort.{u3}} {κ₂ : ι₂ -> Sort.{u2}} (f : forall (i₁ : ι₁), (κ₁ i₁) -> (forall (i₂ : ι₂), (κ₂ i₂) -> α)), Eq.{succ u1} α (supᵢ.{u1, u5} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι₁ (fun (i₁ : ι₁) => supᵢ.{u1, u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) (κ₁ i₁) (fun (j₁ : κ₁ i₁) => supᵢ.{u1, u4} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι₂ (fun (i₂ : ι₂) => supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) (κ₂ i₂) (fun (j₂ : κ₂ i₂) => f i₁ j₁ i₂ j₂))))) (supᵢ.{u1, u4} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι₂ (fun (i₂ : ι₂) => supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) (κ₂ i₂) (fun (j₂ : κ₂ i₂) => supᵢ.{u1, u5} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι₁ (fun (i₁ : ι₁) => supᵢ.{u1, u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) (κ₁ i₁) (fun (j₁ : κ₁ i₁) => f i₁ j₁ i₂ j₂)))))
-Case conversion may be inaccurate. Consider using '#align supr₂_comm supᵢ₂_commₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι₁ : Sort.{u5}} {ι₂ : Sort.{u4}} {κ₁ : ι₁ -> Sort.{u3}} {κ₂ : ι₂ -> Sort.{u2}} (f : forall (i₁ : ι₁), (κ₁ i₁) -> (forall (i₂ : ι₂), (κ₂ i₂) -> α)), Eq.{succ u1} α (iSup.{u1, u5} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι₁ (fun (i₁ : ι₁) => iSup.{u1, u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) (κ₁ i₁) (fun (j₁ : κ₁ i₁) => iSup.{u1, u4} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι₂ (fun (i₂ : ι₂) => iSup.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) (κ₂ i₂) (fun (j₂ : κ₂ i₂) => f i₁ j₁ i₂ j₂))))) (iSup.{u1, u4} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι₂ (fun (i₂ : ι₂) => iSup.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) (κ₂ i₂) (fun (j₂ : κ₂ i₂) => iSup.{u1, u5} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι₁ (fun (i₁ : ι₁) => iSup.{u1, u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) (κ₁ i₁) (fun (j₁ : κ₁ i₁) => f i₁ j₁ i₂ j₂)))))
+Case conversion may be inaccurate. Consider using '#align supr₂_comm iSup₂_commₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i₁ j₁ i₂ j₂) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i₂ j₂ i₁ j₁) -/
-theorem supᵢ₂_comm {ι₁ ι₂ : Sort _} {κ₁ : ι₁ → Sort _} {κ₂ : ι₂ → Sort _}
+theorem iSup₂_comm {ι₁ ι₂ : Sort _} {κ₁ : ι₁ → Sort _} {κ₂ : ι₂ → Sort _}
     (f : ∀ i₁, κ₁ i₁ → ∀ i₂, κ₂ i₂ → α) :
     (⨆ (i₁) (j₁) (i₂) (j₂), f i₁ j₁ i₂ j₂) = ⨆ (i₂) (j₂) (i₁) (j₁), f i₁ j₁ i₂ j₂ := by
-  simp only [@supᵢ_comm _ (κ₁ _), @supᵢ_comm _ ι₁]
-#align supr₂_comm supᵢ₂_comm
+  simp only [@iSup_comm _ (κ₁ _), @iSup_comm _ ι₁]
+#align supr₂_comm iSup₂_comm
 
-/- warning: infi₂_comm -> infᵢ₂_comm is a dubious translation:
+/- warning: infi₂_comm -> iInf₂_comm is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι₁ : Sort.{u2}} {ι₂ : Sort.{u3}} {κ₁ : ι₁ -> Sort.{u4}} {κ₂ : ι₂ -> Sort.{u5}} (f : forall (i₁ : ι₁), (κ₁ i₁) -> (forall (i₂ : ι₂), (κ₂ i₂) -> α)), Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι₁ (fun (i₁ : ι₁) => infᵢ.{u1, u4} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ₁ i₁) (fun (j₁ : κ₁ i₁) => infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι₂ (fun (i₂ : ι₂) => infᵢ.{u1, u5} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ₂ i₂) (fun (j₂ : κ₂ i₂) => f i₁ j₁ i₂ j₂))))) (infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι₂ (fun (i₂ : ι₂) => infᵢ.{u1, u5} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ₂ i₂) (fun (j₂ : κ₂ i₂) => infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι₁ (fun (i₁ : ι₁) => infᵢ.{u1, u4} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ₁ i₁) (fun (j₁ : κ₁ i₁) => f i₁ j₁ i₂ j₂)))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι₁ : Sort.{u2}} {ι₂ : Sort.{u3}} {κ₁ : ι₁ -> Sort.{u4}} {κ₂ : ι₂ -> Sort.{u5}} (f : forall (i₁ : ι₁), (κ₁ i₁) -> (forall (i₂ : ι₂), (κ₂ i₂) -> α)), Eq.{succ u1} α (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι₁ (fun (i₁ : ι₁) => iInf.{u1, u4} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ₁ i₁) (fun (j₁ : κ₁ i₁) => iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι₂ (fun (i₂ : ι₂) => iInf.{u1, u5} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ₂ i₂) (fun (j₂ : κ₂ i₂) => f i₁ j₁ i₂ j₂))))) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι₂ (fun (i₂ : ι₂) => iInf.{u1, u5} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ₂ i₂) (fun (j₂ : κ₂ i₂) => iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι₁ (fun (i₁ : ι₁) => iInf.{u1, u4} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (κ₁ i₁) (fun (j₁ : κ₁ i₁) => f i₁ j₁ i₂ j₂)))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι₁ : Sort.{u5}} {ι₂ : Sort.{u4}} {κ₁ : ι₁ -> Sort.{u3}} {κ₂ : ι₂ -> Sort.{u2}} (f : forall (i₁ : ι₁), (κ₁ i₁) -> (forall (i₂ : ι₂), (κ₂ i₂) -> α)), Eq.{succ u1} α (infᵢ.{u1, u5} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι₁ (fun (i₁ : ι₁) => infᵢ.{u1, u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) (κ₁ i₁) (fun (j₁ : κ₁ i₁) => infᵢ.{u1, u4} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι₂ (fun (i₂ : ι₂) => infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) (κ₂ i₂) (fun (j₂ : κ₂ i₂) => f i₁ j₁ i₂ j₂))))) (infᵢ.{u1, u4} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι₂ (fun (i₂ : ι₂) => infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) (κ₂ i₂) (fun (j₂ : κ₂ i₂) => infᵢ.{u1, u5} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι₁ (fun (i₁ : ι₁) => infᵢ.{u1, u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) (κ₁ i₁) (fun (j₁ : κ₁ i₁) => f i₁ j₁ i₂ j₂)))))
-Case conversion may be inaccurate. Consider using '#align infi₂_comm infᵢ₂_commₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι₁ : Sort.{u5}} {ι₂ : Sort.{u4}} {κ₁ : ι₁ -> Sort.{u3}} {κ₂ : ι₂ -> Sort.{u2}} (f : forall (i₁ : ι₁), (κ₁ i₁) -> (forall (i₂ : ι₂), (κ₂ i₂) -> α)), Eq.{succ u1} α (iInf.{u1, u5} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι₁ (fun (i₁ : ι₁) => iInf.{u1, u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) (κ₁ i₁) (fun (j₁ : κ₁ i₁) => iInf.{u1, u4} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι₂ (fun (i₂ : ι₂) => iInf.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) (κ₂ i₂) (fun (j₂ : κ₂ i₂) => f i₁ j₁ i₂ j₂))))) (iInf.{u1, u4} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι₂ (fun (i₂ : ι₂) => iInf.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) (κ₂ i₂) (fun (j₂ : κ₂ i₂) => iInf.{u1, u5} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι₁ (fun (i₁ : ι₁) => iInf.{u1, u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) (κ₁ i₁) (fun (j₁ : κ₁ i₁) => f i₁ j₁ i₂ j₂)))))
+Case conversion may be inaccurate. Consider using '#align infi₂_comm iInf₂_commₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i₁ j₁ i₂ j₂) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i₂ j₂ i₁ j₁) -/
-theorem infᵢ₂_comm {ι₁ ι₂ : Sort _} {κ₁ : ι₁ → Sort _} {κ₂ : ι₂ → Sort _}
+theorem iInf₂_comm {ι₁ ι₂ : Sort _} {κ₁ : ι₁ → Sort _} {κ₂ : ι₂ → Sort _}
     (f : ∀ i₁, κ₁ i₁ → ∀ i₂, κ₂ i₂ → α) :
     (⨅ (i₁) (j₁) (i₂) (j₂), f i₁ j₁ i₂ j₂) = ⨅ (i₂) (j₂) (i₁) (j₁), f i₁ j₁ i₂ j₂ := by
-  simp only [@infᵢ_comm _ (κ₁ _), @infᵢ_comm _ ι₁]
-#align infi₂_comm infᵢ₂_comm
+  simp only [@iInf_comm _ (κ₁ _), @iInf_comm _ ι₁]
+#align infi₂_comm iInf₂_comm
 
-/- warning: supr_supr_eq_left -> supᵢ_supᵢ_eq_left is a dubious translation:
+/- warning: supr_supr_eq_left -> iSup_iSup_eq_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : β} {f : forall (x : β), (Eq.{succ u2} β x b) -> α}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Eq.{succ u2} β x b) (fun (h : Eq.{succ u2} β x b) => f x h))) (f b (rfl.{succ u2} β b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : β} {f : forall (x : β), (Eq.{succ u2} β x b) -> α}, Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Eq.{succ u2} β x b) (fun (h : Eq.{succ u2} β x b) => f x h))) (f b (rfl.{succ u2} β b))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : β} {f : forall (x : β), (Eq.{succ u2} β x b) -> α}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Eq.{succ u2} β x b) (fun (h : Eq.{succ u2} β x b) => f x h))) (f b (rfl.{succ u2} β b))
-Case conversion may be inaccurate. Consider using '#align supr_supr_eq_left supᵢ_supᵢ_eq_leftₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : β} {f : forall (x : β), (Eq.{succ u2} β x b) -> α}, Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Eq.{succ u2} β x b) (fun (h : Eq.{succ u2} β x b) => f x h))) (f b (rfl.{succ u2} β b))
+Case conversion may be inaccurate. Consider using '#align supr_supr_eq_left iSup_iSup_eq_leftₓ'. -/
 /- TODO: this is strange. In the proof below, we get exactly the desired
    among the equalities, but close does not get it.
 begin
@@ -2153,164 +2153,164 @@ begin
 end
 -/
 @[simp]
-theorem supᵢ_supᵢ_eq_left {b : β} {f : ∀ x : β, x = b → α} : (⨆ x, ⨆ h : x = b, f x h) = f b rfl :=
-  (@le_supᵢ₂ _ _ _ _ f b rfl).antisymm'
-    (supᵢ_le fun c =>
-      supᵢ_le <| by
+theorem iSup_iSup_eq_left {b : β} {f : ∀ x : β, x = b → α} : (⨆ x, ⨆ h : x = b, f x h) = f b rfl :=
+  (@le_iSup₂ _ _ _ _ f b rfl).antisymm'
+    (iSup_le fun c =>
+      iSup_le <| by
         rintro rfl
         rfl)
-#align supr_supr_eq_left supᵢ_supᵢ_eq_left
+#align supr_supr_eq_left iSup_iSup_eq_left
 
-/- warning: infi_infi_eq_left -> infᵢ_infᵢ_eq_left is a dubious translation:
+/- warning: infi_infi_eq_left -> iInf_iInf_eq_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : β} {f : forall (x : β), (Eq.{succ u2} β x b) -> α}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Eq.{succ u2} β x b) (fun (h : Eq.{succ u2} β x b) => f x h))) (f b (rfl.{succ u2} β b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : β} {f : forall (x : β), (Eq.{succ u2} β x b) -> α}, Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Eq.{succ u2} β x b) (fun (h : Eq.{succ u2} β x b) => f x h))) (f b (rfl.{succ u2} β b))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : β} {f : forall (x : β), (Eq.{succ u2} β x b) -> α}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Eq.{succ u2} β x b) (fun (h : Eq.{succ u2} β x b) => f x h))) (f b (rfl.{succ u2} β b))
-Case conversion may be inaccurate. Consider using '#align infi_infi_eq_left infᵢ_infᵢ_eq_leftₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : β} {f : forall (x : β), (Eq.{succ u2} β x b) -> α}, Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Eq.{succ u2} β x b) (fun (h : Eq.{succ u2} β x b) => f x h))) (f b (rfl.{succ u2} β b))
+Case conversion may be inaccurate. Consider using '#align infi_infi_eq_left iInf_iInf_eq_leftₓ'. -/
 @[simp]
-theorem infᵢ_infᵢ_eq_left {b : β} {f : ∀ x : β, x = b → α} : (⨅ x, ⨅ h : x = b, f x h) = f b rfl :=
-  @supᵢ_supᵢ_eq_left αᵒᵈ _ _ _ _
-#align infi_infi_eq_left infᵢ_infᵢ_eq_left
+theorem iInf_iInf_eq_left {b : β} {f : ∀ x : β, x = b → α} : (⨅ x, ⨅ h : x = b, f x h) = f b rfl :=
+  @iSup_iSup_eq_left αᵒᵈ _ _ _ _
+#align infi_infi_eq_left iInf_iInf_eq_left
 
-/- warning: supr_supr_eq_right -> supᵢ_supᵢ_eq_right is a dubious translation:
+/- warning: supr_supr_eq_right -> iSup_iSup_eq_right is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : β} {f : forall (x : β), (Eq.{succ u2} β b x) -> α}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Eq.{succ u2} β b x) (fun (h : Eq.{succ u2} β b x) => f x h))) (f b (rfl.{succ u2} β b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : β} {f : forall (x : β), (Eq.{succ u2} β b x) -> α}, Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Eq.{succ u2} β b x) (fun (h : Eq.{succ u2} β b x) => f x h))) (f b (rfl.{succ u2} β b))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : β} {f : forall (x : β), (Eq.{succ u2} β b x) -> α}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Eq.{succ u2} β b x) (fun (h : Eq.{succ u2} β b x) => f x h))) (f b (rfl.{succ u2} β b))
-Case conversion may be inaccurate. Consider using '#align supr_supr_eq_right supᵢ_supᵢ_eq_rightₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : β} {f : forall (x : β), (Eq.{succ u2} β b x) -> α}, Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Eq.{succ u2} β b x) (fun (h : Eq.{succ u2} β b x) => f x h))) (f b (rfl.{succ u2} β b))
+Case conversion may be inaccurate. Consider using '#align supr_supr_eq_right iSup_iSup_eq_rightₓ'. -/
 @[simp]
-theorem supᵢ_supᵢ_eq_right {b : β} {f : ∀ x : β, b = x → α} : (⨆ x, ⨆ h : b = x, f x h) = f b rfl :=
-  (le_supᵢ₂ b rfl).antisymm'
-    (supᵢ₂_le fun c => by
+theorem iSup_iSup_eq_right {b : β} {f : ∀ x : β, b = x → α} : (⨆ x, ⨆ h : b = x, f x h) = f b rfl :=
+  (le_iSup₂ b rfl).antisymm'
+    (iSup₂_le fun c => by
       rintro rfl
       rfl)
-#align supr_supr_eq_right supᵢ_supᵢ_eq_right
+#align supr_supr_eq_right iSup_iSup_eq_right
 
-/- warning: infi_infi_eq_right -> infᵢ_infᵢ_eq_right is a dubious translation:
+/- warning: infi_infi_eq_right -> iInf_iInf_eq_right is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : β} {f : forall (x : β), (Eq.{succ u2} β b x) -> α}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Eq.{succ u2} β b x) (fun (h : Eq.{succ u2} β b x) => f x h))) (f b (rfl.{succ u2} β b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : β} {f : forall (x : β), (Eq.{succ u2} β b x) -> α}, Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Eq.{succ u2} β b x) (fun (h : Eq.{succ u2} β b x) => f x h))) (f b (rfl.{succ u2} β b))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : β} {f : forall (x : β), (Eq.{succ u2} β b x) -> α}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Eq.{succ u2} β b x) (fun (h : Eq.{succ u2} β b x) => f x h))) (f b (rfl.{succ u2} β b))
-Case conversion may be inaccurate. Consider using '#align infi_infi_eq_right infᵢ_infᵢ_eq_rightₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {b : β} {f : forall (x : β), (Eq.{succ u2} β b x) -> α}, Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Eq.{succ u2} β b x) (fun (h : Eq.{succ u2} β b x) => f x h))) (f b (rfl.{succ u2} β b))
+Case conversion may be inaccurate. Consider using '#align infi_infi_eq_right iInf_iInf_eq_rightₓ'. -/
 @[simp]
-theorem infᵢ_infᵢ_eq_right {b : β} {f : ∀ x : β, b = x → α} : (⨅ x, ⨅ h : b = x, f x h) = f b rfl :=
-  @supᵢ_supᵢ_eq_right αᵒᵈ _ _ _ _
-#align infi_infi_eq_right infᵢ_infᵢ_eq_right
+theorem iInf_iInf_eq_right {b : β} {f : ∀ x : β, b = x → α} : (⨅ x, ⨅ h : b = x, f x h) = f b rfl :=
+  @iSup_iSup_eq_right αᵒᵈ _ _ _ _
+#align infi_infi_eq_right iInf_iInf_eq_right
 
 attribute [ematch] le_refl
 
-/- warning: supr_subtype -> supᵢ_subtype is a dubious translation:
+/- warning: supr_subtype -> iSup_subtype is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : (Subtype.{u2} ι p) -> α}, Eq.{succ u1} α (supᵢ.{u1, max 1 u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Subtype.{u2} ι p) f) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f (Subtype.mk.{u2} ι p i h))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : (Subtype.{u2} ι p) -> α}, Eq.{succ u1} α (iSup.{u1, max 1 u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Subtype.{u2} ι p) f) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f (Subtype.mk.{u2} ι p i h))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : (Subtype.{u2} ι p) -> α}, Eq.{succ u1} α (supᵢ.{u1, max 1 u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Subtype.{u2} ι p) f) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => f (Subtype.mk.{u2} ι p i h))))
-Case conversion may be inaccurate. Consider using '#align supr_subtype supᵢ_subtypeₓ'. -/
-theorem supᵢ_subtype {p : ι → Prop} {f : Subtype p → α} : supᵢ f = ⨆ (i) (h : p i), f ⟨i, h⟩ :=
-  le_antisymm (supᵢ_le fun ⟨i, h⟩ => le_supᵢ₂ i h) (supᵢ₂_le fun i h => le_supᵢ _ _)
-#align supr_subtype supᵢ_subtype
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : (Subtype.{u2} ι p) -> α}, Eq.{succ u1} α (iSup.{u1, max 1 u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Subtype.{u2} ι p) f) (iSup.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => f (Subtype.mk.{u2} ι p i h))))
+Case conversion may be inaccurate. Consider using '#align supr_subtype iSup_subtypeₓ'. -/
+theorem iSup_subtype {p : ι → Prop} {f : Subtype p → α} : iSup f = ⨆ (i) (h : p i), f ⟨i, h⟩ :=
+  le_antisymm (iSup_le fun ⟨i, h⟩ => le_iSup₂ i h) (iSup₂_le fun i h => le_iSup _ _)
+#align supr_subtype iSup_subtype
 
-/- warning: infi_subtype -> infᵢ_subtype is a dubious translation:
+/- warning: infi_subtype -> iInf_subtype is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : (Subtype.{u2} ι p) -> α}, Eq.{succ u1} α (infᵢ.{u1, max 1 u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Subtype.{u2} ι p) f) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f (Subtype.mk.{u2} ι p i h))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : (Subtype.{u2} ι p) -> α}, Eq.{succ u1} α (iInf.{u1, max 1 u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Subtype.{u2} ι p) f) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f (Subtype.mk.{u2} ι p i h))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : (Subtype.{u2} ι p) -> α}, Eq.{succ u1} α (infᵢ.{u1, max 1 u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Subtype.{u2} ι p) f) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => f (Subtype.mk.{u2} ι p i h))))
-Case conversion may be inaccurate. Consider using '#align infi_subtype infᵢ_subtypeₓ'. -/
-theorem infᵢ_subtype : ∀ {p : ι → Prop} {f : Subtype p → α}, infᵢ f = ⨅ (i) (h : p i), f ⟨i, h⟩ :=
-  @supᵢ_subtype αᵒᵈ _ _
-#align infi_subtype infᵢ_subtype
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : (Subtype.{u2} ι p) -> α}, Eq.{succ u1} α (iInf.{u1, max 1 u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Subtype.{u2} ι p) f) (iInf.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => f (Subtype.mk.{u2} ι p i h))))
+Case conversion may be inaccurate. Consider using '#align infi_subtype iInf_subtypeₓ'. -/
+theorem iInf_subtype : ∀ {p : ι → Prop} {f : Subtype p → α}, iInf f = ⨅ (i) (h : p i), f ⟨i, h⟩ :=
+  @iSup_subtype αᵒᵈ _ _
+#align infi_subtype iInf_subtype
 
-/- warning: supr_subtype' -> supᵢ_subtype' is a dubious translation:
+/- warning: supr_subtype' -> iSup_subtype' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α}, Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) (supᵢ.{u1, max 1 u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Subtype.{u2} ι p) (fun (x : Subtype.{u2} ι p) => f ((fun (a : Sort.{max 1 u2}) (b : Sort.{u2}) [self : HasLiftT.{max 1 u2, u2} a b] => self.0) (Subtype.{u2} ι p) ι (HasLiftT.mk.{max 1 u2, u2} (Subtype.{u2} ι p) ι (CoeTCₓ.coe.{max 1 u2, u2} (Subtype.{u2} ι p) ι (coeBase.{max 1 u2, u2} (Subtype.{u2} ι p) ι (coeSubtype.{u2} ι (fun (x : ι) => p x))))) x) (Subtype.property.{u2} ι p x)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α}, Eq.{succ u1} α (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) (iSup.{u1, max 1 u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Subtype.{u2} ι p) (fun (x : Subtype.{u2} ι p) => f ((fun (a : Sort.{max 1 u2}) (b : Sort.{u2}) [self : HasLiftT.{max 1 u2, u2} a b] => self.0) (Subtype.{u2} ι p) ι (HasLiftT.mk.{max 1 u2, u2} (Subtype.{u2} ι p) ι (CoeTCₓ.coe.{max 1 u2, u2} (Subtype.{u2} ι p) ι (coeBase.{max 1 u2, u2} (Subtype.{u2} ι p) ι (coeSubtype.{u2} ι (fun (x : ι) => p x))))) x) (Subtype.property.{u2} ι p x)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α}, Eq.{succ u2} α (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i h))) (supᵢ.{u2, max 1 u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Subtype.{u1} ι p) (fun (x : Subtype.{u1} ι p) => f (Subtype.val.{u1} ι p x) (Subtype.property.{u1} ι p x)))
-Case conversion may be inaccurate. Consider using '#align supr_subtype' supᵢ_subtype'ₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α}, Eq.{succ u2} α (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i h))) (iSup.{u2, max 1 u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Subtype.{u1} ι p) (fun (x : Subtype.{u1} ι p) => f (Subtype.val.{u1} ι p x) (Subtype.property.{u1} ι p x)))
+Case conversion may be inaccurate. Consider using '#align supr_subtype' iSup_subtype'ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i h) -/
-theorem supᵢ_subtype' {p : ι → Prop} {f : ∀ i, p i → α} :
+theorem iSup_subtype' {p : ι → Prop} {f : ∀ i, p i → α} :
     (⨆ (i) (h), f i h) = ⨆ x : Subtype p, f x x.property :=
-  (@supᵢ_subtype _ _ _ p fun x => f x.val x.property).symm
-#align supr_subtype' supᵢ_subtype'
+  (@iSup_subtype _ _ _ p fun x => f x.val x.property).symm
+#align supr_subtype' iSup_subtype'
 
-/- warning: infi_subtype' -> infᵢ_subtype' is a dubious translation:
+/- warning: infi_subtype' -> iInf_subtype' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α}, Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) (infᵢ.{u1, max 1 u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Subtype.{u2} ι p) (fun (x : Subtype.{u2} ι p) => f ((fun (a : Sort.{max 1 u2}) (b : Sort.{u2}) [self : HasLiftT.{max 1 u2, u2} a b] => self.0) (Subtype.{u2} ι p) ι (HasLiftT.mk.{max 1 u2, u2} (Subtype.{u2} ι p) ι (CoeTCₓ.coe.{max 1 u2, u2} (Subtype.{u2} ι p) ι (coeBase.{max 1 u2, u2} (Subtype.{u2} ι p) ι (coeSubtype.{u2} ι (fun (x : ι) => p x))))) x) (Subtype.property.{u2} ι p x)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α}, Eq.{succ u1} α (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) (iInf.{u1, max 1 u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Subtype.{u2} ι p) (fun (x : Subtype.{u2} ι p) => f ((fun (a : Sort.{max 1 u2}) (b : Sort.{u2}) [self : HasLiftT.{max 1 u2, u2} a b] => self.0) (Subtype.{u2} ι p) ι (HasLiftT.mk.{max 1 u2, u2} (Subtype.{u2} ι p) ι (CoeTCₓ.coe.{max 1 u2, u2} (Subtype.{u2} ι p) ι (coeBase.{max 1 u2, u2} (Subtype.{u2} ι p) ι (coeSubtype.{u2} ι (fun (x : ι) => p x))))) x) (Subtype.property.{u2} ι p x)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α}, Eq.{succ u2} α (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i h))) (infᵢ.{u2, max 1 u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Subtype.{u1} ι p) (fun (x : Subtype.{u1} ι p) => f (Subtype.val.{u1} ι p x) (Subtype.property.{u1} ι p x)))
-Case conversion may be inaccurate. Consider using '#align infi_subtype' infᵢ_subtype'ₓ'. -/
-theorem infᵢ_subtype' {p : ι → Prop} {f : ∀ i, p i → α} :
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α}, Eq.{succ u2} α (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => iInf.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i h))) (iInf.{u2, max 1 u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Subtype.{u1} ι p) (fun (x : Subtype.{u1} ι p) => f (Subtype.val.{u1} ι p x) (Subtype.property.{u1} ι p x)))
+Case conversion may be inaccurate. Consider using '#align infi_subtype' iInf_subtype'ₓ'. -/
+theorem iInf_subtype' {p : ι → Prop} {f : ∀ i, p i → α} :
     (⨅ (i) (h : p i), f i h) = ⨅ x : Subtype p, f x x.property :=
-  (@infᵢ_subtype _ _ _ p fun x => f x.val x.property).symm
-#align infi_subtype' infᵢ_subtype'
+  (@iInf_subtype _ _ _ p fun x => f x.val x.property).symm
+#align infi_subtype' iInf_subtype'
 
-/- warning: supr_subtype'' -> supᵢ_subtype'' is a dubious translation:
+/- warning: supr_subtype'' -> iSup_subtype'' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Type.{u2}} (s : Set.{u2} ι) (f : ι -> α), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeSubtype.{succ u2} ι (fun (x : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) x s))))) i))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (t : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) t s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) t s) => f t)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Type.{u2}} (s : Set.{u2} ι) (f : ι -> α), Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeSubtype.{succ u2} ι (fun (x : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) x s))))) i))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (t : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) t s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) t s) => f t)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Type.{u2}} (s : Set.{u2} ι) (f : ι -> α), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Set.Elem.{u2} ι s) (fun (i : Set.Elem.{u2} ι s) => f (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x s) i))) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (t : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) t s) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) t s) => f t)))
-Case conversion may be inaccurate. Consider using '#align supr_subtype'' supᵢ_subtype''ₓ'. -/
-theorem supᵢ_subtype'' {ι} (s : Set ι) (f : ι → α) : (⨆ i : s, f i) = ⨆ (t : ι) (H : t ∈ s), f t :=
-  supᵢ_subtype
-#align supr_subtype'' supᵢ_subtype''
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Type.{u2}} (s : Set.{u2} ι) (f : ι -> α), Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Set.Elem.{u2} ι s) (fun (i : Set.Elem.{u2} ι s) => f (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x s) i))) (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (t : ι) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) t s) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) t s) => f t)))
+Case conversion may be inaccurate. Consider using '#align supr_subtype'' iSup_subtype''ₓ'. -/
+theorem iSup_subtype'' {ι} (s : Set ι) (f : ι → α) : (⨆ i : s, f i) = ⨆ (t : ι) (H : t ∈ s), f t :=
+  iSup_subtype
+#align supr_subtype'' iSup_subtype''
 
-/- warning: infi_subtype'' -> infᵢ_subtype'' is a dubious translation:
+/- warning: infi_subtype'' -> iInf_subtype'' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Type.{u2}} (s : Set.{u2} ι) (f : ι -> α), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeSubtype.{succ u2} ι (fun (x : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) x s))))) i))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (t : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) t s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) t s) => f t)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Type.{u2}} (s : Set.{u2} ι) (f : ι -> α), Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeSubtype.{succ u2} ι (fun (x : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) x s))))) i))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (t : ι) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) t s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) t s) => f t)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Type.{u2}} (s : Set.{u2} ι) (f : ι -> α), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Set.Elem.{u2} ι s) (fun (i : Set.Elem.{u2} ι s) => f (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x s) i))) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (t : ι) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) t s) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) t s) => f t)))
-Case conversion may be inaccurate. Consider using '#align infi_subtype'' infᵢ_subtype''ₓ'. -/
-theorem infᵢ_subtype'' {ι} (s : Set ι) (f : ι → α) : (⨅ i : s, f i) = ⨅ (t : ι) (H : t ∈ s), f t :=
-  infᵢ_subtype
-#align infi_subtype'' infᵢ_subtype''
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Type.{u2}} (s : Set.{u2} ι) (f : ι -> α), Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Set.Elem.{u2} ι s) (fun (i : Set.Elem.{u2} ι s) => f (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x s) i))) (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (t : ι) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) t s) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) t s) => f t)))
+Case conversion may be inaccurate. Consider using '#align infi_subtype'' iInf_subtype''ₓ'. -/
+theorem iInf_subtype'' {ι} (s : Set ι) (f : ι → α) : (⨅ i : s, f i) = ⨅ (t : ι) (H : t ∈ s), f t :=
+  iInf_subtype
+#align infi_subtype'' iInf_subtype''
 
-/- warning: bsupr_const -> bsupᵢ_const is a dubious translation:
+/- warning: bsupr_const -> biSup_const is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Type.{u2}} {a : α} {s : Set.{u2} ι}, (Set.Nonempty.{u2} ι s) -> (Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) => a))) a)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Type.{u2}} {a : α} {s : Set.{u2} ι}, (Set.Nonempty.{u2} ι s) -> (Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) => a))) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Type.{u2}} {a : α} {s : Set.{u2} ι}, (Set.Nonempty.{u2} ι s) -> (Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) => a))) a)
-Case conversion may be inaccurate. Consider using '#align bsupr_const bsupᵢ_constₓ'. -/
-theorem bsupᵢ_const {ι : Sort _} {a : α} {s : Set ι} (hs : s.Nonempty) : (⨆ i ∈ s, a) = a :=
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Type.{u2}} {a : α} {s : Set.{u2} ι}, (Set.Nonempty.{u2} ι s) -> (Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) => a))) a)
+Case conversion may be inaccurate. Consider using '#align bsupr_const biSup_constₓ'. -/
+theorem biSup_const {ι : Sort _} {a : α} {s : Set ι} (hs : s.Nonempty) : (⨆ i ∈ s, a) = a :=
   by
   haveI : Nonempty s := set.nonempty_coe_sort.mpr hs
-  rw [← supᵢ_subtype'', supᵢ_const]
-#align bsupr_const bsupᵢ_const
+  rw [← iSup_subtype'', iSup_const]
+#align bsupr_const biSup_const
 
-/- warning: binfi_const -> binfᵢ_const is a dubious translation:
+/- warning: binfi_const -> biInf_const is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Type.{u2}} {a : α} {s : Set.{u2} ι}, (Set.Nonempty.{u2} ι s) -> (Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) => a))) a)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Type.{u2}} {a : α} {s : Set.{u2} ι}, (Set.Nonempty.{u2} ι s) -> (Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) => a))) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Type.{u2}} {a : α} {s : Set.{u2} ι}, (Set.Nonempty.{u2} ι s) -> (Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) => a))) a)
-Case conversion may be inaccurate. Consider using '#align binfi_const binfᵢ_constₓ'. -/
-theorem binfᵢ_const {ι : Sort _} {a : α} {s : Set ι} (hs : s.Nonempty) : (⨅ i ∈ s, a) = a :=
-  @bsupᵢ_const αᵒᵈ _ ι _ s hs
-#align binfi_const binfᵢ_const
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {ι : Type.{u2}} {a : α} {s : Set.{u2} ι}, (Set.Nonempty.{u2} ι s) -> (Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) (fun (H : Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) => a))) a)
+Case conversion may be inaccurate. Consider using '#align binfi_const biInf_constₓ'. -/
+theorem biInf_const {ι : Sort _} {a : α} {s : Set ι} (hs : s.Nonempty) : (⨅ i ∈ s, a) = a :=
+  @biSup_const αᵒᵈ _ ι _ s hs
+#align binfi_const biInf_const
 
-/- warning: supr_sup_eq -> supᵢ_sup_eq is a dubious translation:
+/- warning: supr_sup_eq -> iSup_sup_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) (g x))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => f x)) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => g x)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, Eq.{succ u1} α (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) (g x))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => f x)) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => g x)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, Eq.{succ u2} α (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (x : ι) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f x) (g x))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (x : ι) => f x)) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (x : ι) => g x)))
-Case conversion may be inaccurate. Consider using '#align supr_sup_eq supᵢ_sup_eqₓ'. -/
-theorem supᵢ_sup_eq : (⨆ x, f x ⊔ g x) = (⨆ x, f x) ⊔ ⨆ x, g x :=
-  le_antisymm (supᵢ_le fun i => sup_le_sup (le_supᵢ _ _) <| le_supᵢ _ _)
-    (sup_le (supᵢ_mono fun i => le_sup_left) <| supᵢ_mono fun i => le_sup_right)
-#align supr_sup_eq supᵢ_sup_eq
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, Eq.{succ u2} α (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (x : ι) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f x) (g x))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (x : ι) => f x)) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (x : ι) => g x)))
+Case conversion may be inaccurate. Consider using '#align supr_sup_eq iSup_sup_eqₓ'. -/
+theorem iSup_sup_eq : (⨆ x, f x ⊔ g x) = (⨆ x, f x) ⊔ ⨆ x, g x :=
+  le_antisymm (iSup_le fun i => sup_le_sup (le_iSup _ _) <| le_iSup _ _)
+    (sup_le (iSup_mono fun i => le_sup_left) <| iSup_mono fun i => le_sup_right)
+#align supr_sup_eq iSup_sup_eq
 
-/- warning: infi_inf_eq -> infᵢ_inf_eq is a dubious translation:
+/- warning: infi_inf_eq -> iInf_inf_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) (g x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f x)) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => g x)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, Eq.{succ u1} α (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) (g x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f x)) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => g x)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, Eq.{succ u2} α (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f x) (g x))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => f x)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => g x)))
-Case conversion may be inaccurate. Consider using '#align infi_inf_eq infᵢ_inf_eqₓ'. -/
-theorem infᵢ_inf_eq : (⨅ x, f x ⊓ g x) = (⨅ x, f x) ⊓ ⨅ x, g x :=
-  @supᵢ_sup_eq αᵒᵈ _ _ _ _
-#align infi_inf_eq infᵢ_inf_eq
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, Eq.{succ u2} α (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f x) (g x))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => f x)) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => g x)))
+Case conversion may be inaccurate. Consider using '#align infi_inf_eq iInf_inf_eqₓ'. -/
+theorem iInf_inf_eq : (⨅ x, f x ⊓ g x) = (⨅ x, f x) ⊓ ⨅ x, g x :=
+  @iSup_sup_eq αᵒᵈ _ _ _ _
+#align infi_inf_eq iInf_inf_eq
 
-/- warning: supr_sup -> supᵢ_sup is a dubious translation:
+/- warning: supr_sup -> iSup_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => f x)) a) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => f x)) a) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) a))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (x : ι) => f x)) a) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (x : ι) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) a))
-Case conversion may be inaccurate. Consider using '#align supr_sup supᵢ_supₓ'. -/
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iSup.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (x : ι) => f x)) a) (iSup.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (x : ι) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) a))
+Case conversion may be inaccurate. Consider using '#align supr_sup iSup_supₓ'. -/
 /- TODO: here is another example where more flexible pattern matching
    might help.
 
@@ -2319,963 +2319,963 @@ begin
   safe, pose h := f a ⊓ g a, begin [smt] ematch, ematch  end
 end
 -/
-theorem supᵢ_sup [Nonempty ι] {f : ι → α} {a : α} : (⨆ x, f x) ⊔ a = ⨆ x, f x ⊔ a := by
-  rw [supᵢ_sup_eq, supᵢ_const]
-#align supr_sup supᵢ_sup
+theorem iSup_sup [Nonempty ι] {f : ι → α} {a : α} : (⨆ x, f x) ⊔ a = ⨆ x, f x ⊔ a := by
+  rw [iSup_sup_eq, iSup_const]
+#align supr_sup iSup_sup
 
-/- warning: infi_inf -> infᵢ_inf is a dubious translation:
+/- warning: infi_inf -> iInf_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f x)) a) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f x)) a) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) a))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (x : ι) => f x)) a) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (x : ι) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f x) a))
-Case conversion may be inaccurate. Consider using '#align infi_inf infᵢ_infₓ'. -/
-theorem infᵢ_inf [Nonempty ι] {f : ι → α} {a : α} : (⨅ x, f x) ⊓ a = ⨅ x, f x ⊓ a := by
-  rw [infᵢ_inf_eq, infᵢ_const]
-#align infi_inf infᵢ_inf
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (iInf.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (x : ι) => f x)) a) (iInf.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (x : ι) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f x) a))
+Case conversion may be inaccurate. Consider using '#align infi_inf iInf_infₓ'. -/
+theorem iInf_inf [Nonempty ι] {f : ι → α} {a : α} : (⨅ x, f x) ⊓ a = ⨅ x, f x ⊓ a := by
+  rw [iInf_inf_eq, iInf_const]
+#align infi_inf iInf_inf
 
-/- warning: sup_supr -> sup_supᵢ is a dubious translation:
+/- warning: sup_supr -> sup_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => f x))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f x)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => f x))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f x)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (x : ι) => f x))) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (x : ι) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f x)))
-Case conversion may be inaccurate. Consider using '#align sup_supr sup_supᵢₓ'. -/
-theorem sup_supᵢ [Nonempty ι] {f : ι → α} {a : α} : (a ⊔ ⨆ x, f x) = ⨆ x, a ⊔ f x := by
-  rw [supᵢ_sup_eq, supᵢ_const]
-#align sup_supr sup_supᵢ
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (iSup.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (x : ι) => f x))) (iSup.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (x : ι) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f x)))
+Case conversion may be inaccurate. Consider using '#align sup_supr sup_iSupₓ'. -/
+theorem sup_iSup [Nonempty ι] {f : ι → α} {a : α} : (a ⊔ ⨆ x, f x) = ⨆ x, a ⊔ f x := by
+  rw [iSup_sup_eq, iSup_const]
+#align sup_supr sup_iSup
 
-/- warning: inf_infi -> inf_infᵢ is a dubious translation:
+/- warning: inf_infi -> inf_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f x))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f x)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f x))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f x)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (x : ι) => f x))) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (x : ι) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (f x)))
-Case conversion may be inaccurate. Consider using '#align inf_infi inf_infᵢₓ'. -/
-theorem inf_infᵢ [Nonempty ι] {f : ι → α} {a : α} : (a ⊓ ⨅ x, f x) = ⨅ x, a ⊓ f x := by
-  rw [infᵢ_inf_eq, infᵢ_const]
-#align inf_infi inf_infᵢ
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (iInf.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (x : ι) => f x))) (iInf.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (x : ι) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (f x)))
+Case conversion may be inaccurate. Consider using '#align inf_infi inf_iInfₓ'. -/
+theorem inf_iInf [Nonempty ι] {f : ι → α} {a : α} : (a ⊓ ⨅ x, f x) = ⨅ x, a ⊓ f x := by
+  rw [iInf_inf_eq, iInf_const]
+#align inf_infi inf_iInf
 
-/- warning: bsupr_sup -> bsupᵢ_sup is a dubious translation:
+/- warning: bsupr_sup -> biSup_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) a) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i h) a))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) a) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i h) a))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => f i h))) a) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i h) a))))
-Case conversion may be inaccurate. Consider using '#align bsupr_sup bsupᵢ_supₓ'. -/
-theorem bsupᵢ_sup {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iSup.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => f i h))) a) (iSup.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i h) a))))
+Case conversion may be inaccurate. Consider using '#align bsupr_sup biSup_supₓ'. -/
+theorem biSup_sup {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
     (⨆ (i) (h : p i), f i h) ⊔ a = ⨆ (i) (h : p i), f i h ⊔ a := by
   haveI : Nonempty { i // p i } :=
       let ⟨i, hi⟩ := h
       ⟨⟨i, hi⟩⟩ <;>
-    rw [supᵢ_subtype', supᵢ_subtype', supᵢ_sup]
-#align bsupr_sup bsupᵢ_sup
+    rw [iSup_subtype', iSup_subtype', iSup_sup]
+#align bsupr_sup biSup_sup
 
-/- warning: sup_bsupr -> sup_bsupᵢ is a dubious translation:
+/- warning: sup_bsupr -> sup_biSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h)))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f i h)))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h)))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f i h)))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => f i h)))) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f i h)))))
-Case conversion may be inaccurate. Consider using '#align sup_bsupr sup_bsupᵢₓ'. -/
-theorem sup_bsupᵢ {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (iSup.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => f i h)))) (iSup.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f i h)))))
+Case conversion may be inaccurate. Consider using '#align sup_bsupr sup_biSupₓ'. -/
+theorem sup_biSup {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
     (a ⊔ ⨆ (i) (h : p i), f i h) = ⨆ (i) (h : p i), a ⊔ f i h := by
-  simpa only [sup_comm] using bsupᵢ_sup h
-#align sup_bsupr sup_bsupᵢ
+  simpa only [sup_comm] using biSup_sup h
+#align sup_bsupr sup_biSup
 
-/- warning: binfi_inf -> binfᵢ_inf is a dubious translation:
+/- warning: binfi_inf -> biInf_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) a) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i h) a))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) a) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i h) a))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => f i h))) a) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f i h) a))))
-Case conversion may be inaccurate. Consider using '#align binfi_inf binfᵢ_infₓ'. -/
-theorem binfᵢ_inf {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (iInf.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => f i h))) a) (iInf.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f i h) a))))
+Case conversion may be inaccurate. Consider using '#align binfi_inf biInf_infₓ'. -/
+theorem biInf_inf {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
     (⨅ (i) (h : p i), f i h) ⊓ a = ⨅ (i) (h : p i), f i h ⊓ a :=
-  @bsupᵢ_sup αᵒᵈ ι _ p f _ h
-#align binfi_inf binfᵢ_inf
+  @biSup_sup αᵒᵈ ι _ p f _ h
+#align binfi_inf biInf_inf
 
-/- warning: inf_binfi -> inf_binfᵢ is a dubious translation:
+/- warning: inf_binfi -> inf_biInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h)))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f i h)))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h)))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f i h)))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => f i h)))) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (f i h)))))
-Case conversion may be inaccurate. Consider using '#align inf_binfi inf_binfᵢₓ'. -/
-theorem inf_binfᵢ {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (iInf.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => f i h)))) (iInf.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (f i h)))))
+Case conversion may be inaccurate. Consider using '#align inf_binfi inf_biInfₓ'. -/
+theorem inf_biInf {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
     (a ⊓ ⨅ (i) (h : p i), f i h) = ⨅ (i) (h : p i), a ⊓ f i h :=
-  @sup_bsupᵢ αᵒᵈ ι _ p f _ h
-#align inf_binfi inf_binfᵢ
+  @sup_biSup αᵒᵈ ι _ p f _ h
+#align inf_binfi inf_biInf
 
 /-! ### `supr` and `infi` under `Prop` -/
 
 
-/- warning: supr_false -> supᵢ_false is a dubious translation:
+/- warning: supr_false -> iSup_false is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : False -> α}, Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) False s) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : False -> α}, Eq.{succ u1} α (iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) False s) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : False -> α}, Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) False s) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align supr_false supᵢ_falseₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : False -> α}, Eq.{succ u1} α (iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) False s) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align supr_false iSup_falseₓ'. -/
 @[simp]
-theorem supᵢ_false {s : False → α} : supᵢ s = ⊥ :=
-  le_antisymm (supᵢ_le fun i => False.elim i) bot_le
-#align supr_false supᵢ_false
+theorem iSup_false {s : False → α} : iSup s = ⊥ :=
+  le_antisymm (iSup_le fun i => False.elim i) bot_le
+#align supr_false iSup_false
 
-/- warning: infi_false -> infᵢ_false is a dubious translation:
+/- warning: infi_false -> iInf_false is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : False -> α}, Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) False s) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : False -> α}, Eq.{succ u1} α (iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) False s) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : False -> α}, Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) False s) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align infi_false infᵢ_falseₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : False -> α}, Eq.{succ u1} α (iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) False s) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align infi_false iInf_falseₓ'. -/
 @[simp]
-theorem infᵢ_false {s : False → α} : infᵢ s = ⊤ :=
-  le_antisymm le_top (le_infᵢ fun i => False.elim i)
-#align infi_false infᵢ_false
+theorem iInf_false {s : False → α} : iInf s = ⊤ :=
+  le_antisymm le_top (le_iInf fun i => False.elim i)
+#align infi_false iInf_false
 
-/- warning: supr_true -> supᵢ_true is a dubious translation:
+/- warning: supr_true -> iSup_true is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : True -> α}, Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) True s) (s trivial)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : True -> α}, Eq.{succ u1} α (iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) True s) (s trivial)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : True -> α}, Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) True s) (s trivial)
-Case conversion may be inaccurate. Consider using '#align supr_true supᵢ_trueₓ'. -/
-theorem supᵢ_true {s : True → α} : supᵢ s = s trivial :=
-  supᵢ_pos trivial
-#align supr_true supᵢ_true
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : True -> α}, Eq.{succ u1} α (iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) True s) (s trivial)
+Case conversion may be inaccurate. Consider using '#align supr_true iSup_trueₓ'. -/
+theorem iSup_true {s : True → α} : iSup s = s trivial :=
+  iSup_pos trivial
+#align supr_true iSup_true
 
-/- warning: infi_true -> infᵢ_true is a dubious translation:
+/- warning: infi_true -> iInf_true is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : True -> α}, Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) True s) (s trivial)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : True -> α}, Eq.{succ u1} α (iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) True s) (s trivial)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : True -> α}, Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) True s) (s trivial)
-Case conversion may be inaccurate. Consider using '#align infi_true infᵢ_trueₓ'. -/
-theorem infᵢ_true {s : True → α} : infᵢ s = s trivial :=
-  infᵢ_pos trivial
-#align infi_true infᵢ_true
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : True -> α}, Eq.{succ u1} α (iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) True s) (s trivial)
+Case conversion may be inaccurate. Consider using '#align infi_true iInf_trueₓ'. -/
+theorem iInf_true {s : True → α} : iInf s = s trivial :=
+  iInf_pos trivial
+#align infi_true iInf_true
 
-/- warning: supr_exists -> supᵢ_exists is a dubious translation:
+/- warning: supr_exists -> iSup_exists is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : (Exists.{u2} ι p) -> α}, Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Exists.{u2} ι p) (fun (x : Exists.{u2} ι p) => f x)) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f (Exists.intro.{u2} ι p i h))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : (Exists.{u2} ι p) -> α}, Eq.{succ u1} α (iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Exists.{u2} ι p) (fun (x : Exists.{u2} ι p) => f x)) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f (Exists.intro.{u2} ι p i h))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : (Exists.{u2} ι p) -> α}, Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Exists.{u2} ι p) (fun (x : Exists.{u2} ι p) => f x)) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => f (Exists.intro.{u2} ι p i h))))
-Case conversion may be inaccurate. Consider using '#align supr_exists supᵢ_existsₓ'. -/
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : (Exists.{u2} ι p) -> α}, Eq.{succ u1} α (iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Exists.{u2} ι p) (fun (x : Exists.{u2} ι p) => f x)) (iSup.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => f (Exists.intro.{u2} ι p i h))))
+Case conversion may be inaccurate. Consider using '#align supr_exists iSup_existsₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i h) -/
 @[simp]
-theorem supᵢ_exists {p : ι → Prop} {f : Exists p → α} : (⨆ x, f x) = ⨆ (i) (h), f ⟨i, h⟩ :=
-  le_antisymm (supᵢ_le fun ⟨i, h⟩ => le_supᵢ₂ i h) (supᵢ₂_le fun i h => le_supᵢ _ _)
-#align supr_exists supᵢ_exists
+theorem iSup_exists {p : ι → Prop} {f : Exists p → α} : (⨆ x, f x) = ⨆ (i) (h), f ⟨i, h⟩ :=
+  le_antisymm (iSup_le fun ⟨i, h⟩ => le_iSup₂ i h) (iSup₂_le fun i h => le_iSup _ _)
+#align supr_exists iSup_exists
 
-/- warning: infi_exists -> infᵢ_exists is a dubious translation:
+/- warning: infi_exists -> iInf_exists is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : (Exists.{u2} ι p) -> α}, Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Exists.{u2} ι p) (fun (x : Exists.{u2} ι p) => f x)) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f (Exists.intro.{u2} ι p i h))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : (Exists.{u2} ι p) -> α}, Eq.{succ u1} α (iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Exists.{u2} ι p) (fun (x : Exists.{u2} ι p) => f x)) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f (Exists.intro.{u2} ι p i h))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : (Exists.{u2} ι p) -> α}, Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Exists.{u2} ι p) (fun (x : Exists.{u2} ι p) => f x)) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => f (Exists.intro.{u2} ι p i h))))
-Case conversion may be inaccurate. Consider using '#align infi_exists infᵢ_existsₓ'. -/
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : (Exists.{u2} ι p) -> α}, Eq.{succ u1} α (iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Exists.{u2} ι p) (fun (x : Exists.{u2} ι p) => f x)) (iInf.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => f (Exists.intro.{u2} ι p i h))))
+Case conversion may be inaccurate. Consider using '#align infi_exists iInf_existsₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i h) -/
 @[simp]
-theorem infᵢ_exists {p : ι → Prop} {f : Exists p → α} : (⨅ x, f x) = ⨅ (i) (h), f ⟨i, h⟩ :=
-  @supᵢ_exists αᵒᵈ _ _ _ _
-#align infi_exists infᵢ_exists
+theorem iInf_exists {p : ι → Prop} {f : Exists p → α} : (⨅ x, f x) = ⨅ (i) (h), f ⟨i, h⟩ :=
+  @iSup_exists αᵒᵈ _ _ _ _
+#align infi_exists iInf_exists
 
-/- warning: supr_and -> supᵢ_and is a dubious translation:
+/- warning: supr_and -> iSup_and is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (And p q) -> α}, Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (And p q) s) (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) p (fun (h₁ : p) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) q (fun (h₂ : q) => s (And.intro p q h₁ h₂))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (And p q) -> α}, Eq.{succ u1} α (iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (And p q) s) (iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) p (fun (h₁ : p) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) q (fun (h₂ : q) => s (And.intro p q h₁ h₂))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (And p q) -> α}, Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (And p q) s) (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) p (fun (h₁ : p) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) q (fun (h₂ : q) => s (And.intro p q h₁ h₂))))
-Case conversion may be inaccurate. Consider using '#align supr_and supᵢ_andₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (And p q) -> α}, Eq.{succ u1} α (iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (And p q) s) (iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) p (fun (h₁ : p) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) q (fun (h₂ : q) => s (And.intro p q h₁ h₂))))
+Case conversion may be inaccurate. Consider using '#align supr_and iSup_andₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (h₁ h₂) -/
-theorem supᵢ_and {p q : Prop} {s : p ∧ q → α} : supᵢ s = ⨆ (h₁) (h₂), s ⟨h₁, h₂⟩ :=
-  le_antisymm (supᵢ_le fun ⟨i, h⟩ => le_supᵢ₂ i h) (supᵢ₂_le fun i h => le_supᵢ _ _)
-#align supr_and supᵢ_and
+theorem iSup_and {p q : Prop} {s : p ∧ q → α} : iSup s = ⨆ (h₁) (h₂), s ⟨h₁, h₂⟩ :=
+  le_antisymm (iSup_le fun ⟨i, h⟩ => le_iSup₂ i h) (iSup₂_le fun i h => le_iSup _ _)
+#align supr_and iSup_and
 
-/- warning: infi_and -> infᵢ_and is a dubious translation:
+/- warning: infi_and -> iInf_and is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (And p q) -> α}, Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (And p q) s) (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) p (fun (h₁ : p) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) q (fun (h₂ : q) => s (And.intro p q h₁ h₂))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (And p q) -> α}, Eq.{succ u1} α (iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (And p q) s) (iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) p (fun (h₁ : p) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) q (fun (h₂ : q) => s (And.intro p q h₁ h₂))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (And p q) -> α}, Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (And p q) s) (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) p (fun (h₁ : p) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) q (fun (h₂ : q) => s (And.intro p q h₁ h₂))))
-Case conversion may be inaccurate. Consider using '#align infi_and infᵢ_andₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (And p q) -> α}, Eq.{succ u1} α (iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (And p q) s) (iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) p (fun (h₁ : p) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) q (fun (h₂ : q) => s (And.intro p q h₁ h₂))))
+Case conversion may be inaccurate. Consider using '#align infi_and iInf_andₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (h₁ h₂) -/
-theorem infᵢ_and {p q : Prop} {s : p ∧ q → α} : infᵢ s = ⨅ (h₁) (h₂), s ⟨h₁, h₂⟩ :=
-  @supᵢ_and αᵒᵈ _ _ _ _
-#align infi_and infᵢ_and
+theorem iInf_and {p q : Prop} {s : p ∧ q → α} : iInf s = ⨅ (h₁) (h₂), s ⟨h₁, h₂⟩ :=
+  @iSup_and αᵒᵈ _ _ _ _
+#align infi_and iInf_and
 
-/- warning: supr_and' -> supᵢ_and' is a dubious translation:
+/- warning: supr_and' -> iSup_and' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : p -> q -> α}, Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) p (fun (h₁ : p) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) q (fun (h₂ : q) => s h₁ h₂))) (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (And p q) (fun (h : And p q) => s (And.left p q h) (And.right p q h)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : p -> q -> α}, Eq.{succ u1} α (iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) p (fun (h₁ : p) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) q (fun (h₂ : q) => s h₁ h₂))) (iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (And p q) (fun (h : And p q) => s (And.left p q h) (And.right p q h)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : p -> q -> α}, Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) p (fun (h₁ : p) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) q (fun (h₂ : q) => s h₁ h₂))) (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (And p q) (fun (h : And p q) => s (And.left p q h) (And.right p q h)))
-Case conversion may be inaccurate. Consider using '#align supr_and' supᵢ_and'ₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : p -> q -> α}, Eq.{succ u1} α (iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) p (fun (h₁ : p) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) q (fun (h₂ : q) => s h₁ h₂))) (iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (And p q) (fun (h : And p q) => s (And.left p q h) (And.right p q h)))
+Case conversion may be inaccurate. Consider using '#align supr_and' iSup_and'ₓ'. -/
 /-- The symmetric case of `supr_and`, useful for rewriting into a supremum over a conjunction -/
-theorem supᵢ_and' {p q : Prop} {s : p → q → α} :
+theorem iSup_and' {p q : Prop} {s : p → q → α} :
     (⨆ (h₁ : p) (h₂ : q), s h₁ h₂) = ⨆ h : p ∧ q, s h.1 h.2 :=
-  Eq.symm supᵢ_and
-#align supr_and' supᵢ_and'
+  Eq.symm iSup_and
+#align supr_and' iSup_and'
 
-/- warning: infi_and' -> infᵢ_and' is a dubious translation:
+/- warning: infi_and' -> iInf_and' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : p -> q -> α}, Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) p (fun (h₁ : p) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) q (fun (h₂ : q) => s h₁ h₂))) (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (And p q) (fun (h : And p q) => s (And.left p q h) (And.right p q h)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : p -> q -> α}, Eq.{succ u1} α (iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) p (fun (h₁ : p) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) q (fun (h₂ : q) => s h₁ h₂))) (iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (And p q) (fun (h : And p q) => s (And.left p q h) (And.right p q h)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : p -> q -> α}, Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) p (fun (h₁ : p) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) q (fun (h₂ : q) => s h₁ h₂))) (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (And p q) (fun (h : And p q) => s (And.left p q h) (And.right p q h)))
-Case conversion may be inaccurate. Consider using '#align infi_and' infᵢ_and'ₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : p -> q -> α}, Eq.{succ u1} α (iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) p (fun (h₁ : p) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) q (fun (h₂ : q) => s h₁ h₂))) (iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (And p q) (fun (h : And p q) => s (And.left p q h) (And.right p q h)))
+Case conversion may be inaccurate. Consider using '#align infi_and' iInf_and'ₓ'. -/
 /-- The symmetric case of `infi_and`, useful for rewriting into a infimum over a conjunction -/
-theorem infᵢ_and' {p q : Prop} {s : p → q → α} :
+theorem iInf_and' {p q : Prop} {s : p → q → α} :
     (⨅ (h₁ : p) (h₂ : q), s h₁ h₂) = ⨅ h : p ∧ q, s h.1 h.2 :=
-  Eq.symm infᵢ_and
-#align infi_and' infᵢ_and'
+  Eq.symm iInf_and
+#align infi_and' iInf_and'
 
-/- warning: supr_or -> supᵢ_or is a dubious translation:
+/- warning: supr_or -> iSup_or is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (Or p q) -> α}, Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Or p q) (fun (x : Or p q) => s x)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) p (fun (i : p) => s (Or.inl p q i))) (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) q (fun (j : q) => s (Or.inr p q j))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (Or p q) -> α}, Eq.{succ u1} α (iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Or p q) (fun (x : Or p q) => s x)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) p (fun (i : p) => s (Or.inl p q i))) (iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) q (fun (j : q) => s (Or.inr p q j))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (Or p q) -> α}, Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Or p q) (fun (x : Or p q) => s x)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) p (fun (i : p) => s (Or.inl p q i))) (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) q (fun (j : q) => s (Or.inr p q j))))
-Case conversion may be inaccurate. Consider using '#align supr_or supᵢ_orₓ'. -/
-theorem supᵢ_or {p q : Prop} {s : p ∨ q → α} :
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (Or p q) -> α}, Eq.{succ u1} α (iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Or p q) (fun (x : Or p q) => s x)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) p (fun (i : p) => s (Or.inl p q i))) (iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) q (fun (j : q) => s (Or.inr p q j))))
+Case conversion may be inaccurate. Consider using '#align supr_or iSup_orₓ'. -/
+theorem iSup_or {p q : Prop} {s : p ∨ q → α} :
     (⨆ x, s x) = (⨆ i, s (Or.inl i)) ⊔ ⨆ j, s (Or.inr j) :=
   le_antisymm
-    (supᵢ_le fun i =>
+    (iSup_le fun i =>
       match i with
-      | Or.inl i => le_sup_of_le_left <| le_supᵢ _ i
-      | Or.inr j => le_sup_of_le_right <| le_supᵢ _ j)
-    (sup_le (supᵢ_comp_le _ _) (supᵢ_comp_le _ _))
-#align supr_or supᵢ_or
+      | Or.inl i => le_sup_of_le_left <| le_iSup _ i
+      | Or.inr j => le_sup_of_le_right <| le_iSup _ j)
+    (sup_le (iSup_comp_le _ _) (iSup_comp_le _ _))
+#align supr_or iSup_or
 
-/- warning: infi_or -> infᵢ_or is a dubious translation:
+/- warning: infi_or -> iInf_or is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (Or p q) -> α}, Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Or p q) (fun (x : Or p q) => s x)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) p (fun (i : p) => s (Or.inl p q i))) (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) q (fun (j : q) => s (Or.inr p q j))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (Or p q) -> α}, Eq.{succ u1} α (iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Or p q) (fun (x : Or p q) => s x)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) p (fun (i : p) => s (Or.inl p q i))) (iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) q (fun (j : q) => s (Or.inr p q j))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (Or p q) -> α}, Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Or p q) (fun (x : Or p q) => s x)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) p (fun (i : p) => s (Or.inl p q i))) (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) q (fun (j : q) => s (Or.inr p q j))))
-Case conversion may be inaccurate. Consider using '#align infi_or infᵢ_orₓ'. -/
-theorem infᵢ_or {p q : Prop} {s : p ∨ q → α} :
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (Or p q) -> α}, Eq.{succ u1} α (iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Or p q) (fun (x : Or p q) => s x)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) p (fun (i : p) => s (Or.inl p q i))) (iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) q (fun (j : q) => s (Or.inr p q j))))
+Case conversion may be inaccurate. Consider using '#align infi_or iInf_orₓ'. -/
+theorem iInf_or {p q : Prop} {s : p ∨ q → α} :
     (⨅ x, s x) = (⨅ i, s (Or.inl i)) ⊓ ⨅ j, s (Or.inr j) :=
-  @supᵢ_or αᵒᵈ _ _ _ _
-#align infi_or infᵢ_or
+  @iSup_or αᵒᵈ _ _ _ _
+#align infi_or iInf_or
 
 section
 
 variable (p : ι → Prop) [DecidablePred p]
 
-/- warning: supr_dite -> supᵢ_dite is a dubious translation:
+/- warning: supr_dite -> iSup_dite is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u2} ι p] (f : forall (i : ι), (p i) -> α) (g : forall (i : ι), (Not (p i)) -> α), Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => dite.{succ u1} α (p i) (_inst_2 i) (fun (h : p i) => f i h) (fun (h : Not (p i)) => g i h))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => g i h))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u2} ι p] (f : forall (i : ι), (p i) -> α) (g : forall (i : ι), (Not (p i)) -> α), Eq.{succ u1} α (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => dite.{succ u1} α (p i) (_inst_2 i) (fun (h : p i) => f i h) (fun (h : Not (p i)) => g i h))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => g i h))))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u1} ι p] (f : forall (i : ι), (p i) -> α) (g : forall (i : ι), (Not (p i)) -> α), Eq.{succ u2} α (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => dite.{succ u2} α (p i) (_inst_2 i) (fun (h : p i) => f i h) (fun (h : Not (p i)) => g i h))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i h))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => g i h))))
-Case conversion may be inaccurate. Consider using '#align supr_dite supᵢ_diteₓ'. -/
-theorem supᵢ_dite (f : ∀ i, p i → α) (g : ∀ i, ¬p i → α) :
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u1} ι p] (f : forall (i : ι), (p i) -> α) (g : forall (i : ι), (Not (p i)) -> α), Eq.{succ u2} α (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => dite.{succ u2} α (p i) (_inst_2 i) (fun (h : p i) => f i h) (fun (h : Not (p i)) => g i h))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i h))) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => g i h))))
+Case conversion may be inaccurate. Consider using '#align supr_dite iSup_diteₓ'. -/
+theorem iSup_dite (f : ∀ i, p i → α) (g : ∀ i, ¬p i → α) :
     (⨆ i, if h : p i then f i h else g i h) = (⨆ (i) (h : p i), f i h) ⊔ ⨆ (i) (h : ¬p i), g i h :=
   by
-  rw [← supᵢ_sup_eq]
+  rw [← iSup_sup_eq]
   congr 1 with i
   split_ifs with h <;> simp [h]
-#align supr_dite supᵢ_dite
+#align supr_dite iSup_dite
 
-/- warning: infi_dite -> infᵢ_dite is a dubious translation:
+/- warning: infi_dite -> iInf_dite is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u2} ι p] (f : forall (i : ι), (p i) -> α) (g : forall (i : ι), (Not (p i)) -> α), Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => dite.{succ u1} α (p i) (_inst_2 i) (fun (h : p i) => f i h) (fun (h : Not (p i)) => g i h))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => g i h))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u2} ι p] (f : forall (i : ι), (p i) -> α) (g : forall (i : ι), (Not (p i)) -> α), Eq.{succ u1} α (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => dite.{succ u1} α (p i) (_inst_2 i) (fun (h : p i) => f i h) (fun (h : Not (p i)) => g i h))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => g i h))))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u1} ι p] (f : forall (i : ι), (p i) -> α) (g : forall (i : ι), (Not (p i)) -> α), Eq.{succ u2} α (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => dite.{succ u2} α (p i) (_inst_2 i) (fun (h : p i) => f i h) (fun (h : Not (p i)) => g i h))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i h))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => g i h))))
-Case conversion may be inaccurate. Consider using '#align infi_dite infᵢ_diteₓ'. -/
-theorem infᵢ_dite (f : ∀ i, p i → α) (g : ∀ i, ¬p i → α) :
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u1} ι p] (f : forall (i : ι), (p i) -> α) (g : forall (i : ι), (Not (p i)) -> α), Eq.{succ u2} α (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => dite.{succ u2} α (p i) (_inst_2 i) (fun (h : p i) => f i h) (fun (h : Not (p i)) => g i h))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => iInf.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i h))) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => iInf.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => g i h))))
+Case conversion may be inaccurate. Consider using '#align infi_dite iInf_diteₓ'. -/
+theorem iInf_dite (f : ∀ i, p i → α) (g : ∀ i, ¬p i → α) :
     (⨅ i, if h : p i then f i h else g i h) = (⨅ (i) (h : p i), f i h) ⊓ ⨅ (i) (h : ¬p i), g i h :=
-  supᵢ_dite p (show ∀ i, p i → αᵒᵈ from f) g
-#align infi_dite infᵢ_dite
+  iSup_dite p (show ∀ i, p i → αᵒᵈ from f) g
+#align infi_dite iInf_dite
 
-/- warning: supr_ite -> supᵢ_ite is a dubious translation:
+/- warning: supr_ite -> iSup_ite is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u2} ι p] (f : ι -> α) (g : ι -> α), Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => ite.{succ u1} α (p i) (_inst_2 i) (f i) (g i))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => g i))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u2} ι p] (f : ι -> α) (g : ι -> α), Eq.{succ u1} α (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => ite.{succ u1} α (p i) (_inst_2 i) (f i) (g i))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => g i))))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u1} ι p] (f : ι -> α) (g : ι -> α), Eq.{succ u2} α (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => ite.{succ u2} α (p i) (_inst_2 i) (f i) (g i))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => g i))))
-Case conversion may be inaccurate. Consider using '#align supr_ite supᵢ_iteₓ'. -/
-theorem supᵢ_ite (f g : ι → α) :
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u1} ι p] (f : ι -> α) (g : ι -> α), Eq.{succ u2} α (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => ite.{succ u2} α (p i) (_inst_2 i) (f i) (g i))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => g i))))
+Case conversion may be inaccurate. Consider using '#align supr_ite iSup_iteₓ'. -/
+theorem iSup_ite (f g : ι → α) :
     (⨆ i, if p i then f i else g i) = (⨆ (i) (h : p i), f i) ⊔ ⨆ (i) (h : ¬p i), g i :=
-  supᵢ_dite _ _ _
-#align supr_ite supᵢ_ite
+  iSup_dite _ _ _
+#align supr_ite iSup_ite
 
-/- warning: infi_ite -> infᵢ_ite is a dubious translation:
+/- warning: infi_ite -> iInf_ite is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u2} ι p] (f : ι -> α) (g : ι -> α), Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => ite.{succ u1} α (p i) (_inst_2 i) (f i) (g i))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => g i))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u2} ι p] (f : ι -> α) (g : ι -> α), Eq.{succ u1} α (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => ite.{succ u1} α (p i) (_inst_2 i) (f i) (g i))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => g i))))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u1} ι p] (f : ι -> α) (g : ι -> α), Eq.{succ u2} α (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => ite.{succ u2} α (p i) (_inst_2 i) (f i) (g i))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => g i))))
-Case conversion may be inaccurate. Consider using '#align infi_ite infᵢ_iteₓ'. -/
-theorem infᵢ_ite (f g : ι → α) :
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u1} ι p] (f : ι -> α) (g : ι -> α), Eq.{succ u2} α (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => ite.{succ u2} α (p i) (_inst_2 i) (f i) (g i))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => iInf.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => iInf.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => g i))))
+Case conversion may be inaccurate. Consider using '#align infi_ite iInf_iteₓ'. -/
+theorem iInf_ite (f g : ι → α) :
     (⨅ i, if p i then f i else g i) = (⨅ (i) (h : p i), f i) ⊓ ⨅ (i) (h : ¬p i), g i :=
-  infᵢ_dite _ _ _
-#align infi_ite infᵢ_ite
+  iInf_dite _ _ _
+#align infi_ite iInf_ite
 
 end
 
-/- warning: supr_range -> supᵢ_range is a dubious translation:
+/- warning: supr_range -> iSup_range is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {g : β -> α} {f : ι -> β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (b : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Set.range.{u2, u3} β ι f)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Set.range.{u2, u3} β ι f)) => g b))) (supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => g (f i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {g : β -> α} {f : ι -> β}, Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (b : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Set.range.{u2, u3} β ι f)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Set.range.{u2, u3} β ι f)) => g b))) (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => g (f i)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {g : β -> α} {f : ι -> β}, Eq.{succ u3} α (supᵢ.{u3, succ u2} α (CompleteLattice.toSupSet.{u3} α _inst_1) β (fun (b : β) => supᵢ.{u3, 0} α (CompleteLattice.toSupSet.{u3} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Set.range.{u2, u1} β ι f)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Set.range.{u2, u1} β ι f)) => g b))) (supᵢ.{u3, u1} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => g (f i)))
-Case conversion may be inaccurate. Consider using '#align supr_range supᵢ_rangeₓ'. -/
-theorem supᵢ_range {g : β → α} {f : ι → β} : (⨆ b ∈ range f, g b) = ⨆ i, g (f i) := by
-  rw [← supᵢ_subtype'', supᵢ_range']
-#align supr_range supᵢ_range
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {g : β -> α} {f : ι -> β}, Eq.{succ u3} α (iSup.{u3, succ u2} α (CompleteLattice.toSupSet.{u3} α _inst_1) β (fun (b : β) => iSup.{u3, 0} α (CompleteLattice.toSupSet.{u3} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Set.range.{u2, u1} β ι f)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Set.range.{u2, u1} β ι f)) => g b))) (iSup.{u3, u1} α (CompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => g (f i)))
+Case conversion may be inaccurate. Consider using '#align supr_range iSup_rangeₓ'. -/
+theorem iSup_range {g : β → α} {f : ι → β} : (⨆ b ∈ range f, g b) = ⨆ i, g (f i) := by
+  rw [← iSup_subtype'', iSup_range']
+#align supr_range iSup_range
 
-/- warning: infi_range -> infᵢ_range is a dubious translation:
+/- warning: infi_range -> iInf_range is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {g : β -> α} {f : ι -> β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (b : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Set.range.{u2, u3} β ι f)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Set.range.{u2, u3} β ι f)) => g b))) (infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => g (f i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {g : β -> α} {f : ι -> β}, Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (b : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Set.range.{u2, u3} β ι f)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Set.range.{u2, u3} β ι f)) => g b))) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => g (f i)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {g : β -> α} {f : ι -> β}, Eq.{succ u3} α (infᵢ.{u3, succ u2} α (CompleteLattice.toInfSet.{u3} α _inst_1) β (fun (b : β) => infᵢ.{u3, 0} α (CompleteLattice.toInfSet.{u3} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Set.range.{u2, u1} β ι f)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Set.range.{u2, u1} β ι f)) => g b))) (infᵢ.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => g (f i)))
-Case conversion may be inaccurate. Consider using '#align infi_range infᵢ_rangeₓ'. -/
-theorem infᵢ_range : ∀ {g : β → α} {f : ι → β}, (⨅ b ∈ range f, g b) = ⨅ i, g (f i) :=
-  @supᵢ_range αᵒᵈ _ _ _
-#align infi_range infᵢ_range
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u3} α] {g : β -> α} {f : ι -> β}, Eq.{succ u3} α (iInf.{u3, succ u2} α (CompleteLattice.toInfSet.{u3} α _inst_1) β (fun (b : β) => iInf.{u3, 0} α (CompleteLattice.toInfSet.{u3} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Set.range.{u2, u1} β ι f)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Set.range.{u2, u1} β ι f)) => g b))) (iInf.{u3, u1} α (CompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => g (f i)))
+Case conversion may be inaccurate. Consider using '#align infi_range iInf_rangeₓ'. -/
+theorem iInf_range : ∀ {g : β → α} {f : ι → β}, (⨅ b ∈ range f, g b) = ⨅ i, g (f i) :=
+  @iSup_range αᵒᵈ _ _ _
+#align infi_range iInf_range
 
-/- warning: Sup_image -> supₛ_image is a dubious translation:
+/- warning: Sup_image -> sSup_image is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u2} β} {f : β -> α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Set.image.{u2, u1} β α f s)) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (a : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) => f a)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u2} β} {f : β -> α}, Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Set.image.{u2, u1} β α f s)) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (a : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) => f a)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u2} β} {f : β -> α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Set.image.{u2, u1} β α f s)) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (a : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) a s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) a s) => f a)))
-Case conversion may be inaccurate. Consider using '#align Sup_image supₛ_imageₓ'. -/
-theorem supₛ_image {s : Set β} {f : β → α} : supₛ (f '' s) = ⨆ a ∈ s, f a := by
-  rw [← supᵢ_subtype'', supₛ_image']
-#align Sup_image supₛ_image
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u2} β} {f : β -> α}, Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Set.image.{u2, u1} β α f s)) (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (a : β) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) a s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) a s) => f a)))
+Case conversion may be inaccurate. Consider using '#align Sup_image sSup_imageₓ'. -/
+theorem sSup_image {s : Set β} {f : β → α} : sSup (f '' s) = ⨆ a ∈ s, f a := by
+  rw [← iSup_subtype'', sSup_image']
+#align Sup_image sSup_image
 
-/- warning: Inf_image -> infₛ_image is a dubious translation:
+/- warning: Inf_image -> sInf_image is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u2} β} {f : β -> α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Set.image.{u2, u1} β α f s)) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (a : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) => f a)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u2} β} {f : β -> α}, Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Set.image.{u2, u1} β α f s)) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (a : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) => f a)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u2} β} {f : β -> α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Set.image.{u2, u1} β α f s)) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (a : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) a s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) a s) => f a)))
-Case conversion may be inaccurate. Consider using '#align Inf_image infₛ_imageₓ'. -/
-theorem infₛ_image {s : Set β} {f : β → α} : infₛ (f '' s) = ⨅ a ∈ s, f a :=
-  @supₛ_image αᵒᵈ _ _ _ _
-#align Inf_image infₛ_image
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u2} β} {f : β -> α}, Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Set.image.{u2, u1} β α f s)) (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (a : β) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) a s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) a s) => f a)))
+Case conversion may be inaccurate. Consider using '#align Inf_image sInf_imageₓ'. -/
+theorem sInf_image {s : Set β} {f : β → α} : sInf (f '' s) = ⨅ a ∈ s, f a :=
+  @sSup_image αᵒᵈ _ _ _ _
+#align Inf_image sInf_image
 
-/- warning: supr_emptyset -> supᵢ_emptyset is a dubious translation:
+/- warning: supr_emptyset -> iSup_emptyset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (EmptyCollection.emptyCollection.{u2} (Set.{u2} β) (Set.hasEmptyc.{u2} β))) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (EmptyCollection.emptyCollection.{u2} (Set.{u2} β) (Set.hasEmptyc.{u2} β))) => f x))) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α}, Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (EmptyCollection.emptyCollection.{u2} (Set.{u2} β) (Set.hasEmptyc.{u2} β))) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (EmptyCollection.emptyCollection.{u2} (Set.{u2} β) (Set.hasEmptyc.{u2} β))) => f x))) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α}, Eq.{succ u2} α (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (x : β) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (EmptyCollection.emptyCollection.{u1} (Set.{u1} β) (Set.instEmptyCollectionSet.{u1} β))) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (EmptyCollection.emptyCollection.{u1} (Set.{u1} β) (Set.instEmptyCollectionSet.{u1} β))) => f x))) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align supr_emptyset supᵢ_emptysetₓ'. -/
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α}, Eq.{succ u2} α (iSup.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (x : β) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (EmptyCollection.emptyCollection.{u1} (Set.{u1} β) (Set.instEmptyCollectionSet.{u1} β))) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (EmptyCollection.emptyCollection.{u1} (Set.{u1} β) (Set.instEmptyCollectionSet.{u1} β))) => f x))) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align supr_emptyset iSup_emptysetₓ'. -/
 /-
 ### supr and infi under set constructions
 -/
-theorem supᵢ_emptyset {f : β → α} : (⨆ x ∈ (∅ : Set β), f x) = ⊥ := by simp
-#align supr_emptyset supᵢ_emptyset
+theorem iSup_emptyset {f : β → α} : (⨆ x ∈ (∅ : Set β), f x) = ⊥ := by simp
+#align supr_emptyset iSup_emptyset
 
-/- warning: infi_emptyset -> infᵢ_emptyset is a dubious translation:
+/- warning: infi_emptyset -> iInf_emptyset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (EmptyCollection.emptyCollection.{u2} (Set.{u2} β) (Set.hasEmptyc.{u2} β))) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (EmptyCollection.emptyCollection.{u2} (Set.{u2} β) (Set.hasEmptyc.{u2} β))) => f x))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α}, Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (EmptyCollection.emptyCollection.{u2} (Set.{u2} β) (Set.hasEmptyc.{u2} β))) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (EmptyCollection.emptyCollection.{u2} (Set.{u2} β) (Set.hasEmptyc.{u2} β))) => f x))) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α}, Eq.{succ u2} α (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (x : β) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (EmptyCollection.emptyCollection.{u1} (Set.{u1} β) (Set.instEmptyCollectionSet.{u1} β))) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (EmptyCollection.emptyCollection.{u1} (Set.{u1} β) (Set.instEmptyCollectionSet.{u1} β))) => f x))) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align infi_emptyset infᵢ_emptysetₓ'. -/
-theorem infᵢ_emptyset {f : β → α} : (⨅ x ∈ (∅ : Set β), f x) = ⊤ := by simp
-#align infi_emptyset infᵢ_emptyset
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α}, Eq.{succ u2} α (iInf.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (x : β) => iInf.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (EmptyCollection.emptyCollection.{u1} (Set.{u1} β) (Set.instEmptyCollectionSet.{u1} β))) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (EmptyCollection.emptyCollection.{u1} (Set.{u1} β) (Set.instEmptyCollectionSet.{u1} β))) => f x))) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align infi_emptyset iInf_emptysetₓ'. -/
+theorem iInf_emptyset {f : β → α} : (⨅ x ∈ (∅ : Set β), f x) = ⊤ := by simp
+#align infi_emptyset iInf_emptyset
 
-/- warning: supr_univ -> supᵢ_univ is a dubious translation:
+/- warning: supr_univ -> iSup_univ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Set.univ.{u2} β)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Set.univ.{u2} β)) => f x))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => f x))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α}, Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Set.univ.{u2} β)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Set.univ.{u2} β)) => f x))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => f x))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α}, Eq.{succ u2} α (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (x : β) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Set.univ.{u1} β)) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Set.univ.{u1} β)) => f x))) (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (x : β) => f x))
-Case conversion may be inaccurate. Consider using '#align supr_univ supᵢ_univₓ'. -/
-theorem supᵢ_univ {f : β → α} : (⨆ x ∈ (univ : Set β), f x) = ⨆ x, f x := by simp
-#align supr_univ supᵢ_univ
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α}, Eq.{succ u2} α (iSup.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (x : β) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Set.univ.{u1} β)) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Set.univ.{u1} β)) => f x))) (iSup.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (x : β) => f x))
+Case conversion may be inaccurate. Consider using '#align supr_univ iSup_univₓ'. -/
+theorem iSup_univ {f : β → α} : (⨆ x ∈ (univ : Set β), f x) = ⨆ x, f x := by simp
+#align supr_univ iSup_univ
 
-/- warning: infi_univ -> infᵢ_univ is a dubious translation:
+/- warning: infi_univ -> iInf_univ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Set.univ.{u2} β)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Set.univ.{u2} β)) => f x))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => f x))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α}, Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Set.univ.{u2} β)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Set.univ.{u2} β)) => f x))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => f x))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α}, Eq.{succ u2} α (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (x : β) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Set.univ.{u1} β)) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Set.univ.{u1} β)) => f x))) (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (x : β) => f x))
-Case conversion may be inaccurate. Consider using '#align infi_univ infᵢ_univₓ'. -/
-theorem infᵢ_univ {f : β → α} : (⨅ x ∈ (univ : Set β), f x) = ⨅ x, f x := by simp
-#align infi_univ infᵢ_univ
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α}, Eq.{succ u2} α (iInf.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (x : β) => iInf.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Set.univ.{u1} β)) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Set.univ.{u1} β)) => f x))) (iInf.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (x : β) => f x))
+Case conversion may be inaccurate. Consider using '#align infi_univ iInf_univₓ'. -/
+theorem iInf_univ {f : β → α} : (⨅ x ∈ (univ : Set β), f x) = ⨅ x, f x := by simp
+#align infi_univ iInf_univ
 
-/- warning: supr_union -> supᵢ_union is a dubious translation:
+/- warning: supr_union -> iSup_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.hasUnion.{u2} β) s t)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.hasUnion.{u2} β) s t)) => f x))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) => f x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.hasUnion.{u2} β) s t)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.hasUnion.{u2} β) s t)) => f x))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) => f x))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.instUnionSet.{u2} β) s t)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.instUnionSet.{u2} β) s t)) => f x))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) => f x))))
-Case conversion may be inaccurate. Consider using '#align supr_union supᵢ_unionₓ'. -/
-theorem supᵢ_union {f : β → α} {s t : Set β} : (⨆ x ∈ s ∪ t, f x) = (⨆ x ∈ s, f x) ⊔ ⨆ x ∈ t, f x :=
-  by simp_rw [mem_union, supᵢ_or, supᵢ_sup_eq]
-#align supr_union supᵢ_union
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.instUnionSet.{u2} β) s t)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.instUnionSet.{u2} β) s t)) => f x))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))) (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) => f x))))
+Case conversion may be inaccurate. Consider using '#align supr_union iSup_unionₓ'. -/
+theorem iSup_union {f : β → α} {s t : Set β} : (⨆ x ∈ s ∪ t, f x) = (⨆ x ∈ s, f x) ⊔ ⨆ x ∈ t, f x :=
+  by simp_rw [mem_union, iSup_or, iSup_sup_eq]
+#align supr_union iSup_union
 
-/- warning: infi_union -> infᵢ_union is a dubious translation:
+/- warning: infi_union -> iInf_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.hasUnion.{u2} β) s t)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.hasUnion.{u2} β) s t)) => f x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) => f x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.hasUnion.{u2} β) s t)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.hasUnion.{u2} β) s t)) => f x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) => f x))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.instUnionSet.{u2} β) s t)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.instUnionSet.{u2} β) s t)) => f x))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) => f x))))
-Case conversion may be inaccurate. Consider using '#align infi_union infᵢ_unionₓ'. -/
-theorem infᵢ_union {f : β → α} {s t : Set β} : (⨅ x ∈ s ∪ t, f x) = (⨅ x ∈ s, f x) ⊓ ⨅ x ∈ t, f x :=
-  @supᵢ_union αᵒᵈ _ _ _ _ _
-#align infi_union infᵢ_union
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.instUnionSet.{u2} β) s t)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.instUnionSet.{u2} β) s t)) => f x))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))) (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) => f x))))
+Case conversion may be inaccurate. Consider using '#align infi_union iInf_unionₓ'. -/
+theorem iInf_union {f : β → α} {s t : Set β} : (⨅ x ∈ s ∪ t, f x) = (⨅ x ∈ s, f x) ⊓ ⨅ x ∈ t, f x :=
+  @iSup_union αᵒᵈ _ _ _ _ _
+#align infi_union iInf_union
 
-/- warning: supr_split -> supᵢ_split is a dubious translation:
+/- warning: supr_split -> iSup_split is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : β -> α) (p : β -> Prop), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => f i)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => f i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : β -> α) (p : β -> Prop), Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => f i)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => f i))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (p : β -> Prop), Eq.{succ u2} α (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => f i)) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => f i))))
-Case conversion may be inaccurate. Consider using '#align supr_split supᵢ_splitₓ'. -/
-theorem supᵢ_split (f : β → α) (p : β → Prop) :
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (p : β -> Prop), Eq.{succ u2} α (iSup.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => f i)) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (iSup.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (iSup.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => f i))))
+Case conversion may be inaccurate. Consider using '#align supr_split iSup_splitₓ'. -/
+theorem iSup_split (f : β → α) (p : β → Prop) :
     (⨆ i, f i) = (⨆ (i) (h : p i), f i) ⊔ ⨆ (i) (h : ¬p i), f i := by
-  simpa [Classical.em] using @supᵢ_union _ _ _ f { i | p i } { i | ¬p i }
-#align supr_split supᵢ_split
+  simpa [Classical.em] using @iSup_union _ _ _ f { i | p i } { i | ¬p i }
+#align supr_split iSup_split
 
-/- warning: infi_split -> infᵢ_split is a dubious translation:
+/- warning: infi_split -> iInf_split is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : β -> α) (p : β -> Prop), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => f i)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => f i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : β -> α) (p : β -> Prop), Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => f i)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => f i))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (p : β -> Prop), Eq.{succ u2} α (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => f i)) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => f i))))
-Case conversion may be inaccurate. Consider using '#align infi_split infᵢ_splitₓ'. -/
-theorem infᵢ_split :
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (p : β -> Prop), Eq.{succ u2} α (iInf.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => f i)) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (iInf.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => iInf.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (iInf.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => iInf.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => f i))))
+Case conversion may be inaccurate. Consider using '#align infi_split iInf_splitₓ'. -/
+theorem iInf_split :
     ∀ (f : β → α) (p : β → Prop), (⨅ i, f i) = (⨅ (i) (h : p i), f i) ⊓ ⨅ (i) (h : ¬p i), f i :=
-  @supᵢ_split αᵒᵈ _ _
-#align infi_split infᵢ_split
+  @iSup_split αᵒᵈ _ _
+#align infi_split iInf_split
 
-/- warning: supr_split_single -> supᵢ_split_single is a dubious translation:
+/- warning: supr_split_single -> iSup_split_single is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : β -> α) (i₀ : β), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => f i)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i₀) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Ne.{succ u2} β i i₀) (fun (h : Ne.{succ u2} β i i₀) => f i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : β -> α) (i₀ : β), Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => f i)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i₀) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Ne.{succ u2} β i i₀) (fun (h : Ne.{succ u2} β i i₀) => f i))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (i₀ : β), Eq.{succ u2} α (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => f i)) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f i₀) (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Ne.{succ u1} β i i₀) (fun (h : Ne.{succ u1} β i i₀) => f i))))
-Case conversion may be inaccurate. Consider using '#align supr_split_single supᵢ_split_singleₓ'. -/
-theorem supᵢ_split_single (f : β → α) (i₀ : β) : (⨆ i, f i) = f i₀ ⊔ ⨆ (i) (h : i ≠ i₀), f i :=
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (i₀ : β), Eq.{succ u2} α (iSup.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => f i)) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f i₀) (iSup.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Ne.{succ u1} β i i₀) (fun (h : Ne.{succ u1} β i i₀) => f i))))
+Case conversion may be inaccurate. Consider using '#align supr_split_single iSup_split_singleₓ'. -/
+theorem iSup_split_single (f : β → α) (i₀ : β) : (⨆ i, f i) = f i₀ ⊔ ⨆ (i) (h : i ≠ i₀), f i :=
   by
-  convert supᵢ_split _ _
+  convert iSup_split _ _
   simp
-#align supr_split_single supᵢ_split_single
+#align supr_split_single iSup_split_single
 
-/- warning: infi_split_single -> infᵢ_split_single is a dubious translation:
+/- warning: infi_split_single -> iInf_split_single is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : β -> α) (i₀ : β), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => f i)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i₀) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Ne.{succ u2} β i i₀) (fun (h : Ne.{succ u2} β i i₀) => f i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : β -> α) (i₀ : β), Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => f i)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i₀) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Ne.{succ u2} β i i₀) (fun (h : Ne.{succ u2} β i i₀) => f i))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (i₀ : β), Eq.{succ u2} α (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => f i)) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f i₀) (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Ne.{succ u1} β i i₀) (fun (h : Ne.{succ u1} β i i₀) => f i))))
-Case conversion may be inaccurate. Consider using '#align infi_split_single infᵢ_split_singleₓ'. -/
-theorem infᵢ_split_single (f : β → α) (i₀ : β) : (⨅ i, f i) = f i₀ ⊓ ⨅ (i) (h : i ≠ i₀), f i :=
-  @supᵢ_split_single αᵒᵈ _ _ _ _
-#align infi_split_single infᵢ_split_single
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (i₀ : β), Eq.{succ u2} α (iInf.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => f i)) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f i₀) (iInf.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => iInf.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Ne.{succ u1} β i i₀) (fun (h : Ne.{succ u1} β i i₀) => f i))))
+Case conversion may be inaccurate. Consider using '#align infi_split_single iInf_split_singleₓ'. -/
+theorem iInf_split_single (f : β → α) (i₀ : β) : (⨅ i, f i) = f i₀ ⊓ ⨅ (i) (h : i ≠ i₀), f i :=
+  @iSup_split_single αᵒᵈ _ _ _ _
+#align infi_split_single iInf_split_single
 
-/- warning: supr_le_supr_of_subset -> supᵢ_le_supᵢ_of_subset is a dubious translation:
+/- warning: supr_le_supr_of_subset -> iSup_le_iSup_of_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, (HasSubset.Subset.{u2} (Set.{u2} β) (Set.hasSubset.{u2} β) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) => f x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, (HasSubset.Subset.{u2} (Set.{u2} β) (Set.hasSubset.{u2} β) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) => f x))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, (HasSubset.Subset.{u2} (Set.{u2} β) (Set.instHasSubsetSet.{u2} β) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) => f x))))
-Case conversion may be inaccurate. Consider using '#align supr_le_supr_of_subset supᵢ_le_supᵢ_of_subsetₓ'. -/
-theorem supᵢ_le_supᵢ_of_subset {f : β → α} {s t : Set β} : s ⊆ t → (⨆ x ∈ s, f x) ≤ ⨆ x ∈ t, f x :=
-  bsupᵢ_mono
-#align supr_le_supr_of_subset supᵢ_le_supᵢ_of_subset
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, (HasSubset.Subset.{u2} (Set.{u2} β) (Set.instHasSubsetSet.{u2} β) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))) (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) => f x))))
+Case conversion may be inaccurate. Consider using '#align supr_le_supr_of_subset iSup_le_iSup_of_subsetₓ'. -/
+theorem iSup_le_iSup_of_subset {f : β → α} {s t : Set β} : s ⊆ t → (⨆ x ∈ s, f x) ≤ ⨆ x ∈ t, f x :=
+  biSup_mono
+#align supr_le_supr_of_subset iSup_le_iSup_of_subset
 
-/- warning: infi_le_infi_of_subset -> infᵢ_le_infᵢ_of_subset is a dubious translation:
+/- warning: infi_le_infi_of_subset -> iInf_le_iInf_of_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, (HasSubset.Subset.{u2} (Set.{u2} β) (Set.hasSubset.{u2} β) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) => f x))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, (HasSubset.Subset.{u2} (Set.{u2} β) (Set.hasSubset.{u2} β) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) => f x))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, (HasSubset.Subset.{u2} (Set.{u2} β) (Set.instHasSubsetSet.{u2} β) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) => f x))) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))))
-Case conversion may be inaccurate. Consider using '#align infi_le_infi_of_subset infᵢ_le_infᵢ_of_subsetₓ'. -/
-theorem infᵢ_le_infᵢ_of_subset {f : β → α} {s t : Set β} : s ⊆ t → (⨅ x ∈ t, f x) ≤ ⨅ x ∈ s, f x :=
-  binfᵢ_mono
-#align infi_le_infi_of_subset infᵢ_le_infᵢ_of_subset
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, (HasSubset.Subset.{u2} (Set.{u2} β) (Set.instHasSubsetSet.{u2} β) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) => f x))) (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))))
+Case conversion may be inaccurate. Consider using '#align infi_le_infi_of_subset iInf_le_iInf_of_subsetₓ'. -/
+theorem iInf_le_iInf_of_subset {f : β → α} {s t : Set β} : s ⊆ t → (⨅ x ∈ t, f x) ≤ ⨅ x ∈ s, f x :=
+  biInf_mono
+#align infi_le_infi_of_subset iInf_le_iInf_of_subset
 
-/- warning: supr_insert -> supᵢ_insert is a dubious translation:
+/- warning: supr_insert -> iSup_insert is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {b : β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) b s)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) b s)) => f x))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f b) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {b : β}, Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) b s)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) b s)) => f x))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f b) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {b : β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.instInsertSet.{u2} β) b s)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.instInsertSet.{u2} β) b s)) => f x))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f b) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))))
-Case conversion may be inaccurate. Consider using '#align supr_insert supᵢ_insertₓ'. -/
-theorem supᵢ_insert {f : β → α} {s : Set β} {b : β} :
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {b : β}, Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.instInsertSet.{u2} β) b s)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.instInsertSet.{u2} β) b s)) => f x))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f b) (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))))
+Case conversion may be inaccurate. Consider using '#align supr_insert iSup_insertₓ'. -/
+theorem iSup_insert {f : β → α} {s : Set β} {b : β} :
     (⨆ x ∈ insert b s, f x) = f b ⊔ ⨆ x ∈ s, f x :=
-  Eq.trans supᵢ_union <| congr_arg (fun x => x ⊔ ⨆ x ∈ s, f x) supᵢ_supᵢ_eq_left
-#align supr_insert supᵢ_insert
+  Eq.trans iSup_union <| congr_arg (fun x => x ⊔ ⨆ x ∈ s, f x) iSup_iSup_eq_left
+#align supr_insert iSup_insert
 
-/- warning: infi_insert -> infᵢ_insert is a dubious translation:
+/- warning: infi_insert -> iInf_insert is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {b : β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) b s)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) b s)) => f x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f b) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {b : β}, Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) b s)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) b s)) => f x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f b) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {b : β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.instInsertSet.{u2} β) b s)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.instInsertSet.{u2} β) b s)) => f x))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f b) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))))
-Case conversion may be inaccurate. Consider using '#align infi_insert infᵢ_insertₓ'. -/
-theorem infᵢ_insert {f : β → α} {s : Set β} {b : β} :
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {b : β}, Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.instInsertSet.{u2} β) b s)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.instInsertSet.{u2} β) b s)) => f x))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f b) (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))))
+Case conversion may be inaccurate. Consider using '#align infi_insert iInf_insertₓ'. -/
+theorem iInf_insert {f : β → α} {s : Set β} {b : β} :
     (⨅ x ∈ insert b s, f x) = f b ⊓ ⨅ x ∈ s, f x :=
-  Eq.trans infᵢ_union <| congr_arg (fun x => x ⊓ ⨅ x ∈ s, f x) infᵢ_infᵢ_eq_left
-#align infi_insert infᵢ_insert
+  Eq.trans iInf_union <| congr_arg (fun x => x ⊓ ⨅ x ∈ s, f x) iInf_iInf_eq_left
+#align infi_insert iInf_insert
 
-/- warning: supr_singleton -> supᵢ_singleton is a dubious translation:
+/- warning: supr_singleton -> iSup_singleton is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {b : β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b)) => f x))) (f b)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {b : β}, Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b)) => f x))) (f b)
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α} {b : β}, Eq.{succ u2} α (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (x : β) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b)) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b)) => f x))) (f b)
-Case conversion may be inaccurate. Consider using '#align supr_singleton supᵢ_singletonₓ'. -/
-theorem supᵢ_singleton {f : β → α} {b : β} : (⨆ x ∈ (singleton b : Set β), f x) = f b := by simp
-#align supr_singleton supᵢ_singleton
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α} {b : β}, Eq.{succ u2} α (iSup.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (x : β) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b)) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b)) => f x))) (f b)
+Case conversion may be inaccurate. Consider using '#align supr_singleton iSup_singletonₓ'. -/
+theorem iSup_singleton {f : β → α} {b : β} : (⨆ x ∈ (singleton b : Set β), f x) = f b := by simp
+#align supr_singleton iSup_singleton
 
-/- warning: infi_singleton -> infᵢ_singleton is a dubious translation:
+/- warning: infi_singleton -> iInf_singleton is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {b : β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b)) => f x))) (f b)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {b : β}, Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b)) => f x))) (f b)
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α} {b : β}, Eq.{succ u2} α (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (x : β) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b)) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b)) => f x))) (f b)
-Case conversion may be inaccurate. Consider using '#align infi_singleton infᵢ_singletonₓ'. -/
-theorem infᵢ_singleton {f : β → α} {b : β} : (⨅ x ∈ (singleton b : Set β), f x) = f b := by simp
-#align infi_singleton infᵢ_singleton
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α} {b : β}, Eq.{succ u2} α (iInf.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (x : β) => iInf.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b)) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b)) => f x))) (f b)
+Case conversion may be inaccurate. Consider using '#align infi_singleton iInf_singletonₓ'. -/
+theorem iInf_singleton {f : β → α} {b : β} : (⨅ x ∈ (singleton b : Set β), f x) = f b := by simp
+#align infi_singleton iInf_singleton
 
-/- warning: supr_pair -> supᵢ_pair is a dubious translation:
+/- warning: supr_pair -> iSup_pair is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {a : β} {b : β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) a (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b))) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) a (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b))) => f x))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f a) (f b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {a : β} {b : β}, Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) a (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b))) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) a (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b))) => f x))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f a) (f b))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α} {a : β} {b : β}, Eq.{succ u2} α (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (x : β) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Insert.insert.{u1, u1} β (Set.{u1} β) (Set.instInsertSet.{u1} β) a (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b))) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Insert.insert.{u1, u1} β (Set.{u1} β) (Set.instInsertSet.{u1} β) a (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b))) => f x))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f a) (f b))
-Case conversion may be inaccurate. Consider using '#align supr_pair supᵢ_pairₓ'. -/
-theorem supᵢ_pair {f : β → α} {a b : β} : (⨆ x ∈ ({a, b} : Set β), f x) = f a ⊔ f b := by
-  rw [supᵢ_insert, supᵢ_singleton]
-#align supr_pair supᵢ_pair
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α} {a : β} {b : β}, Eq.{succ u2} α (iSup.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (x : β) => iSup.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Insert.insert.{u1, u1} β (Set.{u1} β) (Set.instInsertSet.{u1} β) a (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b))) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Insert.insert.{u1, u1} β (Set.{u1} β) (Set.instInsertSet.{u1} β) a (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b))) => f x))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f a) (f b))
+Case conversion may be inaccurate. Consider using '#align supr_pair iSup_pairₓ'. -/
+theorem iSup_pair {f : β → α} {a b : β} : (⨆ x ∈ ({a, b} : Set β), f x) = f a ⊔ f b := by
+  rw [iSup_insert, iSup_singleton]
+#align supr_pair iSup_pair
 
-/- warning: infi_pair -> infᵢ_pair is a dubious translation:
+/- warning: infi_pair -> iInf_pair is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {a : β} {b : β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) a (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b))) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) a (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b))) => f x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f a) (f b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {a : β} {b : β}, Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) a (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b))) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) a (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b))) => f x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f a) (f b))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α} {a : β} {b : β}, Eq.{succ u2} α (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (x : β) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Insert.insert.{u1, u1} β (Set.{u1} β) (Set.instInsertSet.{u1} β) a (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b))) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Insert.insert.{u1, u1} β (Set.{u1} β) (Set.instInsertSet.{u1} β) a (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b))) => f x))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f a) (f b))
-Case conversion may be inaccurate. Consider using '#align infi_pair infᵢ_pairₓ'. -/
-theorem infᵢ_pair {f : β → α} {a b : β} : (⨅ x ∈ ({a, b} : Set β), f x) = f a ⊓ f b := by
-  rw [infᵢ_insert, infᵢ_singleton]
-#align infi_pair infᵢ_pair
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α} {a : β} {b : β}, Eq.{succ u2} α (iInf.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (x : β) => iInf.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Insert.insert.{u1, u1} β (Set.{u1} β) (Set.instInsertSet.{u1} β) a (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b))) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Insert.insert.{u1, u1} β (Set.{u1} β) (Set.instInsertSet.{u1} β) a (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b))) => f x))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f a) (f b))
+Case conversion may be inaccurate. Consider using '#align infi_pair iInf_pairₓ'. -/
+theorem iInf_pair {f : β → α} {a b : β} : (⨅ x ∈ ({a, b} : Set β), f x) = f a ⊓ f b := by
+  rw [iInf_insert, iInf_singleton]
+#align infi_pair iInf_pair
 
-/- warning: supr_image -> supᵢ_image is a dubious translation:
+/- warning: supr_image -> iSup_image is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {γ : Type.{u3}} {f : β -> γ} {g : γ -> α} {t : Set.{u2} β}, Eq.{succ u1} α (supᵢ.{u1, succ u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) γ (fun (c : γ) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) c (Set.image.{u2, u3} β γ f t)) (fun (H : Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) c (Set.image.{u2, u3} β γ f t)) => g c))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (b : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b t) => g (f b))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {γ : Type.{u3}} {f : β -> γ} {g : γ -> α} {t : Set.{u2} β}, Eq.{succ u1} α (iSup.{u1, succ u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) γ (fun (c : γ) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) c (Set.image.{u2, u3} β γ f t)) (fun (H : Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) c (Set.image.{u2, u3} β γ f t)) => g c))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (b : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b t) => g (f b))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {γ : Type.{u3}} {f : β -> γ} {g : γ -> α} {t : Set.{u2} β}, Eq.{succ u1} α (supᵢ.{u1, succ u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) γ (fun (c : γ) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u3, u3} γ (Set.{u3} γ) (Set.instMembershipSet.{u3} γ) c (Set.image.{u2, u3} β γ f t)) (fun (H : Membership.mem.{u3, u3} γ (Set.{u3} γ) (Set.instMembershipSet.{u3} γ) c (Set.image.{u2, u3} β γ f t)) => g c))) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (b : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b t) => g (f b))))
-Case conversion may be inaccurate. Consider using '#align supr_image supᵢ_imageₓ'. -/
-theorem supᵢ_image {γ} {f : β → γ} {g : γ → α} {t : Set β} :
-    (⨆ c ∈ f '' t, g c) = ⨆ b ∈ t, g (f b) := by rw [← supₛ_image, ← supₛ_image, ← image_comp]
-#align supr_image supᵢ_image
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {γ : Type.{u3}} {f : β -> γ} {g : γ -> α} {t : Set.{u2} β}, Eq.{succ u1} α (iSup.{u1, succ u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) γ (fun (c : γ) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u3, u3} γ (Set.{u3} γ) (Set.instMembershipSet.{u3} γ) c (Set.image.{u2, u3} β γ f t)) (fun (H : Membership.mem.{u3, u3} γ (Set.{u3} γ) (Set.instMembershipSet.{u3} γ) c (Set.image.{u2, u3} β γ f t)) => g c))) (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (b : β) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b t) => g (f b))))
+Case conversion may be inaccurate. Consider using '#align supr_image iSup_imageₓ'. -/
+theorem iSup_image {γ} {f : β → γ} {g : γ → α} {t : Set β} :
+    (⨆ c ∈ f '' t, g c) = ⨆ b ∈ t, g (f b) := by rw [← sSup_image, ← sSup_image, ← image_comp]
+#align supr_image iSup_image
 
-/- warning: infi_image -> infᵢ_image is a dubious translation:
+/- warning: infi_image -> iInf_image is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {γ : Type.{u3}} {f : β -> γ} {g : γ -> α} {t : Set.{u2} β}, Eq.{succ u1} α (infᵢ.{u1, succ u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) γ (fun (c : γ) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) c (Set.image.{u2, u3} β γ f t)) (fun (H : Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) c (Set.image.{u2, u3} β γ f t)) => g c))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (b : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b t) => g (f b))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {γ : Type.{u3}} {f : β -> γ} {g : γ -> α} {t : Set.{u2} β}, Eq.{succ u1} α (iInf.{u1, succ u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) γ (fun (c : γ) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) c (Set.image.{u2, u3} β γ f t)) (fun (H : Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) c (Set.image.{u2, u3} β γ f t)) => g c))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (b : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b t) => g (f b))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {γ : Type.{u3}} {f : β -> γ} {g : γ -> α} {t : Set.{u2} β}, Eq.{succ u1} α (infᵢ.{u1, succ u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) γ (fun (c : γ) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u3, u3} γ (Set.{u3} γ) (Set.instMembershipSet.{u3} γ) c (Set.image.{u2, u3} β γ f t)) (fun (H : Membership.mem.{u3, u3} γ (Set.{u3} γ) (Set.instMembershipSet.{u3} γ) c (Set.image.{u2, u3} β γ f t)) => g c))) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (b : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b t) => g (f b))))
-Case conversion may be inaccurate. Consider using '#align infi_image infᵢ_imageₓ'. -/
-theorem infᵢ_image :
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {γ : Type.{u3}} {f : β -> γ} {g : γ -> α} {t : Set.{u2} β}, Eq.{succ u1} α (iInf.{u1, succ u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) γ (fun (c : γ) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u3, u3} γ (Set.{u3} γ) (Set.instMembershipSet.{u3} γ) c (Set.image.{u2, u3} β γ f t)) (fun (H : Membership.mem.{u3, u3} γ (Set.{u3} γ) (Set.instMembershipSet.{u3} γ) c (Set.image.{u2, u3} β γ f t)) => g c))) (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (b : β) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b t) => g (f b))))
+Case conversion may be inaccurate. Consider using '#align infi_image iInf_imageₓ'. -/
+theorem iInf_image :
     ∀ {γ} {f : β → γ} {g : γ → α} {t : Set β}, (⨅ c ∈ f '' t, g c) = ⨅ b ∈ t, g (f b) :=
-  @supᵢ_image αᵒᵈ _ _
-#align infi_image infᵢ_image
+  @iSup_image αᵒᵈ _ _
+#align infi_image iInf_image
 
-/- warning: supr_extend_bot -> supᵢ_extend_bot is a dubious translation:
+/- warning: supr_extend_bot -> iSup_extend_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {e : ι -> β}, (Function.Injective.{u3, succ u2} ι β e) -> (forall (f : ι -> α), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (j : β) => Function.extend.{u3, succ u2, succ u1} ι β α e f (Bot.bot.{max u2 u1} (β -> α) (Pi.hasBot.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => CompleteLattice.toHasBot.{u1} α _inst_1))) j)) (supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {e : ι -> β}, (Function.Injective.{u3, succ u2} ι β e) -> (forall (f : ι -> α), Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (j : β) => Function.extend.{u3, succ u2, succ u1} ι β α e f (Bot.bot.{max u2 u1} (β -> α) (Pi.hasBot.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => CompleteLattice.toHasBot.{u1} α _inst_1))) j)) (iSup.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {e : ι -> β}, (Function.Injective.{u3, succ u2} ι β e) -> (forall (f : ι -> α), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (j : β) => Function.extend.{u3, succ u2, succ u1} ι β α e f (Bot.bot.{max u1 u2} (β -> α) (Pi.instBotForAll.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => CompleteLattice.toBot.{u1} α _inst_1))) j)) (supᵢ.{u1, u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => f i)))
-Case conversion may be inaccurate. Consider using '#align supr_extend_bot supᵢ_extend_botₓ'. -/
-theorem supᵢ_extend_bot {e : ι → β} (he : Injective e) (f : ι → α) :
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {e : ι -> β}, (Function.Injective.{u3, succ u2} ι β e) -> (forall (f : ι -> α), Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (j : β) => Function.extend.{u3, succ u2, succ u1} ι β α e f (Bot.bot.{max u1 u2} (β -> α) (Pi.instBotForAll.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => CompleteLattice.toBot.{u1} α _inst_1))) j)) (iSup.{u1, u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => f i)))
+Case conversion may be inaccurate. Consider using '#align supr_extend_bot iSup_extend_botₓ'. -/
+theorem iSup_extend_bot {e : ι → β} (he : Injective e) (f : ι → α) :
     (⨆ j, extend e f ⊥ j) = ⨆ i, f i :=
   by
-  rw [supᵢ_split _ fun j => ∃ i, e i = j]
-  simp (config := { contextual := true }) [he.extend_apply, extend_apply', @supᵢ_comm _ β ι]
-#align supr_extend_bot supᵢ_extend_bot
+  rw [iSup_split _ fun j => ∃ i, e i = j]
+  simp (config := { contextual := true }) [he.extend_apply, extend_apply', @iSup_comm _ β ι]
+#align supr_extend_bot iSup_extend_bot
 
-/- warning: infi_extend_top -> infᵢ_extend_top is a dubious translation:
+/- warning: infi_extend_top -> iInf_extend_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {e : ι -> β}, (Function.Injective.{u3, succ u2} ι β e) -> (forall (f : ι -> α), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (j : β) => Function.extend.{u3, succ u2, succ u1} ι β α e f (Top.top.{max u2 u1} (β -> α) (Pi.hasTop.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => CompleteLattice.toHasTop.{u1} α _inst_1))) j)) (infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι f))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {e : ι -> β}, (Function.Injective.{u3, succ u2} ι β e) -> (forall (f : ι -> α), Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (j : β) => Function.extend.{u3, succ u2, succ u1} ι β α e f (Top.top.{max u2 u1} (β -> α) (Pi.hasTop.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => CompleteLattice.toHasTop.{u1} α _inst_1))) j)) (iInf.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι f))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {e : ι -> β}, (Function.Injective.{u3, succ u2} ι β e) -> (forall (f : ι -> α), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (j : β) => Function.extend.{u3, succ u2, succ u1} ι β α e f (Top.top.{max u1 u2} (β -> α) (Pi.instTopForAll.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => CompleteLattice.toTop.{u1} α _inst_1))) j)) (infᵢ.{u1, u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι f))
-Case conversion may be inaccurate. Consider using '#align infi_extend_top infᵢ_extend_topₓ'. -/
-theorem infᵢ_extend_top {e : ι → β} (he : Injective e) (f : ι → α) :
-    (⨅ j, extend e f ⊤ j) = infᵢ f :=
-  @supᵢ_extend_bot αᵒᵈ _ _ _ _ he _
-#align infi_extend_top infᵢ_extend_top
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] {e : ι -> β}, (Function.Injective.{u3, succ u2} ι β e) -> (forall (f : ι -> α), Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (j : β) => Function.extend.{u3, succ u2, succ u1} ι β α e f (Top.top.{max u1 u2} (β -> α) (Pi.instTopForAll.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => CompleteLattice.toTop.{u1} α _inst_1))) j)) (iInf.{u1, u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι f))
+Case conversion may be inaccurate. Consider using '#align infi_extend_top iInf_extend_topₓ'. -/
+theorem iInf_extend_top {e : ι → β} (he : Injective e) (f : ι → α) :
+    (⨅ j, extend e f ⊤ j) = iInf f :=
+  @iSup_extend_bot αᵒᵈ _ _ _ _ he _
+#align infi_extend_top iInf_extend_top
 
 /-!
 ### `supr` and `infi` under `Type`
 -/
 
 
-/- warning: supr_of_empty' -> supᵢ_of_empty' is a dubious translation:
+/- warning: supr_of_empty' -> iSup_of_empty' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_2 : SupSet.{u1} α] [_inst_3 : IsEmpty.{u2} ι] (f : ι -> α), Eq.{succ u1} α (supᵢ.{u1, u2} α _inst_2 ι f) (SupSet.supₛ.{u1} α _inst_2 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_2 : SupSet.{u1} α] [_inst_3 : IsEmpty.{u2} ι] (f : ι -> α), Eq.{succ u1} α (iSup.{u1, u2} α _inst_2 ι f) (SupSet.sSup.{u1} α _inst_2 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_2 : SupSet.{u2} α] [_inst_3 : IsEmpty.{u1} ι] (f : ι -> α), Eq.{succ u2} α (supᵢ.{u2, u1} α _inst_2 ι f) (SupSet.supₛ.{u2} α _inst_2 (EmptyCollection.emptyCollection.{u2} (Set.{u2} α) (Set.instEmptyCollectionSet.{u2} α)))
-Case conversion may be inaccurate. Consider using '#align supr_of_empty' supᵢ_of_empty'ₓ'. -/
-theorem supᵢ_of_empty' {α ι} [SupSet α] [IsEmpty ι] (f : ι → α) : supᵢ f = supₛ (∅ : Set α) :=
-  congr_arg supₛ (range_eq_empty f)
-#align supr_of_empty' supᵢ_of_empty'
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_2 : SupSet.{u2} α] [_inst_3 : IsEmpty.{u1} ι] (f : ι -> α), Eq.{succ u2} α (iSup.{u2, u1} α _inst_2 ι f) (SupSet.sSup.{u2} α _inst_2 (EmptyCollection.emptyCollection.{u2} (Set.{u2} α) (Set.instEmptyCollectionSet.{u2} α)))
+Case conversion may be inaccurate. Consider using '#align supr_of_empty' iSup_of_empty'ₓ'. -/
+theorem iSup_of_empty' {α ι} [SupSet α] [IsEmpty ι] (f : ι → α) : iSup f = sSup (∅ : Set α) :=
+  congr_arg sSup (range_eq_empty f)
+#align supr_of_empty' iSup_of_empty'
 
-/- warning: infi_of_empty' -> infᵢ_of_empty' is a dubious translation:
+/- warning: infi_of_empty' -> iInf_of_empty' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_2 : InfSet.{u1} α] [_inst_3 : IsEmpty.{u2} ι] (f : ι -> α), Eq.{succ u1} α (infᵢ.{u1, u2} α _inst_2 ι f) (InfSet.infₛ.{u1} α _inst_2 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_2 : InfSet.{u1} α] [_inst_3 : IsEmpty.{u2} ι] (f : ι -> α), Eq.{succ u1} α (iInf.{u1, u2} α _inst_2 ι f) (InfSet.sInf.{u1} α _inst_2 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_2 : InfSet.{u2} α] [_inst_3 : IsEmpty.{u1} ι] (f : ι -> α), Eq.{succ u2} α (infᵢ.{u2, u1} α _inst_2 ι f) (InfSet.infₛ.{u2} α _inst_2 (EmptyCollection.emptyCollection.{u2} (Set.{u2} α) (Set.instEmptyCollectionSet.{u2} α)))
-Case conversion may be inaccurate. Consider using '#align infi_of_empty' infᵢ_of_empty'ₓ'. -/
-theorem infᵢ_of_empty' {α ι} [InfSet α] [IsEmpty ι] (f : ι → α) : infᵢ f = infₛ (∅ : Set α) :=
-  congr_arg infₛ (range_eq_empty f)
-#align infi_of_empty' infᵢ_of_empty'
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_2 : InfSet.{u2} α] [_inst_3 : IsEmpty.{u1} ι] (f : ι -> α), Eq.{succ u2} α (iInf.{u2, u1} α _inst_2 ι f) (InfSet.sInf.{u2} α _inst_2 (EmptyCollection.emptyCollection.{u2} (Set.{u2} α) (Set.instEmptyCollectionSet.{u2} α)))
+Case conversion may be inaccurate. Consider using '#align infi_of_empty' iInf_of_empty'ₓ'. -/
+theorem iInf_of_empty' {α ι} [InfSet α] [IsEmpty ι] (f : ι → α) : iInf f = sInf (∅ : Set α) :=
+  congr_arg sInf (range_eq_empty f)
+#align infi_of_empty' iInf_of_empty'
 
-/- warning: supr_of_empty -> supᵢ_of_empty is a dubious translation:
+/- warning: supr_of_empty -> iSup_of_empty is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsEmpty.{u2} ι] (f : ι -> α), Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι f) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsEmpty.{u2} ι] (f : ι -> α), Eq.{succ u1} α (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι f) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsEmpty.{u2} ι] (f : ι -> α), Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι f) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align supr_of_empty supᵢ_of_emptyₓ'. -/
-theorem supᵢ_of_empty [IsEmpty ι] (f : ι → α) : supᵢ f = ⊥ :=
-  (supᵢ_of_empty' f).trans supₛ_empty
-#align supr_of_empty supᵢ_of_empty
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsEmpty.{u2} ι] (f : ι -> α), Eq.{succ u1} α (iSup.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι f) (Bot.bot.{u1} α (CompleteLattice.toBot.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align supr_of_empty iSup_of_emptyₓ'. -/
+theorem iSup_of_empty [IsEmpty ι] (f : ι → α) : iSup f = ⊥ :=
+  (iSup_of_empty' f).trans sSup_empty
+#align supr_of_empty iSup_of_empty
 
-/- warning: infi_of_empty -> infᵢ_of_empty is a dubious translation:
+/- warning: infi_of_empty -> iInf_of_empty is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsEmpty.{u2} ι] (f : ι -> α), Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι f) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsEmpty.{u2} ι] (f : ι -> α), Eq.{succ u1} α (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι f) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsEmpty.{u2} ι] (f : ι -> α), Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι f) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align infi_of_empty infᵢ_of_emptyₓ'. -/
-theorem infᵢ_of_empty [IsEmpty ι] (f : ι → α) : infᵢ f = ⊤ :=
-  @supᵢ_of_empty αᵒᵈ _ _ _ f
-#align infi_of_empty infᵢ_of_empty
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : IsEmpty.{u2} ι] (f : ι -> α), Eq.{succ u1} α (iInf.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι f) (Top.top.{u1} α (CompleteLattice.toTop.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align infi_of_empty iInf_of_emptyₓ'. -/
+theorem iInf_of_empty [IsEmpty ι] (f : ι → α) : iInf f = ⊤ :=
+  @iSup_of_empty αᵒᵈ _ _ _ f
+#align infi_of_empty iInf_of_empty
 
-/- warning: supr_bool_eq -> supᵢ_bool_eq is a dubious translation:
+/- warning: supr_bool_eq -> iSup_bool_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Bool -> α}, Eq.{succ u1} α (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Bool (fun (b : Bool) => f b)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f Bool.true) (f Bool.false))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Bool -> α}, Eq.{succ u1} α (iSup.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Bool (fun (b : Bool) => f b)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f Bool.true) (f Bool.false))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Bool -> α}, Eq.{succ u1} α (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Bool (fun (b : Bool) => f b)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f Bool.true) (f Bool.false))
-Case conversion may be inaccurate. Consider using '#align supr_bool_eq supᵢ_bool_eqₓ'. -/
-theorem supᵢ_bool_eq {f : Bool → α} : (⨆ b : Bool, f b) = f true ⊔ f false := by
-  rw [supᵢ, Bool.range_eq, supₛ_pair, sup_comm]
-#align supr_bool_eq supᵢ_bool_eq
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Bool -> α}, Eq.{succ u1} α (iSup.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Bool (fun (b : Bool) => f b)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f Bool.true) (f Bool.false))
+Case conversion may be inaccurate. Consider using '#align supr_bool_eq iSup_bool_eqₓ'. -/
+theorem iSup_bool_eq {f : Bool → α} : (⨆ b : Bool, f b) = f true ⊔ f false := by
+  rw [iSup, Bool.range_eq, sSup_pair, sup_comm]
+#align supr_bool_eq iSup_bool_eq
 
-/- warning: infi_bool_eq -> infᵢ_bool_eq is a dubious translation:
+/- warning: infi_bool_eq -> iInf_bool_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Bool -> α}, Eq.{succ u1} α (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Bool (fun (b : Bool) => f b)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f Bool.true) (f Bool.false))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Bool -> α}, Eq.{succ u1} α (iInf.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Bool (fun (b : Bool) => f b)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f Bool.true) (f Bool.false))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Bool -> α}, Eq.{succ u1} α (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Bool (fun (b : Bool) => f b)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f Bool.true) (f Bool.false))
-Case conversion may be inaccurate. Consider using '#align infi_bool_eq infᵢ_bool_eqₓ'. -/
-theorem infᵢ_bool_eq {f : Bool → α} : (⨅ b : Bool, f b) = f true ⊓ f false :=
-  @supᵢ_bool_eq αᵒᵈ _ _
-#align infi_bool_eq infᵢ_bool_eq
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Bool -> α}, Eq.{succ u1} α (iInf.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Bool (fun (b : Bool) => f b)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f Bool.true) (f Bool.false))
+Case conversion may be inaccurate. Consider using '#align infi_bool_eq iInf_bool_eqₓ'. -/
+theorem iInf_bool_eq {f : Bool → α} : (⨅ b : Bool, f b) = f true ⊓ f false :=
+  @iSup_bool_eq αᵒᵈ _ _
+#align infi_bool_eq iInf_bool_eq
 
-/- warning: sup_eq_supr -> sup_eq_supᵢ is a dubious translation:
+/- warning: sup_eq_supr -> sup_eq_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (x : α) (y : α), Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) x y) (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Bool (fun (b : Bool) => cond.{u1} α b x y))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (x : α) (y : α), Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) x y) (iSup.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Bool (fun (b : Bool) => cond.{u1} α b x y))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (x : α) (y : α), Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) x y) (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Bool (fun (b : Bool) => cond.{u1} α b x y))
-Case conversion may be inaccurate. Consider using '#align sup_eq_supr sup_eq_supᵢₓ'. -/
-theorem sup_eq_supᵢ (x y : α) : x ⊔ y = ⨆ b : Bool, cond b x y := by
-  rw [supᵢ_bool_eq, Bool.cond_true, Bool.cond_false]
-#align sup_eq_supr sup_eq_supᵢ
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (x : α) (y : α), Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) x y) (iSup.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Bool (fun (b : Bool) => cond.{u1} α b x y))
+Case conversion may be inaccurate. Consider using '#align sup_eq_supr sup_eq_iSupₓ'. -/
+theorem sup_eq_iSup (x y : α) : x ⊔ y = ⨆ b : Bool, cond b x y := by
+  rw [iSup_bool_eq, Bool.cond_true, Bool.cond_false]
+#align sup_eq_supr sup_eq_iSup
 
-/- warning: inf_eq_infi -> inf_eq_infᵢ is a dubious translation:
+/- warning: inf_eq_infi -> inf_eq_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (x : α) (y : α), Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) x y) (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Bool (fun (b : Bool) => cond.{u1} α b x y))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (x : α) (y : α), Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) x y) (iInf.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Bool (fun (b : Bool) => cond.{u1} α b x y))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (x : α) (y : α), Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) x y) (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Bool (fun (b : Bool) => cond.{u1} α b x y))
-Case conversion may be inaccurate. Consider using '#align inf_eq_infi inf_eq_infᵢₓ'. -/
-theorem inf_eq_infᵢ (x y : α) : x ⊓ y = ⨅ b : Bool, cond b x y :=
-  @sup_eq_supᵢ αᵒᵈ _ _ _
-#align inf_eq_infi inf_eq_infᵢ
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (x : α) (y : α), Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) x y) (iInf.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Bool (fun (b : Bool) => cond.{u1} α b x y))
+Case conversion may be inaccurate. Consider using '#align inf_eq_infi inf_eq_iInfₓ'. -/
+theorem inf_eq_iInf (x y : α) : x ⊓ y = ⨅ b : Bool, cond b x y :=
+  @sup_eq_iSup αᵒᵈ _ _ _
+#align inf_eq_infi inf_eq_iInf
 
-/- warning: is_glb_binfi -> isGLB_binfᵢ is a dubious translation:
+/- warning: is_glb_binfi -> isGLB_biInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u2} β} {f : β -> α}, IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Set.image.{u2, u1} β α f s) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u2} β} {f : β -> α}, IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Set.image.{u2, u1} β α f s) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u2} β} {f : β -> α}, IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Set.image.{u2, u1} β α f s) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x)))
-Case conversion may be inaccurate. Consider using '#align is_glb_binfi isGLB_binfᵢₓ'. -/
-theorem isGLB_binfᵢ {s : Set β} {f : β → α} : IsGLB (f '' s) (⨅ x ∈ s, f x) := by
-  simpa only [range_comp, Subtype.range_coe, infᵢ_subtype'] using @isGLB_infᵢ α s _ (f ∘ coe)
-#align is_glb_binfi isGLB_binfᵢ
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u2} β} {f : β -> α}, IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Set.image.{u2, u1} β α f s) (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x)))
+Case conversion may be inaccurate. Consider using '#align is_glb_binfi isGLB_biInfₓ'. -/
+theorem isGLB_biInf {s : Set β} {f : β → α} : IsGLB (f '' s) (⨅ x ∈ s, f x) := by
+  simpa only [range_comp, Subtype.range_coe, iInf_subtype'] using @isGLB_iInf α s _ (f ∘ coe)
+#align is_glb_binfi isGLB_biInf
 
-/- warning: is_lub_bsupr -> isLUB_bsupᵢ is a dubious translation:
+/- warning: is_lub_bsupr -> isLUB_biSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u2} β} {f : β -> α}, IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Set.image.{u2, u1} β α f s) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u2} β} {f : β -> α}, IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Set.image.{u2, u1} β α f s) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u2} β} {f : β -> α}, IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Set.image.{u2, u1} β α f s) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x)))
-Case conversion may be inaccurate. Consider using '#align is_lub_bsupr isLUB_bsupᵢₓ'. -/
-theorem isLUB_bsupᵢ {s : Set β} {f : β → α} : IsLUB (f '' s) (⨆ x ∈ s, f x) := by
-  simpa only [range_comp, Subtype.range_coe, supᵢ_subtype'] using @isLUB_supᵢ α s _ (f ∘ coe)
-#align is_lub_bsupr isLUB_bsupᵢ
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u2} β} {f : β -> α}, IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) (Set.image.{u2, u1} β α f s) (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x)))
+Case conversion may be inaccurate. Consider using '#align is_lub_bsupr isLUB_biSupₓ'. -/
+theorem isLUB_biSup {s : Set β} {f : β → α} : IsLUB (f '' s) (⨆ x ∈ s, f x) := by
+  simpa only [range_comp, Subtype.range_coe, iSup_subtype'] using @isLUB_iSup α s _ (f ∘ coe)
+#align is_lub_bsupr isLUB_biSup
 
-/- warning: supr_sigma -> supᵢ_sigma is a dubious translation:
+/- warning: supr_sigma -> iSup_sigma is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : β -> Type.{u3}} {f : (Sigma.{u2, u3} β p) -> α}, Eq.{succ u1} α (supᵢ.{u1, max (succ u2) (succ u3)} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Sigma.{u2, u3} β p) (fun (x : Sigma.{u2, u3} β p) => f x)) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => supᵢ.{u1, succ u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (j : p i) => f (Sigma.mk.{u2, u3} β p i j))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : β -> Type.{u3}} {f : (Sigma.{u2, u3} β p) -> α}, Eq.{succ u1} α (iSup.{u1, max (succ u2) (succ u3)} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Sigma.{u2, u3} β p) (fun (x : Sigma.{u2, u3} β p) => f x)) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => iSup.{u1, succ u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (j : p i) => f (Sigma.mk.{u2, u3} β p i j))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : β -> Type.{u3}} {f : (Sigma.{u2, u3} β p) -> α}, Eq.{succ u1} α (supᵢ.{u1, max (succ u2) (succ u3)} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Sigma.{u2, u3} β p) (fun (x : Sigma.{u2, u3} β p) => f x)) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (i : β) => supᵢ.{u1, succ u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (j : p i) => f (Sigma.mk.{u2, u3} β p i j))))
-Case conversion may be inaccurate. Consider using '#align supr_sigma supᵢ_sigmaₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : β -> Type.{u3}} {f : (Sigma.{u2, u3} β p) -> α}, Eq.{succ u1} α (iSup.{u1, max (succ u2) (succ u3)} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Sigma.{u2, u3} β p) (fun (x : Sigma.{u2, u3} β p) => f x)) (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (i : β) => iSup.{u1, succ u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (j : p i) => f (Sigma.mk.{u2, u3} β p i j))))
+Case conversion may be inaccurate. Consider using '#align supr_sigma iSup_sigmaₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem supᵢ_sigma {p : β → Type _} {f : Sigma p → α} : (⨆ x, f x) = ⨆ (i) (j), f ⟨i, j⟩ :=
-  eq_of_forall_ge_iff fun c => by simp only [supᵢ_le_iff, Sigma.forall]
-#align supr_sigma supᵢ_sigma
+theorem iSup_sigma {p : β → Type _} {f : Sigma p → α} : (⨆ x, f x) = ⨆ (i) (j), f ⟨i, j⟩ :=
+  eq_of_forall_ge_iff fun c => by simp only [iSup_le_iff, Sigma.forall]
+#align supr_sigma iSup_sigma
 
-/- warning: infi_sigma -> infᵢ_sigma is a dubious translation:
+/- warning: infi_sigma -> iInf_sigma is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : β -> Type.{u3}} {f : (Sigma.{u2, u3} β p) -> α}, Eq.{succ u1} α (infᵢ.{u1, max (succ u2) (succ u3)} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Sigma.{u2, u3} β p) (fun (x : Sigma.{u2, u3} β p) => f x)) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => infᵢ.{u1, succ u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (j : p i) => f (Sigma.mk.{u2, u3} β p i j))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : β -> Type.{u3}} {f : (Sigma.{u2, u3} β p) -> α}, Eq.{succ u1} α (iInf.{u1, max (succ u2) (succ u3)} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Sigma.{u2, u3} β p) (fun (x : Sigma.{u2, u3} β p) => f x)) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => iInf.{u1, succ u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (j : p i) => f (Sigma.mk.{u2, u3} β p i j))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : β -> Type.{u3}} {f : (Sigma.{u2, u3} β p) -> α}, Eq.{succ u1} α (infᵢ.{u1, max (succ u2) (succ u3)} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Sigma.{u2, u3} β p) (fun (x : Sigma.{u2, u3} β p) => f x)) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (i : β) => infᵢ.{u1, succ u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (j : p i) => f (Sigma.mk.{u2, u3} β p i j))))
-Case conversion may be inaccurate. Consider using '#align infi_sigma infᵢ_sigmaₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : β -> Type.{u3}} {f : (Sigma.{u2, u3} β p) -> α}, Eq.{succ u1} α (iInf.{u1, max (succ u2) (succ u3)} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Sigma.{u2, u3} β p) (fun (x : Sigma.{u2, u3} β p) => f x)) (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (i : β) => iInf.{u1, succ u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (j : p i) => f (Sigma.mk.{u2, u3} β p i j))))
+Case conversion may be inaccurate. Consider using '#align infi_sigma iInf_sigmaₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem infᵢ_sigma {p : β → Type _} {f : Sigma p → α} : (⨅ x, f x) = ⨅ (i) (j), f ⟨i, j⟩ :=
-  @supᵢ_sigma αᵒᵈ _ _ _ _
-#align infi_sigma infᵢ_sigma
+theorem iInf_sigma {p : β → Type _} {f : Sigma p → α} : (⨅ x, f x) = ⨅ (i) (j), f ⟨i, j⟩ :=
+  @iSup_sigma αᵒᵈ _ _ _ _
+#align infi_sigma iInf_sigma
 
-/- warning: supr_prod -> supᵢ_prod is a dubious translation:
+/- warning: supr_prod -> iSup_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : (Prod.{u2, u3} β γ) -> α}, Eq.{succ u1} α (supᵢ.{u1, max (succ u2) (succ u3)} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Prod.{u2, u3} β γ) (fun (x : Prod.{u2, u3} β γ) => f x)) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => supᵢ.{u1, succ u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) γ (fun (j : γ) => f (Prod.mk.{u2, u3} β γ i j))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : (Prod.{u2, u3} β γ) -> α}, Eq.{succ u1} α (iSup.{u1, max (succ u2) (succ u3)} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Prod.{u2, u3} β γ) (fun (x : Prod.{u2, u3} β γ) => f x)) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => iSup.{u1, succ u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) γ (fun (j : γ) => f (Prod.mk.{u2, u3} β γ i j))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : (Prod.{u3, u2} β γ) -> α}, Eq.{succ u1} α (supᵢ.{u1, max (succ u3) (succ u2)} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Prod.{u3, u2} β γ) (fun (x : Prod.{u3, u2} β γ) => f x)) (supᵢ.{u1, succ u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (i : β) => supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) γ (fun (j : γ) => f (Prod.mk.{u3, u2} β γ i j))))
-Case conversion may be inaccurate. Consider using '#align supr_prod supᵢ_prodₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : (Prod.{u3, u2} β γ) -> α}, Eq.{succ u1} α (iSup.{u1, max (succ u3) (succ u2)} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Prod.{u3, u2} β γ) (fun (x : Prod.{u3, u2} β γ) => f x)) (iSup.{u1, succ u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (i : β) => iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) γ (fun (j : γ) => f (Prod.mk.{u3, u2} β γ i j))))
+Case conversion may be inaccurate. Consider using '#align supr_prod iSup_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem supᵢ_prod {f : β × γ → α} : (⨆ x, f x) = ⨆ (i) (j), f (i, j) :=
-  eq_of_forall_ge_iff fun c => by simp only [supᵢ_le_iff, Prod.forall]
-#align supr_prod supᵢ_prod
+theorem iSup_prod {f : β × γ → α} : (⨆ x, f x) = ⨆ (i) (j), f (i, j) :=
+  eq_of_forall_ge_iff fun c => by simp only [iSup_le_iff, Prod.forall]
+#align supr_prod iSup_prod
 
-/- warning: infi_prod -> infᵢ_prod is a dubious translation:
+/- warning: infi_prod -> iInf_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : (Prod.{u2, u3} β γ) -> α}, Eq.{succ u1} α (infᵢ.{u1, max (succ u2) (succ u3)} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Prod.{u2, u3} β γ) (fun (x : Prod.{u2, u3} β γ) => f x)) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => infᵢ.{u1, succ u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) γ (fun (j : γ) => f (Prod.mk.{u2, u3} β γ i j))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : (Prod.{u2, u3} β γ) -> α}, Eq.{succ u1} α (iInf.{u1, max (succ u2) (succ u3)} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Prod.{u2, u3} β γ) (fun (x : Prod.{u2, u3} β γ) => f x)) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => iInf.{u1, succ u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) γ (fun (j : γ) => f (Prod.mk.{u2, u3} β γ i j))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : (Prod.{u3, u2} β γ) -> α}, Eq.{succ u1} α (infᵢ.{u1, max (succ u3) (succ u2)} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Prod.{u3, u2} β γ) (fun (x : Prod.{u3, u2} β γ) => f x)) (infᵢ.{u1, succ u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (i : β) => infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) γ (fun (j : γ) => f (Prod.mk.{u3, u2} β γ i j))))
-Case conversion may be inaccurate. Consider using '#align infi_prod infᵢ_prodₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : (Prod.{u3, u2} β γ) -> α}, Eq.{succ u1} α (iInf.{u1, max (succ u3) (succ u2)} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Prod.{u3, u2} β γ) (fun (x : Prod.{u3, u2} β γ) => f x)) (iInf.{u1, succ u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (i : β) => iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) γ (fun (j : γ) => f (Prod.mk.{u3, u2} β γ i j))))
+Case conversion may be inaccurate. Consider using '#align infi_prod iInf_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i j) -/
-theorem infᵢ_prod {f : β × γ → α} : (⨅ x, f x) = ⨅ (i) (j), f (i, j) :=
-  @supᵢ_prod αᵒᵈ _ _ _ _
-#align infi_prod infᵢ_prod
+theorem iInf_prod {f : β × γ → α} : (⨅ x, f x) = ⨅ (i) (j), f (i, j) :=
+  @iSup_prod αᵒᵈ _ _ _ _
+#align infi_prod iInf_prod
 
-/- warning: bsupr_prod -> bsupᵢ_prod is a dubious translation:
+/- warning: bsupr_prod -> biSup_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : (Prod.{u2, u3} β γ) -> α} {s : Set.{u2} β} {t : Set.{u3} γ}, Eq.{succ u1} α (supᵢ.{u1, succ (max u2 u3)} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Prod.{u2, u3} β γ) (fun (x : Prod.{u2, u3} β γ) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} β γ) (Set.{max u2 u3} (Prod.{u2, u3} β γ)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} β γ)) x (Set.prod.{u2, u3} β γ s t)) (fun (H : Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} β γ) (Set.{max u2 u3} (Prod.{u2, u3} β γ)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} β γ)) x (Set.prod.{u2, u3} β γ s t)) => f x))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (a : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) => supᵢ.{u1, succ u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) γ (fun (b : γ) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) b t) (fun (H : Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) b t) => f (Prod.mk.{u2, u3} β γ a b))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : (Prod.{u2, u3} β γ) -> α} {s : Set.{u2} β} {t : Set.{u3} γ}, Eq.{succ u1} α (iSup.{u1, succ (max u2 u3)} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Prod.{u2, u3} β γ) (fun (x : Prod.{u2, u3} β γ) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} β γ) (Set.{max u2 u3} (Prod.{u2, u3} β γ)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} β γ)) x (Set.prod.{u2, u3} β γ s t)) (fun (H : Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} β γ) (Set.{max u2 u3} (Prod.{u2, u3} β γ)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} β γ)) x (Set.prod.{u2, u3} β γ s t)) => f x))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (a : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) => iSup.{u1, succ u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) γ (fun (b : γ) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) b t) (fun (H : Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) b t) => f (Prod.mk.{u2, u3} β γ a b))))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : (Prod.{u3, u2} β γ) -> α} {s : Set.{u3} β} {t : Set.{u2} γ}, Eq.{succ u1} α (supᵢ.{u1, succ (max u3 u2)} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Prod.{u3, u2} β γ) (fun (x : Prod.{u3, u2} β γ) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{max u3 u2, max u2 u3} (Prod.{u3, u2} β γ) (Set.{max u2 u3} (Prod.{u3, u2} β γ)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} β γ)) x (Set.prod.{u3, u2} β γ s t)) (fun (H : Membership.mem.{max u3 u2, max u2 u3} (Prod.{u3, u2} β γ) (Set.{max u2 u3} (Prod.{u3, u2} β γ)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} β γ)) x (Set.prod.{u3, u2} β γ s t)) => f x))) (supᵢ.{u1, succ u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (a : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a s) (fun (H : Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a s) => supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) γ (fun (b : γ) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} γ (Set.{u2} γ) (Set.instMembershipSet.{u2} γ) b t) (fun (H : Membership.mem.{u2, u2} γ (Set.{u2} γ) (Set.instMembershipSet.{u2} γ) b t) => f (Prod.mk.{u3, u2} β γ a b))))))
-Case conversion may be inaccurate. Consider using '#align bsupr_prod bsupᵢ_prodₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : (Prod.{u3, u2} β γ) -> α} {s : Set.{u3} β} {t : Set.{u2} γ}, Eq.{succ u1} α (iSup.{u1, succ (max u3 u2)} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Prod.{u3, u2} β γ) (fun (x : Prod.{u3, u2} β γ) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{max u3 u2, max u2 u3} (Prod.{u3, u2} β γ) (Set.{max u2 u3} (Prod.{u3, u2} β γ)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} β γ)) x (Set.prod.{u3, u2} β γ s t)) (fun (H : Membership.mem.{max u3 u2, max u2 u3} (Prod.{u3, u2} β γ) (Set.{max u2 u3} (Prod.{u3, u2} β γ)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} β γ)) x (Set.prod.{u3, u2} β γ s t)) => f x))) (iSup.{u1, succ u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (a : β) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a s) (fun (H : Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a s) => iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) γ (fun (b : γ) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} γ (Set.{u2} γ) (Set.instMembershipSet.{u2} γ) b t) (fun (H : Membership.mem.{u2, u2} γ (Set.{u2} γ) (Set.instMembershipSet.{u2} γ) b t) => f (Prod.mk.{u3, u2} β γ a b))))))
+Case conversion may be inaccurate. Consider using '#align bsupr_prod biSup_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-theorem bsupᵢ_prod {f : β × γ → α} {s : Set β} {t : Set γ} :
+theorem biSup_prod {f : β × γ → α} {s : Set β} {t : Set γ} :
     (⨆ x ∈ s ×ˢ t, f x) = ⨆ (a ∈ s) (b ∈ t), f (a, b) :=
   by
-  simp_rw [supᵢ_prod, mem_prod, supᵢ_and]
-  exact supᵢ_congr fun _ => supᵢ_comm
-#align bsupr_prod bsupᵢ_prod
+  simp_rw [iSup_prod, mem_prod, iSup_and]
+  exact iSup_congr fun _ => iSup_comm
+#align bsupr_prod biSup_prod
 
-/- warning: binfi_prod -> binfᵢ_prod is a dubious translation:
+/- warning: binfi_prod -> biInf_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : (Prod.{u2, u3} β γ) -> α} {s : Set.{u2} β} {t : Set.{u3} γ}, Eq.{succ u1} α (infᵢ.{u1, succ (max u2 u3)} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Prod.{u2, u3} β γ) (fun (x : Prod.{u2, u3} β γ) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} β γ) (Set.{max u2 u3} (Prod.{u2, u3} β γ)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} β γ)) x (Set.prod.{u2, u3} β γ s t)) (fun (H : Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} β γ) (Set.{max u2 u3} (Prod.{u2, u3} β γ)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} β γ)) x (Set.prod.{u2, u3} β γ s t)) => f x))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (a : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) => infᵢ.{u1, succ u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) γ (fun (b : γ) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) b t) (fun (H : Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) b t) => f (Prod.mk.{u2, u3} β γ a b))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : (Prod.{u2, u3} β γ) -> α} {s : Set.{u2} β} {t : Set.{u3} γ}, Eq.{succ u1} α (iInf.{u1, succ (max u2 u3)} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Prod.{u2, u3} β γ) (fun (x : Prod.{u2, u3} β γ) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} β γ) (Set.{max u2 u3} (Prod.{u2, u3} β γ)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} β γ)) x (Set.prod.{u2, u3} β γ s t)) (fun (H : Membership.Mem.{max u2 u3, max u2 u3} (Prod.{u2, u3} β γ) (Set.{max u2 u3} (Prod.{u2, u3} β γ)) (Set.hasMem.{max u2 u3} (Prod.{u2, u3} β γ)) x (Set.prod.{u2, u3} β γ s t)) => f x))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (a : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) => iInf.{u1, succ u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) γ (fun (b : γ) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) b t) (fun (H : Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) b t) => f (Prod.mk.{u2, u3} β γ a b))))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : (Prod.{u3, u2} β γ) -> α} {s : Set.{u3} β} {t : Set.{u2} γ}, Eq.{succ u1} α (infᵢ.{u1, succ (max u3 u2)} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Prod.{u3, u2} β γ) (fun (x : Prod.{u3, u2} β γ) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{max u3 u2, max u2 u3} (Prod.{u3, u2} β γ) (Set.{max u2 u3} (Prod.{u3, u2} β γ)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} β γ)) x (Set.prod.{u3, u2} β γ s t)) (fun (H : Membership.mem.{max u3 u2, max u2 u3} (Prod.{u3, u2} β γ) (Set.{max u2 u3} (Prod.{u3, u2} β γ)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} β γ)) x (Set.prod.{u3, u2} β γ s t)) => f x))) (infᵢ.{u1, succ u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (a : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a s) (fun (H : Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a s) => infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) γ (fun (b : γ) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} γ (Set.{u2} γ) (Set.instMembershipSet.{u2} γ) b t) (fun (H : Membership.mem.{u2, u2} γ (Set.{u2} γ) (Set.instMembershipSet.{u2} γ) b t) => f (Prod.mk.{u3, u2} β γ a b))))))
-Case conversion may be inaccurate. Consider using '#align binfi_prod binfᵢ_prodₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : (Prod.{u3, u2} β γ) -> α} {s : Set.{u3} β} {t : Set.{u2} γ}, Eq.{succ u1} α (iInf.{u1, succ (max u3 u2)} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Prod.{u3, u2} β γ) (fun (x : Prod.{u3, u2} β γ) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{max u3 u2, max u2 u3} (Prod.{u3, u2} β γ) (Set.{max u2 u3} (Prod.{u3, u2} β γ)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} β γ)) x (Set.prod.{u3, u2} β γ s t)) (fun (H : Membership.mem.{max u3 u2, max u2 u3} (Prod.{u3, u2} β γ) (Set.{max u2 u3} (Prod.{u3, u2} β γ)) (Set.instMembershipSet.{max u3 u2} (Prod.{u3, u2} β γ)) x (Set.prod.{u3, u2} β γ s t)) => f x))) (iInf.{u1, succ u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (a : β) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a s) (fun (H : Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a s) => iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) γ (fun (b : γ) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} γ (Set.{u2} γ) (Set.instMembershipSet.{u2} γ) b t) (fun (H : Membership.mem.{u2, u2} γ (Set.{u2} γ) (Set.instMembershipSet.{u2} γ) b t) => f (Prod.mk.{u3, u2} β γ a b))))))
+Case conversion may be inaccurate. Consider using '#align binfi_prod biInf_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-theorem binfᵢ_prod {f : β × γ → α} {s : Set β} {t : Set γ} :
+theorem biInf_prod {f : β × γ → α} {s : Set β} {t : Set γ} :
     (⨅ x ∈ s ×ˢ t, f x) = ⨅ (a ∈ s) (b ∈ t), f (a, b) :=
-  @bsupᵢ_prod αᵒᵈ _ _ _ _ _ _
-#align binfi_prod binfᵢ_prod
+  @biSup_prod αᵒᵈ _ _ _ _ _ _
+#align binfi_prod biInf_prod
 
-/- warning: supr_sum -> supᵢ_sum is a dubious translation:
+/- warning: supr_sum -> iSup_sum is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : (Sum.{u2, u3} β γ) -> α}, Eq.{succ u1} α (supᵢ.{u1, max (succ u2) (succ u3)} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Sum.{u2, u3} β γ) (fun (x : Sum.{u2, u3} β γ) => f x)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => f (Sum.inl.{u2, u3} β γ i))) (supᵢ.{u1, succ u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) γ (fun (j : γ) => f (Sum.inr.{u2, u3} β γ j))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : (Sum.{u2, u3} β γ) -> α}, Eq.{succ u1} α (iSup.{u1, max (succ u2) (succ u3)} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Sum.{u2, u3} β γ) (fun (x : Sum.{u2, u3} β γ) => f x)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => f (Sum.inl.{u2, u3} β γ i))) (iSup.{u1, succ u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) γ (fun (j : γ) => f (Sum.inr.{u2, u3} β γ j))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : (Sum.{u3, u2} β γ) -> α}, Eq.{succ u1} α (supᵢ.{u1, max (succ u3) (succ u2)} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Sum.{u3, u2} β γ) (fun (x : Sum.{u3, u2} β γ) => f x)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, succ u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (i : β) => f (Sum.inl.{u3, u2} β γ i))) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) γ (fun (j : γ) => f (Sum.inr.{u3, u2} β γ j))))
-Case conversion may be inaccurate. Consider using '#align supr_sum supᵢ_sumₓ'. -/
-theorem supᵢ_sum {f : Sum β γ → α} : (⨆ x, f x) = (⨆ i, f (Sum.inl i)) ⊔ ⨆ j, f (Sum.inr j) :=
-  eq_of_forall_ge_iff fun c => by simp only [sup_le_iff, supᵢ_le_iff, Sum.forall]
-#align supr_sum supᵢ_sum
+  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : (Sum.{u3, u2} β γ) -> α}, Eq.{succ u1} α (iSup.{u1, max (succ u3) (succ u2)} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Sum.{u3, u2} β γ) (fun (x : Sum.{u3, u2} β γ) => f x)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iSup.{u1, succ u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (i : β) => f (Sum.inl.{u3, u2} β γ i))) (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) γ (fun (j : γ) => f (Sum.inr.{u3, u2} β γ j))))
+Case conversion may be inaccurate. Consider using '#align supr_sum iSup_sumₓ'. -/
+theorem iSup_sum {f : Sum β γ → α} : (⨆ x, f x) = (⨆ i, f (Sum.inl i)) ⊔ ⨆ j, f (Sum.inr j) :=
+  eq_of_forall_ge_iff fun c => by simp only [sup_le_iff, iSup_le_iff, Sum.forall]
+#align supr_sum iSup_sum
 
-/- warning: infi_sum -> infᵢ_sum is a dubious translation:
+/- warning: infi_sum -> iInf_sum is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : (Sum.{u2, u3} β γ) -> α}, Eq.{succ u1} α (infᵢ.{u1, max (succ u2) (succ u3)} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Sum.{u2, u3} β γ) (fun (x : Sum.{u2, u3} β γ) => f x)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => f (Sum.inl.{u2, u3} β γ i))) (infᵢ.{u1, succ u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) γ (fun (j : γ) => f (Sum.inr.{u2, u3} β γ j))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : (Sum.{u2, u3} β γ) -> α}, Eq.{succ u1} α (iInf.{u1, max (succ u2) (succ u3)} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Sum.{u2, u3} β γ) (fun (x : Sum.{u2, u3} β γ) => f x)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => f (Sum.inl.{u2, u3} β γ i))) (iInf.{u1, succ u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) γ (fun (j : γ) => f (Sum.inr.{u2, u3} β γ j))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : (Sum.{u3, u2} β γ) -> α}, Eq.{succ u1} α (infᵢ.{u1, max (succ u3) (succ u2)} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Sum.{u3, u2} β γ) (fun (x : Sum.{u3, u2} β γ) => f x)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (infᵢ.{u1, succ u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (i : β) => f (Sum.inl.{u3, u2} β γ i))) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) γ (fun (j : γ) => f (Sum.inr.{u3, u2} β γ j))))
-Case conversion may be inaccurate. Consider using '#align infi_sum infᵢ_sumₓ'. -/
-theorem infᵢ_sum {f : Sum β γ → α} : (⨅ x, f x) = (⨅ i, f (Sum.inl i)) ⊓ ⨅ j, f (Sum.inr j) :=
-  @supᵢ_sum αᵒᵈ _ _ _ _
-#align infi_sum infᵢ_sum
+  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : (Sum.{u3, u2} β γ) -> α}, Eq.{succ u1} α (iInf.{u1, max (succ u3) (succ u2)} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Sum.{u3, u2} β γ) (fun (x : Sum.{u3, u2} β γ) => f x)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (iInf.{u1, succ u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (i : β) => f (Sum.inl.{u3, u2} β γ i))) (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) γ (fun (j : γ) => f (Sum.inr.{u3, u2} β γ j))))
+Case conversion may be inaccurate. Consider using '#align infi_sum iInf_sumₓ'. -/
+theorem iInf_sum {f : Sum β γ → α} : (⨅ x, f x) = (⨅ i, f (Sum.inl i)) ⊓ ⨅ j, f (Sum.inr j) :=
+  @iSup_sum αᵒᵈ _ _ _ _
+#align infi_sum iInf_sum
 
-/- warning: supr_option -> supᵢ_option is a dubious translation:
+/- warning: supr_option -> iSup_option is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : (Option.{u2} β) -> α), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Option.{u2} β) (fun (o : Option.{u2} β) => f o)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f (Option.none.{u2} β)) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (b : β) => f (Option.some.{u2} β b))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : (Option.{u2} β) -> α), Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Option.{u2} β) (fun (o : Option.{u2} β) => f o)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f (Option.none.{u2} β)) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (b : β) => f (Option.some.{u2} β b))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : (Option.{u2} β) -> α), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Option.{u2} β) (fun (o : Option.{u2} β) => f o)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f (Option.none.{u2} β)) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (b : β) => f (Option.some.{u2} β b))))
-Case conversion may be inaccurate. Consider using '#align supr_option supᵢ_optionₓ'. -/
-theorem supᵢ_option (f : Option β → α) : (⨆ o, f o) = f none ⊔ ⨆ b, f (Option.some b) :=
-  eq_of_forall_ge_iff fun c => by simp only [supᵢ_le_iff, sup_le_iff, Option.forall]
-#align supr_option supᵢ_option
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : (Option.{u2} β) -> α), Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Option.{u2} β) (fun (o : Option.{u2} β) => f o)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f (Option.none.{u2} β)) (iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (b : β) => f (Option.some.{u2} β b))))
+Case conversion may be inaccurate. Consider using '#align supr_option iSup_optionₓ'. -/
+theorem iSup_option (f : Option β → α) : (⨆ o, f o) = f none ⊔ ⨆ b, f (Option.some b) :=
+  eq_of_forall_ge_iff fun c => by simp only [iSup_le_iff, sup_le_iff, Option.forall]
+#align supr_option iSup_option
 
-/- warning: infi_option -> infᵢ_option is a dubious translation:
+/- warning: infi_option -> iInf_option is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : (Option.{u2} β) -> α), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Option.{u2} β) (fun (o : Option.{u2} β) => f o)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f (Option.none.{u2} β)) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (b : β) => f (Option.some.{u2} β b))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : (Option.{u2} β) -> α), Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Option.{u2} β) (fun (o : Option.{u2} β) => f o)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f (Option.none.{u2} β)) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (b : β) => f (Option.some.{u2} β b))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : (Option.{u2} β) -> α), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Option.{u2} β) (fun (o : Option.{u2} β) => f o)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f (Option.none.{u2} β)) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (b : β) => f (Option.some.{u2} β b))))
-Case conversion may be inaccurate. Consider using '#align infi_option infᵢ_optionₓ'. -/
-theorem infᵢ_option (f : Option β → α) : (⨅ o, f o) = f none ⊓ ⨅ b, f (Option.some b) :=
-  @supᵢ_option αᵒᵈ _ _ _
-#align infi_option infᵢ_option
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : (Option.{u2} β) -> α), Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Option.{u2} β) (fun (o : Option.{u2} β) => f o)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f (Option.none.{u2} β)) (iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (b : β) => f (Option.some.{u2} β b))))
+Case conversion may be inaccurate. Consider using '#align infi_option iInf_optionₓ'. -/
+theorem iInf_option (f : Option β → α) : (⨅ o, f o) = f none ⊓ ⨅ b, f (Option.some b) :=
+  @iSup_option αᵒᵈ _ _ _
+#align infi_option iInf_option
 
-/- warning: supr_option_elim -> supᵢ_option_elim is a dubious translation:
+/- warning: supr_option_elim -> iSup_option_elim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (a : α) (f : β -> α), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Option.{u2} β) (fun (o : Option.{u2} β) => Option.elim'.{u2, u1} β α a f o)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (b : β) => f b)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (a : α) (f : β -> α), Eq.{succ u1} α (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Option.{u2} β) (fun (o : Option.{u2} β) => Option.elim'.{u2, u1} β α a f o)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (b : β) => f b)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (a : α) (f : β -> α), Eq.{succ u2} α (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Option.{u1} β) (fun (o : Option.{u1} β) => Option.elim.{u1, succ u2} β α o a f)) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) a (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (b : β) => f b)))
-Case conversion may be inaccurate. Consider using '#align supr_option_elim supᵢ_option_elimₓ'. -/
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (a : α) (f : β -> α), Eq.{succ u2} α (iSup.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Option.{u1} β) (fun (o : Option.{u1} β) => Option.elim.{u1, succ u2} β α o a f)) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) a (iSup.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (b : β) => f b)))
+Case conversion may be inaccurate. Consider using '#align supr_option_elim iSup_option_elimₓ'. -/
 /-- A version of `supr_option` useful for rewriting right-to-left. -/
-theorem supᵢ_option_elim (a : α) (f : β → α) : (⨆ o : Option β, o.elim a f) = a ⊔ ⨆ b, f b := by
-  simp [supᵢ_option]
-#align supr_option_elim supᵢ_option_elim
+theorem iSup_option_elim (a : α) (f : β → α) : (⨆ o : Option β, o.elim a f) = a ⊔ ⨆ b, f b := by
+  simp [iSup_option]
+#align supr_option_elim iSup_option_elim
 
-/- warning: infi_option_elim -> infᵢ_option_elim is a dubious translation:
+/- warning: infi_option_elim -> iInf_option_elim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (a : α) (f : β -> α), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Option.{u2} β) (fun (o : Option.{u2} β) => Option.elim'.{u2, u1} β α a f o)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (b : β) => f b)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (a : α) (f : β -> α), Eq.{succ u1} α (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Option.{u2} β) (fun (o : Option.{u2} β) => Option.elim'.{u2, u1} β α a f o)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (b : β) => f b)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (a : α) (f : β -> α), Eq.{succ u2} α (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Option.{u1} β) (fun (o : Option.{u1} β) => Option.elim.{u1, succ u2} β α o a f)) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) a (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (b : β) => f b)))
-Case conversion may be inaccurate. Consider using '#align infi_option_elim infᵢ_option_elimₓ'. -/
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (a : α) (f : β -> α), Eq.{succ u2} α (iInf.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Option.{u1} β) (fun (o : Option.{u1} β) => Option.elim.{u1, succ u2} β α o a f)) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) a (iInf.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (b : β) => f b)))
+Case conversion may be inaccurate. Consider using '#align infi_option_elim iInf_option_elimₓ'. -/
 /-- A version of `infi_option` useful for rewriting right-to-left. -/
-theorem infᵢ_option_elim (a : α) (f : β → α) : (⨅ o : Option β, o.elim a f) = a ⊓ ⨅ b, f b :=
-  @supᵢ_option_elim αᵒᵈ _ _ _ _
-#align infi_option_elim infᵢ_option_elim
+theorem iInf_option_elim (a : α) (f : β → α) : (⨅ o : Option β, o.elim a f) = a ⊓ ⨅ b, f b :=
+  @iSup_option_elim αᵒᵈ _ _ _ _
+#align infi_option_elim iInf_option_elim
 
-/- warning: supr_ne_bot_subtype -> supᵢ_ne_bot_subtype is a dubious translation:
+/- warning: supr_ne_bot_subtype -> iSup_ne_bot_subtype 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} α (supᵢ.{u1, max 1 u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))) (fun (i : Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))) => f ((fun (a : Sort.{max 1 u2}) (b : Sort.{u2}) [self : HasLiftT.{max 1 u2, u2} a b] => self.0) (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))) ι (HasLiftT.mk.{max 1 u2, u2} (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))) ι (CoeTCₓ.coe.{max 1 u2, u2} (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))) ι (coeBase.{max 1 u2, u2} (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))) ι (coeSubtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))))))) i))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α), Eq.{succ u1} α (iSup.{u1, max 1 u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))) (fun (i : Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))) => f ((fun (a : Sort.{max 1 u2}) (b : Sort.{u2}) [self : HasLiftT.{max 1 u2, u2} a b] => self.0) (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))) ι (HasLiftT.mk.{max 1 u2, u2} (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))) ι (CoeTCₓ.coe.{max 1 u2, u2} (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))) ι (coeBase.{max 1 u2, u2} (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1)))) ι (coeSubtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α _inst_1))))))) i))) (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => 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} α (supᵢ.{u2, max 1 u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Subtype.{u1} ι (fun (i : ι) => Ne.{succ u2} α (f i) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α _inst_1)))) (fun (i : Subtype.{u1} ι (fun (i : ι) => Ne.{succ u2} α (f i) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α _inst_1)))) => f (Subtype.val.{u1} ι (fun (i : ι) => Ne.{succ u2} α (f i) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α _inst_1))) i))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))
-Case conversion may be inaccurate. Consider using '#align supr_ne_bot_subtype supᵢ_ne_bot_subtypeₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α), Eq.{succ u2} α (iSup.{u2, max 1 u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Subtype.{u1} ι (fun (i : ι) => Ne.{succ u2} α (f i) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α _inst_1)))) (fun (i : Subtype.{u1} ι (fun (i : ι) => Ne.{succ u2} α (f i) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α _inst_1)))) => f (Subtype.val.{u1} ι (fun (i : ι) => Ne.{succ u2} α (f i) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α _inst_1))) i))) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))
+Case conversion may be inaccurate. Consider using '#align supr_ne_bot_subtype iSup_ne_bot_subtypeₓ'. -/
 /-- When taking the supremum of `f : ι → α`, the elements of `ι` on which `f` gives `⊥` can be
 dropped, without changing the result. -/
-theorem supᵢ_ne_bot_subtype (f : ι → α) : (⨆ i : { i // f i ≠ ⊥ }, f i) = ⨆ i, f i :=
+theorem iSup_ne_bot_subtype (f : ι → α) : (⨆ i : { i // f i ≠ ⊥ }, f i) = ⨆ i, f i :=
   by
   by_cases htriv : ∀ i, f i = ⊥
-  · simp only [supᵢ_bot, (funext htriv : f = _)]
-  refine' (supᵢ_comp_le f _).antisymm (supᵢ_mono' fun i => _)
+  · simp only [iSup_bot, (funext htriv : f = _)]
+  refine' (iSup_comp_le f _).antisymm (iSup_mono' fun i => _)
   by_cases hi : f i = ⊥
   · rw [hi]
     obtain ⟨i₀, hi₀⟩ := not_forall.mp htriv
     exact ⟨⟨i₀, hi₀⟩, bot_le⟩
   · exact ⟨⟨i, hi⟩, rfl.le⟩
-#align supr_ne_bot_subtype supᵢ_ne_bot_subtype
+#align supr_ne_bot_subtype iSup_ne_bot_subtype
 
-/- warning: infi_ne_top_subtype -> infᵢ_ne_top_subtype is a dubious translation:
+/- warning: infi_ne_top_subtype -> iInf_ne_top_subtype 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} α (infᵢ.{u1, max 1 u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))) (fun (i : Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))) => f ((fun (a : Sort.{max 1 u2}) (b : Sort.{u2}) [self : HasLiftT.{max 1 u2, u2} a b] => self.0) (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))) ι (HasLiftT.mk.{max 1 u2, u2} (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))) ι (CoeTCₓ.coe.{max 1 u2, u2} (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))) ι (coeBase.{max 1 u2, u2} (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))) ι (coeSubtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))))))) i))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => f i))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α), Eq.{succ u1} α (iInf.{u1, max 1 u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))) (fun (i : Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))) => f ((fun (a : Sort.{max 1 u2}) (b : Sort.{u2}) [self : HasLiftT.{max 1 u2, u2} a b] => self.0) (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))) ι (HasLiftT.mk.{max 1 u2, u2} (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))) ι (CoeTCₓ.coe.{max 1 u2, u2} (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))) ι (coeBase.{max 1 u2, u2} (Subtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1)))) ι (coeSubtype.{u2} ι (fun (i : ι) => Ne.{succ u1} α (f i) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α _inst_1))))))) i))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => 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} α (infᵢ.{u2, max 1 u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Subtype.{u1} ι (fun (i : ι) => Ne.{succ u2} α (f i) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α _inst_1)))) (fun (i : Subtype.{u1} ι (fun (i : ι) => Ne.{succ u2} α (f i) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α _inst_1)))) => f (Subtype.val.{u1} ι (fun (i : ι) => Ne.{succ u2} α (f i) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α _inst_1))) i))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i))
-Case conversion may be inaccurate. Consider using '#align infi_ne_top_subtype infᵢ_ne_top_subtypeₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α), Eq.{succ u2} α (iInf.{u2, max 1 u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Subtype.{u1} ι (fun (i : ι) => Ne.{succ u2} α (f i) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α _inst_1)))) (fun (i : Subtype.{u1} ι (fun (i : ι) => Ne.{succ u2} α (f i) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α _inst_1)))) => f (Subtype.val.{u1} ι (fun (i : ι) => Ne.{succ u2} α (f i) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α _inst_1))) i))) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i))
+Case conversion may be inaccurate. Consider using '#align infi_ne_top_subtype iInf_ne_top_subtypeₓ'. -/
 /-- When taking the infimum of `f : ι → α`, the elements of `ι` on which `f` gives `⊤` can be
 dropped, without changing the result. -/
-theorem infᵢ_ne_top_subtype (f : ι → α) : (⨅ i : { i // f i ≠ ⊤ }, f i) = ⨅ i, f i :=
-  @supᵢ_ne_bot_subtype αᵒᵈ ι _ f
-#align infi_ne_top_subtype infᵢ_ne_top_subtype
+theorem iInf_ne_top_subtype (f : ι → α) : (⨅ i : { i // f i ≠ ⊤ }, f i) = ⨅ i, f i :=
+  @iSup_ne_bot_subtype αᵒᵈ ι _ f
+#align infi_ne_top_subtype iInf_ne_top_subtype
 
-/- warning: Sup_image2 -> supₛ_image2 is a dubious translation:
+/- warning: Sup_image2 -> sSup_image2 is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> γ -> α} {s : Set.{u2} β} {t : Set.{u3} γ}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Set.image2.{u2, u3, u1} β γ α f s t)) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (a : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) => supᵢ.{u1, succ u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) γ (fun (b : γ) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) b t) (fun (H : Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) b t) => f a b)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> γ -> α} {s : Set.{u2} β} {t : Set.{u3} γ}, Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Set.image2.{u2, u3, u1} β γ α f s t)) (iSup.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (a : β) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) => iSup.{u1, succ u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) γ (fun (b : γ) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) b t) (fun (H : Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) b t) => f a b)))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> γ -> α} {s : Set.{u3} β} {t : Set.{u2} γ}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Set.image2.{u3, u2, u1} β γ α f s t)) (supᵢ.{u1, succ u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (a : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a s) (fun (H : Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a s) => supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) γ (fun (b : γ) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} γ (Set.{u2} γ) (Set.instMembershipSet.{u2} γ) b t) (fun (H : Membership.mem.{u2, u2} γ (Set.{u2} γ) (Set.instMembershipSet.{u2} γ) b t) => f a b)))))
-Case conversion may be inaccurate. Consider using '#align Sup_image2 supₛ_image2ₓ'. -/
-theorem supₛ_image2 {f : β → γ → α} {s : Set β} {t : Set γ} :
-    supₛ (image2 f s t) = ⨆ (a ∈ s) (b ∈ t), f a b := by rw [← image_prod, supₛ_image, bsupᵢ_prod]
-#align Sup_image2 supₛ_image2
+  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> γ -> α} {s : Set.{u3} β} {t : Set.{u2} γ}, Eq.{succ u1} α (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Set.image2.{u3, u2, u1} β γ α f s t)) (iSup.{u1, succ u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (a : β) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a s) (fun (H : Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a s) => iSup.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) γ (fun (b : γ) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} γ (Set.{u2} γ) (Set.instMembershipSet.{u2} γ) b t) (fun (H : Membership.mem.{u2, u2} γ (Set.{u2} γ) (Set.instMembershipSet.{u2} γ) b t) => f a b)))))
+Case conversion may be inaccurate. Consider using '#align Sup_image2 sSup_image2ₓ'. -/
+theorem sSup_image2 {f : β → γ → α} {s : Set β} {t : Set γ} :
+    sSup (image2 f s t) = ⨆ (a ∈ s) (b ∈ t), f a b := by rw [← image_prod, sSup_image, biSup_prod]
+#align Sup_image2 sSup_image2
 
-/- warning: Inf_image2 -> infₛ_image2 is a dubious translation:
+/- warning: Inf_image2 -> sInf_image2 is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> γ -> α} {s : Set.{u2} β} {t : Set.{u3} γ}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Set.image2.{u2, u3, u1} β γ α f s t)) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (a : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) => infᵢ.{u1, succ u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) γ (fun (b : γ) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) b t) (fun (H : Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) b t) => f a b)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> γ -> α} {s : Set.{u2} β} {t : Set.{u3} γ}, Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Set.image2.{u2, u3, u1} β γ α f s t)) (iInf.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (a : β) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) a s) => iInf.{u1, succ u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) γ (fun (b : γ) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) b t) (fun (H : Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) b t) => f a b)))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> γ -> α} {s : Set.{u3} β} {t : Set.{u2} γ}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Set.image2.{u3, u2, u1} β γ α f s t)) (infᵢ.{u1, succ u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (a : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a s) (fun (H : Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a s) => infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) γ (fun (b : γ) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} γ (Set.{u2} γ) (Set.instMembershipSet.{u2} γ) b t) (fun (H : Membership.mem.{u2, u2} γ (Set.{u2} γ) (Set.instMembershipSet.{u2} γ) b t) => f a b)))))
-Case conversion may be inaccurate. Consider using '#align Inf_image2 infₛ_image2ₓ'. -/
-theorem infₛ_image2 {f : β → γ → α} {s : Set β} {t : Set γ} :
-    infₛ (image2 f s t) = ⨅ (a ∈ s) (b ∈ t), f a b := by rw [← image_prod, infₛ_image, binfᵢ_prod]
-#align Inf_image2 infₛ_image2
+  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> γ -> α} {s : Set.{u3} β} {t : Set.{u2} γ}, Eq.{succ u1} α (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Set.image2.{u3, u2, u1} β γ α f s t)) (iInf.{u1, succ u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (a : β) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a s) (fun (H : Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) a s) => iInf.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) γ (fun (b : γ) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} γ (Set.{u2} γ) (Set.instMembershipSet.{u2} γ) b t) (fun (H : Membership.mem.{u2, u2} γ (Set.{u2} γ) (Set.instMembershipSet.{u2} γ) b t) => f a b)))))
+Case conversion may be inaccurate. Consider using '#align Inf_image2 sInf_image2ₓ'. -/
+theorem sInf_image2 {f : β → γ → α} {s : Set β} {t : Set γ} :
+    sInf (image2 f s t) = ⨅ (a ∈ s) (b ∈ t), f a b := by rw [← image_prod, sInf_image, biInf_prod]
+#align Inf_image2 sInf_image2
 
 /-!
 ### `supr` and `infi` under `ℕ`
 -/
 
 
-/- warning: supr_ge_eq_supr_nat_add -> supᵢ_ge_eq_supᵢ_nat_add is a dubious translation:
+/- warning: supr_ge_eq_supr_nat_add -> iSup_ge_eq_iSup_nat_add is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α) (n : Nat), Eq.{succ u1} α (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (GE.ge.{0} Nat Nat.hasLe i n) (fun (H : GE.ge.{0} Nat Nat.hasLe i n) => u i))) (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i n)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α) (n : Nat), Eq.{succ u1} α (iSup.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (GE.ge.{0} Nat Nat.hasLe i n) (fun (H : GE.ge.{0} Nat Nat.hasLe i n) => u i))) (iSup.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i n)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α) (n : Nat), Eq.{succ u1} α (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (GE.ge.{0} Nat instLENat i n) (fun (H : GE.ge.{0} Nat instLENat i n) => u i))) (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i n)))
-Case conversion may be inaccurate. Consider using '#align supr_ge_eq_supr_nat_add supᵢ_ge_eq_supᵢ_nat_addₓ'. -/
-theorem supᵢ_ge_eq_supᵢ_nat_add (u : ℕ → α) (n : ℕ) : (⨆ i ≥ n, u i) = ⨆ i, u (i + n) :=
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α) (n : Nat), Eq.{succ u1} α (iSup.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (GE.ge.{0} Nat instLENat i n) (fun (H : GE.ge.{0} Nat instLENat i n) => u i))) (iSup.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i n)))
+Case conversion may be inaccurate. Consider using '#align supr_ge_eq_supr_nat_add iSup_ge_eq_iSup_nat_addₓ'. -/
+theorem iSup_ge_eq_iSup_nat_add (u : ℕ → α) (n : ℕ) : (⨆ i ≥ n, u i) = ⨆ i, u (i + n) :=
   by
-  apply le_antisymm <;> simp only [supᵢ_le_iff]
+  apply le_antisymm <;> simp only [iSup_le_iff]
   ·
     exact fun i hi =>
-      le_supₛ
+      le_sSup
         ⟨i - n, by
           dsimp only
           rw [Nat.sub_add_cancel hi]⟩
-  · exact fun i => le_supₛ ⟨i + n, supᵢ_pos (Nat.le_add_left _ _)⟩
-#align supr_ge_eq_supr_nat_add supᵢ_ge_eq_supᵢ_nat_add
+  · exact fun i => le_sSup ⟨i + n, iSup_pos (Nat.le_add_left _ _)⟩
+#align supr_ge_eq_supr_nat_add iSup_ge_eq_iSup_nat_add
 
-/- warning: infi_ge_eq_infi_nat_add -> infᵢ_ge_eq_infᵢ_nat_add is a dubious translation:
+/- warning: infi_ge_eq_infi_nat_add -> iInf_ge_eq_iInf_nat_add is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α) (n : Nat), Eq.{succ u1} α (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (GE.ge.{0} Nat Nat.hasLe i n) (fun (H : GE.ge.{0} Nat Nat.hasLe i n) => u i))) (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i n)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α) (n : Nat), Eq.{succ u1} α (iInf.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (GE.ge.{0} Nat Nat.hasLe i n) (fun (H : GE.ge.{0} Nat Nat.hasLe i n) => u i))) (iInf.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i n)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α) (n : Nat), Eq.{succ u1} α (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (GE.ge.{0} Nat instLENat i n) (fun (H : GE.ge.{0} Nat instLENat i n) => u i))) (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i n)))
-Case conversion may be inaccurate. Consider using '#align infi_ge_eq_infi_nat_add infᵢ_ge_eq_infᵢ_nat_addₓ'. -/
-theorem infᵢ_ge_eq_infᵢ_nat_add (u : ℕ → α) (n : ℕ) : (⨅ i ≥ n, u i) = ⨅ i, u (i + n) :=
-  @supᵢ_ge_eq_supᵢ_nat_add αᵒᵈ _ _ _
-#align infi_ge_eq_infi_nat_add infᵢ_ge_eq_infᵢ_nat_add
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α) (n : Nat), Eq.{succ u1} α (iInf.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (GE.ge.{0} Nat instLENat i n) (fun (H : GE.ge.{0} Nat instLENat i n) => u i))) (iInf.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i n)))
+Case conversion may be inaccurate. Consider using '#align infi_ge_eq_infi_nat_add iInf_ge_eq_iInf_nat_addₓ'. -/
+theorem iInf_ge_eq_iInf_nat_add (u : ℕ → α) (n : ℕ) : (⨅ i ≥ n, u i) = ⨅ i, u (i + n) :=
+  @iSup_ge_eq_iSup_nat_add αᵒᵈ _ _ _
+#align infi_ge_eq_infi_nat_add iInf_ge_eq_iInf_nat_add
 
-/- warning: monotone.supr_nat_add -> Monotone.supᵢ_nat_add is a dubious translation:
+/- warning: monotone.supr_nat_add -> Monotone.iSup_nat_add is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Nat -> α}, (Monotone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (SemilatticeInf.toPartialOrder.{0} Nat (Lattice.toSemilatticeInf.{0} Nat (LinearOrder.toLattice.{0} Nat Nat.linearOrder)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f) -> (forall (k : Nat), Eq.{succ u1} α (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (n : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n k))) (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (n : Nat) => f n)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Nat -> α}, (Monotone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (SemilatticeInf.toPartialOrder.{0} Nat (Lattice.toSemilatticeInf.{0} Nat (LinearOrder.toLattice.{0} Nat Nat.linearOrder)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f) -> (forall (k : Nat), Eq.{succ u1} α (iSup.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (n : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n k))) (iSup.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (n : Nat) => f n)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Nat -> α}, (Monotone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (SemilatticeInf.toPartialOrder.{0} Nat (Lattice.toSemilatticeInf.{0} Nat (DistribLattice.toLattice.{0} Nat instDistribLatticeNat)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f) -> (forall (k : Nat), Eq.{succ u1} α (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (n : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n k))) (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (n : Nat) => f n)))
-Case conversion may be inaccurate. Consider using '#align monotone.supr_nat_add Monotone.supᵢ_nat_addₓ'. -/
-theorem Monotone.supᵢ_nat_add {f : ℕ → α} (hf : Monotone f) (k : ℕ) : (⨆ n, f (n + k)) = ⨆ n, f n :=
-  le_antisymm (supᵢ_le fun i => le_supᵢ _ (i + k)) <| supᵢ_mono fun i => hf <| Nat.le_add_right i k
-#align monotone.supr_nat_add Monotone.supᵢ_nat_add
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Nat -> α}, (Monotone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (SemilatticeInf.toPartialOrder.{0} Nat (Lattice.toSemilatticeInf.{0} Nat (DistribLattice.toLattice.{0} Nat instDistribLatticeNat)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f) -> (forall (k : Nat), Eq.{succ u1} α (iSup.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (n : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n k))) (iSup.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (n : Nat) => f n)))
+Case conversion may be inaccurate. Consider using '#align monotone.supr_nat_add Monotone.iSup_nat_addₓ'. -/
+theorem Monotone.iSup_nat_add {f : ℕ → α} (hf : Monotone f) (k : ℕ) : (⨆ n, f (n + k)) = ⨆ n, f n :=
+  le_antisymm (iSup_le fun i => le_iSup _ (i + k)) <| iSup_mono fun i => hf <| Nat.le_add_right i k
+#align monotone.supr_nat_add Monotone.iSup_nat_add
 
-/- warning: antitone.infi_nat_add -> Antitone.infᵢ_nat_add is a dubious translation:
+/- warning: antitone.infi_nat_add -> Antitone.iInf_nat_add is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Nat -> α}, (Antitone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (SemilatticeInf.toPartialOrder.{0} Nat (Lattice.toSemilatticeInf.{0} Nat (LinearOrder.toLattice.{0} Nat Nat.linearOrder)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f) -> (forall (k : Nat), Eq.{succ u1} α (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (n : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n k))) (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (n : Nat) => f n)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Nat -> α}, (Antitone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (SemilatticeInf.toPartialOrder.{0} Nat (Lattice.toSemilatticeInf.{0} Nat (LinearOrder.toLattice.{0} Nat Nat.linearOrder)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f) -> (forall (k : Nat), Eq.{succ u1} α (iInf.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (n : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n k))) (iInf.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (n : Nat) => f n)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Nat -> α}, (Antitone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (SemilatticeInf.toPartialOrder.{0} Nat (Lattice.toSemilatticeInf.{0} Nat (DistribLattice.toLattice.{0} Nat instDistribLatticeNat)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f) -> (forall (k : Nat), Eq.{succ u1} α (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (n : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n k))) (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (n : Nat) => f n)))
-Case conversion may be inaccurate. Consider using '#align antitone.infi_nat_add Antitone.infᵢ_nat_addₓ'. -/
-theorem Antitone.infᵢ_nat_add {f : ℕ → α} (hf : Antitone f) (k : ℕ) : (⨅ n, f (n + k)) = ⨅ n, f n :=
-  hf.dual_right.supᵢ_nat_add k
-#align antitone.infi_nat_add Antitone.infᵢ_nat_add
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Nat -> α}, (Antitone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (SemilatticeInf.toPartialOrder.{0} Nat (Lattice.toSemilatticeInf.{0} Nat (DistribLattice.toLattice.{0} Nat instDistribLatticeNat)))) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) f) -> (forall (k : Nat), Eq.{succ u1} α (iInf.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (n : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n k))) (iInf.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (n : Nat) => f n)))
+Case conversion may be inaccurate. Consider using '#align antitone.infi_nat_add Antitone.iInf_nat_addₓ'. -/
+theorem Antitone.iInf_nat_add {f : ℕ → α} (hf : Antitone f) (k : ℕ) : (⨅ n, f (n + k)) = ⨅ n, f n :=
+  hf.dual_right.iSup_nat_add k
+#align antitone.infi_nat_add Antitone.iInf_nat_add
 
-/- warning: supr_infi_ge_nat_add -> supᵢ_infᵢ_ge_nat_add is a dubious translation:
+/- warning: supr_infi_ge_nat_add -> iSup_iInf_ge_nat_add is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α) (k : Nat), Eq.{succ u1} α (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (n : Nat) => infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (GE.ge.{0} Nat Nat.hasLe i n) (fun (H : GE.ge.{0} Nat Nat.hasLe i n) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i k))))) (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (n : Nat) => infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (GE.ge.{0} Nat Nat.hasLe i n) (fun (H : GE.ge.{0} Nat Nat.hasLe i n) => f i))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α) (k : Nat), Eq.{succ u1} α (iSup.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (n : Nat) => iInf.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (GE.ge.{0} Nat Nat.hasLe i n) (fun (H : GE.ge.{0} Nat Nat.hasLe i n) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i k))))) (iSup.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (n : Nat) => iInf.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (GE.ge.{0} Nat Nat.hasLe i n) (fun (H : GE.ge.{0} Nat Nat.hasLe i n) => f i))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α) (k : Nat), Eq.{succ u1} α (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (n : Nat) => infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (GE.ge.{0} Nat instLENat i n) (fun (H : GE.ge.{0} Nat instLENat i n) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i k))))) (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (n : Nat) => infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (GE.ge.{0} Nat instLENat i n) (fun (H : GE.ge.{0} Nat instLENat i n) => f i))))
-Case conversion may be inaccurate. Consider using '#align supr_infi_ge_nat_add supᵢ_infᵢ_ge_nat_addₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α) (k : Nat), Eq.{succ u1} α (iSup.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (n : Nat) => iInf.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (GE.ge.{0} Nat instLENat i n) (fun (H : GE.ge.{0} Nat instLENat i n) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i k))))) (iSup.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (n : Nat) => iInf.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (GE.ge.{0} Nat instLENat i n) (fun (H : GE.ge.{0} Nat instLENat i n) => f i))))
+Case conversion may be inaccurate. Consider using '#align supr_infi_ge_nat_add iSup_iInf_ge_nat_addₓ'. -/
 @[simp]
-theorem supᵢ_infᵢ_ge_nat_add (f : ℕ → α) (k : ℕ) : (⨆ n, ⨅ i ≥ n, f (i + k)) = ⨆ n, ⨅ i ≥ n, f i :=
+theorem iSup_iInf_ge_nat_add (f : ℕ → α) (k : ℕ) : (⨆ n, ⨅ i ≥ n, f (i + k)) = ⨆ n, ⨅ i ≥ n, f i :=
   by
-  have hf : Monotone fun n => ⨅ i ≥ n, f i := fun n m h => binfᵢ_mono fun i => h.trans
-  rw [← Monotone.supᵢ_nat_add hf k]
-  · simp_rw [infᵢ_ge_eq_infᵢ_nat_add, ← Nat.add_assoc]
-#align supr_infi_ge_nat_add supᵢ_infᵢ_ge_nat_add
+  have hf : Monotone fun n => ⨅ i ≥ n, f i := fun n m h => biInf_mono fun i => h.trans
+  rw [← Monotone.iSup_nat_add hf k]
+  · simp_rw [iInf_ge_eq_iInf_nat_add, ← Nat.add_assoc]
+#align supr_infi_ge_nat_add iSup_iInf_ge_nat_add
 
-/- warning: infi_supr_ge_nat_add -> infᵢ_supᵢ_ge_nat_add is a dubious translation:
+/- warning: infi_supr_ge_nat_add -> iInf_iSup_ge_nat_add is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α) (k : Nat), Eq.{succ u1} α (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (n : Nat) => supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (GE.ge.{0} Nat Nat.hasLe i n) (fun (H : GE.ge.{0} Nat Nat.hasLe i n) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i k))))) (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (n : Nat) => supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (GE.ge.{0} Nat Nat.hasLe i n) (fun (H : GE.ge.{0} Nat Nat.hasLe i n) => f i))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α) (k : Nat), Eq.{succ u1} α (iInf.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (n : Nat) => iSup.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (GE.ge.{0} Nat Nat.hasLe i n) (fun (H : GE.ge.{0} Nat Nat.hasLe i n) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i k))))) (iInf.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (n : Nat) => iSup.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (GE.ge.{0} Nat Nat.hasLe i n) (fun (H : GE.ge.{0} Nat Nat.hasLe i n) => f i))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α) (k : Nat), Eq.{succ u1} α (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (n : Nat) => supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (GE.ge.{0} Nat instLENat i n) (fun (H : GE.ge.{0} Nat instLENat i n) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i k))))) (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (n : Nat) => supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (GE.ge.{0} Nat instLENat i n) (fun (H : GE.ge.{0} Nat instLENat i n) => f i))))
-Case conversion may be inaccurate. Consider using '#align infi_supr_ge_nat_add infᵢ_supᵢ_ge_nat_addₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α) (k : Nat), Eq.{succ u1} α (iInf.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (n : Nat) => iSup.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (GE.ge.{0} Nat instLENat i n) (fun (H : GE.ge.{0} Nat instLENat i n) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i k))))) (iInf.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (n : Nat) => iSup.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (GE.ge.{0} Nat instLENat i n) (fun (H : GE.ge.{0} Nat instLENat i n) => f i))))
+Case conversion may be inaccurate. Consider using '#align infi_supr_ge_nat_add iInf_iSup_ge_nat_addₓ'. -/
 @[simp]
-theorem infᵢ_supᵢ_ge_nat_add :
+theorem iInf_iSup_ge_nat_add :
     ∀ (f : ℕ → α) (k : ℕ), (⨅ n, ⨆ i ≥ n, f (i + k)) = ⨅ n, ⨆ i ≥ n, f i :=
-  @supᵢ_infᵢ_ge_nat_add αᵒᵈ _
-#align infi_supr_ge_nat_add infᵢ_supᵢ_ge_nat_add
+  @iSup_iInf_ge_nat_add αᵒᵈ _
+#align infi_supr_ge_nat_add iInf_iSup_ge_nat_add
 
-/- warning: sup_supr_nat_succ -> sup_supᵢ_nat_succ is a dubious translation:
+/- warning: sup_supr_nat_succ -> sup_iSup_nat_succ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α), Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (u (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => u i))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α), Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (u (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (iSup.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (iSup.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => u i))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α), Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (u (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => u i))
-Case conversion may be inaccurate. Consider using '#align sup_supr_nat_succ sup_supᵢ_nat_succₓ'. -/
-theorem sup_supᵢ_nat_succ (u : ℕ → α) : (u 0 ⊔ ⨆ i, u (i + 1)) = ⨆ i, u i :=
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α), Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (u (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (iSup.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (iSup.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => u i))
+Case conversion may be inaccurate. Consider using '#align sup_supr_nat_succ sup_iSup_nat_succₓ'. -/
+theorem sup_iSup_nat_succ (u : ℕ → α) : (u 0 ⊔ ⨆ i, u (i + 1)) = ⨆ i, u i :=
   calc
     (u 0 ⊔ ⨆ i, u (i + 1)) = ⨆ x ∈ {0} ∪ range Nat.succ, u x := by
-      rw [supᵢ_union, supᵢ_singleton, supᵢ_range]
-    _ = ⨆ i, u i := by rw [Nat.zero_union_range_succ, supᵢ_univ]
+      rw [iSup_union, iSup_singleton, iSup_range]
+    _ = ⨆ i, u i := by rw [Nat.zero_union_range_succ, iSup_univ]
     
-#align sup_supr_nat_succ sup_supᵢ_nat_succ
+#align sup_supr_nat_succ sup_iSup_nat_succ
 
-/- warning: inf_infi_nat_succ -> inf_infᵢ_nat_succ is a dubious translation:
+/- warning: inf_infi_nat_succ -> inf_iInf_nat_succ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α), Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (u (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => u i))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α), Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (u (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (iInf.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (iInf.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => u i))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α), Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (u (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => u i))
-Case conversion may be inaccurate. Consider using '#align inf_infi_nat_succ inf_infᵢ_nat_succₓ'. -/
-theorem inf_infᵢ_nat_succ (u : ℕ → α) : (u 0 ⊓ ⨅ i, u (i + 1)) = ⨅ i, u i :=
-  @sup_supᵢ_nat_succ αᵒᵈ _ u
-#align inf_infi_nat_succ inf_infᵢ_nat_succ
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α), Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (u (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (iInf.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (iInf.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => u i))
+Case conversion may be inaccurate. Consider using '#align inf_infi_nat_succ inf_iInf_nat_succₓ'. -/
+theorem inf_iInf_nat_succ (u : ℕ → α) : (u 0 ⊓ ⨅ i, u (i + 1)) = ⨅ i, u i :=
+  @sup_iSup_nat_succ αᵒᵈ _ u
+#align inf_infi_nat_succ inf_iInf_nat_succ
 
-/- warning: infi_nat_gt_zero_eq -> infᵢ_nat_gt_zero_eq is a dubious translation:
+/- warning: infi_nat_gt_zero_eq -> iInf_nat_gt_zero_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α), Eq.{succ u1} α (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (GT.gt.{0} Nat Nat.hasLt i (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (fun (H : GT.gt.{0} Nat Nat.hasLt i (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) => f i))) (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α), Eq.{succ u1} α (iInf.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (GT.gt.{0} Nat Nat.hasLt i (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (fun (H : GT.gt.{0} Nat Nat.hasLt i (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) => f i))) (iInf.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α), Eq.{succ u1} α (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (GT.gt.{0} Nat instLTNat i (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (fun (H : GT.gt.{0} Nat instLTNat i (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) => f i))) (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
-Case conversion may be inaccurate. Consider using '#align infi_nat_gt_zero_eq infᵢ_nat_gt_zero_eqₓ'. -/
-theorem infᵢ_nat_gt_zero_eq (f : ℕ → α) : (⨅ i > 0, f i) = ⨅ i, f (i + 1) :=
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α), Eq.{succ u1} α (iInf.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (GT.gt.{0} Nat instLTNat i (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (fun (H : GT.gt.{0} Nat instLTNat i (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) => f i))) (iInf.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
+Case conversion may be inaccurate. Consider using '#align infi_nat_gt_zero_eq iInf_nat_gt_zero_eqₓ'. -/
+theorem iInf_nat_gt_zero_eq (f : ℕ → α) : (⨅ i > 0, f i) = ⨅ i, f (i + 1) :=
   by
-  rw [← infᵢ_range, Nat.range_succ]
+  rw [← iInf_range, Nat.range_succ]
   simp only [mem_set_of]
-#align infi_nat_gt_zero_eq infᵢ_nat_gt_zero_eq
+#align infi_nat_gt_zero_eq iInf_nat_gt_zero_eq
 
-/- warning: supr_nat_gt_zero_eq -> supᵢ_nat_gt_zero_eq is a dubious translation:
+/- warning: supr_nat_gt_zero_eq -> iSup_nat_gt_zero_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α), Eq.{succ u1} α (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (GT.gt.{0} Nat Nat.hasLt i (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (fun (H : GT.gt.{0} Nat Nat.hasLt i (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) => f i))) (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α), Eq.{succ u1} α (iSup.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (GT.gt.{0} Nat Nat.hasLt i (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (fun (H : GT.gt.{0} Nat Nat.hasLt i (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) => f i))) (iSup.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α), Eq.{succ u1} α (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (GT.gt.{0} Nat instLTNat i (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (fun (H : GT.gt.{0} Nat instLTNat i (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) => f i))) (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
-Case conversion may be inaccurate. Consider using '#align supr_nat_gt_zero_eq supᵢ_nat_gt_zero_eqₓ'. -/
-theorem supᵢ_nat_gt_zero_eq (f : ℕ → α) : (⨆ i > 0, f i) = ⨆ i, f (i + 1) :=
-  @infᵢ_nat_gt_zero_eq αᵒᵈ _ f
-#align supr_nat_gt_zero_eq supᵢ_nat_gt_zero_eq
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (f : Nat -> α), Eq.{succ u1} α (iSup.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (GT.gt.{0} Nat instLTNat i (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (fun (H : GT.gt.{0} Nat instLTNat i (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) => f i))) (iSup.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))
+Case conversion may be inaccurate. Consider using '#align supr_nat_gt_zero_eq iSup_nat_gt_zero_eqₓ'. -/
+theorem iSup_nat_gt_zero_eq (f : ℕ → α) : (⨆ i > 0, f i) = ⨆ i, f (i + 1) :=
+  @iInf_nat_gt_zero_eq αᵒᵈ _ f
+#align supr_nat_gt_zero_eq iSup_nat_gt_zero_eq
 
 end
 
@@ -3283,25 +3283,25 @@ section CompleteLinearOrder
 
 variable [CompleteLinearOrder α]
 
-/- warning: supr_eq_top -> supᵢ_eq_top is a dubious translation:
+/- warning: supr_eq_top -> iSup_eq_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] (f : ι -> α), Iff (Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι f) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (f i))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] (f : ι -> α), Iff (Eq.{succ u1} α (iSup.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι f) (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (f i))))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLinearOrder.{u2} α] (f : ι -> α), Iff (Eq.{succ u2} α (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)) ι f) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (forall (b : α), (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) b (Top.top.{u2} α (CompleteLattice.toTop.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) -> (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) b (f i))))
-Case conversion may be inaccurate. Consider using '#align supr_eq_top supᵢ_eq_topₓ'. -/
-theorem supᵢ_eq_top (f : ι → α) : supᵢ f = ⊤ ↔ ∀ b < ⊤, ∃ i, b < f i := by
-  simp only [← supₛ_range, supₛ_eq_top, Set.exists_range_iff]
-#align supr_eq_top supᵢ_eq_top
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLinearOrder.{u2} α] (f : ι -> α), Iff (Eq.{succ u2} α (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)) ι f) (Top.top.{u2} α (CompleteLattice.toTop.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (forall (b : α), (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) b (Top.top.{u2} α (CompleteLattice.toTop.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) -> (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) b (f i))))
+Case conversion may be inaccurate. Consider using '#align supr_eq_top iSup_eq_topₓ'. -/
+theorem iSup_eq_top (f : ι → α) : iSup f = ⊤ ↔ ∀ b < ⊤, ∃ i, b < f i := by
+  simp only [← sSup_range, sSup_eq_top, Set.exists_range_iff]
+#align supr_eq_top iSup_eq_top
 
-/- warning: infi_eq_bot -> infᵢ_eq_bot is a dubious translation:
+/- warning: infi_eq_bot -> iInf_eq_bot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] (f : ι -> α), Iff (Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι f) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (f i) b)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] (f : ι -> α), Iff (Eq.{succ u1} α (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι f) (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (forall (b : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) b (Bot.bot.{u1} α (CompleteLattice.toHasBot.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))) (f i) b)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLinearOrder.{u2} α] (f : ι -> α), Iff (Eq.{succ u2} α (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)) ι f) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (forall (b : α), (GT.gt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) b (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) -> (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) (f i) b)))
-Case conversion may be inaccurate. Consider using '#align infi_eq_bot infᵢ_eq_botₓ'. -/
-theorem infᵢ_eq_bot (f : ι → α) : infᵢ f = ⊥ ↔ ∀ b > ⊥, ∃ i, f i < b := by
-  simp only [← infₛ_range, infₛ_eq_bot, Set.exists_range_iff]
-#align infi_eq_bot infᵢ_eq_bot
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLinearOrder.{u2} α] (f : ι -> α), Iff (Eq.{succ u2} α (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)) ι f) (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (forall (b : α), (GT.gt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) b (Bot.bot.{u2} α (CompleteLattice.toBot.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) -> (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))) (f i) b)))
+Case conversion may be inaccurate. Consider using '#align infi_eq_bot iInf_eq_botₓ'. -/
+theorem iInf_eq_bot (f : ι → α) : iInf f = ⊥ ↔ ∀ b > ⊥, ∃ i, f i < b := by
+  simp only [← sInf_range, sInf_eq_bot, Set.exists_range_iff]
+#align infi_eq_bot iInf_eq_bot
 
 end CompleteLinearOrder
 
@@ -3314,10 +3314,10 @@ end CompleteLinearOrder
 instance Prop.completeLattice : CompleteLattice Prop :=
   { Prop.boundedOrder,
     Prop.distribLattice with
-    supₛ := fun s => ∃ a ∈ s, a
+    sSup := fun s => ∃ a ∈ s, a
     le_sup := fun s a h p => ⟨a, h, p⟩
     sup_le := fun s a h ⟨b, h', p⟩ => h b h' p
-    infₛ := fun s => ∀ a, a ∈ s → a
+    sInf := fun s => ∀ a, a ∈ s → a
     inf_le := fun s a h p => p a h
     le_inf := fun s a h p b hb => h b hb p }
 #align Prop.complete_lattice Prop.completeLattice
@@ -3329,50 +3329,50 @@ noncomputable instance Prop.completeLinearOrder : CompleteLinearOrder Prop :=
 #align Prop.complete_linear_order Prop.completeLinearOrder
 -/
 
-/- warning: Sup_Prop_eq -> supₛ_Prop_eq is a dubious translation:
+/- warning: Sup_Prop_eq -> sSup_Prop_eq is a dubious translation:
 lean 3 declaration is
-  forall {s : Set.{0} Prop}, Eq.{1} Prop (SupSet.supₛ.{0} Prop (CompleteSemilatticeSup.toHasSup.{0} Prop (CompleteLattice.toCompleteSemilatticeSup.{0} Prop Prop.completeLattice)) s) (Exists.{1} Prop (fun (p : Prop) => Exists.{0} (Membership.Mem.{0, 0} Prop (Set.{0} Prop) (Set.hasMem.{0} Prop) p s) (fun (H : Membership.Mem.{0, 0} Prop (Set.{0} Prop) (Set.hasMem.{0} Prop) p s) => p)))
+  forall {s : Set.{0} Prop}, Eq.{1} Prop (SupSet.sSup.{0} Prop (CompleteSemilatticeSup.toHasSup.{0} Prop (CompleteLattice.toCompleteSemilatticeSup.{0} Prop Prop.completeLattice)) s) (Exists.{1} Prop (fun (p : Prop) => Exists.{0} (Membership.Mem.{0, 0} Prop (Set.{0} Prop) (Set.hasMem.{0} Prop) p s) (fun (H : Membership.Mem.{0, 0} Prop (Set.{0} Prop) (Set.hasMem.{0} Prop) p s) => p)))
 but is expected to have type
-  forall {s : Set.{0} Prop}, Eq.{1} Prop (SupSet.supₛ.{0} Prop (CompleteLattice.toSupSet.{0} Prop Prop.completeLattice) s) (Exists.{1} Prop (fun (p : Prop) => And (Membership.mem.{0, 0} Prop (Set.{0} Prop) (Set.instMembershipSet.{0} Prop) p s) p))
-Case conversion may be inaccurate. Consider using '#align Sup_Prop_eq supₛ_Prop_eqₓ'. -/
+  forall {s : Set.{0} Prop}, Eq.{1} Prop (SupSet.sSup.{0} Prop (CompleteLattice.toSupSet.{0} Prop Prop.completeLattice) s) (Exists.{1} Prop (fun (p : Prop) => And (Membership.mem.{0, 0} Prop (Set.{0} Prop) (Set.instMembershipSet.{0} Prop) p s) p))
+Case conversion may be inaccurate. Consider using '#align Sup_Prop_eq sSup_Prop_eqₓ'. -/
 @[simp]
-theorem supₛ_Prop_eq {s : Set Prop} : supₛ s = ∃ p ∈ s, p :=
+theorem sSup_Prop_eq {s : Set Prop} : sSup s = ∃ p ∈ s, p :=
   rfl
-#align Sup_Prop_eq supₛ_Prop_eq
+#align Sup_Prop_eq sSup_Prop_eq
 
-/- warning: Inf_Prop_eq -> infₛ_Prop_eq is a dubious translation:
+/- warning: Inf_Prop_eq -> sInf_Prop_eq is a dubious translation:
 lean 3 declaration is
-  forall {s : Set.{0} Prop}, Eq.{1} Prop (InfSet.infₛ.{0} Prop (CompleteSemilatticeInf.toHasInf.{0} Prop (CompleteLattice.toCompleteSemilatticeInf.{0} Prop Prop.completeLattice)) s) (forall (p : Prop), (Membership.Mem.{0, 0} Prop (Set.{0} Prop) (Set.hasMem.{0} Prop) p s) -> p)
+  forall {s : Set.{0} Prop}, Eq.{1} Prop (InfSet.sInf.{0} Prop (CompleteSemilatticeInf.toHasInf.{0} Prop (CompleteLattice.toCompleteSemilatticeInf.{0} Prop Prop.completeLattice)) s) (forall (p : Prop), (Membership.Mem.{0, 0} Prop (Set.{0} Prop) (Set.hasMem.{0} Prop) p s) -> p)
 but is expected to have type
-  forall {s : Set.{0} Prop}, Eq.{1} Prop (InfSet.infₛ.{0} Prop (CompleteLattice.toInfSet.{0} Prop Prop.completeLattice) s) (forall (p : Prop), (Membership.mem.{0, 0} Prop (Set.{0} Prop) (Set.instMembershipSet.{0} Prop) p s) -> p)
-Case conversion may be inaccurate. Consider using '#align Inf_Prop_eq infₛ_Prop_eqₓ'. -/
+  forall {s : Set.{0} Prop}, Eq.{1} Prop (InfSet.sInf.{0} Prop (CompleteLattice.toInfSet.{0} Prop Prop.completeLattice) s) (forall (p : Prop), (Membership.mem.{0, 0} Prop (Set.{0} Prop) (Set.instMembershipSet.{0} Prop) p s) -> p)
+Case conversion may be inaccurate. Consider using '#align Inf_Prop_eq sInf_Prop_eqₓ'. -/
 @[simp]
-theorem infₛ_Prop_eq {s : Set Prop} : infₛ s = ∀ p ∈ s, p :=
+theorem sInf_Prop_eq {s : Set Prop} : sInf s = ∀ p ∈ s, p :=
   rfl
-#align Inf_Prop_eq infₛ_Prop_eq
+#align Inf_Prop_eq sInf_Prop_eq
 
-/- warning: supr_Prop_eq -> supᵢ_Prop_eq is a dubious translation:
+/- warning: supr_Prop_eq -> iSup_Prop_eq is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {p : ι -> Prop}, Eq.{1} Prop (supᵢ.{0, u1} Prop (CompleteSemilatticeSup.toHasSup.{0} Prop (CompleteLattice.toCompleteSemilatticeSup.{0} Prop Prop.completeLattice)) ι (fun (i : ι) => p i)) (Exists.{u1} ι (fun (i : ι) => p i))
+  forall {ι : Sort.{u1}} {p : ι -> Prop}, Eq.{1} Prop (iSup.{0, u1} Prop (CompleteSemilatticeSup.toHasSup.{0} Prop (CompleteLattice.toCompleteSemilatticeSup.{0} Prop Prop.completeLattice)) ι (fun (i : ι) => p i)) (Exists.{u1} ι (fun (i : ι) => p i))
 but is expected to have type
-  forall {ι : Sort.{u1}} {p : ι -> Prop}, Eq.{1} Prop (supᵢ.{0, u1} Prop (CompleteLattice.toSupSet.{0} Prop Prop.completeLattice) ι (fun (i : ι) => p i)) (Exists.{u1} ι (fun (i : ι) => p i))
-Case conversion may be inaccurate. Consider using '#align supr_Prop_eq supᵢ_Prop_eqₓ'. -/
+  forall {ι : Sort.{u1}} {p : ι -> Prop}, Eq.{1} Prop (iSup.{0, u1} Prop (CompleteLattice.toSupSet.{0} Prop Prop.completeLattice) ι (fun (i : ι) => p i)) (Exists.{u1} ι (fun (i : ι) => p i))
+Case conversion may be inaccurate. Consider using '#align supr_Prop_eq iSup_Prop_eqₓ'. -/
 @[simp]
-theorem supᵢ_Prop_eq {p : ι → Prop} : (⨆ i, p i) = ∃ i, p i :=
+theorem iSup_Prop_eq {p : ι → Prop} : (⨆ i, p i) = ∃ i, p i :=
   le_antisymm (fun ⟨q, ⟨i, (Eq : p i = q)⟩, hq⟩ => ⟨i, Eq.symm ▸ hq⟩) fun ⟨i, hi⟩ =>
     ⟨p i, ⟨i, rfl⟩, hi⟩
-#align supr_Prop_eq supᵢ_Prop_eq
+#align supr_Prop_eq iSup_Prop_eq
 
-/- warning: infi_Prop_eq -> infᵢ_Prop_eq is a dubious translation:
+/- warning: infi_Prop_eq -> iInf_Prop_eq is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {p : ι -> Prop}, Eq.{1} Prop (infᵢ.{0, u1} Prop (CompleteSemilatticeInf.toHasInf.{0} Prop (CompleteLattice.toCompleteSemilatticeInf.{0} Prop Prop.completeLattice)) ι (fun (i : ι) => p i)) (forall (i : ι), p i)
+  forall {ι : Sort.{u1}} {p : ι -> Prop}, Eq.{1} Prop (iInf.{0, u1} Prop (CompleteSemilatticeInf.toHasInf.{0} Prop (CompleteLattice.toCompleteSemilatticeInf.{0} Prop Prop.completeLattice)) ι (fun (i : ι) => p i)) (forall (i : ι), p i)
 but is expected to have type
-  forall {ι : Sort.{u1}} {p : ι -> Prop}, Eq.{1} Prop (infᵢ.{0, u1} Prop (CompleteLattice.toInfSet.{0} Prop Prop.completeLattice) ι (fun (i : ι) => p i)) (forall (i : ι), p i)
-Case conversion may be inaccurate. Consider using '#align infi_Prop_eq infᵢ_Prop_eqₓ'. -/
+  forall {ι : Sort.{u1}} {p : ι -> Prop}, Eq.{1} Prop (iInf.{0, u1} Prop (CompleteLattice.toInfSet.{0} Prop Prop.completeLattice) ι (fun (i : ι) => p i)) (forall (i : ι), p i)
+Case conversion may be inaccurate. Consider using '#align infi_Prop_eq iInf_Prop_eqₓ'. -/
 @[simp]
-theorem infᵢ_Prop_eq {p : ι → Prop} : (⨅ i, p i) = ∀ i, p i :=
+theorem iInf_Prop_eq {p : ι → Prop} : (⨅ i, p i) = ∀ i, p i :=
   le_antisymm (fun h i => h _ ⟨i, rfl⟩) fun h p ⟨i, Eq⟩ => Eq ▸ h i
-#align infi_Prop_eq infᵢ_Prop_eq
+#align infi_Prop_eq iInf_Prop_eq
 
 #print Pi.supSet /-
 instance Pi.supSet {α : Type _} {β : α → Type _} [∀ i, SupSet (β i)] : SupSet (∀ i, β i) :=
@@ -3390,137 +3390,137 @@ instance Pi.infSet {α : Type _} {β : α → Type _} [∀ i, InfSet (β i)] : I
 instance Pi.completeLattice {α : Type _} {β : α → Type _} [∀ i, CompleteLattice (β i)] :
     CompleteLattice (∀ i, β i) :=
   { Pi.boundedOrder, Pi.lattice with
-    supₛ := supₛ
-    infₛ := infₛ
-    le_sup := fun s f hf i => le_supᵢ (fun f : s => (f : ∀ i, β i) i) ⟨f, hf⟩
-    inf_le := fun s f hf i => infᵢ_le (fun f : s => (f : ∀ i, β i) i) ⟨f, hf⟩
-    sup_le := fun s f hf i => supᵢ_le fun g => hf g g.2 i
-    le_inf := fun s f hf i => le_infᵢ fun g => hf g g.2 i }
+    sSup := sSup
+    sInf := sInf
+    le_sup := fun s f hf i => le_iSup (fun f : s => (f : ∀ i, β i) i) ⟨f, hf⟩
+    inf_le := fun s f hf i => iInf_le (fun f : s => (f : ∀ i, β i) i) ⟨f, hf⟩
+    sup_le := fun s f hf i => iSup_le fun g => hf g g.2 i
+    le_inf := fun s f hf i => le_iInf fun g => hf g g.2 i }
 #align pi.complete_lattice Pi.completeLattice
 -/
 
-/- warning: Sup_apply -> supₛ_apply is a dubious translation:
+/- warning: Sup_apply -> sSup_apply is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : α -> Type.{u2}} [_inst_1 : forall (i : α), SupSet.{u2} (β i)] {s : Set.{max u1 u2} (forall (a : α), β a)} {a : α}, Eq.{succ u2} (β a) (SupSet.supₛ.{max u1 u2} (forall (a : α), β a) (Pi.supSet.{u1, u2} α (fun (a : α) => β a) (fun (i : α) => _inst_1 i)) s a) (supᵢ.{u2, succ (max u1 u2)} (β a) (_inst_1 a) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (fun (f : coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) => (fun (a : Type.{max u1 u2}) (b : Sort.{max (succ u1) (succ u2)}) [self : HasLiftT.{succ (max u1 u2), max (succ u1) (succ u2)} a b] => self.0) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (forall (a : α), β a) (HasLiftT.mk.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (forall (a : α), β a) (CoeTCₓ.coe.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (forall (a : α), β a) (coeBase.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (forall (a : α), β a) (coeSubtype.{max (succ u1) (succ u2)} (forall (a : α), β a) (fun (x : forall (a : α), β a) => Membership.Mem.{max u1 u2, max u1 u2} (forall (a : α), β a) (Set.{max u1 u2} (forall (a : α), β a)) (Set.hasMem.{max u1 u2} (forall (a : α), β a)) x s))))) f a))
+  forall {α : Type.{u1}} {β : α -> Type.{u2}} [_inst_1 : forall (i : α), SupSet.{u2} (β i)] {s : Set.{max u1 u2} (forall (a : α), β a)} {a : α}, Eq.{succ u2} (β a) (SupSet.sSup.{max u1 u2} (forall (a : α), β a) (Pi.supSet.{u1, u2} α (fun (a : α) => β a) (fun (i : α) => _inst_1 i)) s a) (iSup.{u2, succ (max u1 u2)} (β a) (_inst_1 a) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (fun (f : coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) => (fun (a : Type.{max u1 u2}) (b : Sort.{max (succ u1) (succ u2)}) [self : HasLiftT.{succ (max u1 u2), max (succ u1) (succ u2)} a b] => self.0) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (forall (a : α), β a) (HasLiftT.mk.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (forall (a : α), β a) (CoeTCₓ.coe.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (forall (a : α), β a) (coeBase.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (forall (a : α), β a) (coeSubtype.{max (succ u1) (succ u2)} (forall (a : α), β a) (fun (x : forall (a : α), β a) => Membership.Mem.{max u1 u2, max u1 u2} (forall (a : α), β a) (Set.{max u1 u2} (forall (a : α), β a)) (Set.hasMem.{max u1 u2} (forall (a : α), β a)) x s))))) f a))
 but is expected to have type
-  forall {α : Type.{u2}} {β : α -> Type.{u1}} [_inst_1 : forall (i : α), SupSet.{u1} (β i)] {s : Set.{max u2 u1} (forall (a : α), β a)} {a : α}, Eq.{succ u1} (β a) (SupSet.supₛ.{max u2 u1} (forall (a : α), β a) (Pi.supSet.{u2, u1} α (fun (a : α) => β a) (fun (i : α) => _inst_1 i)) s a) (supᵢ.{u1, max (succ u2) (succ u1)} (β a) (_inst_1 a) (Set.Elem.{max u2 u1} (forall (a : α), β a) s) (fun (f : Set.Elem.{max u2 u1} (forall (a : α), β a) s) => Subtype.val.{succ (max u2 u1)} (forall (a : α), β a) (fun (x : forall (a : α), β a) => Membership.mem.{max u2 u1, max u2 u1} (forall (a : α), β a) (Set.{max u2 u1} (forall (a : α), β a)) (Set.instMembershipSet.{max u2 u1} (forall (a : α), β a)) x s) f a))
-Case conversion may be inaccurate. Consider using '#align Sup_apply supₛ_applyₓ'. -/
-theorem supₛ_apply {α : Type _} {β : α → Type _} [∀ i, SupSet (β i)] {s : Set (∀ a, β a)} {a : α} :
-    (supₛ s) a = ⨆ f : s, (f : ∀ a, β a) a :=
+  forall {α : Type.{u2}} {β : α -> Type.{u1}} [_inst_1 : forall (i : α), SupSet.{u1} (β i)] {s : Set.{max u2 u1} (forall (a : α), β a)} {a : α}, Eq.{succ u1} (β a) (SupSet.sSup.{max u2 u1} (forall (a : α), β a) (Pi.supSet.{u2, u1} α (fun (a : α) => β a) (fun (i : α) => _inst_1 i)) s a) (iSup.{u1, max (succ u2) (succ u1)} (β a) (_inst_1 a) (Set.Elem.{max u2 u1} (forall (a : α), β a) s) (fun (f : Set.Elem.{max u2 u1} (forall (a : α), β a) s) => Subtype.val.{succ (max u2 u1)} (forall (a : α), β a) (fun (x : forall (a : α), β a) => Membership.mem.{max u2 u1, max u2 u1} (forall (a : α), β a) (Set.{max u2 u1} (forall (a : α), β a)) (Set.instMembershipSet.{max u2 u1} (forall (a : α), β a)) x s) f a))
+Case conversion may be inaccurate. Consider using '#align Sup_apply sSup_applyₓ'. -/
+theorem sSup_apply {α : Type _} {β : α → Type _} [∀ i, SupSet (β i)] {s : Set (∀ a, β a)} {a : α} :
+    (sSup s) a = ⨆ f : s, (f : ∀ a, β a) a :=
   rfl
-#align Sup_apply supₛ_apply
+#align Sup_apply sSup_apply
 
-/- warning: Inf_apply -> infₛ_apply is a dubious translation:
+/- warning: Inf_apply -> sInf_apply is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : α -> Type.{u2}} [_inst_1 : forall (i : α), InfSet.{u2} (β i)] {s : Set.{max u1 u2} (forall (a : α), β a)} {a : α}, Eq.{succ u2} (β a) (InfSet.infₛ.{max u1 u2} (forall (a : α), β a) (Pi.infSet.{u1, u2} α (fun (a : α) => β a) (fun (i : α) => _inst_1 i)) s a) (infᵢ.{u2, succ (max u1 u2)} (β a) (_inst_1 a) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (fun (f : coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) => (fun (a : Type.{max u1 u2}) (b : Sort.{max (succ u1) (succ u2)}) [self : HasLiftT.{succ (max u1 u2), max (succ u1) (succ u2)} a b] => self.0) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (forall (a : α), β a) (HasLiftT.mk.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (forall (a : α), β a) (CoeTCₓ.coe.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (forall (a : α), β a) (coeBase.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (forall (a : α), β a) (coeSubtype.{max (succ u1) (succ u2)} (forall (a : α), β a) (fun (x : forall (a : α), β a) => Membership.Mem.{max u1 u2, max u1 u2} (forall (a : α), β a) (Set.{max u1 u2} (forall (a : α), β a)) (Set.hasMem.{max u1 u2} (forall (a : α), β a)) x s))))) f a))
+  forall {α : Type.{u1}} {β : α -> Type.{u2}} [_inst_1 : forall (i : α), InfSet.{u2} (β i)] {s : Set.{max u1 u2} (forall (a : α), β a)} {a : α}, Eq.{succ u2} (β a) (InfSet.sInf.{max u1 u2} (forall (a : α), β a) (Pi.infSet.{u1, u2} α (fun (a : α) => β a) (fun (i : α) => _inst_1 i)) s a) (iInf.{u2, succ (max u1 u2)} (β a) (_inst_1 a) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (fun (f : coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) => (fun (a : Type.{max u1 u2}) (b : Sort.{max (succ u1) (succ u2)}) [self : HasLiftT.{succ (max u1 u2), max (succ u1) (succ u2)} a b] => self.0) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (forall (a : α), β a) (HasLiftT.mk.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (forall (a : α), β a) (CoeTCₓ.coe.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (forall (a : α), β a) (coeBase.{succ (max u1 u2), max (succ u1) (succ u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Set.{max u1 u2} (forall (a : α), β a)) Type.{max u1 u2} (Set.hasCoeToSort.{max u1 u2} (forall (a : α), β a)) s) (forall (a : α), β a) (coeSubtype.{max (succ u1) (succ u2)} (forall (a : α), β a) (fun (x : forall (a : α), β a) => Membership.Mem.{max u1 u2, max u1 u2} (forall (a : α), β a) (Set.{max u1 u2} (forall (a : α), β a)) (Set.hasMem.{max u1 u2} (forall (a : α), β a)) x s))))) f a))
 but is expected to have type
-  forall {α : Type.{u2}} {β : α -> Type.{u1}} [_inst_1 : forall (i : α), InfSet.{u1} (β i)] {s : Set.{max u2 u1} (forall (a : α), β a)} {a : α}, Eq.{succ u1} (β a) (InfSet.infₛ.{max u2 u1} (forall (a : α), β a) (Pi.infSet.{u2, u1} α (fun (a : α) => β a) (fun (i : α) => _inst_1 i)) s a) (infᵢ.{u1, max (succ u2) (succ u1)} (β a) (_inst_1 a) (Set.Elem.{max u2 u1} (forall (a : α), β a) s) (fun (f : Set.Elem.{max u2 u1} (forall (a : α), β a) s) => Subtype.val.{succ (max u2 u1)} (forall (a : α), β a) (fun (x : forall (a : α), β a) => Membership.mem.{max u2 u1, max u2 u1} (forall (a : α), β a) (Set.{max u2 u1} (forall (a : α), β a)) (Set.instMembershipSet.{max u2 u1} (forall (a : α), β a)) x s) f a))
-Case conversion may be inaccurate. Consider using '#align Inf_apply infₛ_applyₓ'. -/
-theorem infₛ_apply {α : Type _} {β : α → Type _} [∀ i, InfSet (β i)] {s : Set (∀ a, β a)} {a : α} :
-    infₛ s a = ⨅ f : s, (f : ∀ a, β a) a :=
+  forall {α : Type.{u2}} {β : α -> Type.{u1}} [_inst_1 : forall (i : α), InfSet.{u1} (β i)] {s : Set.{max u2 u1} (forall (a : α), β a)} {a : α}, Eq.{succ u1} (β a) (InfSet.sInf.{max u2 u1} (forall (a : α), β a) (Pi.infSet.{u2, u1} α (fun (a : α) => β a) (fun (i : α) => _inst_1 i)) s a) (iInf.{u1, max (succ u2) (succ u1)} (β a) (_inst_1 a) (Set.Elem.{max u2 u1} (forall (a : α), β a) s) (fun (f : Set.Elem.{max u2 u1} (forall (a : α), β a) s) => Subtype.val.{succ (max u2 u1)} (forall (a : α), β a) (fun (x : forall (a : α), β a) => Membership.mem.{max u2 u1, max u2 u1} (forall (a : α), β a) (Set.{max u2 u1} (forall (a : α), β a)) (Set.instMembershipSet.{max u2 u1} (forall (a : α), β a)) x s) f a))
+Case conversion may be inaccurate. Consider using '#align Inf_apply sInf_applyₓ'. -/
+theorem sInf_apply {α : Type _} {β : α → Type _} [∀ i, InfSet (β i)] {s : Set (∀ a, β a)} {a : α} :
+    sInf s a = ⨅ f : s, (f : ∀ a, β a) a :=
   rfl
-#align Inf_apply infₛ_apply
+#align Inf_apply sInf_apply
 
-/- warning: supr_apply -> supᵢ_apply is a dubious translation:
+/- warning: supr_apply -> iSup_apply is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : α -> Type.{u2}} {ι : Sort.{u3}} [_inst_1 : forall (i : α), SupSet.{u2} (β i)] {f : ι -> (forall (a : α), β a)} {a : α}, Eq.{succ u2} (β a) (supᵢ.{max u1 u2, u3} (forall (a : α), β a) (Pi.supSet.{u1, u2} α (fun (a : α) => β a) (fun (i : α) => _inst_1 i)) ι (fun (i : ι) => f i) a) (supᵢ.{u2, u3} (β a) (_inst_1 a) ι (fun (i : ι) => f i a))
+  forall {α : Type.{u1}} {β : α -> Type.{u2}} {ι : Sort.{u3}} [_inst_1 : forall (i : α), SupSet.{u2} (β i)] {f : ι -> (forall (a : α), β a)} {a : α}, Eq.{succ u2} (β a) (iSup.{max u1 u2, u3} (forall (a : α), β a) (Pi.supSet.{u1, u2} α (fun (a : α) => β a) (fun (i : α) => _inst_1 i)) ι (fun (i : ι) => f i) a) (iSup.{u2, u3} (β a) (_inst_1 a) ι (fun (i : ι) => f i a))
 but is expected to have type
-  forall {α : Type.{u3}} {β : α -> Type.{u2}} {ι : Sort.{u1}} [_inst_1 : forall (i : α), SupSet.{u2} (β i)] {f : ι -> (forall (a : α), β a)} {a : α}, Eq.{succ u2} (β a) (supᵢ.{max u3 u2, u1} (forall (a : α), β a) (Pi.supSet.{u3, u2} α (fun (a : α) => β a) (fun (i : α) => _inst_1 i)) ι (fun (i : ι) => f i) a) (supᵢ.{u2, u1} (β a) (_inst_1 a) ι (fun (i : ι) => f i a))
-Case conversion may be inaccurate. Consider using '#align supr_apply supᵢ_applyₓ'. -/
+  forall {α : Type.{u3}} {β : α -> Type.{u2}} {ι : Sort.{u1}} [_inst_1 : forall (i : α), SupSet.{u2} (β i)] {f : ι -> (forall (a : α), β a)} {a : α}, Eq.{succ u2} (β a) (iSup.{max u3 u2, u1} (forall (a : α), β a) (Pi.supSet.{u3, u2} α (fun (a : α) => β a) (fun (i : α) => _inst_1 i)) ι (fun (i : ι) => f i) a) (iSup.{u2, u1} (β a) (_inst_1 a) ι (fun (i : ι) => f i a))
+Case conversion may be inaccurate. Consider using '#align supr_apply iSup_applyₓ'. -/
 @[simp]
-theorem supᵢ_apply {α : Type _} {β : α → Type _} {ι : Sort _} [∀ i, SupSet (β i)] {f : ι → ∀ a, β a}
+theorem iSup_apply {α : Type _} {β : α → Type _} {ι : Sort _} [∀ i, SupSet (β i)] {f : ι → ∀ a, β a}
     {a : α} : (⨆ i, f i) a = ⨆ i, f i a := by
-  rw [supᵢ, supₛ_apply, supᵢ, supᵢ, ← image_eq_range (fun f : ∀ i, β i => f a) (range f), ←
+  rw [iSup, sSup_apply, iSup, iSup, ← image_eq_range (fun f : ∀ i, β i => f a) (range f), ←
     range_comp]
-#align supr_apply supᵢ_apply
+#align supr_apply iSup_apply
 
-/- warning: infi_apply -> infᵢ_apply is a dubious translation:
+/- warning: infi_apply -> iInf_apply is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : α -> Type.{u2}} {ι : Sort.{u3}} [_inst_1 : forall (i : α), InfSet.{u2} (β i)] {f : ι -> (forall (a : α), β a)} {a : α}, Eq.{succ u2} (β a) (infᵢ.{max u1 u2, u3} (forall (a : α), β a) (Pi.infSet.{u1, u2} α (fun (a : α) => β a) (fun (i : α) => _inst_1 i)) ι (fun (i : ι) => f i) a) (infᵢ.{u2, u3} (β a) (_inst_1 a) ι (fun (i : ι) => f i a))
+  forall {α : Type.{u1}} {β : α -> Type.{u2}} {ι : Sort.{u3}} [_inst_1 : forall (i : α), InfSet.{u2} (β i)] {f : ι -> (forall (a : α), β a)} {a : α}, Eq.{succ u2} (β a) (iInf.{max u1 u2, u3} (forall (a : α), β a) (Pi.infSet.{u1, u2} α (fun (a : α) => β a) (fun (i : α) => _inst_1 i)) ι (fun (i : ι) => f i) a) (iInf.{u2, u3} (β a) (_inst_1 a) ι (fun (i : ι) => f i a))
 but is expected to have type
-  forall {α : Type.{u3}} {β : α -> Type.{u2}} {ι : Sort.{u1}} [_inst_1 : forall (i : α), InfSet.{u2} (β i)] {f : ι -> (forall (a : α), β a)} {a : α}, Eq.{succ u2} (β a) (infᵢ.{max u3 u2, u1} (forall (a : α), β a) (Pi.infSet.{u3, u2} α (fun (a : α) => β a) (fun (i : α) => _inst_1 i)) ι (fun (i : ι) => f i) a) (infᵢ.{u2, u1} (β a) (_inst_1 a) ι (fun (i : ι) => f i a))
-Case conversion may be inaccurate. Consider using '#align infi_apply infᵢ_applyₓ'. -/
+  forall {α : Type.{u3}} {β : α -> Type.{u2}} {ι : Sort.{u1}} [_inst_1 : forall (i : α), InfSet.{u2} (β i)] {f : ι -> (forall (a : α), β a)} {a : α}, Eq.{succ u2} (β a) (iInf.{max u3 u2, u1} (forall (a : α), β a) (Pi.infSet.{u3, u2} α (fun (a : α) => β a) (fun (i : α) => _inst_1 i)) ι (fun (i : ι) => f i) a) (iInf.{u2, u1} (β a) (_inst_1 a) ι (fun (i : ι) => f i a))
+Case conversion may be inaccurate. Consider using '#align infi_apply iInf_applyₓ'. -/
 @[simp]
-theorem infᵢ_apply {α : Type _} {β : α → Type _} {ι : Sort _} [∀ i, InfSet (β i)] {f : ι → ∀ a, β a}
+theorem iInf_apply {α : Type _} {β : α → Type _} {ι : Sort _} [∀ i, InfSet (β i)] {f : ι → ∀ a, β a}
     {a : α} : (⨅ i, f i) a = ⨅ i, f i a :=
-  @supᵢ_apply α (fun i => (β i)ᵒᵈ) _ _ _ _
-#align infi_apply infᵢ_apply
+  @iSup_apply α (fun i => (β i)ᵒᵈ) _ _ _ _
+#align infi_apply iInf_apply
 
-/- warning: unary_relation_Sup_iff -> unary_relation_supₛ_iff is a dubious translation:
+/- warning: unary_relation_Sup_iff -> unary_relation_sSup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} (s : Set.{u1} (α -> Prop)) {a : α}, Iff (SupSet.supₛ.{u1} (α -> Prop) (Pi.supSet.{u1, 0} α (fun (ᾰ : α) => Prop) (fun (i : α) => CompleteSemilatticeSup.toHasSup.{0} Prop (CompleteLattice.toCompleteSemilatticeSup.{0} Prop Prop.completeLattice))) s a) (Exists.{succ u1} (α -> Prop) (fun (r : α -> Prop) => And (Membership.Mem.{u1, u1} (α -> Prop) (Set.{u1} (α -> Prop)) (Set.hasMem.{u1} (α -> Prop)) r s) (r a)))
+  forall {α : Type.{u1}} (s : Set.{u1} (α -> Prop)) {a : α}, Iff (SupSet.sSup.{u1} (α -> Prop) (Pi.supSet.{u1, 0} α (fun (ᾰ : α) => Prop) (fun (i : α) => CompleteSemilatticeSup.toHasSup.{0} Prop (CompleteLattice.toCompleteSemilatticeSup.{0} Prop Prop.completeLattice))) s a) (Exists.{succ u1} (α -> Prop) (fun (r : α -> Prop) => And (Membership.Mem.{u1, u1} (α -> Prop) (Set.{u1} (α -> Prop)) (Set.hasMem.{u1} (α -> Prop)) r s) (r a)))
 but is expected to have type
-  forall {α : Type.{u1}} (s : Set.{u1} (α -> Prop)) {a : α}, Iff (SupSet.supₛ.{u1} (α -> Prop) (Pi.supSet.{u1, 0} α (fun (ᾰ : α) => Prop) (fun (i : α) => CompleteLattice.toSupSet.{0} Prop Prop.completeLattice)) s a) (Exists.{succ u1} (α -> Prop) (fun (r : α -> Prop) => And (Membership.mem.{u1, u1} (α -> Prop) (Set.{u1} (α -> Prop)) (Set.instMembershipSet.{u1} (α -> Prop)) r s) (r a)))
-Case conversion may be inaccurate. Consider using '#align unary_relation_Sup_iff unary_relation_supₛ_iffₓ'. -/
-theorem unary_relation_supₛ_iff {α : Type _} (s : Set (α → Prop)) {a : α} :
-    supₛ s a ↔ ∃ r : α → Prop, r ∈ s ∧ r a :=
+  forall {α : Type.{u1}} (s : Set.{u1} (α -> Prop)) {a : α}, Iff (SupSet.sSup.{u1} (α -> Prop) (Pi.supSet.{u1, 0} α (fun (ᾰ : α) => Prop) (fun (i : α) => CompleteLattice.toSupSet.{0} Prop Prop.completeLattice)) s a) (Exists.{succ u1} (α -> Prop) (fun (r : α -> Prop) => And (Membership.mem.{u1, u1} (α -> Prop) (Set.{u1} (α -> Prop)) (Set.instMembershipSet.{u1} (α -> Prop)) r s) (r a)))
+Case conversion may be inaccurate. Consider using '#align unary_relation_Sup_iff unary_relation_sSup_iffₓ'. -/
+theorem unary_relation_sSup_iff {α : Type _} (s : Set (α → Prop)) {a : α} :
+    sSup s a ↔ ∃ r : α → Prop, r ∈ s ∧ r a :=
   by
   unfold Sup
   simp [← eq_iff_iff]
-#align unary_relation_Sup_iff unary_relation_supₛ_iff
+#align unary_relation_Sup_iff unary_relation_sSup_iff
 
-/- warning: unary_relation_Inf_iff -> unary_relation_infₛ_iff is a dubious translation:
+/- warning: unary_relation_Inf_iff -> unary_relation_sInf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} (s : Set.{u1} (α -> Prop)) {a : α}, Iff (InfSet.infₛ.{u1} (α -> Prop) (Pi.infSet.{u1, 0} α (fun (ᾰ : α) => Prop) (fun (i : α) => CompleteSemilatticeInf.toHasInf.{0} Prop (CompleteLattice.toCompleteSemilatticeInf.{0} Prop Prop.completeLattice))) s a) (forall (r : α -> Prop), (Membership.Mem.{u1, u1} (α -> Prop) (Set.{u1} (α -> Prop)) (Set.hasMem.{u1} (α -> Prop)) r s) -> (r a))
+  forall {α : Type.{u1}} (s : Set.{u1} (α -> Prop)) {a : α}, Iff (InfSet.sInf.{u1} (α -> Prop) (Pi.infSet.{u1, 0} α (fun (ᾰ : α) => Prop) (fun (i : α) => CompleteSemilatticeInf.toHasInf.{0} Prop (CompleteLattice.toCompleteSemilatticeInf.{0} Prop Prop.completeLattice))) s a) (forall (r : α -> Prop), (Membership.Mem.{u1, u1} (α -> Prop) (Set.{u1} (α -> Prop)) (Set.hasMem.{u1} (α -> Prop)) r s) -> (r a))
 but is expected to have type
-  forall {α : Type.{u1}} (s : Set.{u1} (α -> Prop)) {a : α}, Iff (InfSet.infₛ.{u1} (α -> Prop) (Pi.infSet.{u1, 0} α (fun (ᾰ : α) => Prop) (fun (i : α) => CompleteLattice.toInfSet.{0} Prop Prop.completeLattice)) s a) (forall (r : α -> Prop), (Membership.mem.{u1, u1} (α -> Prop) (Set.{u1} (α -> Prop)) (Set.instMembershipSet.{u1} (α -> Prop)) r s) -> (r a))
-Case conversion may be inaccurate. Consider using '#align unary_relation_Inf_iff unary_relation_infₛ_iffₓ'. -/
-theorem unary_relation_infₛ_iff {α : Type _} (s : Set (α → Prop)) {a : α} :
-    infₛ s a ↔ ∀ r : α → Prop, r ∈ s → r a :=
+  forall {α : Type.{u1}} (s : Set.{u1} (α -> Prop)) {a : α}, Iff (InfSet.sInf.{u1} (α -> Prop) (Pi.infSet.{u1, 0} α (fun (ᾰ : α) => Prop) (fun (i : α) => CompleteLattice.toInfSet.{0} Prop Prop.completeLattice)) s a) (forall (r : α -> Prop), (Membership.mem.{u1, u1} (α -> Prop) (Set.{u1} (α -> Prop)) (Set.instMembershipSet.{u1} (α -> Prop)) r s) -> (r a))
+Case conversion may be inaccurate. Consider using '#align unary_relation_Inf_iff unary_relation_sInf_iffₓ'. -/
+theorem unary_relation_sInf_iff {α : Type _} (s : Set (α → Prop)) {a : α} :
+    sInf s a ↔ ∀ r : α → Prop, r ∈ s → r a :=
   by
   unfold Inf
   simp [← eq_iff_iff]
-#align unary_relation_Inf_iff unary_relation_infₛ_iff
+#align unary_relation_Inf_iff unary_relation_sInf_iff
 
-/- warning: binary_relation_Sup_iff -> binary_relation_supₛ_iff is a dubious translation:
+/- warning: binary_relation_Sup_iff -> binary_relation_sSup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} (s : Set.{max u1 u2} (α -> β -> Prop)) {a : α} {b : β}, Iff (SupSet.supₛ.{max u1 u2} (α -> β -> Prop) (Pi.supSet.{u1, u2} α (fun (ᾰ : α) => β -> Prop) (fun (i : α) => Pi.supSet.{u2, 0} β (fun (ᾰ : β) => Prop) (fun (i : β) => CompleteSemilatticeSup.toHasSup.{0} Prop (CompleteLattice.toCompleteSemilatticeSup.{0} Prop Prop.completeLattice)))) s a b) (Exists.{max (succ u1) (succ u2)} (α -> β -> Prop) (fun (r : α -> β -> Prop) => And (Membership.Mem.{max u1 u2, max u1 u2} (α -> β -> Prop) (Set.{max u1 u2} (α -> β -> Prop)) (Set.hasMem.{max u1 u2} (α -> β -> Prop)) r s) (r a b)))
+  forall {α : Type.{u1}} {β : Type.{u2}} (s : Set.{max u1 u2} (α -> β -> Prop)) {a : α} {b : β}, Iff (SupSet.sSup.{max u1 u2} (α -> β -> Prop) (Pi.supSet.{u1, u2} α (fun (ᾰ : α) => β -> Prop) (fun (i : α) => Pi.supSet.{u2, 0} β (fun (ᾰ : β) => Prop) (fun (i : β) => CompleteSemilatticeSup.toHasSup.{0} Prop (CompleteLattice.toCompleteSemilatticeSup.{0} Prop Prop.completeLattice)))) s a b) (Exists.{max (succ u1) (succ u2)} (α -> β -> Prop) (fun (r : α -> β -> Prop) => And (Membership.Mem.{max u1 u2, max u1 u2} (α -> β -> Prop) (Set.{max u1 u2} (α -> β -> Prop)) (Set.hasMem.{max u1 u2} (α -> β -> Prop)) r s) (r a b)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (s : Set.{max u2 u1} (α -> β -> Prop)) {a : α} {b : β}, Iff (SupSet.supₛ.{max u2 u1} (α -> β -> Prop) (Pi.supSet.{u2, u1} α (fun (ᾰ : α) => β -> Prop) (fun (i : α) => Pi.supSet.{u1, 0} β (fun (ᾰ : β) => Prop) (fun (i : β) => CompleteLattice.toSupSet.{0} Prop Prop.completeLattice))) s a b) (Exists.{max (succ u2) (succ u1)} (α -> β -> Prop) (fun (r : α -> β -> Prop) => And (Membership.mem.{max u2 u1, max u2 u1} (α -> β -> Prop) (Set.{max u2 u1} (α -> β -> Prop)) (Set.instMembershipSet.{max u2 u1} (α -> β -> Prop)) r s) (r a b)))
-Case conversion may be inaccurate. Consider using '#align binary_relation_Sup_iff binary_relation_supₛ_iffₓ'. -/
-theorem binary_relation_supₛ_iff {α β : Type _} (s : Set (α → β → Prop)) {a : α} {b : β} :
-    supₛ s a b ↔ ∃ r : α → β → Prop, r ∈ s ∧ r a b :=
+  forall {α : Type.{u2}} {β : Type.{u1}} (s : Set.{max u2 u1} (α -> β -> Prop)) {a : α} {b : β}, Iff (SupSet.sSup.{max u2 u1} (α -> β -> Prop) (Pi.supSet.{u2, u1} α (fun (ᾰ : α) => β -> Prop) (fun (i : α) => Pi.supSet.{u1, 0} β (fun (ᾰ : β) => Prop) (fun (i : β) => CompleteLattice.toSupSet.{0} Prop Prop.completeLattice))) s a b) (Exists.{max (succ u2) (succ u1)} (α -> β -> Prop) (fun (r : α -> β -> Prop) => And (Membership.mem.{max u2 u1, max u2 u1} (α -> β -> Prop) (Set.{max u2 u1} (α -> β -> Prop)) (Set.instMembershipSet.{max u2 u1} (α -> β -> Prop)) r s) (r a b)))
+Case conversion may be inaccurate. Consider using '#align binary_relation_Sup_iff binary_relation_sSup_iffₓ'. -/
+theorem binary_relation_sSup_iff {α β : Type _} (s : Set (α → β → Prop)) {a : α} {b : β} :
+    sSup s a b ↔ ∃ r : α → β → Prop, r ∈ s ∧ r a b :=
   by
   unfold Sup
   simp [← eq_iff_iff]
-#align binary_relation_Sup_iff binary_relation_supₛ_iff
+#align binary_relation_Sup_iff binary_relation_sSup_iff
 
-/- warning: binary_relation_Inf_iff -> binary_relation_infₛ_iff is a dubious translation:
+/- warning: binary_relation_Inf_iff -> binary_relation_sInf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} (s : Set.{max u1 u2} (α -> β -> Prop)) {a : α} {b : β}, Iff (InfSet.infₛ.{max u1 u2} (α -> β -> Prop) (Pi.infSet.{u1, u2} α (fun (ᾰ : α) => β -> Prop) (fun (i : α) => Pi.infSet.{u2, 0} β (fun (ᾰ : β) => Prop) (fun (i : β) => CompleteSemilatticeInf.toHasInf.{0} Prop (CompleteLattice.toCompleteSemilatticeInf.{0} Prop Prop.completeLattice)))) s a b) (forall (r : α -> β -> Prop), (Membership.Mem.{max u1 u2, max u1 u2} (α -> β -> Prop) (Set.{max u1 u2} (α -> β -> Prop)) (Set.hasMem.{max u1 u2} (α -> β -> Prop)) r s) -> (r a b))
+  forall {α : Type.{u1}} {β : Type.{u2}} (s : Set.{max u1 u2} (α -> β -> Prop)) {a : α} {b : β}, Iff (InfSet.sInf.{max u1 u2} (α -> β -> Prop) (Pi.infSet.{u1, u2} α (fun (ᾰ : α) => β -> Prop) (fun (i : α) => Pi.infSet.{u2, 0} β (fun (ᾰ : β) => Prop) (fun (i : β) => CompleteSemilatticeInf.toHasInf.{0} Prop (CompleteLattice.toCompleteSemilatticeInf.{0} Prop Prop.completeLattice)))) s a b) (forall (r : α -> β -> Prop), (Membership.Mem.{max u1 u2, max u1 u2} (α -> β -> Prop) (Set.{max u1 u2} (α -> β -> Prop)) (Set.hasMem.{max u1 u2} (α -> β -> Prop)) r s) -> (r a b))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (s : Set.{max u2 u1} (α -> β -> Prop)) {a : α} {b : β}, Iff (InfSet.infₛ.{max u2 u1} (α -> β -> Prop) (Pi.infSet.{u2, u1} α (fun (ᾰ : α) => β -> Prop) (fun (i : α) => Pi.infSet.{u1, 0} β (fun (ᾰ : β) => Prop) (fun (i : β) => CompleteLattice.toInfSet.{0} Prop Prop.completeLattice))) s a b) (forall (r : α -> β -> Prop), (Membership.mem.{max u2 u1, max u2 u1} (α -> β -> Prop) (Set.{max u2 u1} (α -> β -> Prop)) (Set.instMembershipSet.{max u2 u1} (α -> β -> Prop)) r s) -> (r a b))
-Case conversion may be inaccurate. Consider using '#align binary_relation_Inf_iff binary_relation_infₛ_iffₓ'. -/
-theorem binary_relation_infₛ_iff {α β : Type _} (s : Set (α → β → Prop)) {a : α} {b : β} :
-    infₛ s a b ↔ ∀ r : α → β → Prop, r ∈ s → r a b :=
+  forall {α : Type.{u2}} {β : Type.{u1}} (s : Set.{max u2 u1} (α -> β -> Prop)) {a : α} {b : β}, Iff (InfSet.sInf.{max u2 u1} (α -> β -> Prop) (Pi.infSet.{u2, u1} α (fun (ᾰ : α) => β -> Prop) (fun (i : α) => Pi.infSet.{u1, 0} β (fun (ᾰ : β) => Prop) (fun (i : β) => CompleteLattice.toInfSet.{0} Prop Prop.completeLattice))) s a b) (forall (r : α -> β -> Prop), (Membership.mem.{max u2 u1, max u2 u1} (α -> β -> Prop) (Set.{max u2 u1} (α -> β -> Prop)) (Set.instMembershipSet.{max u2 u1} (α -> β -> Prop)) r s) -> (r a b))
+Case conversion may be inaccurate. Consider using '#align binary_relation_Inf_iff binary_relation_sInf_iffₓ'. -/
+theorem binary_relation_sInf_iff {α β : Type _} (s : Set (α → β → Prop)) {a : α} {b : β} :
+    sInf s a b ↔ ∀ r : α → β → Prop, r ∈ s → r a b :=
   by
   unfold Inf
   simp [← eq_iff_iff]
-#align binary_relation_Inf_iff binary_relation_infₛ_iff
+#align binary_relation_Inf_iff binary_relation_sInf_iff
 
 section CompleteLattice
 
 variable [Preorder α] [CompleteLattice β]
 
-/- warning: monotone_Sup_of_monotone -> monotone_supₛ_of_monotone is a dubious translation:
+/- warning: monotone_Sup_of_monotone -> monotone_sSup_of_monotone is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{max u1 u2} (α -> β)}, (forall (f : α -> β), (Membership.Mem.{max u1 u2, max u1 u2} (α -> β) (Set.{max u1 u2} (α -> β)) (Set.hasMem.{max u1 u2} (α -> β)) f s) -> (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f)) -> (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) (SupSet.supₛ.{max u1 u2} (α -> β) (Pi.supSet.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2))) s))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{max u1 u2} (α -> β)}, (forall (f : α -> β), (Membership.Mem.{max u1 u2, max u1 u2} (α -> β) (Set.{max u1 u2} (α -> β)) (Set.hasMem.{max u1 u2} (α -> β)) f s) -> (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f)) -> (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) (SupSet.sSup.{max u1 u2} (α -> β) (Pi.supSet.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2))) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : CompleteLattice.{u1} β] {s : Set.{max u2 u1} (α -> β)}, (forall (f : α -> β), (Membership.mem.{max u2 u1, max u2 u1} (α -> β) (Set.{max u2 u1} (α -> β)) (Set.instMembershipSet.{max u2 u1} (α -> β)) f s) -> (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (CompleteSemilatticeInf.toPartialOrder.{u1} β (CompleteLattice.toCompleteSemilatticeInf.{u1} β _inst_2))) f)) -> (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (CompleteSemilatticeInf.toPartialOrder.{u1} β (CompleteLattice.toCompleteSemilatticeInf.{u1} β _inst_2))) (SupSet.supₛ.{max u1 u2} (α -> β) (Pi.supSet.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => CompleteLattice.toSupSet.{u1} β _inst_2)) s))
-Case conversion may be inaccurate. Consider using '#align monotone_Sup_of_monotone monotone_supₛ_of_monotoneₓ'. -/
-theorem monotone_supₛ_of_monotone {s : Set (α → β)} (m_s : ∀ f ∈ s, Monotone f) :
-    Monotone (supₛ s) := fun x y h => supᵢ_mono fun f => m_s f f.2 h
-#align monotone_Sup_of_monotone monotone_supₛ_of_monotone
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : CompleteLattice.{u1} β] {s : Set.{max u2 u1} (α -> β)}, (forall (f : α -> β), (Membership.mem.{max u2 u1, max u2 u1} (α -> β) (Set.{max u2 u1} (α -> β)) (Set.instMembershipSet.{max u2 u1} (α -> β)) f s) -> (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (CompleteSemilatticeInf.toPartialOrder.{u1} β (CompleteLattice.toCompleteSemilatticeInf.{u1} β _inst_2))) f)) -> (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (CompleteSemilatticeInf.toPartialOrder.{u1} β (CompleteLattice.toCompleteSemilatticeInf.{u1} β _inst_2))) (SupSet.sSup.{max u1 u2} (α -> β) (Pi.supSet.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => CompleteLattice.toSupSet.{u1} β _inst_2)) s))
+Case conversion may be inaccurate. Consider using '#align monotone_Sup_of_monotone monotone_sSup_of_monotoneₓ'. -/
+theorem monotone_sSup_of_monotone {s : Set (α → β)} (m_s : ∀ f ∈ s, Monotone f) :
+    Monotone (sSup s) := fun x y h => iSup_mono fun f => m_s f f.2 h
+#align monotone_Sup_of_monotone monotone_sSup_of_monotone
 
-/- warning: monotone_Inf_of_monotone -> monotone_infₛ_of_monotone is a dubious translation:
+/- warning: monotone_Inf_of_monotone -> monotone_sInf_of_monotone is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{max u1 u2} (α -> β)}, (forall (f : α -> β), (Membership.Mem.{max u1 u2, max u1 u2} (α -> β) (Set.{max u1 u2} (α -> β)) (Set.hasMem.{max u1 u2} (α -> β)) f s) -> (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f)) -> (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) (InfSet.infₛ.{max u1 u2} (α -> β) (Pi.infSet.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) s))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {s : Set.{max u1 u2} (α -> β)}, (forall (f : α -> β), (Membership.Mem.{max u1 u2, max u1 u2} (α -> β) (Set.{max u1 u2} (α -> β)) (Set.hasMem.{max u1 u2} (α -> β)) f s) -> (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) f)) -> (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) (InfSet.sInf.{max u1 u2} (α -> β) (Pi.infSet.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : CompleteLattice.{u1} β] {s : Set.{max u2 u1} (α -> β)}, (forall (f : α -> β), (Membership.mem.{max u2 u1, max u2 u1} (α -> β) (Set.{max u2 u1} (α -> β)) (Set.instMembershipSet.{max u2 u1} (α -> β)) f s) -> (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (CompleteSemilatticeInf.toPartialOrder.{u1} β (CompleteLattice.toCompleteSemilatticeInf.{u1} β _inst_2))) f)) -> (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (CompleteSemilatticeInf.toPartialOrder.{u1} β (CompleteLattice.toCompleteSemilatticeInf.{u1} β _inst_2))) (InfSet.infₛ.{max u1 u2} (α -> β) (Pi.infSet.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => CompleteLattice.toInfSet.{u1} β _inst_2)) s))
-Case conversion may be inaccurate. Consider using '#align monotone_Inf_of_monotone monotone_infₛ_of_monotoneₓ'. -/
-theorem monotone_infₛ_of_monotone {s : Set (α → β)} (m_s : ∀ f ∈ s, Monotone f) :
-    Monotone (infₛ s) := fun x y h => infᵢ_mono fun f => m_s f f.2 h
-#align monotone_Inf_of_monotone monotone_infₛ_of_monotone
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : CompleteLattice.{u1} β] {s : Set.{max u2 u1} (α -> β)}, (forall (f : α -> β), (Membership.mem.{max u2 u1, max u2 u1} (α -> β) (Set.{max u2 u1} (α -> β)) (Set.instMembershipSet.{max u2 u1} (α -> β)) f s) -> (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (CompleteSemilatticeInf.toPartialOrder.{u1} β (CompleteLattice.toCompleteSemilatticeInf.{u1} β _inst_2))) f)) -> (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (CompleteSemilatticeInf.toPartialOrder.{u1} β (CompleteLattice.toCompleteSemilatticeInf.{u1} β _inst_2))) (InfSet.sInf.{max u1 u2} (α -> β) (Pi.infSet.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => CompleteLattice.toInfSet.{u1} β _inst_2)) s))
+Case conversion may be inaccurate. Consider using '#align monotone_Inf_of_monotone monotone_sInf_of_monotoneₓ'. -/
+theorem monotone_sInf_of_monotone {s : Set (α → β)} (m_s : ∀ f ∈ s, Monotone f) :
+    Monotone (sInf s) := fun x y h => iInf_mono fun f => m_s f f.2 h
+#align monotone_Inf_of_monotone monotone_sInf_of_monotone
 
 end CompleteLattice
 
@@ -3529,156 +3529,156 @@ namespace Prod
 variable (α β)
 
 instance [SupSet α] [SupSet β] : SupSet (α × β) :=
-  ⟨fun s => (supₛ (Prod.fst '' s), supₛ (Prod.snd '' s))⟩
+  ⟨fun s => (sSup (Prod.fst '' s), sSup (Prod.snd '' s))⟩
 
 instance [InfSet α] [InfSet β] : InfSet (α × β) :=
-  ⟨fun s => (infₛ (Prod.fst '' s), infₛ (Prod.snd '' s))⟩
+  ⟨fun s => (sInf (Prod.fst '' s), sInf (Prod.snd '' s))⟩
 
 variable {α β}
 
-/- warning: prod.fst_Inf -> Prod.fst_infₛ is a dubious translation:
+/- warning: prod.fst_Inf -> Prod.fst_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : InfSet.{u1} α] [_inst_2 : InfSet.{u2} β] (s : Set.{max u1 u2} (Prod.{u1, u2} α β)), Eq.{succ u1} α (Prod.fst.{u1, u2} α β (InfSet.infₛ.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasInf.{u1, u2} α β _inst_1 _inst_2) s)) (InfSet.infₛ.{u1} α _inst_1 (Set.image.{max u1 u2, u1} (Prod.{u1, u2} α β) α (Prod.fst.{u1, u2} α β) s))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : InfSet.{u1} α] [_inst_2 : InfSet.{u2} β] (s : Set.{max u1 u2} (Prod.{u1, u2} α β)), Eq.{succ u1} α (Prod.fst.{u1, u2} α β (InfSet.sInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasInf.{u1, u2} α β _inst_1 _inst_2) s)) (InfSet.sInf.{u1} α _inst_1 (Set.image.{max u1 u2, u1} (Prod.{u1, u2} α β) α (Prod.fst.{u1, u2} α β) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : InfSet.{u2} α] [_inst_2 : InfSet.{u1} β] (s : Set.{max u1 u2} (Prod.{u2, u1} α β)), Eq.{succ u2} α (Prod.fst.{u2, u1} α β (InfSet.infₛ.{max u2 u1} (Prod.{u2, u1} α β) (Prod.infSet.{u2, u1} α β _inst_1 _inst_2) s)) (InfSet.infₛ.{u2} α _inst_1 (Set.image.{max u1 u2, u2} (Prod.{u2, u1} α β) α (Prod.fst.{u2, u1} α β) s))
-Case conversion may be inaccurate. Consider using '#align prod.fst_Inf Prod.fst_infₛₓ'. -/
-theorem fst_infₛ [InfSet α] [InfSet β] (s : Set (α × β)) : (infₛ s).fst = infₛ (Prod.fst '' s) :=
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : InfSet.{u2} α] [_inst_2 : InfSet.{u1} β] (s : Set.{max u1 u2} (Prod.{u2, u1} α β)), Eq.{succ u2} α (Prod.fst.{u2, u1} α β (InfSet.sInf.{max u2 u1} (Prod.{u2, u1} α β) (Prod.infSet.{u2, u1} α β _inst_1 _inst_2) s)) (InfSet.sInf.{u2} α _inst_1 (Set.image.{max u1 u2, u2} (Prod.{u2, u1} α β) α (Prod.fst.{u2, u1} α β) s))
+Case conversion may be inaccurate. Consider using '#align prod.fst_Inf Prod.fst_sInfₓ'. -/
+theorem fst_sInf [InfSet α] [InfSet β] (s : Set (α × β)) : (sInf s).fst = sInf (Prod.fst '' s) :=
   rfl
-#align prod.fst_Inf Prod.fst_infₛ
+#align prod.fst_Inf Prod.fst_sInf
 
-/- warning: prod.snd_Inf -> Prod.snd_infₛ is a dubious translation:
+/- warning: prod.snd_Inf -> Prod.snd_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : InfSet.{u1} α] [_inst_2 : InfSet.{u2} β] (s : Set.{max u1 u2} (Prod.{u1, u2} α β)), Eq.{succ u2} β (Prod.snd.{u1, u2} α β (InfSet.infₛ.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasInf.{u1, u2} α β _inst_1 _inst_2) s)) (InfSet.infₛ.{u2} β _inst_2 (Set.image.{max u1 u2, u2} (Prod.{u1, u2} α β) β (Prod.snd.{u1, u2} α β) s))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : InfSet.{u1} α] [_inst_2 : InfSet.{u2} β] (s : Set.{max u1 u2} (Prod.{u1, u2} α β)), Eq.{succ u2} β (Prod.snd.{u1, u2} α β (InfSet.sInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasInf.{u1, u2} α β _inst_1 _inst_2) s)) (InfSet.sInf.{u2} β _inst_2 (Set.image.{max u1 u2, u2} (Prod.{u1, u2} α β) β (Prod.snd.{u1, u2} α β) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : InfSet.{u2} α] [_inst_2 : InfSet.{u1} β] (s : Set.{max u1 u2} (Prod.{u2, u1} α β)), Eq.{succ u1} β (Prod.snd.{u2, u1} α β (InfSet.infₛ.{max u2 u1} (Prod.{u2, u1} α β) (Prod.infSet.{u2, u1} α β _inst_1 _inst_2) s)) (InfSet.infₛ.{u1} β _inst_2 (Set.image.{max u1 u2, u1} (Prod.{u2, u1} α β) β (Prod.snd.{u2, u1} α β) s))
-Case conversion may be inaccurate. Consider using '#align prod.snd_Inf Prod.snd_infₛₓ'. -/
-theorem snd_infₛ [InfSet α] [InfSet β] (s : Set (α × β)) : (infₛ s).snd = infₛ (Prod.snd '' s) :=
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : InfSet.{u2} α] [_inst_2 : InfSet.{u1} β] (s : Set.{max u1 u2} (Prod.{u2, u1} α β)), Eq.{succ u1} β (Prod.snd.{u2, u1} α β (InfSet.sInf.{max u2 u1} (Prod.{u2, u1} α β) (Prod.infSet.{u2, u1} α β _inst_1 _inst_2) s)) (InfSet.sInf.{u1} β _inst_2 (Set.image.{max u1 u2, u1} (Prod.{u2, u1} α β) β (Prod.snd.{u2, u1} α β) s))
+Case conversion may be inaccurate. Consider using '#align prod.snd_Inf Prod.snd_sInfₓ'. -/
+theorem snd_sInf [InfSet α] [InfSet β] (s : Set (α × β)) : (sInf s).snd = sInf (Prod.snd '' s) :=
   rfl
-#align prod.snd_Inf Prod.snd_infₛ
+#align prod.snd_Inf Prod.snd_sInf
 
-/- warning: prod.swap_Inf -> Prod.swap_infₛ is a dubious translation:
+/- warning: prod.swap_Inf -> Prod.swap_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : InfSet.{u1} α] [_inst_2 : InfSet.{u2} β] (s : Set.{max u1 u2} (Prod.{u1, u2} α β)), Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} β α) (Prod.swap.{u1, u2} α β (InfSet.infₛ.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasInf.{u1, u2} α β _inst_1 _inst_2) s)) (InfSet.infₛ.{max u2 u1} (Prod.{u2, u1} β α) (Prod.hasInf.{u2, u1} β α _inst_2 _inst_1) (Set.image.{max u1 u2, max u2 u1} (Prod.{u1, u2} α β) (Prod.{u2, u1} β α) (Prod.swap.{u1, u2} α β) s))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : InfSet.{u1} α] [_inst_2 : InfSet.{u2} β] (s : Set.{max u1 u2} (Prod.{u1, u2} α β)), Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} β α) (Prod.swap.{u1, u2} α β (InfSet.sInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasInf.{u1, u2} α β _inst_1 _inst_2) s)) (InfSet.sInf.{max u2 u1} (Prod.{u2, u1} β α) (Prod.hasInf.{u2, u1} β α _inst_2 _inst_1) (Set.image.{max u1 u2, max u2 u1} (Prod.{u1, u2} α β) (Prod.{u2, u1} β α) (Prod.swap.{u1, u2} α β) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : InfSet.{u2} α] [_inst_2 : InfSet.{u1} β] (s : Set.{max u1 u2} (Prod.{u2, u1} α β)), Eq.{max (succ u2) (succ u1)} (Prod.{u1, u2} β α) (Prod.swap.{u2, u1} α β (InfSet.infₛ.{max u2 u1} (Prod.{u2, u1} α β) (Prod.infSet.{u2, u1} α β _inst_1 _inst_2) s)) (InfSet.infₛ.{max u1 u2} (Prod.{u1, u2} β α) (Prod.infSet.{u1, u2} β α _inst_2 _inst_1) (Set.image.{max u1 u2, max u1 u2} (Prod.{u2, u1} α β) (Prod.{u1, u2} β α) (Prod.swap.{u2, u1} α β) s))
-Case conversion may be inaccurate. Consider using '#align prod.swap_Inf Prod.swap_infₛₓ'. -/
-theorem swap_infₛ [InfSet α] [InfSet β] (s : Set (α × β)) : (infₛ s).symm = infₛ (Prod.swap '' s) :=
-  ext (congr_arg infₛ <| image_comp Prod.fst swap s : _)
-    (congr_arg infₛ <| image_comp Prod.snd swap s : _)
-#align prod.swap_Inf Prod.swap_infₛ
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : InfSet.{u2} α] [_inst_2 : InfSet.{u1} β] (s : Set.{max u1 u2} (Prod.{u2, u1} α β)), Eq.{max (succ u2) (succ u1)} (Prod.{u1, u2} β α) (Prod.swap.{u2, u1} α β (InfSet.sInf.{max u2 u1} (Prod.{u2, u1} α β) (Prod.infSet.{u2, u1} α β _inst_1 _inst_2) s)) (InfSet.sInf.{max u1 u2} (Prod.{u1, u2} β α) (Prod.infSet.{u1, u2} β α _inst_2 _inst_1) (Set.image.{max u1 u2, max u1 u2} (Prod.{u2, u1} α β) (Prod.{u1, u2} β α) (Prod.swap.{u2, u1} α β) s))
+Case conversion may be inaccurate. Consider using '#align prod.swap_Inf Prod.swap_sInfₓ'. -/
+theorem swap_sInf [InfSet α] [InfSet β] (s : Set (α × β)) : (sInf s).symm = sInf (Prod.swap '' s) :=
+  ext (congr_arg sInf <| image_comp Prod.fst swap s : _)
+    (congr_arg sInf <| image_comp Prod.snd swap s : _)
+#align prod.swap_Inf Prod.swap_sInf
 
-/- warning: prod.fst_Sup -> Prod.fst_supₛ is a dubious translation:
+/- warning: prod.fst_Sup -> Prod.fst_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SupSet.{u1} α] [_inst_2 : SupSet.{u2} β] (s : Set.{max u1 u2} (Prod.{u1, u2} α β)), Eq.{succ u1} α (Prod.fst.{u1, u2} α β (SupSet.supₛ.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasSup.{u1, u2} α β _inst_1 _inst_2) s)) (SupSet.supₛ.{u1} α _inst_1 (Set.image.{max u1 u2, u1} (Prod.{u1, u2} α β) α (Prod.fst.{u1, u2} α β) s))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SupSet.{u1} α] [_inst_2 : SupSet.{u2} β] (s : Set.{max u1 u2} (Prod.{u1, u2} α β)), Eq.{succ u1} α (Prod.fst.{u1, u2} α β (SupSet.sSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasSup.{u1, u2} α β _inst_1 _inst_2) s)) (SupSet.sSup.{u1} α _inst_1 (Set.image.{max u1 u2, u1} (Prod.{u1, u2} α β) α (Prod.fst.{u1, u2} α β) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SupSet.{u2} α] [_inst_2 : SupSet.{u1} β] (s : Set.{max u1 u2} (Prod.{u2, u1} α β)), Eq.{succ u2} α (Prod.fst.{u2, u1} α β (SupSet.supₛ.{max u2 u1} (Prod.{u2, u1} α β) (Prod.supSet.{u2, u1} α β _inst_1 _inst_2) s)) (SupSet.supₛ.{u2} α _inst_1 (Set.image.{max u1 u2, u2} (Prod.{u2, u1} α β) α (Prod.fst.{u2, u1} α β) s))
-Case conversion may be inaccurate. Consider using '#align prod.fst_Sup Prod.fst_supₛₓ'. -/
-theorem fst_supₛ [SupSet α] [SupSet β] (s : Set (α × β)) : (supₛ s).fst = supₛ (Prod.fst '' s) :=
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SupSet.{u2} α] [_inst_2 : SupSet.{u1} β] (s : Set.{max u1 u2} (Prod.{u2, u1} α β)), Eq.{succ u2} α (Prod.fst.{u2, u1} α β (SupSet.sSup.{max u2 u1} (Prod.{u2, u1} α β) (Prod.supSet.{u2, u1} α β _inst_1 _inst_2) s)) (SupSet.sSup.{u2} α _inst_1 (Set.image.{max u1 u2, u2} (Prod.{u2, u1} α β) α (Prod.fst.{u2, u1} α β) s))
+Case conversion may be inaccurate. Consider using '#align prod.fst_Sup Prod.fst_sSupₓ'. -/
+theorem fst_sSup [SupSet α] [SupSet β] (s : Set (α × β)) : (sSup s).fst = sSup (Prod.fst '' s) :=
   rfl
-#align prod.fst_Sup Prod.fst_supₛ
+#align prod.fst_Sup Prod.fst_sSup
 
-/- warning: prod.snd_Sup -> Prod.snd_supₛ is a dubious translation:
+/- warning: prod.snd_Sup -> Prod.snd_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SupSet.{u1} α] [_inst_2 : SupSet.{u2} β] (s : Set.{max u1 u2} (Prod.{u1, u2} α β)), Eq.{succ u2} β (Prod.snd.{u1, u2} α β (SupSet.supₛ.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasSup.{u1, u2} α β _inst_1 _inst_2) s)) (SupSet.supₛ.{u2} β _inst_2 (Set.image.{max u1 u2, u2} (Prod.{u1, u2} α β) β (Prod.snd.{u1, u2} α β) s))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SupSet.{u1} α] [_inst_2 : SupSet.{u2} β] (s : Set.{max u1 u2} (Prod.{u1, u2} α β)), Eq.{succ u2} β (Prod.snd.{u1, u2} α β (SupSet.sSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasSup.{u1, u2} α β _inst_1 _inst_2) s)) (SupSet.sSup.{u2} β _inst_2 (Set.image.{max u1 u2, u2} (Prod.{u1, u2} α β) β (Prod.snd.{u1, u2} α β) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SupSet.{u2} α] [_inst_2 : SupSet.{u1} β] (s : Set.{max u1 u2} (Prod.{u2, u1} α β)), Eq.{succ u1} β (Prod.snd.{u2, u1} α β (SupSet.supₛ.{max u2 u1} (Prod.{u2, u1} α β) (Prod.supSet.{u2, u1} α β _inst_1 _inst_2) s)) (SupSet.supₛ.{u1} β _inst_2 (Set.image.{max u1 u2, u1} (Prod.{u2, u1} α β) β (Prod.snd.{u2, u1} α β) s))
-Case conversion may be inaccurate. Consider using '#align prod.snd_Sup Prod.snd_supₛₓ'. -/
-theorem snd_supₛ [SupSet α] [SupSet β] (s : Set (α × β)) : (supₛ s).snd = supₛ (Prod.snd '' s) :=
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SupSet.{u2} α] [_inst_2 : SupSet.{u1} β] (s : Set.{max u1 u2} (Prod.{u2, u1} α β)), Eq.{succ u1} β (Prod.snd.{u2, u1} α β (SupSet.sSup.{max u2 u1} (Prod.{u2, u1} α β) (Prod.supSet.{u2, u1} α β _inst_1 _inst_2) s)) (SupSet.sSup.{u1} β _inst_2 (Set.image.{max u1 u2, u1} (Prod.{u2, u1} α β) β (Prod.snd.{u2, u1} α β) s))
+Case conversion may be inaccurate. Consider using '#align prod.snd_Sup Prod.snd_sSupₓ'. -/
+theorem snd_sSup [SupSet α] [SupSet β] (s : Set (α × β)) : (sSup s).snd = sSup (Prod.snd '' s) :=
   rfl
-#align prod.snd_Sup Prod.snd_supₛ
+#align prod.snd_Sup Prod.snd_sSup
 
-/- warning: prod.swap_Sup -> Prod.swap_supₛ is a dubious translation:
+/- warning: prod.swap_Sup -> Prod.swap_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SupSet.{u1} α] [_inst_2 : SupSet.{u2} β] (s : Set.{max u1 u2} (Prod.{u1, u2} α β)), Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} β α) (Prod.swap.{u1, u2} α β (SupSet.supₛ.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasSup.{u1, u2} α β _inst_1 _inst_2) s)) (SupSet.supₛ.{max u2 u1} (Prod.{u2, u1} β α) (Prod.hasSup.{u2, u1} β α _inst_2 _inst_1) (Set.image.{max u1 u2, max u2 u1} (Prod.{u1, u2} α β) (Prod.{u2, u1} β α) (Prod.swap.{u1, u2} α β) s))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SupSet.{u1} α] [_inst_2 : SupSet.{u2} β] (s : Set.{max u1 u2} (Prod.{u1, u2} α β)), Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} β α) (Prod.swap.{u1, u2} α β (SupSet.sSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasSup.{u1, u2} α β _inst_1 _inst_2) s)) (SupSet.sSup.{max u2 u1} (Prod.{u2, u1} β α) (Prod.hasSup.{u2, u1} β α _inst_2 _inst_1) (Set.image.{max u1 u2, max u2 u1} (Prod.{u1, u2} α β) (Prod.{u2, u1} β α) (Prod.swap.{u1, u2} α β) s))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SupSet.{u2} α] [_inst_2 : SupSet.{u1} β] (s : Set.{max u1 u2} (Prod.{u2, u1} α β)), Eq.{max (succ u2) (succ u1)} (Prod.{u1, u2} β α) (Prod.swap.{u2, u1} α β (SupSet.supₛ.{max u2 u1} (Prod.{u2, u1} α β) (Prod.supSet.{u2, u1} α β _inst_1 _inst_2) s)) (SupSet.supₛ.{max u1 u2} (Prod.{u1, u2} β α) (Prod.supSet.{u1, u2} β α _inst_2 _inst_1) (Set.image.{max u1 u2, max u1 u2} (Prod.{u2, u1} α β) (Prod.{u1, u2} β α) (Prod.swap.{u2, u1} α β) s))
-Case conversion may be inaccurate. Consider using '#align prod.swap_Sup Prod.swap_supₛₓ'. -/
-theorem swap_supₛ [SupSet α] [SupSet β] (s : Set (α × β)) : (supₛ s).symm = supₛ (Prod.swap '' s) :=
-  ext (congr_arg supₛ <| image_comp Prod.fst swap s : _)
-    (congr_arg supₛ <| image_comp Prod.snd swap s : _)
-#align prod.swap_Sup Prod.swap_supₛ
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SupSet.{u2} α] [_inst_2 : SupSet.{u1} β] (s : Set.{max u1 u2} (Prod.{u2, u1} α β)), Eq.{max (succ u2) (succ u1)} (Prod.{u1, u2} β α) (Prod.swap.{u2, u1} α β (SupSet.sSup.{max u2 u1} (Prod.{u2, u1} α β) (Prod.supSet.{u2, u1} α β _inst_1 _inst_2) s)) (SupSet.sSup.{max u1 u2} (Prod.{u1, u2} β α) (Prod.supSet.{u1, u2} β α _inst_2 _inst_1) (Set.image.{max u1 u2, max u1 u2} (Prod.{u2, u1} α β) (Prod.{u1, u2} β α) (Prod.swap.{u2, u1} α β) s))
+Case conversion may be inaccurate. Consider using '#align prod.swap_Sup Prod.swap_sSupₓ'. -/
+theorem swap_sSup [SupSet α] [SupSet β] (s : Set (α × β)) : (sSup s).symm = sSup (Prod.swap '' s) :=
+  ext (congr_arg sSup <| image_comp Prod.fst swap s : _)
+    (congr_arg sSup <| image_comp Prod.snd swap s : _)
+#align prod.swap_Sup Prod.swap_sSup
 
-/- warning: prod.fst_infi -> Prod.fst_infᵢ is a dubious translation:
+/- warning: prod.fst_infi -> Prod.fst_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : InfSet.{u1} α] [_inst_2 : InfSet.{u2} β] (f : ι -> (Prod.{u1, u2} α β)), Eq.{succ u1} α (Prod.fst.{u1, u2} α β (infᵢ.{max u1 u2, u3} (Prod.{u1, u2} α β) (Prod.hasInf.{u1, u2} α β _inst_1 _inst_2) ι f)) (infᵢ.{u1, u3} α _inst_1 ι (fun (i : ι) => Prod.fst.{u1, u2} α β (f i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : InfSet.{u1} α] [_inst_2 : InfSet.{u2} β] (f : ι -> (Prod.{u1, u2} α β)), Eq.{succ u1} α (Prod.fst.{u1, u2} α β (iInf.{max u1 u2, u3} (Prod.{u1, u2} α β) (Prod.hasInf.{u1, u2} α β _inst_1 _inst_2) ι f)) (iInf.{u1, u3} α _inst_1 ι (fun (i : ι) => Prod.fst.{u1, u2} α β (f i)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : InfSet.{u3} α] [_inst_2 : InfSet.{u2} β] (f : ι -> (Prod.{u3, u2} α β)), Eq.{succ u3} α (Prod.fst.{u3, u2} α β (infᵢ.{max u3 u2, u1} (Prod.{u3, u2} α β) (Prod.infSet.{u3, u2} α β _inst_1 _inst_2) ι f)) (infᵢ.{u3, u1} α _inst_1 ι (fun (i : ι) => Prod.fst.{u3, u2} α β (f i)))
-Case conversion may be inaccurate. Consider using '#align prod.fst_infi Prod.fst_infᵢₓ'. -/
-theorem fst_infᵢ [InfSet α] [InfSet β] (f : ι → α × β) : (infᵢ f).fst = ⨅ i, (f i).fst :=
-  congr_arg infₛ (range_comp _ _).symm
-#align prod.fst_infi Prod.fst_infᵢ
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : InfSet.{u3} α] [_inst_2 : InfSet.{u2} β] (f : ι -> (Prod.{u3, u2} α β)), Eq.{succ u3} α (Prod.fst.{u3, u2} α β (iInf.{max u3 u2, u1} (Prod.{u3, u2} α β) (Prod.infSet.{u3, u2} α β _inst_1 _inst_2) ι f)) (iInf.{u3, u1} α _inst_1 ι (fun (i : ι) => Prod.fst.{u3, u2} α β (f i)))
+Case conversion may be inaccurate. Consider using '#align prod.fst_infi Prod.fst_iInfₓ'. -/
+theorem fst_iInf [InfSet α] [InfSet β] (f : ι → α × β) : (iInf f).fst = ⨅ i, (f i).fst :=
+  congr_arg sInf (range_comp _ _).symm
+#align prod.fst_infi Prod.fst_iInf
 
-/- warning: prod.snd_infi -> Prod.snd_infᵢ is a dubious translation:
+/- warning: prod.snd_infi -> Prod.snd_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : InfSet.{u1} α] [_inst_2 : InfSet.{u2} β] (f : ι -> (Prod.{u1, u2} α β)), Eq.{succ u2} β (Prod.snd.{u1, u2} α β (infᵢ.{max u1 u2, u3} (Prod.{u1, u2} α β) (Prod.hasInf.{u1, u2} α β _inst_1 _inst_2) ι f)) (infᵢ.{u2, u3} β _inst_2 ι (fun (i : ι) => Prod.snd.{u1, u2} α β (f i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : InfSet.{u1} α] [_inst_2 : InfSet.{u2} β] (f : ι -> (Prod.{u1, u2} α β)), Eq.{succ u2} β (Prod.snd.{u1, u2} α β (iInf.{max u1 u2, u3} (Prod.{u1, u2} α β) (Prod.hasInf.{u1, u2} α β _inst_1 _inst_2) ι f)) (iInf.{u2, u3} β _inst_2 ι (fun (i : ι) => Prod.snd.{u1, u2} α β (f i)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : InfSet.{u3} α] [_inst_2 : InfSet.{u2} β] (f : ι -> (Prod.{u3, u2} α β)), Eq.{succ u2} β (Prod.snd.{u3, u2} α β (infᵢ.{max u3 u2, u1} (Prod.{u3, u2} α β) (Prod.infSet.{u3, u2} α β _inst_1 _inst_2) ι f)) (infᵢ.{u2, u1} β _inst_2 ι (fun (i : ι) => Prod.snd.{u3, u2} α β (f i)))
-Case conversion may be inaccurate. Consider using '#align prod.snd_infi Prod.snd_infᵢₓ'. -/
-theorem snd_infᵢ [InfSet α] [InfSet β] (f : ι → α × β) : (infᵢ f).snd = ⨅ i, (f i).snd :=
-  congr_arg infₛ (range_comp _ _).symm
-#align prod.snd_infi Prod.snd_infᵢ
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : InfSet.{u3} α] [_inst_2 : InfSet.{u2} β] (f : ι -> (Prod.{u3, u2} α β)), Eq.{succ u2} β (Prod.snd.{u3, u2} α β (iInf.{max u3 u2, u1} (Prod.{u3, u2} α β) (Prod.infSet.{u3, u2} α β _inst_1 _inst_2) ι f)) (iInf.{u2, u1} β _inst_2 ι (fun (i : ι) => Prod.snd.{u3, u2} α β (f i)))
+Case conversion may be inaccurate. Consider using '#align prod.snd_infi Prod.snd_iInfₓ'. -/
+theorem snd_iInf [InfSet α] [InfSet β] (f : ι → α × β) : (iInf f).snd = ⨅ i, (f i).snd :=
+  congr_arg sInf (range_comp _ _).symm
+#align prod.snd_infi Prod.snd_iInf
 
-/- warning: prod.swap_infi -> Prod.swap_infᵢ is a dubious translation:
+/- warning: prod.swap_infi -> Prod.swap_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : InfSet.{u1} α] [_inst_2 : InfSet.{u2} β] (f : ι -> (Prod.{u1, u2} α β)), Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} β α) (Prod.swap.{u1, u2} α β (infᵢ.{max u1 u2, u3} (Prod.{u1, u2} α β) (Prod.hasInf.{u1, u2} α β _inst_1 _inst_2) ι f)) (infᵢ.{max u2 u1, u3} (Prod.{u2, u1} β α) (Prod.hasInf.{u2, u1} β α _inst_2 _inst_1) ι (fun (i : ι) => Prod.swap.{u1, u2} α β (f i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : InfSet.{u1} α] [_inst_2 : InfSet.{u2} β] (f : ι -> (Prod.{u1, u2} α β)), Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} β α) (Prod.swap.{u1, u2} α β (iInf.{max u1 u2, u3} (Prod.{u1, u2} α β) (Prod.hasInf.{u1, u2} α β _inst_1 _inst_2) ι f)) (iInf.{max u2 u1, u3} (Prod.{u2, u1} β α) (Prod.hasInf.{u2, u1} β α _inst_2 _inst_1) ι (fun (i : ι) => Prod.swap.{u1, u2} α β (f i)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : InfSet.{u3} α] [_inst_2 : InfSet.{u2} β] (f : ι -> (Prod.{u3, u2} α β)), Eq.{max (succ u3) (succ u2)} (Prod.{u2, u3} β α) (Prod.swap.{u3, u2} α β (infᵢ.{max u3 u2, u1} (Prod.{u3, u2} α β) (Prod.infSet.{u3, u2} α β _inst_1 _inst_2) ι f)) (infᵢ.{max u3 u2, u1} (Prod.{u2, u3} β α) (Prod.infSet.{u2, u3} β α _inst_2 _inst_1) ι (fun (i : ι) => Prod.swap.{u3, u2} α β (f i)))
-Case conversion may be inaccurate. Consider using '#align prod.swap_infi Prod.swap_infᵢₓ'. -/
-theorem swap_infᵢ [InfSet α] [InfSet β] (f : ι → α × β) : (infᵢ f).symm = ⨅ i, (f i).symm := by
-  simp_rw [infᵢ, swap_Inf, range_comp]
-#align prod.swap_infi Prod.swap_infᵢ
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : InfSet.{u3} α] [_inst_2 : InfSet.{u2} β] (f : ι -> (Prod.{u3, u2} α β)), Eq.{max (succ u3) (succ u2)} (Prod.{u2, u3} β α) (Prod.swap.{u3, u2} α β (iInf.{max u3 u2, u1} (Prod.{u3, u2} α β) (Prod.infSet.{u3, u2} α β _inst_1 _inst_2) ι f)) (iInf.{max u3 u2, u1} (Prod.{u2, u3} β α) (Prod.infSet.{u2, u3} β α _inst_2 _inst_1) ι (fun (i : ι) => Prod.swap.{u3, u2} α β (f i)))
+Case conversion may be inaccurate. Consider using '#align prod.swap_infi Prod.swap_iInfₓ'. -/
+theorem swap_iInf [InfSet α] [InfSet β] (f : ι → α × β) : (iInf f).symm = ⨅ i, (f i).symm := by
+  simp_rw [iInf, swap_Inf, range_comp]
+#align prod.swap_infi Prod.swap_iInf
 
-/- warning: prod.infi_mk -> Prod.infᵢ_mk is a dubious translation:
+/- warning: prod.infi_mk -> Prod.iInf_mk is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : InfSet.{u1} α] [_inst_2 : InfSet.{u2} β] (f : ι -> α) (g : ι -> β), Eq.{succ (max u1 u2)} (Prod.{u1, u2} α β) (infᵢ.{max u1 u2, u3} (Prod.{u1, u2} α β) (Prod.hasInf.{u1, u2} α β _inst_1 _inst_2) ι (fun (i : ι) => Prod.mk.{u1, u2} α β (f i) (g i))) (Prod.mk.{u1, u2} α β (infᵢ.{u1, u3} α _inst_1 ι (fun (i : ι) => f i)) (infᵢ.{u2, u3} β _inst_2 ι (fun (i : ι) => g i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : InfSet.{u1} α] [_inst_2 : InfSet.{u2} β] (f : ι -> α) (g : ι -> β), Eq.{succ (max u1 u2)} (Prod.{u1, u2} α β) (iInf.{max u1 u2, u3} (Prod.{u1, u2} α β) (Prod.hasInf.{u1, u2} α β _inst_1 _inst_2) ι (fun (i : ι) => Prod.mk.{u1, u2} α β (f i) (g i))) (Prod.mk.{u1, u2} α β (iInf.{u1, u3} α _inst_1 ι (fun (i : ι) => f i)) (iInf.{u2, u3} β _inst_2 ι (fun (i : ι) => g i)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : InfSet.{u3} α] [_inst_2 : InfSet.{u2} β] (f : ι -> α) (g : ι -> β), Eq.{max (succ u3) (succ u2)} (Prod.{u3, u2} α β) (infᵢ.{max u2 u3, u1} (Prod.{u3, u2} α β) (Prod.infSet.{u3, u2} α β _inst_1 _inst_2) ι (fun (i : ι) => Prod.mk.{u3, u2} α β (f i) (g i))) (Prod.mk.{u3, u2} α β (infᵢ.{u3, u1} α _inst_1 ι (fun (i : ι) => f i)) (infᵢ.{u2, u1} β _inst_2 ι (fun (i : ι) => g i)))
-Case conversion may be inaccurate. Consider using '#align prod.infi_mk Prod.infᵢ_mkₓ'. -/
-theorem infᵢ_mk [InfSet α] [InfSet β] (f : ι → α) (g : ι → β) :
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : InfSet.{u3} α] [_inst_2 : InfSet.{u2} β] (f : ι -> α) (g : ι -> β), Eq.{max (succ u3) (succ u2)} (Prod.{u3, u2} α β) (iInf.{max u2 u3, u1} (Prod.{u3, u2} α β) (Prod.infSet.{u3, u2} α β _inst_1 _inst_2) ι (fun (i : ι) => Prod.mk.{u3, u2} α β (f i) (g i))) (Prod.mk.{u3, u2} α β (iInf.{u3, u1} α _inst_1 ι (fun (i : ι) => f i)) (iInf.{u2, u1} β _inst_2 ι (fun (i : ι) => g i)))
+Case conversion may be inaccurate. Consider using '#align prod.infi_mk Prod.iInf_mkₓ'. -/
+theorem iInf_mk [InfSet α] [InfSet β] (f : ι → α) (g : ι → β) :
     (⨅ i, (f i, g i)) = (⨅ i, f i, ⨅ i, g i) :=
-  congr_arg₂ Prod.mk (fst_infᵢ _) (snd_infᵢ _)
-#align prod.infi_mk Prod.infᵢ_mk
+  congr_arg₂ Prod.mk (fst_iInf _) (snd_iInf _)
+#align prod.infi_mk Prod.iInf_mk
 
-/- warning: prod.fst_supr -> Prod.fst_supᵢ is a dubious translation:
+/- warning: prod.fst_supr -> Prod.fst_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SupSet.{u1} α] [_inst_2 : SupSet.{u2} β] (f : ι -> (Prod.{u1, u2} α β)), Eq.{succ u1} α (Prod.fst.{u1, u2} α β (supᵢ.{max u1 u2, u3} (Prod.{u1, u2} α β) (Prod.hasSup.{u1, u2} α β _inst_1 _inst_2) ι f)) (supᵢ.{u1, u3} α _inst_1 ι (fun (i : ι) => Prod.fst.{u1, u2} α β (f i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SupSet.{u1} α] [_inst_2 : SupSet.{u2} β] (f : ι -> (Prod.{u1, u2} α β)), Eq.{succ u1} α (Prod.fst.{u1, u2} α β (iSup.{max u1 u2, u3} (Prod.{u1, u2} α β) (Prod.hasSup.{u1, u2} α β _inst_1 _inst_2) ι f)) (iSup.{u1, u3} α _inst_1 ι (fun (i : ι) => Prod.fst.{u1, u2} α β (f i)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : SupSet.{u3} α] [_inst_2 : SupSet.{u2} β] (f : ι -> (Prod.{u3, u2} α β)), Eq.{succ u3} α (Prod.fst.{u3, u2} α β (supᵢ.{max u3 u2, u1} (Prod.{u3, u2} α β) (Prod.supSet.{u3, u2} α β _inst_1 _inst_2) ι f)) (supᵢ.{u3, u1} α _inst_1 ι (fun (i : ι) => Prod.fst.{u3, u2} α β (f i)))
-Case conversion may be inaccurate. Consider using '#align prod.fst_supr Prod.fst_supᵢₓ'. -/
-theorem fst_supᵢ [SupSet α] [SupSet β] (f : ι → α × β) : (supᵢ f).fst = ⨆ i, (f i).fst :=
-  congr_arg supₛ (range_comp _ _).symm
-#align prod.fst_supr Prod.fst_supᵢ
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : SupSet.{u3} α] [_inst_2 : SupSet.{u2} β] (f : ι -> (Prod.{u3, u2} α β)), Eq.{succ u3} α (Prod.fst.{u3, u2} α β (iSup.{max u3 u2, u1} (Prod.{u3, u2} α β) (Prod.supSet.{u3, u2} α β _inst_1 _inst_2) ι f)) (iSup.{u3, u1} α _inst_1 ι (fun (i : ι) => Prod.fst.{u3, u2} α β (f i)))
+Case conversion may be inaccurate. Consider using '#align prod.fst_supr Prod.fst_iSupₓ'. -/
+theorem fst_iSup [SupSet α] [SupSet β] (f : ι → α × β) : (iSup f).fst = ⨆ i, (f i).fst :=
+  congr_arg sSup (range_comp _ _).symm
+#align prod.fst_supr Prod.fst_iSup
 
-/- warning: prod.snd_supr -> Prod.snd_supᵢ is a dubious translation:
+/- warning: prod.snd_supr -> Prod.snd_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SupSet.{u1} α] [_inst_2 : SupSet.{u2} β] (f : ι -> (Prod.{u1, u2} α β)), Eq.{succ u2} β (Prod.snd.{u1, u2} α β (supᵢ.{max u1 u2, u3} (Prod.{u1, u2} α β) (Prod.hasSup.{u1, u2} α β _inst_1 _inst_2) ι f)) (supᵢ.{u2, u3} β _inst_2 ι (fun (i : ι) => Prod.snd.{u1, u2} α β (f i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SupSet.{u1} α] [_inst_2 : SupSet.{u2} β] (f : ι -> (Prod.{u1, u2} α β)), Eq.{succ u2} β (Prod.snd.{u1, u2} α β (iSup.{max u1 u2, u3} (Prod.{u1, u2} α β) (Prod.hasSup.{u1, u2} α β _inst_1 _inst_2) ι f)) (iSup.{u2, u3} β _inst_2 ι (fun (i : ι) => Prod.snd.{u1, u2} α β (f i)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : SupSet.{u3} α] [_inst_2 : SupSet.{u2} β] (f : ι -> (Prod.{u3, u2} α β)), Eq.{succ u2} β (Prod.snd.{u3, u2} α β (supᵢ.{max u3 u2, u1} (Prod.{u3, u2} α β) (Prod.supSet.{u3, u2} α β _inst_1 _inst_2) ι f)) (supᵢ.{u2, u1} β _inst_2 ι (fun (i : ι) => Prod.snd.{u3, u2} α β (f i)))
-Case conversion may be inaccurate. Consider using '#align prod.snd_supr Prod.snd_supᵢₓ'. -/
-theorem snd_supᵢ [SupSet α] [SupSet β] (f : ι → α × β) : (supᵢ f).snd = ⨆ i, (f i).snd :=
-  congr_arg supₛ (range_comp _ _).symm
-#align prod.snd_supr Prod.snd_supᵢ
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : SupSet.{u3} α] [_inst_2 : SupSet.{u2} β] (f : ι -> (Prod.{u3, u2} α β)), Eq.{succ u2} β (Prod.snd.{u3, u2} α β (iSup.{max u3 u2, u1} (Prod.{u3, u2} α β) (Prod.supSet.{u3, u2} α β _inst_1 _inst_2) ι f)) (iSup.{u2, u1} β _inst_2 ι (fun (i : ι) => Prod.snd.{u3, u2} α β (f i)))
+Case conversion may be inaccurate. Consider using '#align prod.snd_supr Prod.snd_iSupₓ'. -/
+theorem snd_iSup [SupSet α] [SupSet β] (f : ι → α × β) : (iSup f).snd = ⨆ i, (f i).snd :=
+  congr_arg sSup (range_comp _ _).symm
+#align prod.snd_supr Prod.snd_iSup
 
-/- warning: prod.swap_supr -> Prod.swap_supᵢ is a dubious translation:
+/- warning: prod.swap_supr -> Prod.swap_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SupSet.{u1} α] [_inst_2 : SupSet.{u2} β] (f : ι -> (Prod.{u1, u2} α β)), Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} β α) (Prod.swap.{u1, u2} α β (supᵢ.{max u1 u2, u3} (Prod.{u1, u2} α β) (Prod.hasSup.{u1, u2} α β _inst_1 _inst_2) ι f)) (supᵢ.{max u2 u1, u3} (Prod.{u2, u1} β α) (Prod.hasSup.{u2, u1} β α _inst_2 _inst_1) ι (fun (i : ι) => Prod.swap.{u1, u2} α β (f i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SupSet.{u1} α] [_inst_2 : SupSet.{u2} β] (f : ι -> (Prod.{u1, u2} α β)), Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} β α) (Prod.swap.{u1, u2} α β (iSup.{max u1 u2, u3} (Prod.{u1, u2} α β) (Prod.hasSup.{u1, u2} α β _inst_1 _inst_2) ι f)) (iSup.{max u2 u1, u3} (Prod.{u2, u1} β α) (Prod.hasSup.{u2, u1} β α _inst_2 _inst_1) ι (fun (i : ι) => Prod.swap.{u1, u2} α β (f i)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : SupSet.{u3} α] [_inst_2 : SupSet.{u2} β] (f : ι -> (Prod.{u3, u2} α β)), Eq.{max (succ u3) (succ u2)} (Prod.{u2, u3} β α) (Prod.swap.{u3, u2} α β (supᵢ.{max u3 u2, u1} (Prod.{u3, u2} α β) (Prod.supSet.{u3, u2} α β _inst_1 _inst_2) ι f)) (supᵢ.{max u3 u2, u1} (Prod.{u2, u3} β α) (Prod.supSet.{u2, u3} β α _inst_2 _inst_1) ι (fun (i : ι) => Prod.swap.{u3, u2} α β (f i)))
-Case conversion may be inaccurate. Consider using '#align prod.swap_supr Prod.swap_supᵢₓ'. -/
-theorem swap_supᵢ [SupSet α] [SupSet β] (f : ι → α × β) : (supᵢ f).symm = ⨆ i, (f i).symm := by
-  simp_rw [supᵢ, swap_Sup, range_comp]
-#align prod.swap_supr Prod.swap_supᵢ
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : SupSet.{u3} α] [_inst_2 : SupSet.{u2} β] (f : ι -> (Prod.{u3, u2} α β)), Eq.{max (succ u3) (succ u2)} (Prod.{u2, u3} β α) (Prod.swap.{u3, u2} α β (iSup.{max u3 u2, u1} (Prod.{u3, u2} α β) (Prod.supSet.{u3, u2} α β _inst_1 _inst_2) ι f)) (iSup.{max u3 u2, u1} (Prod.{u2, u3} β α) (Prod.supSet.{u2, u3} β α _inst_2 _inst_1) ι (fun (i : ι) => Prod.swap.{u3, u2} α β (f i)))
+Case conversion may be inaccurate. Consider using '#align prod.swap_supr Prod.swap_iSupₓ'. -/
+theorem swap_iSup [SupSet α] [SupSet β] (f : ι → α × β) : (iSup f).symm = ⨆ i, (f i).symm := by
+  simp_rw [iSup, swap_Sup, range_comp]
+#align prod.swap_supr Prod.swap_iSup
 
-/- warning: prod.supr_mk -> Prod.supᵢ_mk is a dubious translation:
+/- warning: prod.supr_mk -> Prod.iSup_mk is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SupSet.{u1} α] [_inst_2 : SupSet.{u2} β] (f : ι -> α) (g : ι -> β), Eq.{succ (max u1 u2)} (Prod.{u1, u2} α β) (supᵢ.{max u1 u2, u3} (Prod.{u1, u2} α β) (Prod.hasSup.{u1, u2} α β _inst_1 _inst_2) ι (fun (i : ι) => Prod.mk.{u1, u2} α β (f i) (g i))) (Prod.mk.{u1, u2} α β (supᵢ.{u1, u3} α _inst_1 ι (fun (i : ι) => f i)) (supᵢ.{u2, u3} β _inst_2 ι (fun (i : ι) => g i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : SupSet.{u1} α] [_inst_2 : SupSet.{u2} β] (f : ι -> α) (g : ι -> β), Eq.{succ (max u1 u2)} (Prod.{u1, u2} α β) (iSup.{max u1 u2, u3} (Prod.{u1, u2} α β) (Prod.hasSup.{u1, u2} α β _inst_1 _inst_2) ι (fun (i : ι) => Prod.mk.{u1, u2} α β (f i) (g i))) (Prod.mk.{u1, u2} α β (iSup.{u1, u3} α _inst_1 ι (fun (i : ι) => f i)) (iSup.{u2, u3} β _inst_2 ι (fun (i : ι) => g i)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : SupSet.{u3} α] [_inst_2 : SupSet.{u2} β] (f : ι -> α) (g : ι -> β), Eq.{max (succ u3) (succ u2)} (Prod.{u3, u2} α β) (supᵢ.{max u2 u3, u1} (Prod.{u3, u2} α β) (Prod.supSet.{u3, u2} α β _inst_1 _inst_2) ι (fun (i : ι) => Prod.mk.{u3, u2} α β (f i) (g i))) (Prod.mk.{u3, u2} α β (supᵢ.{u3, u1} α _inst_1 ι (fun (i : ι) => f i)) (supᵢ.{u2, u1} β _inst_2 ι (fun (i : ι) => g i)))
-Case conversion may be inaccurate. Consider using '#align prod.supr_mk Prod.supᵢ_mkₓ'. -/
-theorem supᵢ_mk [SupSet α] [SupSet β] (f : ι → α) (g : ι → β) :
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : SupSet.{u3} α] [_inst_2 : SupSet.{u2} β] (f : ι -> α) (g : ι -> β), Eq.{max (succ u3) (succ u2)} (Prod.{u3, u2} α β) (iSup.{max u2 u3, u1} (Prod.{u3, u2} α β) (Prod.supSet.{u3, u2} α β _inst_1 _inst_2) ι (fun (i : ι) => Prod.mk.{u3, u2} α β (f i) (g i))) (Prod.mk.{u3, u2} α β (iSup.{u3, u1} α _inst_1 ι (fun (i : ι) => f i)) (iSup.{u2, u1} β _inst_2 ι (fun (i : ι) => g i)))
+Case conversion may be inaccurate. Consider using '#align prod.supr_mk Prod.iSup_mkₓ'. -/
+theorem iSup_mk [SupSet α] [SupSet β] (f : ι → α) (g : ι → β) :
     (⨆ i, (f i, g i)) = (⨆ i, f i, ⨆ i, g i) :=
-  congr_arg₂ Prod.mk (fst_supᵢ _) (snd_supᵢ _)
-#align prod.supr_mk Prod.supᵢ_mk
+  congr_arg₂ Prod.mk (fst_iSup _) (snd_iSup _)
+#align prod.supr_mk Prod.iSup_mk
 
 variable (α β)
 
@@ -3686,138 +3686,138 @@ instance [CompleteLattice α] [CompleteLattice β] : CompleteLattice (α × β)
   { Prod.lattice α β, Prod.boundedOrder α β, Prod.hasSup α β,
     Prod.hasInf α
       β with
-    le_sup := fun s p hab => ⟨le_supₛ <| mem_image_of_mem _ hab, le_supₛ <| mem_image_of_mem _ hab⟩
+    le_sup := fun s p hab => ⟨le_sSup <| mem_image_of_mem _ hab, le_sSup <| mem_image_of_mem _ hab⟩
     sup_le := fun s p h =>
-      ⟨supₛ_le <| ball_image_of_ball fun p hp => (h p hp).1,
-        supₛ_le <| ball_image_of_ball fun p hp => (h p hp).2⟩
-    inf_le := fun s p hab => ⟨infₛ_le <| mem_image_of_mem _ hab, infₛ_le <| mem_image_of_mem _ hab⟩
+      ⟨sSup_le <| ball_image_of_ball fun p hp => (h p hp).1,
+        sSup_le <| ball_image_of_ball fun p hp => (h p hp).2⟩
+    inf_le := fun s p hab => ⟨sInf_le <| mem_image_of_mem _ hab, sInf_le <| mem_image_of_mem _ hab⟩
     le_inf := fun s p h =>
-      ⟨le_infₛ <| ball_image_of_ball fun p hp => (h p hp).1,
-        le_infₛ <| ball_image_of_ball fun p hp => (h p hp).2⟩ }
+      ⟨le_sInf <| ball_image_of_ball fun p hp => (h p hp).1,
+        le_sInf <| ball_image_of_ball fun p hp => (h p hp).2⟩ }
 
 end Prod
 
-/- warning: Inf_prod -> infₛ_prod is a dubious translation:
+/- warning: Inf_prod -> sInf_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : InfSet.{u1} α] [_inst_2 : InfSet.{u2} β] {s : Set.{u1} α} {t : Set.{u2} β}, (Set.Nonempty.{u1} α s) -> (Set.Nonempty.{u2} β t) -> (Eq.{succ (max u1 u2)} (Prod.{u1, u2} α β) (InfSet.infₛ.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasInf.{u1, u2} α β _inst_1 _inst_2) (Set.prod.{u1, u2} α β s t)) (Prod.mk.{u1, u2} α β (InfSet.infₛ.{u1} α _inst_1 s) (InfSet.infₛ.{u2} β _inst_2 t)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : InfSet.{u1} α] [_inst_2 : InfSet.{u2} β] {s : Set.{u1} α} {t : Set.{u2} β}, (Set.Nonempty.{u1} α s) -> (Set.Nonempty.{u2} β t) -> (Eq.{succ (max u1 u2)} (Prod.{u1, u2} α β) (InfSet.sInf.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasInf.{u1, u2} α β _inst_1 _inst_2) (Set.prod.{u1, u2} α β s t)) (Prod.mk.{u1, u2} α β (InfSet.sInf.{u1} α _inst_1 s) (InfSet.sInf.{u2} β _inst_2 t)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : InfSet.{u2} α] [_inst_2 : InfSet.{u1} β] {s : Set.{u2} α} {t : Set.{u1} β}, (Set.Nonempty.{u2} α s) -> (Set.Nonempty.{u1} β t) -> (Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} α β) (InfSet.infₛ.{max u1 u2} (Prod.{u2, u1} α β) (Prod.infSet.{u2, u1} α β _inst_1 _inst_2) (Set.prod.{u2, u1} α β s t)) (Prod.mk.{u2, u1} α β (InfSet.infₛ.{u2} α _inst_1 s) (InfSet.infₛ.{u1} β _inst_2 t)))
-Case conversion may be inaccurate. Consider using '#align Inf_prod infₛ_prodₓ'. -/
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : InfSet.{u2} α] [_inst_2 : InfSet.{u1} β] {s : Set.{u2} α} {t : Set.{u1} β}, (Set.Nonempty.{u2} α s) -> (Set.Nonempty.{u1} β t) -> (Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} α β) (InfSet.sInf.{max u1 u2} (Prod.{u2, u1} α β) (Prod.infSet.{u2, u1} α β _inst_1 _inst_2) (Set.prod.{u2, u1} α β s t)) (Prod.mk.{u2, u1} α β (InfSet.sInf.{u2} α _inst_1 s) (InfSet.sInf.{u1} β _inst_2 t)))
+Case conversion may be inaccurate. Consider using '#align Inf_prod sInf_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-theorem infₛ_prod [InfSet α] [InfSet β] {s : Set α} {t : Set β} (hs : s.Nonempty)
-    (ht : t.Nonempty) : infₛ (s ×ˢ t) = (infₛ s, infₛ t) :=
-  congr_arg₂ Prod.mk (congr_arg infₛ <| fst_image_prod _ ht) (congr_arg infₛ <| snd_image_prod hs _)
-#align Inf_prod infₛ_prod
+theorem sInf_prod [InfSet α] [InfSet β] {s : Set α} {t : Set β} (hs : s.Nonempty)
+    (ht : t.Nonempty) : sInf (s ×ˢ t) = (sInf s, sInf t) :=
+  congr_arg₂ Prod.mk (congr_arg sInf <| fst_image_prod _ ht) (congr_arg sInf <| snd_image_prod hs _)
+#align Inf_prod sInf_prod
 
-/- warning: Sup_prod -> supₛ_prod is a dubious translation:
+/- warning: Sup_prod -> sSup_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SupSet.{u1} α] [_inst_2 : SupSet.{u2} β] {s : Set.{u1} α} {t : Set.{u2} β}, (Set.Nonempty.{u1} α s) -> (Set.Nonempty.{u2} β t) -> (Eq.{succ (max u1 u2)} (Prod.{u1, u2} α β) (SupSet.supₛ.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasSup.{u1, u2} α β _inst_1 _inst_2) (Set.prod.{u1, u2} α β s t)) (Prod.mk.{u1, u2} α β (SupSet.supₛ.{u1} α _inst_1 s) (SupSet.supₛ.{u2} β _inst_2 t)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SupSet.{u1} α] [_inst_2 : SupSet.{u2} β] {s : Set.{u1} α} {t : Set.{u2} β}, (Set.Nonempty.{u1} α s) -> (Set.Nonempty.{u2} β t) -> (Eq.{succ (max u1 u2)} (Prod.{u1, u2} α β) (SupSet.sSup.{max u1 u2} (Prod.{u1, u2} α β) (Prod.hasSup.{u1, u2} α β _inst_1 _inst_2) (Set.prod.{u1, u2} α β s t)) (Prod.mk.{u1, u2} α β (SupSet.sSup.{u1} α _inst_1 s) (SupSet.sSup.{u2} β _inst_2 t)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SupSet.{u2} α] [_inst_2 : SupSet.{u1} β] {s : Set.{u2} α} {t : Set.{u1} β}, (Set.Nonempty.{u2} α s) -> (Set.Nonempty.{u1} β t) -> (Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} α β) (SupSet.supₛ.{max u1 u2} (Prod.{u2, u1} α β) (Prod.supSet.{u2, u1} α β _inst_1 _inst_2) (Set.prod.{u2, u1} α β s t)) (Prod.mk.{u2, u1} α β (SupSet.supₛ.{u2} α _inst_1 s) (SupSet.supₛ.{u1} β _inst_2 t)))
-Case conversion may be inaccurate. Consider using '#align Sup_prod supₛ_prodₓ'. -/
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SupSet.{u2} α] [_inst_2 : SupSet.{u1} β] {s : Set.{u2} α} {t : Set.{u1} β}, (Set.Nonempty.{u2} α s) -> (Set.Nonempty.{u1} β t) -> (Eq.{max (succ u2) (succ u1)} (Prod.{u2, u1} α β) (SupSet.sSup.{max u1 u2} (Prod.{u2, u1} α β) (Prod.supSet.{u2, u1} α β _inst_1 _inst_2) (Set.prod.{u2, u1} α β s t)) (Prod.mk.{u2, u1} α β (SupSet.sSup.{u2} α _inst_1 s) (SupSet.sSup.{u1} β _inst_2 t)))
+Case conversion may be inaccurate. Consider using '#align Sup_prod sSup_prodₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-theorem supₛ_prod [SupSet α] [SupSet β] {s : Set α} {t : Set β} (hs : s.Nonempty)
-    (ht : t.Nonempty) : supₛ (s ×ˢ t) = (supₛ s, supₛ t) :=
-  congr_arg₂ Prod.mk (congr_arg supₛ <| fst_image_prod _ ht) (congr_arg supₛ <| snd_image_prod hs _)
-#align Sup_prod supₛ_prod
+theorem sSup_prod [SupSet α] [SupSet β] {s : Set α} {t : Set β} (hs : s.Nonempty)
+    (ht : t.Nonempty) : sSup (s ×ˢ t) = (sSup s, sSup t) :=
+  congr_arg₂ Prod.mk (congr_arg sSup <| fst_image_prod _ ht) (congr_arg sSup <| snd_image_prod hs _)
+#align Sup_prod sSup_prod
 
 section CompleteLattice
 
 variable [CompleteLattice α] {a : α} {s : Set α}
 
-/- warning: sup_Inf_le_infi_sup -> sup_infₛ_le_infᵢ_sup is a dubious translation:
+/- warning: sup_Inf_le_infi_sup -> sup_sInf_le_iInf_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)) (infᵢ.{u1, succ u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) α (fun (b : α) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)) (iInf.{u1, succ u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) α (fun (b : α) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)) (infᵢ.{u1, succ u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) α (fun (b : α) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)))
-Case conversion may be inaccurate. Consider using '#align sup_Inf_le_infi_sup sup_infₛ_le_infᵢ_supₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)) (iInf.{u1, succ u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) α (fun (b : α) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)))
+Case conversion may be inaccurate. Consider using '#align sup_Inf_le_infi_sup sup_sInf_le_iInf_supₓ'. -/
 /-- This is a weaker version of `sup_Inf_eq` -/
-theorem sup_infₛ_le_infᵢ_sup : a ⊔ infₛ s ≤ ⨅ b ∈ s, a ⊔ b :=
-  le_infᵢ₂ fun i h => sup_le_sup_left (infₛ_le h) _
-#align sup_Inf_le_infi_sup sup_infₛ_le_infᵢ_sup
+theorem sup_sInf_le_iInf_sup : a ⊔ sInf s ≤ ⨅ b ∈ s, a ⊔ b :=
+  le_iInf₂ fun i h => sup_le_sup_left (sInf_le h) _
+#align sup_Inf_le_infi_sup sup_sInf_le_iInf_sup
 
-/- warning: supr_inf_le_inf_Sup -> supᵢ_inf_le_inf_supₛ is a dubious translation:
+/- warning: supr_inf_le_inf_Sup -> iSup_inf_le_inf_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (supᵢ.{u1, succ u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) α (fun (b : α) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iSup.{u1, succ u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) α (fun (b : α) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (supᵢ.{u1, succ u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) α (fun (b : α) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a b))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align supr_inf_le_inf_Sup supᵢ_inf_le_inf_supₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iSup.{u1, succ u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) α (fun (b : α) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a b))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align supr_inf_le_inf_Sup iSup_inf_le_inf_sSupₓ'. -/
 /-- This is a weaker version of `inf_Sup_eq` -/
-theorem supᵢ_inf_le_inf_supₛ : (⨆ b ∈ s, a ⊓ b) ≤ a ⊓ supₛ s :=
-  @sup_infₛ_le_infᵢ_sup αᵒᵈ _ _ _
-#align supr_inf_le_inf_Sup supᵢ_inf_le_inf_supₛ
+theorem iSup_inf_le_inf_sSup : (⨆ b ∈ s, a ⊓ b) ≤ a ⊓ sSup s :=
+  @sup_sInf_le_iInf_sup αᵒᵈ _ _ _
+#align supr_inf_le_inf_Sup iSup_inf_le_inf_sSup
 
-/- warning: Inf_sup_le_infi_sup -> infₛ_sup_le_infᵢ_sup is a dubious translation:
+/- warning: Inf_sup_le_infi_sup -> sInf_sup_le_iInf_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) a) (infᵢ.{u1, succ u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) α (fun (b : α) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) a) (iInf.{u1, succ u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) α (fun (b : α) => iInf.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) a) (infᵢ.{u1, succ u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) α (fun (b : α) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a)))
-Case conversion may be inaccurate. Consider using '#align Inf_sup_le_infi_sup infₛ_sup_le_infᵢ_supₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) a) (iInf.{u1, succ u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) α (fun (b : α) => iInf.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a)))
+Case conversion may be inaccurate. Consider using '#align Inf_sup_le_infi_sup sInf_sup_le_iInf_supₓ'. -/
 /-- This is a weaker version of `Inf_sup_eq` -/
-theorem infₛ_sup_le_infᵢ_sup : infₛ s ⊔ a ≤ ⨅ b ∈ s, b ⊔ a :=
-  le_infᵢ₂ fun i h => sup_le_sup_right (infₛ_le h) _
-#align Inf_sup_le_infi_sup infₛ_sup_le_infᵢ_sup
+theorem sInf_sup_le_iInf_sup : sInf s ⊔ a ≤ ⨅ b ∈ s, b ⊔ a :=
+  le_iInf₂ fun i h => sup_le_sup_right (sInf_le h) _
+#align Inf_sup_le_infi_sup sInf_sup_le_iInf_sup
 
-/- warning: supr_inf_le_Sup_inf -> supᵢ_inf_le_supₛ_inf is a dubious translation:
+/- warning: supr_inf_le_Sup_inf -> iSup_inf_le_sSup_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (supᵢ.{u1, succ u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) α (fun (b : α) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) a)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iSup.{u1, succ u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) α (fun (b : α) => iSup.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (supᵢ.{u1, succ u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) α (fun (b : α) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) b a))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) a)
-Case conversion may be inaccurate. Consider using '#align supr_inf_le_Sup_inf supᵢ_inf_le_supₛ_infₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (iSup.{u1, succ u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) α (fun (b : α) => iSup.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) b a))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) a)
+Case conversion may be inaccurate. Consider using '#align supr_inf_le_Sup_inf iSup_inf_le_sSup_infₓ'. -/
 /-- This is a weaker version of `Sup_inf_eq` -/
-theorem supᵢ_inf_le_supₛ_inf : (⨆ b ∈ s, b ⊓ a) ≤ supₛ s ⊓ a :=
-  @infₛ_sup_le_infᵢ_sup αᵒᵈ _ _ _
-#align supr_inf_le_Sup_inf supᵢ_inf_le_supₛ_inf
+theorem iSup_inf_le_sSup_inf : (⨆ b ∈ s, b ⊓ a) ≤ sSup s ⊓ a :=
+  @sInf_sup_le_iInf_sup αᵒᵈ _ _ _
+#align supr_inf_le_Sup_inf iSup_inf_le_sSup_inf
 
-/- warning: le_supr_inf_supr -> le_supᵢ_inf_supᵢ is a dubious translation:
+/- warning: le_supr_inf_supr -> le_iSup_inf_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (g : ι -> α), LE.le.{u1} α (Preorder.toLE.{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) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i) (g i))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{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} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => g i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (g : ι -> α), LE.le.{u1} α (Preorder.toLE.{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) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i) (g i))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{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} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => g i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (g : ι -> α), LE.le.{u2} α (Preorder.toLE.{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) => Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f i) (g i))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i)) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => g i)))
-Case conversion may be inaccurate. Consider using '#align le_supr_inf_supr le_supᵢ_inf_supᵢₓ'. -/
-theorem le_supᵢ_inf_supᵢ (f g : ι → α) : (⨆ i, f i ⊓ g i) ≤ (⨆ i, f i) ⊓ ⨆ i, g i :=
-  le_inf (supᵢ_mono fun i => inf_le_left) (supᵢ_mono fun i => inf_le_right)
-#align le_supr_inf_supr le_supᵢ_inf_supᵢ
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (g : ι -> α), LE.le.{u2} α (Preorder.toLE.{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) => Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f i) (g i))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i)) (iSup.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => g i)))
+Case conversion may be inaccurate. Consider using '#align le_supr_inf_supr le_iSup_inf_iSupₓ'. -/
+theorem le_iSup_inf_iSup (f g : ι → α) : (⨆ i, f i ⊓ g i) ≤ (⨆ i, f i) ⊓ ⨆ i, g i :=
+  le_inf (iSup_mono fun i => inf_le_left) (iSup_mono fun i => inf_le_right)
+#align le_supr_inf_supr le_iSup_inf_iSup
 
-/- warning: infi_sup_infi_le -> infᵢ_sup_infᵢ_le is a dubious translation:
+/- warning: infi_sup_infi_le -> iInf_sup_iInf_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (g : ι -> α), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{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} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => g i))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i) (g i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (g : ι -> α), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{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} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => g i))) (iInf.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i) (g i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (g : ι -> α), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => g i))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f i) (g i)))
-Case conversion may be inaccurate. Consider using '#align infi_sup_infi_le infᵢ_sup_infᵢ_leₓ'. -/
-theorem infᵢ_sup_infᵢ_le (f g : ι → α) : ((⨅ i, f i) ⊔ ⨅ i, g i) ≤ ⨅ i, f i ⊔ g i :=
-  @le_supᵢ_inf_supᵢ αᵒᵈ ι _ f g
-#align infi_sup_infi_le infᵢ_sup_infᵢ_le
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (g : ι -> α), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i)) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => g i))) (iInf.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f i) (g i)))
+Case conversion may be inaccurate. Consider using '#align infi_sup_infi_le iInf_sup_iInf_leₓ'. -/
+theorem iInf_sup_iInf_le (f g : ι → α) : ((⨅ i, f i) ⊔ ⨅ i, g i) ≤ ⨅ i, f i ⊔ g i :=
+  @le_iSup_inf_iSup αᵒᵈ ι _ f g
+#align infi_sup_infi_le iInf_sup_iInf_le
 
-/- warning: disjoint_Sup_left -> disjoint_supₛ_left is a dubious translation:
+/- warning: disjoint_Sup_left -> disjoint_sSup_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : Set.{u1} α} {b : α}, (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) a) b) -> (forall {i : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) i a) -> (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) i b))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : Set.{u1} α} {b : α}, (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) a) b) -> (forall {i : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) i a) -> (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) i b))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : Set.{u1} α} {b : α}, (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) a) b) -> (forall {i : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) i a) -> (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) i b))
-Case conversion may be inaccurate. Consider using '#align disjoint_Sup_left disjoint_supₛ_leftₓ'. -/
-theorem disjoint_supₛ_left {a : Set α} {b : α} (d : Disjoint (supₛ a) b) {i} (hi : i ∈ a) :
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : Set.{u1} α} {b : α}, (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) a) b) -> (forall {i : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) i a) -> (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) i b))
+Case conversion may be inaccurate. Consider using '#align disjoint_Sup_left disjoint_sSup_leftₓ'. -/
+theorem disjoint_sSup_left {a : Set α} {b : α} (d : Disjoint (sSup a) b) {i} (hi : i ∈ a) :
     Disjoint i b :=
-  disjoint_iff_inf_le.mpr (supᵢ₂_le_iff.1 (supᵢ_inf_le_supₛ_inf.trans d.le_bot) i hi : _)
-#align disjoint_Sup_left disjoint_supₛ_left
+  disjoint_iff_inf_le.mpr (iSup₂_le_iff.1 (iSup_inf_le_sSup_inf.trans d.le_bot) i hi : _)
+#align disjoint_Sup_left disjoint_sSup_left
 
-/- warning: disjoint_Sup_right -> disjoint_supₛ_right is a dubious translation:
+/- warning: disjoint_Sup_right -> disjoint_sSup_right is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : Set.{u1} α} {b : α}, (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) b (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) a)) -> (forall {i : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) i a) -> (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) b i))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : Set.{u1} α} {b : α}, (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) b (SupSet.sSup.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) a)) -> (forall {i : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) i a) -> (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) b i))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : Set.{u1} α} {b : α}, (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) b (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) a)) -> (forall {i : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) i a) -> (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) b i))
-Case conversion may be inaccurate. Consider using '#align disjoint_Sup_right disjoint_supₛ_rightₓ'. -/
-theorem disjoint_supₛ_right {a : Set α} {b : α} (d : Disjoint b (supₛ a)) {i} (hi : i ∈ a) :
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : Set.{u1} α} {b : α}, (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) b (SupSet.sSup.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) a)) -> (forall {i : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) i a) -> (Disjoint.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (BoundedOrder.toOrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (CompleteLattice.toBoundedOrder.{u1} α _inst_1)) b i))
+Case conversion may be inaccurate. Consider using '#align disjoint_Sup_right disjoint_sSup_rightₓ'. -/
+theorem disjoint_sSup_right {a : Set α} {b : α} (d : Disjoint b (sSup a)) {i} (hi : i ∈ a) :
     Disjoint b i :=
-  disjoint_iff_inf_le.mpr (supᵢ₂_le_iff.mp (supᵢ_inf_le_inf_supₛ.trans d.le_bot) i hi : _)
-#align disjoint_Sup_right disjoint_supₛ_right
+  disjoint_iff_inf_le.mpr (iSup₂_le_iff.mp (iSup_inf_le_inf_sSup.trans d.le_bot) i hi : _)
+#align disjoint_Sup_right disjoint_sSup_right
 
 end CompleteLattice
 
 /- warning: function.injective.complete_lattice -> Function.Injective.completeLattice is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Sup.{u1} α] [_inst_2 : Inf.{u1} α] [_inst_3 : SupSet.{u1} α] [_inst_4 : InfSet.{u1} α] [_inst_5 : Top.{u1} α] [_inst_6 : Bot.{u1} α] [_inst_7 : CompleteLattice.{u2} β] (f : α -> β), (Function.Injective.{succ u1, succ u2} α β f) -> (forall (a : α) (b : α), Eq.{succ u2} β (f (Sup.sup.{u1} α _inst_1 a b)) (Sup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (CompleteLattice.toLattice.{u2} β _inst_7))) (f a) (f b))) -> (forall (a : α) (b : α), Eq.{succ u2} β (f (Inf.inf.{u1} α _inst_2 a b)) (Inf.inf.{u2} β (SemilatticeInf.toHasInf.{u2} β (Lattice.toSemilatticeInf.{u2} β (CompleteLattice.toLattice.{u2} β _inst_7))) (f a) (f b))) -> (forall (s : Set.{u1} α), Eq.{succ u2} β (f (SupSet.supₛ.{u1} α _inst_3 s)) (supᵢ.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_7)) α (fun (a : α) => supᵢ.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_7)) (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) => f a)))) -> (forall (s : Set.{u1} α), Eq.{succ u2} β (f (InfSet.infₛ.{u1} α _inst_4 s)) (infᵢ.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_7)) α (fun (a : α) => infᵢ.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_7)) (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) => f a)))) -> (Eq.{succ u2} β (f (Top.top.{u1} α _inst_5)) (Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β _inst_7))) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α _inst_6)) (Bot.bot.{u2} β (CompleteLattice.toHasBot.{u2} β _inst_7))) -> (CompleteLattice.{u1} α)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Sup.{u1} α] [_inst_2 : Inf.{u1} α] [_inst_3 : SupSet.{u1} α] [_inst_4 : InfSet.{u1} α] [_inst_5 : Top.{u1} α] [_inst_6 : Bot.{u1} α] [_inst_7 : CompleteLattice.{u2} β] (f : α -> β), (Function.Injective.{succ u1, succ u2} α β f) -> (forall (a : α) (b : α), Eq.{succ u2} β (f (Sup.sup.{u1} α _inst_1 a b)) (Sup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (CompleteLattice.toLattice.{u2} β _inst_7))) (f a) (f b))) -> (forall (a : α) (b : α), Eq.{succ u2} β (f (Inf.inf.{u1} α _inst_2 a b)) (Inf.inf.{u2} β (SemilatticeInf.toHasInf.{u2} β (Lattice.toSemilatticeInf.{u2} β (CompleteLattice.toLattice.{u2} β _inst_7))) (f a) (f b))) -> (forall (s : Set.{u1} α), Eq.{succ u2} β (f (SupSet.sSup.{u1} α _inst_3 s)) (iSup.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_7)) α (fun (a : α) => iSup.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_7)) (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) => f a)))) -> (forall (s : Set.{u1} α), Eq.{succ u2} β (f (InfSet.sInf.{u1} α _inst_4 s)) (iInf.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_7)) α (fun (a : α) => iInf.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_7)) (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) => f a)))) -> (Eq.{succ u2} β (f (Top.top.{u1} α _inst_5)) (Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β _inst_7))) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α _inst_6)) (Bot.bot.{u2} β (CompleteLattice.toHasBot.{u2} β _inst_7))) -> (CompleteLattice.{u1} α)
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Sup.{u1} α] [_inst_2 : Inf.{u1} α] [_inst_3 : SupSet.{u1} α] [_inst_4 : InfSet.{u1} α] [_inst_5 : Top.{u1} α] [_inst_6 : Bot.{u1} α] [_inst_7 : CompleteLattice.{u2} β] (f : α -> β), (Function.Injective.{succ u1, succ u2} α β f) -> (forall (a : α) (b : α), Eq.{succ u2} β (f (Sup.sup.{u1} α _inst_1 a b)) (Sup.sup.{u2} β (SemilatticeSup.toSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (CompleteLattice.toLattice.{u2} β _inst_7))) (f a) (f b))) -> (forall (a : α) (b : α), Eq.{succ u2} β (f (Inf.inf.{u1} α _inst_2 a b)) (Inf.inf.{u2} β (Lattice.toInf.{u2} β (CompleteLattice.toLattice.{u2} β _inst_7)) (f a) (f b))) -> (forall (s : Set.{u1} α), Eq.{succ u2} β (f (SupSet.supₛ.{u1} α _inst_3 s)) (supᵢ.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_7) α (fun (a : α) => supᵢ.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_7) (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) => f a)))) -> (forall (s : Set.{u1} α), Eq.{succ u2} β (f (InfSet.infₛ.{u1} α _inst_4 s)) (infᵢ.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_7) α (fun (a : α) => infᵢ.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_7) (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) => f a)))) -> (Eq.{succ u2} β (f (Top.top.{u1} α _inst_5)) (Top.top.{u2} β (CompleteLattice.toTop.{u2} β _inst_7))) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α _inst_6)) (Bot.bot.{u2} β (CompleteLattice.toBot.{u2} β _inst_7))) -> (CompleteLattice.{u1} α)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Sup.{u1} α] [_inst_2 : Inf.{u1} α] [_inst_3 : SupSet.{u1} α] [_inst_4 : InfSet.{u1} α] [_inst_5 : Top.{u1} α] [_inst_6 : Bot.{u1} α] [_inst_7 : CompleteLattice.{u2} β] (f : α -> β), (Function.Injective.{succ u1, succ u2} α β f) -> (forall (a : α) (b : α), Eq.{succ u2} β (f (Sup.sup.{u1} α _inst_1 a b)) (Sup.sup.{u2} β (SemilatticeSup.toSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (CompleteLattice.toLattice.{u2} β _inst_7))) (f a) (f b))) -> (forall (a : α) (b : α), Eq.{succ u2} β (f (Inf.inf.{u1} α _inst_2 a b)) (Inf.inf.{u2} β (Lattice.toInf.{u2} β (CompleteLattice.toLattice.{u2} β _inst_7)) (f a) (f b))) -> (forall (s : Set.{u1} α), Eq.{succ u2} β (f (SupSet.sSup.{u1} α _inst_3 s)) (iSup.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_7) α (fun (a : α) => iSup.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_7) (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) => f a)))) -> (forall (s : Set.{u1} α), Eq.{succ u2} β (f (InfSet.sInf.{u1} α _inst_4 s)) (iInf.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_7) α (fun (a : α) => iInf.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_7) (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) => f a)))) -> (Eq.{succ u2} β (f (Top.top.{u1} α _inst_5)) (Top.top.{u2} β (CompleteLattice.toTop.{u2} β _inst_7))) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α _inst_6)) (Bot.bot.{u2} β (CompleteLattice.toBot.{u2} β _inst_7))) -> (CompleteLattice.{u1} α)
 Case conversion may be inaccurate. Consider using '#align function.injective.complete_lattice Function.Injective.completeLatticeₓ'. -/
 -- See note [reducible non-instances]
 /-- Pullback a `complete_lattice` along an injection. -/
@@ -3825,17 +3825,17 @@ Case conversion may be inaccurate. Consider using '#align function.injective.com
 protected def Function.Injective.completeLattice [Sup α] [Inf α] [SupSet α] [InfSet α] [Top α]
     [Bot α] [CompleteLattice β] (f : α → β) (hf : Function.Injective f)
     (map_sup : ∀ a b, f (a ⊔ b) = f a ⊔ f b) (map_inf : ∀ a b, f (a ⊓ b) = f a ⊓ f b)
-    (map_Sup : ∀ s, f (supₛ s) = ⨆ a ∈ s, f a) (map_Inf : ∀ s, f (infₛ s) = ⨅ a ∈ s, f a)
+    (map_Sup : ∀ s, f (sSup s) = ⨆ a ∈ s, f a) (map_Inf : ∀ s, f (sInf s) = ⨅ a ∈ s, f a)
     (map_top : f ⊤ = ⊤) (map_bot : f ⊥ = ⊥) : CompleteLattice α :=
   {-- we cannot use bounded_order.lift here as the `has_le` instance doesn't exist yet
         hf.Lattice
       f map_sup map_inf with
-    supₛ := supₛ
-    le_sup := fun s a h => (le_supᵢ₂ a h).trans (map_Sup _).ge
-    sup_le := fun s a h => (map_Sup _).trans_le <| supᵢ₂_le h
-    infₛ := infₛ
-    inf_le := fun s a h => (map_Inf _).trans_le <| infᵢ₂_le a h
-    le_inf := fun s a h => (le_infᵢ₂ h).trans (map_Inf _).ge
+    sSup := sSup
+    le_sup := fun s a h => (le_iSup₂ a h).trans (map_Sup _).ge
+    sup_le := fun s a h => (map_Sup _).trans_le <| iSup₂_le h
+    sInf := sInf
+    inf_le := fun s a h => (map_Inf _).trans_le <| iInf₂_le a h
+    le_inf := fun s a h => (le_iInf₂ h).trans (map_Inf _).ge
     top := ⊤
     le_top := fun a => (@le_top β _ _ _).trans map_top.ge
     bot := ⊥

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

@@ -509,10 +509,10 @@ def completeLatticeOfCompleteSemilatticeSup (α : Type _) [CompleteSemilatticeSu
 -/
 
 #print CompleteLinearOrder /-
-/- ./././Mathport/Syntax/Translate/Command.lean:417:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure -/
 /-- A complete linear order is a linear order whose lattice structure is complete. -/
 class CompleteLinearOrder (α : Type _) extends CompleteLattice α,
-  "./././Mathport/Syntax/Translate/Command.lean:417:11: unsupported: advanced extends in structure"
+  "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure"
 #align complete_linear_order CompleteLinearOrder
 -/
 

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

@@ -1706,7 +1706,7 @@ theorem Antitone.le_map_infₛ [CompleteLattice β] {s : Set α} {f : α → β}
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (x : ι -> α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (supᵢ.{u1, u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => x i))) (supᵢ.{u2, u3} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (x i)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : CompleteLattice.{u3} β] (f : OrderIso.{u2, u3} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))))) (x : ι -> α), Eq.{succ u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => x i))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} α β)) (RelEmbedding.toEmbedding.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f)) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => x i))) (supᵢ.{u3, u1} β (CompleteLattice.toSupSet.{u3} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} α β)) (RelEmbedding.toEmbedding.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f)) (x i)))
+  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : CompleteLattice.{u3} β] (f : OrderIso.{u2, u3} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))))) (x : ι -> α), Eq.{succ u3} β (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => x i))) (supᵢ.{u3, u1} β (CompleteLattice.toSupSet.{u3} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (x i)))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_supr OrderIso.map_supᵢₓ'. -/
 theorem OrderIso.map_supᵢ [CompleteLattice β] (f : α ≃o β) (x : ι → α) :
     f (⨆ i, x i) = ⨆ i, f (x i) :=
@@ -1717,7 +1717,7 @@ theorem OrderIso.map_supᵢ [CompleteLattice β] (f : α ≃o β) (x : ι → α
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (x : ι -> α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (infᵢ.{u1, u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => x i))) (infᵢ.{u2, u3} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (x i)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : CompleteLattice.{u3} β] (f : OrderIso.{u2, u3} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))))) (x : ι -> α), Eq.{succ u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => x i))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} α β)) (RelEmbedding.toEmbedding.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => x i))) (infᵢ.{u3, u1} β (CompleteLattice.toInfSet.{u3} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u2, succ u3} (Function.Embedding.{succ u2, succ u3} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u3} α β)) (RelEmbedding.toEmbedding.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f)) (x i)))
+  forall {α : Type.{u2}} {β : Type.{u3}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] [_inst_2 : CompleteLattice.{u3} β] (f : OrderIso.{u2, u3} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2))))) (x : ι -> α), Eq.{succ u3} β (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => x i))) (infᵢ.{u3, u1} β (CompleteLattice.toInfSet.{u3} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} 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 u3, u2, u3} (RelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u3} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (x i)))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_infi OrderIso.map_infᵢₓ'. -/
 theorem OrderIso.map_infᵢ [CompleteLattice β] (f : α ≃o β) (x : ι → α) :
     f (⨅ i, x i) = ⨅ i, f (x i) :=
@@ -1728,7 +1728,7 @@ theorem OrderIso.map_infᵢ [CompleteLattice β] (f : α ≃o β) (x : ι → α
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s)) (supᵢ.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) α (fun (a : α) => supᵢ.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_2)) (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) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f a)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)) (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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f)) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)) (supᵢ.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_2) α (fun (a : α) => supᵢ.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_2) (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) => 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f)) a)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s)) (supᵢ.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_2) α (fun (a : α) => supᵢ.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_2) (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) => 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} 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 order_iso.map_Sup OrderIso.map_supₛₓ'. -/
 theorem OrderIso.map_supₛ [CompleteLattice β] (f : α ≃o β) (s : Set α) :
     f (supₛ s) = ⨆ a ∈ s, f a := by simp only [supₛ_eq_supᵢ, OrderIso.map_supᵢ]
@@ -1738,7 +1738,7 @@ theorem OrderIso.map_supₛ [CompleteLattice β] (f : α ≃o β) (s : Set α) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)) (infᵢ.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) α (fun (a : α) => infᵢ.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)) (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) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))))) f a)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)) (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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f)) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)) (infᵢ.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_2) α (fun (a : α) => infᵢ.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_2) (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) => 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) f)) a)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (f : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (s : Set.{u1} α), Eq.{succ u2} 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) f (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)) (infᵢ.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_2) α (fun (a : α) => infᵢ.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_2) (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) => 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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} 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 order_iso.map_Inf OrderIso.map_infₛₓ'. -/
 theorem OrderIso.map_infₛ [CompleteLattice β] (f : α ≃o β) (s : Set α) :
     f (infₛ s) = ⨅ a ∈ s, f a :=

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

@@ -571,7 +571,7 @@ theorem ofDual_infₛ (s : Set αᵒᵈ) : ofDual (infₛ s) = supₛ (toDual 
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α), Eq.{succ u1} (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => f i))) (infᵢ.{u1, u2} (OrderDual.{u1} α) (OrderDual.hasInf.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1))) ι (fun (i : ι) => coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) (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} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => OrderDual.{u2} α) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (infᵢ.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (f i)))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (infᵢ.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (f i)))
 Case conversion may be inaccurate. Consider using '#align to_dual_supr toDual_supᵢₓ'. -/
 @[simp]
 theorem toDual_supᵢ (f : ι → α) : toDual (⨆ i, f i) = ⨅ i, toDual (f i) :=
@@ -582,7 +582,7 @@ theorem toDual_supᵢ (f : ι → α) : toDual (⨆ i, f i) = ⨅ i, toDual (f i
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α), Eq.{succ u1} (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => f i))) (supᵢ.{u1, u2} (OrderDual.{u1} α) (OrderDual.hasSup.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) ι (fun (i : ι) => coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α) (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} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => OrderDual.{u2} α) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (supᵢ.{u2, u1} (OrderDual.{u2} α) (OrderDual.supSet.{u2} α (CompleteLattice.toInfSet.{u2} α _inst_1)) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (f i)))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i))) (supᵢ.{u2, u1} (OrderDual.{u2} α) (OrderDual.supSet.{u2} α (CompleteLattice.toInfSet.{u2} α _inst_1)) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α) (f i)))
 Case conversion may be inaccurate. Consider using '#align to_dual_infi toDual_infᵢₓ'. -/
 @[simp]
 theorem toDual_infᵢ (f : ι → α) : toDual (⨅ i, f i) = ⨆ i, toDual (f i) :=
@@ -593,7 +593,7 @@ theorem toDual_infᵢ (f : ι → α) : toDual (⨅ i, f i) = ⨆ i, toDual (f i
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> (OrderDual.{u1} α)), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α) (supᵢ.{u1, u2} (OrderDual.{u1} α) (OrderDual.hasSup.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1))) ι (fun (i : ι) => f i))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α) (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> (OrderDual.{u2} α)), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : OrderDual.{u2} α) => α) (supᵢ.{u2, u1} (OrderDual.{u2} α) (OrderDual.supSet.{u2} α (CompleteLattice.toInfSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (supᵢ.{u2, u1} (OrderDual.{u2} α) (OrderDual.supSet.{u2} α (CompleteLattice.toInfSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (f i)))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> (OrderDual.{u2} α)), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) (supᵢ.{u2, u1} (OrderDual.{u2} α) (OrderDual.supSet.{u2} α (CompleteLattice.toInfSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (supᵢ.{u2, u1} (OrderDual.{u2} α) (OrderDual.supSet.{u2} α (CompleteLattice.toInfSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (f i)))
 Case conversion may be inaccurate. Consider using '#align of_dual_supr ofDual_supᵢₓ'. -/
 @[simp]
 theorem ofDual_supᵢ (f : ι → αᵒᵈ) : ofDual (⨆ i, f i) = ⨅ i, ofDual (f i) :=
@@ -604,7 +604,7 @@ theorem ofDual_supᵢ (f : ι → αᵒᵈ) : ofDual (⨆ i, f i) = ⨅ i, ofDua
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> (OrderDual.{u1} α)), Eq.{succ u1} α (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α) (infᵢ.{u1, u2} (OrderDual.{u1} α) (OrderDual.hasInf.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1))) ι (fun (i : ι) => f i))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α) (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> (OrderDual.{u2} α)), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : OrderDual.{u2} α) => α) (infᵢ.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (infᵢ.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (f i)))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> (OrderDual.{u2} α)), Eq.{succ u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) (infᵢ.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (infᵢ.{u2, u1} (OrderDual.{u2} α) (OrderDual.infSet.{u2} α (CompleteLattice.toSupSet.{u2} α _inst_1)) ι (fun (i : ι) => f i))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α) (f i)))
 Case conversion may be inaccurate. Consider using '#align of_dual_infi ofDual_infᵢₓ'. -/
 @[simp]
 theorem ofDual_infᵢ (f : ι → αᵒᵈ) : ofDual (⨅ i, f i) = ⨆ i, ofDual (f i) :=
@@ -988,7 +988,7 @@ theorem Function.Surjective.supᵢ_comp {f : ι → ι'} (hf : Surjective f) (g
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : SupSet.{u1} α] {g : ι' -> α} (e : Equiv.{u2, u3} ι ι'), Eq.{succ u1} α (supᵢ.{u1, u2} α _inst_1 ι (fun (x : ι) => g (coeFn.{max 1 (imax u2 u3) (imax u3 u2), imax u2 u3} (Equiv.{u2, u3} ι ι') (fun (_x : Equiv.{u2, u3} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{u2, u3} ι ι') e x))) (supᵢ.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), Eq.{succ u1} α (supᵢ.{u1, u3} α _inst_1 ι (fun (x : ι) => g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x))) (supᵢ.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y))
+  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), Eq.{succ u1} α (supᵢ.{u1, u3} α _inst_1 ι (fun (x : ι) => g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x))) (supᵢ.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y))
 Case conversion may be inaccurate. Consider using '#align equiv.supr_comp Equiv.supᵢ_compₓ'. -/
 theorem Equiv.supᵢ_comp {g : ι' → α} (e : ι ≃ ι') : (⨆ x, g (e x)) = ⨆ y, g y :=
   e.Surjective.supᵢ_comp _
@@ -1011,7 +1011,7 @@ protected theorem Function.Surjective.supᵢ_congr {g : ι' → α} (h : ι →
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u2, u3} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (coeFn.{max 1 (imax u2 u3) (imax u3 u2), imax u2 u3} (Equiv.{u2, u3} ι ι') (fun (_x : Equiv.{u2, u3} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{u2, u3} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (supᵢ.{u1, u2} α _inst_1 ι (fun (x : ι) => f x)) (supᵢ.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (supᵢ.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (supᵢ.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
+  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : SupSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (supᵢ.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (supᵢ.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
 Case conversion may be inaccurate. Consider using '#align equiv.supr_congr Equiv.supᵢ_congrₓ'. -/
 protected theorem Equiv.supᵢ_congr {g : ι' → α} (e : ι ≃ ι') (h : ∀ x, g (e x) = f x) :
     (⨆ x, f x) = ⨆ y, g y :=
@@ -1108,7 +1108,7 @@ theorem Function.Surjective.infᵢ_comp {f : ι → ι'} (hf : Surjective f) (g
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : InfSet.{u1} α] {g : ι' -> α} (e : Equiv.{u2, u3} ι ι'), Eq.{succ u1} α (infᵢ.{u1, u2} α _inst_1 ι (fun (x : ι) => g (coeFn.{max 1 (imax u2 u3) (imax u3 u2), imax u2 u3} (Equiv.{u2, u3} ι ι') (fun (_x : Equiv.{u2, u3} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{u2, u3} ι ι') e x))) (infᵢ.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), Eq.{succ u1} α (infᵢ.{u1, u3} α _inst_1 ι (fun (x : ι) => g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x))) (infᵢ.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y))
+  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), Eq.{succ u1} α (infᵢ.{u1, u3} α _inst_1 ι (fun (x : ι) => g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x))) (infᵢ.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y))
 Case conversion may be inaccurate. Consider using '#align equiv.infi_comp Equiv.infᵢ_compₓ'. -/
 theorem Equiv.infᵢ_comp {g : ι' → α} (e : ι ≃ ι') : (⨅ x, g (e x)) = ⨅ y, g y :=
   @Equiv.supᵢ_comp αᵒᵈ _ _ _ _ e
@@ -1129,7 +1129,7 @@ protected theorem Function.Surjective.infᵢ_congr {g : ι' → α} (h : ι →
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} {ι' : Sort.{u3}} [_inst_1 : InfSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u2, u3} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (coeFn.{max 1 (imax u2 u3) (imax u3 u2), imax u2 u3} (Equiv.{u2, u3} ι ι') (fun (_x : Equiv.{u2, u3} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{u2, u3} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (infᵢ.{u1, u2} α _inst_1 ι (fun (x : ι) => f x)) (infᵢ.{u1, u3} α _inst_1 ι' (fun (y : ι') => g y)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (infᵢ.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (infᵢ.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
+  forall {α : Type.{u1}} {ι : Sort.{u3}} {ι' : Sort.{u2}} [_inst_1 : InfSet.{u1} α] {f : ι -> α} {g : ι' -> α} (e : Equiv.{u3, u2} ι ι'), (forall (x : ι), Eq.{succ u1} α (g (FunLike.coe.{max (max 1 u3) u2, u3, u2} (Equiv.{u3, u2} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{u3, u2} ι ι') e x)) (f x)) -> (Eq.{succ u1} α (infᵢ.{u1, u3} α _inst_1 ι (fun (x : ι) => f x)) (infᵢ.{u1, u2} α _inst_1 ι' (fun (y : ι') => g y)))
 Case conversion may be inaccurate. Consider using '#align equiv.infi_congr Equiv.infᵢ_congrₓ'. -/
 protected theorem Equiv.infᵢ_congr {g : ι' → α} (e : ι ≃ ι') (h : ∀ x, g (e x) = f x) :
     (⨅ x, f x) = ⨅ y, g y :=

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

@@ -623,9 +623,9 @@ theorem infₛ_le_supₛ (hs : s.Nonempty) : infₛ s ≤ supₛ s :=
 
 /- warning: Sup_union -> supₛ_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align Sup_union supₛ_unionₓ'. -/
 theorem supₛ_union {s t : Set α} : supₛ (s ∪ t) = supₛ s ⊔ supₛ t :=
   ((isLUB_supₛ s).union (isLUB_supₛ t)).supₛ_eq
@@ -633,9 +633,9 @@ theorem supₛ_union {s t : Set α} : supₛ (s ∪ t) = supₛ s ⊔ supₛ t :
 
 /- warning: Inf_union -> infₛ_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align Inf_union infₛ_unionₓ'. -/
 theorem infₛ_union {s t : Set α} : infₛ (s ∪ t) = infₛ s ⊓ infₛ t :=
   ((isGLB_infₛ s).union (isGLB_infₛ t)).infₛ_eq
@@ -643,9 +643,9 @@ theorem infₛ_union {s t : Set α} : infₛ (s ∪ t) = infₛ s ⊓ infₛ t :
 
 /- warning: Sup_inter_le -> supₛ_inter_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{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)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{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)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{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) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{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) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align Sup_inter_le supₛ_inter_leₓ'. -/
 theorem supₛ_inter_le {s t : Set α} : supₛ (s ∩ t) ≤ supₛ s ⊓ supₛ t :=
   supₛ_le fun b hb => le_inf (le_supₛ hb.1) (le_supₛ hb.2)
@@ -653,9 +653,9 @@ theorem supₛ_inter_le {s t : Set α} : supₛ (s ∩ t) ≤ supₛ s ⊓ sup
 
 /- warning: le_Inf_inter -> le_infₛ_inter is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) t)) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) t)) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{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 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) t)) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) t)) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t))
 Case conversion may be inaccurate. Consider using '#align le_Inf_inter le_infₛ_interₓ'. -/
 theorem le_infₛ_inter {s t : Set α} : infₛ s ⊔ infₛ t ≤ infₛ (s ∩ t) :=
   @supₛ_inter_le αᵒᵈ _ _ _
@@ -707,9 +707,9 @@ theorem infₛ_univ : infₛ univ = (⊥ : α) :=
 
 /- warning: Sup_insert -> supₛ_insert is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align Sup_insert supₛ_insertₓ'. -/
 -- TODO(Jeremy): get this automatically
 @[simp]
@@ -719,9 +719,9 @@ theorem supₛ_insert {a : α} {s : Set α} : supₛ (insert a s) = a ⊔ supₛ
 
 /- warning: Inf_insert -> infₛ_insert is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s)) (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align Inf_insert infₛ_insertₓ'. -/
 @[simp]
 theorem infₛ_insert {a : α} {s : Set α} : infₛ (insert a s) = a ⊓ infₛ s :=
@@ -773,9 +773,9 @@ theorem infₛ_diff_singleton_top (s : Set α) : infₛ (s \ {⊤}) = infₛ s :
 
 /- warning: Sup_pair -> supₛ_pair is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {b : α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {b : α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {b : α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {b : α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)
 Case conversion may be inaccurate. Consider using '#align Sup_pair supₛ_pairₓ'. -/
 theorem supₛ_pair {a b : α} : supₛ {a, b} = a ⊔ b :=
   (@isLUB_pair α _ a b).supₛ_eq
@@ -783,9 +783,9 @@ theorem supₛ_pair {a b : α} : supₛ {a, b} = a ⊔ b :=
 
 /- warning: Inf_pair -> infₛ_pair is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {b : α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {b : α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {b : α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a b)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {b : α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a b)
 Case conversion may be inaccurate. Consider using '#align Inf_pair infₛ_pairₓ'. -/
 theorem infₛ_pair {a b : α} : infₛ {a, b} = a ⊓ b :=
   (@isGLB_pair α _ a b).infₛ_eq
@@ -2286,9 +2286,9 @@ theorem binfᵢ_const {ι : Sort _} {a : α} {s : Set ι} (hs : s.Nonempty) : (
 
 /- warning: supr_sup_eq -> supᵢ_sup_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) (g x))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => f x)) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => g x)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) (g x))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => f x)) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => g x)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, Eq.{succ u2} α (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (x : ι) => HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f x) (g x))) (HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (x : ι) => f x)) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (x : ι) => g x)))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, Eq.{succ u2} α (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (x : ι) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f x) (g x))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (x : ι) => f x)) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (x : ι) => g x)))
 Case conversion may be inaccurate. Consider using '#align supr_sup_eq supᵢ_sup_eqₓ'. -/
 theorem supᵢ_sup_eq : (⨆ x, f x ⊔ g x) = (⨆ x, f x) ⊔ ⨆ x, g x :=
   le_antisymm (supᵢ_le fun i => sup_le_sup (le_supᵢ _ _) <| le_supᵢ _ _)
@@ -2297,9 +2297,9 @@ theorem supᵢ_sup_eq : (⨆ x, f x ⊔ g x) = (⨆ x, f x) ⊔ ⨆ x, g x :=
 
 /- warning: infi_inf_eq -> infᵢ_inf_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) (g x))) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f x)) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => g x)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) (g x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f x)) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => g x)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, Eq.{succ u2} α (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => HasInf.inf.{u2} α (Lattice.toHasInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f x) (g x))) (HasInf.inf.{u2} α (Lattice.toHasInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => f x)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => g x)))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, Eq.{succ u2} α (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f x) (g x))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => f x)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (x : ι) => g x)))
 Case conversion may be inaccurate. Consider using '#align infi_inf_eq infᵢ_inf_eqₓ'. -/
 theorem infᵢ_inf_eq : (⨅ x, f x ⊓ g x) = (⨅ x, f x) ⊓ ⨅ x, g x :=
   @supᵢ_sup_eq αᵒᵈ _ _ _ _
@@ -2307,9 +2307,9 @@ theorem infᵢ_inf_eq : (⨅ x, f x ⊓ g x) = (⨅ x, f x) ⊓ ⨅ x, g x :=
 
 /- warning: supr_sup -> supᵢ_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => f x)) a) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => f x)) a) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) a))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (x : ι) => f x)) a) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (x : ι) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (x : ι) => f x)) a) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (x : ι) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) a))
 Case conversion may be inaccurate. Consider using '#align supr_sup supᵢ_supₓ'. -/
 /- TODO: here is another example where more flexible pattern matching
    might help.
@@ -2325,9 +2325,9 @@ theorem supᵢ_sup [Nonempty ι] {f : ι → α} {a : α} : (⨆ x, f x) ⊔ a =
 
 /- warning: infi_inf -> infᵢ_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f x)) a) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f x)) a) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f x) a))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (x : ι) => f x)) a) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (x : ι) => HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f x) a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (x : ι) => f x)) a) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (x : ι) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f x) a))
 Case conversion may be inaccurate. Consider using '#align infi_inf infᵢ_infₓ'. -/
 theorem infᵢ_inf [Nonempty ι] {f : ι → α} {a : α} : (⨅ x, f x) ⊓ a = ⨅ x, f x ⊓ a := by
   rw [infᵢ_inf_eq, infᵢ_const]
@@ -2335,9 +2335,9 @@ theorem infᵢ_inf [Nonempty ι] {f : ι → α} {a : α} : (⨅ x, f x) ⊓ a =
 
 /- warning: sup_supr -> sup_supᵢ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => f x))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f x)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => f x))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (x : ι) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f x)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (x : ι) => f x))) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (x : ι) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f x)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (x : ι) => f x))) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (x : ι) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f x)))
 Case conversion may be inaccurate. Consider using '#align sup_supr sup_supᵢₓ'. -/
 theorem sup_supᵢ [Nonempty ι] {f : ι → α} {a : α} : (a ⊔ ⨆ x, f x) = ⨆ x, a ⊔ f x := by
   rw [supᵢ_sup_eq, supᵢ_const]
@@ -2345,9 +2345,9 @@ theorem sup_supᵢ [Nonempty ι] {f : ι → α} {a : α} : (a ⊔ ⨆ x, f x) =
 
 /- warning: inf_infi -> inf_infᵢ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f x))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f x)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => f x))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (x : ι) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f x)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (x : ι) => f x))) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (x : ι) => HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (f x)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (x : ι) => f x))) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (x : ι) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (f x)))
 Case conversion may be inaccurate. Consider using '#align inf_infi inf_infᵢₓ'. -/
 theorem inf_infᵢ [Nonempty ι] {f : ι → α} {a : α} : (a ⊓ ⨅ x, f x) = ⨅ x, a ⊓ f x := by
   rw [infᵢ_inf_eq, infᵢ_const]
@@ -2355,9 +2355,9 @@ theorem inf_infᵢ [Nonempty ι] {f : ι → α} {a : α} : (a ⊓ ⨅ x, f x) =
 
 /- warning: bsupr_sup -> bsupᵢ_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) a) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i h) a))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) a) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i h) a))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => f i h))) a) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i h) a))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => f i h))) a) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i h) a))))
 Case conversion may be inaccurate. Consider using '#align bsupr_sup bsupᵢ_supₓ'. -/
 theorem bsupᵢ_sup {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
     (⨆ (i) (h : p i), f i h) ⊔ a = ⨆ (i) (h : p i), f i h ⊔ a := by
@@ -2369,9 +2369,9 @@ theorem bsupᵢ_sup {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃
 
 /- warning: sup_bsupr -> sup_bsupᵢ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h)))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f i h)))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h)))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f i h)))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => f i h)))) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f i h)))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => f i h)))) (supᵢ.{u1, u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (p i) (fun (h : p i) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f i h)))))
 Case conversion may be inaccurate. Consider using '#align sup_bsupr sup_bsupᵢₓ'. -/
 theorem sup_bsupᵢ {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
     (a ⊔ ⨆ (i) (h : p i), f i h) = ⨆ (i) (h : p i), a ⊔ f i h := by
@@ -2380,9 +2380,9 @@ theorem sup_bsupᵢ {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃
 
 /- warning: binfi_inf -> binfᵢ_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) a) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i h) a))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) a) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i h) a))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => f i h))) a) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f i h) a))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => f i h))) a) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f i h) a))))
 Case conversion may be inaccurate. Consider using '#align binfi_inf binfᵢ_infₓ'. -/
 theorem binfᵢ_inf {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
     (⨅ (i) (h : p i), f i h) ⊓ a = ⨅ (i) (h : p i), f i h ⊓ a :=
@@ -2391,9 +2391,9 @@ theorem binfᵢ_inf {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃
 
 /- warning: inf_binfi -> inf_binfᵢ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h)))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f i h)))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h)))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (f i h)))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => f i h)))) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (f i h)))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α} {a : α}, (Exists.{u2} ι (fun (i : ι) => p i)) -> (Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => f i h)))) (infᵢ.{u1, u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (p i) (fun (h : p i) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (f i h)))))
 Case conversion may be inaccurate. Consider using '#align inf_binfi inf_binfᵢₓ'. -/
 theorem inf_binfᵢ {p : ι → Prop} {f : ∀ i, p i → α} {a : α} (h : ∃ i, p i) :
     (a ⊓ ⨅ (i) (h : p i), f i h) = ⨅ (i) (h : p i), a ⊓ f i h :=
@@ -2517,9 +2517,9 @@ theorem infᵢ_and' {p q : Prop} {s : p → q → α} :
 
 /- warning: supr_or -> supᵢ_or is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (Or p q) -> α}, Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Or p q) (fun (x : Or p q) => s x)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) p (fun (i : p) => s (Or.inl p q i))) (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) q (fun (j : q) => s (Or.inr p q j))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (Or p q) -> α}, Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Or p q) (fun (x : Or p q) => s x)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) p (fun (i : p) => s (Or.inl p q i))) (supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) q (fun (j : q) => s (Or.inr p q j))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (Or p q) -> α}, Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Or p q) (fun (x : Or p q) => s x)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) p (fun (i : p) => s (Or.inl p q i))) (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) q (fun (j : q) => s (Or.inr p q j))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (Or p q) -> α}, Eq.{succ u1} α (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Or p q) (fun (x : Or p q) => s x)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) p (fun (i : p) => s (Or.inl p q i))) (supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) q (fun (j : q) => s (Or.inr p q j))))
 Case conversion may be inaccurate. Consider using '#align supr_or supᵢ_orₓ'. -/
 theorem supᵢ_or {p q : Prop} {s : p ∨ q → α} :
     (⨆ x, s x) = (⨆ i, s (Or.inl i)) ⊔ ⨆ j, s (Or.inr j) :=
@@ -2533,9 +2533,9 @@ theorem supᵢ_or {p q : Prop} {s : p ∨ q → α} :
 
 /- warning: infi_or -> infᵢ_or is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (Or p q) -> α}, Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Or p q) (fun (x : Or p q) => s x)) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) p (fun (i : p) => s (Or.inl p q i))) (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) q (fun (j : q) => s (Or.inr p q j))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (Or p q) -> α}, Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Or p q) (fun (x : Or p q) => s x)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) p (fun (i : p) => s (Or.inl p q i))) (infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) q (fun (j : q) => s (Or.inr p q j))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (Or p q) -> α}, Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Or p q) (fun (x : Or p q) => s x)) (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) p (fun (i : p) => s (Or.inl p q i))) (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) q (fun (j : q) => s (Or.inr p q j))))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {p : Prop} {q : Prop} {s : (Or p q) -> α}, Eq.{succ u1} α (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Or p q) (fun (x : Or p q) => s x)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) p (fun (i : p) => s (Or.inl p q i))) (infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) q (fun (j : q) => s (Or.inr p q j))))
 Case conversion may be inaccurate. Consider using '#align infi_or infᵢ_orₓ'. -/
 theorem infᵢ_or {p q : Prop} {s : p ∨ q → α} :
     (⨅ x, s x) = (⨅ i, s (Or.inl i)) ⊓ ⨅ j, s (Or.inr j) :=
@@ -2548,9 +2548,9 @@ variable (p : ι → Prop) [DecidablePred p]
 
 /- warning: supr_dite -> supᵢ_dite is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u2} ι p] (f : forall (i : ι), (p i) -> α) (g : forall (i : ι), (Not (p i)) -> α), Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => dite.{succ u1} α (p i) (_inst_2 i) (fun (h : p i) => f i h) (fun (h : Not (p i)) => g i h))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => g i h))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u2} ι p] (f : forall (i : ι), (p i) -> α) (g : forall (i : ι), (Not (p i)) -> α), Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => dite.{succ u1} α (p i) (_inst_2 i) (fun (h : p i) => f i h) (fun (h : Not (p i)) => g i h))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => g i h))))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u1} ι p] (f : forall (i : ι), (p i) -> α) (g : forall (i : ι), (Not (p i)) -> α), Eq.{succ u2} α (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => dite.{succ u2} α (p i) (_inst_2 i) (fun (h : p i) => f i h) (fun (h : Not (p i)) => g i h))) (HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i h))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => g i h))))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u1} ι p] (f : forall (i : ι), (p i) -> α) (g : forall (i : ι), (Not (p i)) -> α), Eq.{succ u2} α (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => dite.{succ u2} α (p i) (_inst_2 i) (fun (h : p i) => f i h) (fun (h : Not (p i)) => g i h))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i h))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => g i h))))
 Case conversion may be inaccurate. Consider using '#align supr_dite supᵢ_diteₓ'. -/
 theorem supᵢ_dite (f : ∀ i, p i → α) (g : ∀ i, ¬p i → α) :
     (⨆ i, if h : p i then f i h else g i h) = (⨆ (i) (h : p i), f i h) ⊔ ⨆ (i) (h : ¬p i), g i h :=
@@ -2562,9 +2562,9 @@ theorem supᵢ_dite (f : ∀ i, p i → α) (g : ∀ i, ¬p i → α) :
 
 /- warning: infi_dite -> infᵢ_dite is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u2} ι p] (f : forall (i : ι), (p i) -> α) (g : forall (i : ι), (Not (p i)) -> α), Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => dite.{succ u1} α (p i) (_inst_2 i) (fun (h : p i) => f i h) (fun (h : Not (p i)) => g i h))) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => g i h))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u2} ι p] (f : forall (i : ι), (p i) -> α) (g : forall (i : ι), (Not (p i)) -> α), Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => dite.{succ u1} α (p i) (_inst_2 i) (fun (h : p i) => f i h) (fun (h : Not (p i)) => g i h))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i h))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => g i h))))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u1} ι p] (f : forall (i : ι), (p i) -> α) (g : forall (i : ι), (Not (p i)) -> α), Eq.{succ u2} α (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => dite.{succ u2} α (p i) (_inst_2 i) (fun (h : p i) => f i h) (fun (h : Not (p i)) => g i h))) (HasInf.inf.{u2} α (Lattice.toHasInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i h))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => g i h))))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u1} ι p] (f : forall (i : ι), (p i) -> α) (g : forall (i : ι), (Not (p i)) -> α), Eq.{succ u2} α (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => dite.{succ u2} α (p i) (_inst_2 i) (fun (h : p i) => f i h) (fun (h : Not (p i)) => g i h))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i h))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => g i h))))
 Case conversion may be inaccurate. Consider using '#align infi_dite infᵢ_diteₓ'. -/
 theorem infᵢ_dite (f : ∀ i, p i → α) (g : ∀ i, ¬p i → α) :
     (⨅ i, if h : p i then f i h else g i h) = (⨅ (i) (h : p i), f i h) ⊓ ⨅ (i) (h : ¬p i), g i h :=
@@ -2573,9 +2573,9 @@ theorem infᵢ_dite (f : ∀ i, p i → α) (g : ∀ i, ¬p i → α) :
 
 /- warning: supr_ite -> supᵢ_ite is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u2} ι p] (f : ι -> α) (g : ι -> α), Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => ite.{succ u1} α (p i) (_inst_2 i) (f i) (g i))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => g i))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u2} ι p] (f : ι -> α) (g : ι -> α), Eq.{succ u1} α (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => ite.{succ u1} α (p i) (_inst_2 i) (f i) (g i))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (supᵢ.{u1, u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => g i))))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u1} ι p] (f : ι -> α) (g : ι -> α), Eq.{succ u2} α (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => ite.{succ u2} α (p i) (_inst_2 i) (f i) (g i))) (HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => g i))))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u1} ι p] (f : ι -> α) (g : ι -> α), Eq.{succ u2} α (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => ite.{succ u2} α (p i) (_inst_2 i) (f i) (g i))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => g i))))
 Case conversion may be inaccurate. Consider using '#align supr_ite supᵢ_iteₓ'. -/
 theorem supᵢ_ite (f g : ι → α) :
     (⨆ i, if p i then f i else g i) = (⨆ (i) (h : p i), f i) ⊔ ⨆ (i) (h : ¬p i), g i :=
@@ -2584,9 +2584,9 @@ theorem supᵢ_ite (f g : ι → α) :
 
 /- warning: infi_ite -> infᵢ_ite is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u2} ι p] (f : ι -> α) (g : ι -> α), Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => ite.{succ u1} α (p i) (_inst_2 i) (f i) (g i))) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => g i))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u2} ι p] (f : ι -> α) (g : ι -> α), Eq.{succ u1} α (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => ite.{succ u1} α (p i) (_inst_2 i) (f i) (g i))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => g i))))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u1} ι p] (f : ι -> α) (g : ι -> α), Eq.{succ u2} α (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => ite.{succ u2} α (p i) (_inst_2 i) (f i) (g i))) (HasInf.inf.{u2} α (Lattice.toHasInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => g i))))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (p : ι -> Prop) [_inst_2 : DecidablePred.{u1} ι p] (f : ι -> α) (g : ι -> α), Eq.{succ u2} α (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => ite.{succ u2} α (p i) (_inst_2 i) (f i) (g i))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => g i))))
 Case conversion may be inaccurate. Consider using '#align infi_ite infᵢ_iteₓ'. -/
 theorem infᵢ_ite (f g : ι → α) :
     (⨅ i, if p i then f i else g i) = (⨅ (i) (h : p i), f i) ⊓ ⨅ (i) (h : ¬p i), g i :=
@@ -2676,9 +2676,9 @@ theorem infᵢ_univ {f : β → α} : (⨅ x ∈ (univ : Set β), f x) = ⨅ x,
 
 /- warning: supr_union -> supᵢ_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.hasUnion.{u2} β) s t)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.hasUnion.{u2} β) s t)) => f x))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) => f x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.hasUnion.{u2} β) s t)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.hasUnion.{u2} β) s t)) => f x))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) => f x))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.instUnionSet.{u2} β) s t)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.instUnionSet.{u2} β) s t)) => f x))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) => f x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.instUnionSet.{u2} β) s t)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.instUnionSet.{u2} β) s t)) => f x))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) => f x))))
 Case conversion may be inaccurate. Consider using '#align supr_union supᵢ_unionₓ'. -/
 theorem supᵢ_union {f : β → α} {s t : Set β} : (⨆ x ∈ s ∪ t, f x) = (⨆ x ∈ s, f x) ⊔ ⨆ x ∈ t, f x :=
   by simp_rw [mem_union, supᵢ_or, supᵢ_sup_eq]
@@ -2686,9 +2686,9 @@ theorem supᵢ_union {f : β → α} {s t : Set β} : (⨆ x ∈ s ∪ t, f x) =
 
 /- warning: infi_union -> infᵢ_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.hasUnion.{u2} β) s t)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.hasUnion.{u2} β) s t)) => f x))) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) => f x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.hasUnion.{u2} β) s t)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.hasUnion.{u2} β) s t)) => f x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x t) => f x))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.instUnionSet.{u2} β) s t)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.instUnionSet.{u2} β) s t)) => f x))) (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) => f x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {t : Set.{u2} β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.instUnionSet.{u2} β) s t)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Union.union.{u2} (Set.{u2} β) (Set.instUnionSet.{u2} β) s t)) => f x))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x t) => f x))))
 Case conversion may be inaccurate. Consider using '#align infi_union infᵢ_unionₓ'. -/
 theorem infᵢ_union {f : β → α} {s t : Set β} : (⨅ x ∈ s ∪ t, f x) = (⨅ x ∈ s, f x) ⊓ ⨅ x ∈ t, f x :=
   @supᵢ_union αᵒᵈ _ _ _ _ _
@@ -2696,9 +2696,9 @@ theorem infᵢ_union {f : β → α} {s t : Set β} : (⨅ x ∈ s ∪ t, f x) =
 
 /- warning: supr_split -> supᵢ_split is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : β -> α) (p : β -> Prop), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => f i)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => f i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : β -> α) (p : β -> Prop), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => f i)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => f i))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (p : β -> Prop), Eq.{succ u2} α (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => f i)) (HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => f i))))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (p : β -> Prop), Eq.{succ u2} α (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => f i)) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => f i))))
 Case conversion may be inaccurate. Consider using '#align supr_split supᵢ_splitₓ'. -/
 theorem supᵢ_split (f : β → α) (p : β → Prop) :
     (⨆ i, f i) = (⨆ (i) (h : p i), f i) ⊔ ⨆ (i) (h : ¬p i), f i := by
@@ -2707,9 +2707,9 @@ theorem supᵢ_split (f : β → α) (p : β → Prop) :
 
 /- warning: infi_split -> infᵢ_split is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : β -> α) (p : β -> Prop), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => f i)) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => f i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : β -> α) (p : β -> Prop), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => f i)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (p i) (fun (h : p i) => f i))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Not (p i)) (fun (h : Not (p i)) => f i))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (p : β -> Prop), Eq.{succ u2} α (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => f i)) (HasInf.inf.{u2} α (Lattice.toHasInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => f i))))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (p : β -> Prop), Eq.{succ u2} α (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => f i)) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (p i) (fun (h : p i) => f i))) (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Not (p i)) (fun (h : Not (p i)) => f i))))
 Case conversion may be inaccurate. Consider using '#align infi_split infᵢ_splitₓ'. -/
 theorem infᵢ_split :
     ∀ (f : β → α) (p : β → Prop), (⨅ i, f i) = (⨅ (i) (h : p i), f i) ⊓ ⨅ (i) (h : ¬p i), f i :=
@@ -2718,9 +2718,9 @@ theorem infᵢ_split :
 
 /- warning: supr_split_single -> supᵢ_split_single is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : β -> α) (i₀ : β), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => f i)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i₀) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Ne.{succ u2} β i i₀) (fun (h : Ne.{succ u2} β i i₀) => f i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : β -> α) (i₀ : β), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => f i)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i₀) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Ne.{succ u2} β i i₀) (fun (h : Ne.{succ u2} β i i₀) => f i))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (i₀ : β), Eq.{succ u2} α (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => f i)) (HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f i₀) (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Ne.{succ u1} β i i₀) (fun (h : Ne.{succ u1} β i i₀) => f i))))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (i₀ : β), Eq.{succ u2} α (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => f i)) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f i₀) (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (i : β) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Ne.{succ u1} β i i₀) (fun (h : Ne.{succ u1} β i i₀) => f i))))
 Case conversion may be inaccurate. Consider using '#align supr_split_single supᵢ_split_singleₓ'. -/
 theorem supᵢ_split_single (f : β → α) (i₀ : β) : (⨆ i, f i) = f i₀ ⊔ ⨆ (i) (h : i ≠ i₀), f i :=
   by
@@ -2730,9 +2730,9 @@ theorem supᵢ_split_single (f : β → α) (i₀ : β) : (⨆ i, f i) = f i₀
 
 /- warning: infi_split_single -> infᵢ_split_single is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : β -> α) (i₀ : β), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => f i)) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i₀) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Ne.{succ u2} β i i₀) (fun (h : Ne.{succ u2} β i i₀) => f i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : β -> α) (i₀ : β), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => f i)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i₀) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Ne.{succ u2} β i i₀) (fun (h : Ne.{succ u2} β i i₀) => f i))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (i₀ : β), Eq.{succ u2} α (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => f i)) (HasInf.inf.{u2} α (Lattice.toHasInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f i₀) (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Ne.{succ u1} β i i₀) (fun (h : Ne.{succ u1} β i i₀) => f i))))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : β -> α) (i₀ : β), Eq.{succ u2} α (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => f i)) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f i₀) (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (i : β) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Ne.{succ u1} β i i₀) (fun (h : Ne.{succ u1} β i i₀) => f i))))
 Case conversion may be inaccurate. Consider using '#align infi_split_single infᵢ_split_singleₓ'. -/
 theorem infᵢ_split_single (f : β → α) (i₀ : β) : (⨅ i, f i) = f i₀ ⊓ ⨅ (i) (h : i ≠ i₀), f i :=
   @supᵢ_split_single αᵒᵈ _ _ _ _
@@ -2760,9 +2760,9 @@ theorem infᵢ_le_infᵢ_of_subset {f : β → α} {s t : Set β} : s ⊆ t →
 
 /- warning: supr_insert -> supᵢ_insert is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {b : β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) b s)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) b s)) => f x))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f b) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {b : β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) b s)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) b s)) => f x))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f b) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {b : β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.instInsertSet.{u2} β) b s)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.instInsertSet.{u2} β) b s)) => f x))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f b) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {b : β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.instInsertSet.{u2} β) b s)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.instInsertSet.{u2} β) b s)) => f x))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f b) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))))
 Case conversion may be inaccurate. Consider using '#align supr_insert supᵢ_insertₓ'. -/
 theorem supᵢ_insert {f : β → α} {s : Set β} {b : β} :
     (⨆ x ∈ insert b s, f x) = f b ⊔ ⨆ x ∈ s, f x :=
@@ -2771,9 +2771,9 @@ theorem supᵢ_insert {f : β → α} {s : Set β} {b : β} :
 
 /- warning: infi_insert -> infᵢ_insert is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {b : β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) b s)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) b s)) => f x))) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f b) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {b : β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) b s)) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) b s)) => f x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f b) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) => f x))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {b : β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.instInsertSet.{u2} β) b s)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.instInsertSet.{u2} β) b s)) => f x))) (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f b) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β} {b : β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.instInsertSet.{u2} β) b s)) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.instInsertSet.{u2} β) b s)) => f x))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f b) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (fun (H : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) => f x))))
 Case conversion may be inaccurate. Consider using '#align infi_insert infᵢ_insertₓ'. -/
 theorem infᵢ_insert {f : β → α} {s : Set β} {b : β} :
     (⨅ x ∈ insert b s, f x) = f b ⊓ ⨅ x ∈ s, f x :=
@@ -2800,9 +2800,9 @@ theorem infᵢ_singleton {f : β → α} {b : β} : (⨅ x ∈ (singleton b : Se
 
 /- warning: supr_pair -> supᵢ_pair is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {a : β} {b : β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) a (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b))) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) a (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b))) => f x))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f a) (f b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {a : β} {b : β}, Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (x : β) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) a (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b))) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) a (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b))) => f x))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f a) (f b))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α} {a : β} {b : β}, Eq.{succ u2} α (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (x : β) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Insert.insert.{u1, u1} β (Set.{u1} β) (Set.instInsertSet.{u1} β) a (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b))) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Insert.insert.{u1, u1} β (Set.{u1} β) (Set.instInsertSet.{u1} β) a (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b))) => f x))) (HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f a) (f b))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α} {a : β} {b : β}, Eq.{succ u2} α (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (x : β) => supᵢ.{u2, 0} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Insert.insert.{u1, u1} β (Set.{u1} β) (Set.instInsertSet.{u1} β) a (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b))) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Insert.insert.{u1, u1} β (Set.{u1} β) (Set.instInsertSet.{u1} β) a (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b))) => f x))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f a) (f b))
 Case conversion may be inaccurate. Consider using '#align supr_pair supᵢ_pairₓ'. -/
 theorem supᵢ_pair {f : β → α} {a b : β} : (⨆ x ∈ ({a, b} : Set β), f x) = f a ⊔ f b := by
   rw [supᵢ_insert, supᵢ_singleton]
@@ -2810,9 +2810,9 @@ theorem supᵢ_pair {f : β → α} {a b : β} : (⨆ x ∈ ({a, b} : Set β), f
 
 /- warning: infi_pair -> infᵢ_pair is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {a : β} {b : β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) a (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b))) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) a (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b))) => f x))) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f a) (f b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : β -> α} {a : β} {b : β}, Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (x : β) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) a (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b))) (fun (H : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (Insert.insert.{u2, u2} β (Set.{u2} β) (Set.hasInsert.{u2} β) a (Singleton.singleton.{u2, u2} β (Set.{u2} β) (Set.hasSingleton.{u2} β) b))) => f x))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f a) (f b))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α} {a : β} {b : β}, Eq.{succ u2} α (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (x : β) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Insert.insert.{u1, u1} β (Set.{u1} β) (Set.instInsertSet.{u1} β) a (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b))) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Insert.insert.{u1, u1} β (Set.{u1} β) (Set.instInsertSet.{u1} β) a (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b))) => f x))) (HasInf.inf.{u2} α (Lattice.toHasInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f a) (f b))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] {f : β -> α} {a : β} {b : β}, Eq.{succ u2} α (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (x : β) => infᵢ.{u2, 0} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Insert.insert.{u1, u1} β (Set.{u1} β) (Set.instInsertSet.{u1} β) a (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b))) (fun (H : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x (Insert.insert.{u1, u1} β (Set.{u1} β) (Set.instInsertSet.{u1} β) a (Singleton.singleton.{u1, u1} β (Set.{u1} β) (Set.instSingletonSet.{u1} β) b))) => f x))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f a) (f b))
 Case conversion may be inaccurate. Consider using '#align infi_pair infᵢ_pairₓ'. -/
 theorem infᵢ_pair {f : β → α} {a b : β} : (⨅ x ∈ ({a, b} : Set β), f x) = f a ⊓ f b := by
   rw [infᵢ_insert, infᵢ_singleton]
@@ -2910,9 +2910,9 @@ theorem infᵢ_of_empty [IsEmpty ι] (f : ι → α) : infᵢ f = ⊤ :=
 
 /- warning: supr_bool_eq -> supᵢ_bool_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Bool -> α}, Eq.{succ u1} α (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Bool (fun (b : Bool) => f b)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f Bool.true) (f Bool.false))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Bool -> α}, Eq.{succ u1} α (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Bool (fun (b : Bool) => f b)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f Bool.true) (f Bool.false))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Bool -> α}, Eq.{succ u1} α (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Bool (fun (b : Bool) => f b)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f Bool.true) (f Bool.false))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Bool -> α}, Eq.{succ u1} α (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Bool (fun (b : Bool) => f b)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f Bool.true) (f Bool.false))
 Case conversion may be inaccurate. Consider using '#align supr_bool_eq supᵢ_bool_eqₓ'. -/
 theorem supᵢ_bool_eq {f : Bool → α} : (⨆ b : Bool, f b) = f true ⊔ f false := by
   rw [supᵢ, Bool.range_eq, supₛ_pair, sup_comm]
@@ -2920,9 +2920,9 @@ theorem supᵢ_bool_eq {f : Bool → α} : (⨆ b : Bool, f b) = f true ⊔ f fa
 
 /- warning: infi_bool_eq -> infᵢ_bool_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Bool -> α}, Eq.{succ u1} α (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Bool (fun (b : Bool) => f b)) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f Bool.true) (f Bool.false))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Bool -> α}, Eq.{succ u1} α (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Bool (fun (b : Bool) => f b)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f Bool.true) (f Bool.false))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Bool -> α}, Eq.{succ u1} α (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Bool (fun (b : Bool) => f b)) (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f Bool.true) (f Bool.false))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {f : Bool -> α}, Eq.{succ u1} α (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Bool (fun (b : Bool) => f b)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f Bool.true) (f Bool.false))
 Case conversion may be inaccurate. Consider using '#align infi_bool_eq infᵢ_bool_eqₓ'. -/
 theorem infᵢ_bool_eq {f : Bool → α} : (⨅ b : Bool, f b) = f true ⊓ f false :=
   @supᵢ_bool_eq αᵒᵈ _ _
@@ -2930,9 +2930,9 @@ theorem infᵢ_bool_eq {f : Bool → α} : (⨅ b : Bool, f b) = f true ⊓ f fa
 
 /- warning: sup_eq_supr -> sup_eq_supᵢ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (x : α) (y : α), Eq.{succ u1} α (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) x y) (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Bool (fun (b : Bool) => cond.{u1} α b x y))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (x : α) (y : α), Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) x y) (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Bool (fun (b : Bool) => cond.{u1} α b x y))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (x : α) (y : α), Eq.{succ u1} α (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) x y) (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Bool (fun (b : Bool) => cond.{u1} α b x y))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (x : α) (y : α), Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) x y) (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Bool (fun (b : Bool) => cond.{u1} α b x y))
 Case conversion may be inaccurate. Consider using '#align sup_eq_supr sup_eq_supᵢₓ'. -/
 theorem sup_eq_supᵢ (x y : α) : x ⊔ y = ⨆ b : Bool, cond b x y := by
   rw [supᵢ_bool_eq, Bool.cond_true, Bool.cond_false]
@@ -2940,9 +2940,9 @@ theorem sup_eq_supᵢ (x y : α) : x ⊔ y = ⨆ b : Bool, cond b x y := by
 
 /- warning: inf_eq_infi -> inf_eq_infᵢ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (x : α) (y : α), Eq.{succ u1} α (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) x y) (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Bool (fun (b : Bool) => cond.{u1} α b x y))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (x : α) (y : α), Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) x y) (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Bool (fun (b : Bool) => cond.{u1} α b x y))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (x : α) (y : α), Eq.{succ u1} α (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) x y) (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Bool (fun (b : Bool) => cond.{u1} α b x y))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (x : α) (y : α), Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) x y) (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Bool (fun (b : Bool) => cond.{u1} α b x y))
 Case conversion may be inaccurate. Consider using '#align inf_eq_infi inf_eq_infᵢₓ'. -/
 theorem inf_eq_infᵢ (x y : α) : x ⊓ y = ⨅ b : Bool, cond b x y :=
   @sup_eq_supᵢ αᵒᵈ _ _ _
@@ -3040,9 +3040,9 @@ theorem binfᵢ_prod {f : β × γ → α} {s : Set β} {t : Set γ} :
 
 /- warning: supr_sum -> supᵢ_sum is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : (Sum.{u2, u3} β γ) -> α}, Eq.{succ u1} α (supᵢ.{u1, max (succ u2) (succ u3)} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Sum.{u2, u3} β γ) (fun (x : Sum.{u2, u3} β γ) => f x)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => f (Sum.inl.{u2, u3} β γ i))) (supᵢ.{u1, succ u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) γ (fun (j : γ) => f (Sum.inr.{u2, u3} β γ j))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : (Sum.{u2, u3} β γ) -> α}, Eq.{succ u1} α (supᵢ.{u1, max (succ u2) (succ u3)} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Sum.{u2, u3} β γ) (fun (x : Sum.{u2, u3} β γ) => f x)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (i : β) => f (Sum.inl.{u2, u3} β γ i))) (supᵢ.{u1, succ u3} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) γ (fun (j : γ) => f (Sum.inr.{u2, u3} β γ j))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : (Sum.{u3, u2} β γ) -> α}, Eq.{succ u1} α (supᵢ.{u1, max (succ u3) (succ u2)} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Sum.{u3, u2} β γ) (fun (x : Sum.{u3, u2} β γ) => f x)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, succ u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (i : β) => f (Sum.inl.{u3, u2} β γ i))) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) γ (fun (j : γ) => f (Sum.inr.{u3, u2} β γ j))))
+  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : (Sum.{u3, u2} β γ) -> α}, Eq.{succ u1} α (supᵢ.{u1, max (succ u3) (succ u2)} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Sum.{u3, u2} β γ) (fun (x : Sum.{u3, u2} β γ) => f x)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (supᵢ.{u1, succ u3} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (i : β) => f (Sum.inl.{u3, u2} β γ i))) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) γ (fun (j : γ) => f (Sum.inr.{u3, u2} β γ j))))
 Case conversion may be inaccurate. Consider using '#align supr_sum supᵢ_sumₓ'. -/
 theorem supᵢ_sum {f : Sum β γ → α} : (⨆ x, f x) = (⨆ i, f (Sum.inl i)) ⊔ ⨆ j, f (Sum.inr j) :=
   eq_of_forall_ge_iff fun c => by simp only [sup_le_iff, supᵢ_le_iff, Sum.forall]
@@ -3050,9 +3050,9 @@ theorem supᵢ_sum {f : Sum β γ → α} : (⨆ x, f x) = (⨆ i, f (Sum.inl i)
 
 /- warning: infi_sum -> infᵢ_sum is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : (Sum.{u2, u3} β γ) -> α}, Eq.{succ u1} α (infᵢ.{u1, max (succ u2) (succ u3)} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Sum.{u2, u3} β γ) (fun (x : Sum.{u2, u3} β γ) => f x)) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => f (Sum.inl.{u2, u3} β γ i))) (infᵢ.{u1, succ u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) γ (fun (j : γ) => f (Sum.inr.{u2, u3} β γ j))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : CompleteLattice.{u1} α] {f : (Sum.{u2, u3} β γ) -> α}, Eq.{succ u1} α (infᵢ.{u1, max (succ u2) (succ u3)} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Sum.{u2, u3} β γ) (fun (x : Sum.{u2, u3} β γ) => f x)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (i : β) => f (Sum.inl.{u2, u3} β γ i))) (infᵢ.{u1, succ u3} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) γ (fun (j : γ) => f (Sum.inr.{u2, u3} β γ j))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : (Sum.{u3, u2} β γ) -> α}, Eq.{succ u1} α (infᵢ.{u1, max (succ u3) (succ u2)} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Sum.{u3, u2} β γ) (fun (x : Sum.{u3, u2} β γ) => f x)) (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (infᵢ.{u1, succ u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (i : β) => f (Sum.inl.{u3, u2} β γ i))) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) γ (fun (j : γ) => f (Sum.inr.{u3, u2} β γ j))))
+  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] {f : (Sum.{u3, u2} β γ) -> α}, Eq.{succ u1} α (infᵢ.{u1, max (succ u3) (succ u2)} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Sum.{u3, u2} β γ) (fun (x : Sum.{u3, u2} β γ) => f x)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (infᵢ.{u1, succ u3} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (i : β) => f (Sum.inl.{u3, u2} β γ i))) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) γ (fun (j : γ) => f (Sum.inr.{u3, u2} β γ j))))
 Case conversion may be inaccurate. Consider using '#align infi_sum infᵢ_sumₓ'. -/
 theorem infᵢ_sum {f : Sum β γ → α} : (⨅ x, f x) = (⨅ i, f (Sum.inl i)) ⊓ ⨅ j, f (Sum.inr j) :=
   @supᵢ_sum αᵒᵈ _ _ _ _
@@ -3060,9 +3060,9 @@ theorem infᵢ_sum {f : Sum β γ → α} : (⨅ x, f x) = (⨅ i, f (Sum.inl i)
 
 /- warning: supr_option -> supᵢ_option is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : (Option.{u2} β) -> α), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Option.{u2} β) (fun (o : Option.{u2} β) => f o)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f (Option.none.{u2} β)) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (b : β) => f (Option.some.{u2} β b))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : (Option.{u2} β) -> α), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Option.{u2} β) (fun (o : Option.{u2} β) => f o)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f (Option.none.{u2} β)) (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (b : β) => f (Option.some.{u2} β b))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : (Option.{u2} β) -> α), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Option.{u2} β) (fun (o : Option.{u2} β) => f o)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f (Option.none.{u2} β)) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (b : β) => f (Option.some.{u2} β b))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : (Option.{u2} β) -> α), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Option.{u2} β) (fun (o : Option.{u2} β) => f o)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f (Option.none.{u2} β)) (supᵢ.{u1, succ u2} α (CompleteLattice.toSupSet.{u1} α _inst_1) β (fun (b : β) => f (Option.some.{u2} β b))))
 Case conversion may be inaccurate. Consider using '#align supr_option supᵢ_optionₓ'. -/
 theorem supᵢ_option (f : Option β → α) : (⨆ o, f o) = f none ⊔ ⨆ b, f (Option.some b) :=
   eq_of_forall_ge_iff fun c => by simp only [supᵢ_le_iff, sup_le_iff, Option.forall]
@@ -3070,9 +3070,9 @@ theorem supᵢ_option (f : Option β → α) : (⨆ o, f o) = f none ⊔ ⨆ b,
 
 /- warning: infi_option -> infᵢ_option is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : (Option.{u2} β) -> α), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Option.{u2} β) (fun (o : Option.{u2} β) => f o)) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f (Option.none.{u2} β)) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (b : β) => f (Option.some.{u2} β b))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : (Option.{u2} β) -> α), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Option.{u2} β) (fun (o : Option.{u2} β) => f o)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f (Option.none.{u2} β)) (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (b : β) => f (Option.some.{u2} β b))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : (Option.{u2} β) -> α), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Option.{u2} β) (fun (o : Option.{u2} β) => f o)) (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f (Option.none.{u2} β)) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (b : β) => f (Option.some.{u2} β b))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : (Option.{u2} β) -> α), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Option.{u2} β) (fun (o : Option.{u2} β) => f o)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (f (Option.none.{u2} β)) (infᵢ.{u1, succ u2} α (CompleteLattice.toInfSet.{u1} α _inst_1) β (fun (b : β) => f (Option.some.{u2} β b))))
 Case conversion may be inaccurate. Consider using '#align infi_option infᵢ_optionₓ'. -/
 theorem infᵢ_option (f : Option β → α) : (⨅ o, f o) = f none ⊓ ⨅ b, f (Option.some b) :=
   @supᵢ_option αᵒᵈ _ _ _
@@ -3080,9 +3080,9 @@ theorem infᵢ_option (f : Option β → α) : (⨅ o, f o) = f none ⊓ ⨅ b,
 
 /- warning: supr_option_elim -> supᵢ_option_elim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (a : α) (f : β -> α), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Option.{u2} β) (fun (o : Option.{u2} β) => Option.elim'.{u2, u1} β α a f o)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (b : β) => f b)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (a : α) (f : β -> α), Eq.{succ u1} α (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Option.{u2} β) (fun (o : Option.{u2} β) => Option.elim'.{u2, u1} β α a f o)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (supᵢ.{u1, succ u2} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) β (fun (b : β) => f b)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (a : α) (f : β -> α), Eq.{succ u2} α (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Option.{u1} β) (fun (o : Option.{u1} β) => Option.elim.{u1, succ u2} β α o a f)) (HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) a (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (b : β) => f b)))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (a : α) (f : β -> α), Eq.{succ u2} α (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) (Option.{u1} β) (fun (o : Option.{u1} β) => Option.elim.{u1, succ u2} β α o a f)) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) a (supᵢ.{u2, succ u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) β (fun (b : β) => f b)))
 Case conversion may be inaccurate. Consider using '#align supr_option_elim supᵢ_option_elimₓ'. -/
 /-- A version of `supr_option` useful for rewriting right-to-left. -/
 theorem supᵢ_option_elim (a : α) (f : β → α) : (⨆ o : Option β, o.elim a f) = a ⊔ ⨆ b, f b := by
@@ -3091,9 +3091,9 @@ theorem supᵢ_option_elim (a : α) (f : β → α) : (⨆ o : Option β, o.elim
 
 /- warning: infi_option_elim -> infᵢ_option_elim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (a : α) (f : β -> α), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Option.{u2} β) (fun (o : Option.{u2} β) => Option.elim'.{u2, u1} β α a f o)) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (b : β) => f b)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u1} α] (a : α) (f : β -> α), Eq.{succ u1} α (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Option.{u2} β) (fun (o : Option.{u2} β) => Option.elim'.{u2, u1} β α a f o)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (infᵢ.{u1, succ u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) β (fun (b : β) => f b)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (a : α) (f : β -> α), Eq.{succ u2} α (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Option.{u1} β) (fun (o : Option.{u1} β) => Option.elim.{u1, succ u2} β α o a f)) (HasInf.inf.{u2} α (Lattice.toHasInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) a (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (b : β) => f b)))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u2} α] (a : α) (f : β -> α), Eq.{succ u2} α (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) (Option.{u1} β) (fun (o : Option.{u1} β) => Option.elim.{u1, succ u2} β α o a f)) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) a (infᵢ.{u2, succ u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) β (fun (b : β) => f b)))
 Case conversion may be inaccurate. Consider using '#align infi_option_elim infᵢ_option_elimₓ'. -/
 /-- A version of `infi_option` useful for rewriting right-to-left. -/
 theorem infᵢ_option_elim (a : α) (f : β → α) : (⨅ o : Option β, o.elim a f) = a ⊓ ⨅ b, f b :=
@@ -3233,9 +3233,9 @@ theorem infᵢ_supᵢ_ge_nat_add :
 
 /- warning: sup_supr_nat_succ -> sup_supᵢ_nat_succ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α), Eq.{succ u1} α (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (u (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => u i))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α), Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (u (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (supᵢ.{u1, 1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) Nat (fun (i : Nat) => u i))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α), Eq.{succ u1} α (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (u (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => u i))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α), Eq.{succ u1} α (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (u (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (supᵢ.{u1, 1} α (CompleteLattice.toSupSet.{u1} α _inst_1) Nat (fun (i : Nat) => u i))
 Case conversion may be inaccurate. Consider using '#align sup_supr_nat_succ sup_supᵢ_nat_succₓ'. -/
 theorem sup_supᵢ_nat_succ (u : ℕ → α) : (u 0 ⊔ ⨆ i, u (i + 1)) = ⨆ i, u i :=
   calc
@@ -3247,9 +3247,9 @@ theorem sup_supᵢ_nat_succ (u : ℕ → α) : (u 0 ⊔ ⨆ i, u (i + 1)) = ⨆
 
 /- warning: inf_infi_nat_succ -> inf_infᵢ_nat_succ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α), Eq.{succ u1} α (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (u (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => u i))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α), Eq.{succ u1} α (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (u (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (infᵢ.{u1, 1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) Nat (fun (i : Nat) => u i))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α), Eq.{succ u1} α (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (u (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => u i))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] (u : Nat -> α), Eq.{succ u1} α (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (u (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => u (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (infᵢ.{u1, 1} α (CompleteLattice.toInfSet.{u1} α _inst_1) Nat (fun (i : Nat) => u i))
 Case conversion may be inaccurate. Consider using '#align inf_infi_nat_succ inf_infᵢ_nat_succₓ'. -/
 theorem inf_infᵢ_nat_succ (u : ℕ → α) : (u 0 ⊓ ⨅ i, u (i + 1)) = ⨅ i, u i :=
   @sup_supᵢ_nat_succ αᵒᵈ _ u
@@ -3727,9 +3727,9 @@ variable [CompleteLattice α] {a : α} {s : Set α}
 
 /- warning: sup_Inf_le_infi_sup -> sup_infₛ_le_infᵢ_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)) (infᵢ.{u1, succ u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) α (fun (b : α) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s)) (infᵢ.{u1, succ u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) α (fun (b : α) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)) (infᵢ.{u1, succ u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) α (fun (b : α) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s)) (infᵢ.{u1, succ u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) α (fun (b : α) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b)))
 Case conversion may be inaccurate. Consider using '#align sup_Inf_le_infi_sup sup_infₛ_le_infᵢ_supₓ'. -/
 /-- This is a weaker version of `sup_Inf_eq` -/
 theorem sup_infₛ_le_infᵢ_sup : a ⊔ infₛ s ≤ ⨅ b ∈ s, a ⊔ b :=
@@ -3738,9 +3738,9 @@ theorem sup_infₛ_le_infᵢ_sup : a ⊔ infₛ s ≤ ⨅ b ∈ s, a ⊔ b :=
 
 /- warning: supr_inf_le_inf_Sup -> supᵢ_inf_le_inf_supₛ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (supᵢ.{u1, succ u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) α (fun (b : α) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b))) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (supᵢ.{u1, succ u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) α (fun (b : α) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a b))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (supᵢ.{u1, succ u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) α (fun (b : α) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a b))) (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (supᵢ.{u1, succ u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) α (fun (b : α) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a b))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) a (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align supr_inf_le_inf_Sup supᵢ_inf_le_inf_supₛₓ'. -/
 /-- This is a weaker version of `inf_Sup_eq` -/
 theorem supᵢ_inf_le_inf_supₛ : (⨆ b ∈ s, a ⊓ b) ≤ a ⊓ supₛ s :=
@@ -3749,9 +3749,9 @@ theorem supᵢ_inf_le_inf_supₛ : (⨆ b ∈ s, a ⊓ b) ≤ a ⊓ supₛ s :=
 
 /- warning: Inf_sup_le_infi_sup -> infₛ_sup_le_infᵢ_sup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) a) (infᵢ.{u1, succ u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) α (fun (b : α) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) s) a) (infᵢ.{u1, succ u1} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) α (fun (b : α) => infᵢ.{u1, 0} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) a) (infᵢ.{u1, succ u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) α (fun (b : α) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) s) a) (infᵢ.{u1, succ u1} α (CompleteLattice.toInfSet.{u1} α _inst_1) α (fun (b : α) => infᵢ.{u1, 0} α (CompleteLattice.toInfSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a)))
 Case conversion may be inaccurate. Consider using '#align Inf_sup_le_infi_sup infₛ_sup_le_infᵢ_supₓ'. -/
 /-- This is a weaker version of `Inf_sup_eq` -/
 theorem infₛ_sup_le_infᵢ_sup : infₛ s ⊔ a ≤ ⨅ b ∈ s, b ⊔ a :=
@@ -3760,9 +3760,9 @@ theorem infₛ_sup_le_infᵢ_sup : infₛ s ⊔ a ≤ ⨅ b ∈ s, b ⊔ a :=
 
 /- warning: supr_inf_le_Sup_inf -> supᵢ_inf_le_supₛ_inf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (supᵢ.{u1, succ u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) α (fun (b : α) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a))) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) a)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (supᵢ.{u1, succ u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) α (fun (b : α) => supᵢ.{u1, 0} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) b a))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) s) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (supᵢ.{u1, succ u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) α (fun (b : α) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) b a))) (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : CompleteLattice.{u1} α] {a : α} {s : Set.{u1} α}, LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (supᵢ.{u1, succ u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) α (fun (b : α) => supᵢ.{u1, 0} α (CompleteLattice.toSupSet.{u1} α _inst_1) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) => Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) b a))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1)) (SupSet.supₛ.{u1} α (CompleteLattice.toSupSet.{u1} α _inst_1) s) a)
 Case conversion may be inaccurate. Consider using '#align supr_inf_le_Sup_inf supᵢ_inf_le_supₛ_infₓ'. -/
 /-- This is a weaker version of `Sup_inf_eq` -/
 theorem supᵢ_inf_le_supₛ_inf : (⨆ b ∈ s, b ⊓ a) ≤ supₛ s ⊓ a :=
@@ -3771,9 +3771,9 @@ theorem supᵢ_inf_le_supₛ_inf : (⨆ b ∈ s, b ⊓ a) ≤ supₛ s ⊓ a :=
 
 /- warning: le_supr_inf_supr -> le_supᵢ_inf_supᵢ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (g : ι -> α), LE.le.{u1} α (Preorder.toLE.{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) => HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i) (g i))) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{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} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => g i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (g : ι -> α), LE.le.{u1} α (Preorder.toLE.{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) => Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i) (g i))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (CompleteLattice.toLattice.{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} α (CompleteSemilatticeSup.toHasSup.{u1} α (CompleteLattice.toCompleteSemilatticeSup.{u1} α _inst_1)) ι (fun (i : ι) => g i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (g : ι -> α), LE.le.{u2} α (Preorder.toLE.{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) => HasInf.inf.{u2} α (Lattice.toHasInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f i) (g i))) (HasInf.inf.{u2} α (Lattice.toHasInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i)) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => g i)))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (g : ι -> α), LE.le.{u2} α (Preorder.toLE.{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) => Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (f i) (g i))) (Inf.inf.{u2} α (Lattice.toInf.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1)) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => f i)) (supᵢ.{u2, u1} α (CompleteLattice.toSupSet.{u2} α _inst_1) ι (fun (i : ι) => g i)))
 Case conversion may be inaccurate. Consider using '#align le_supr_inf_supr le_supᵢ_inf_supᵢₓ'. -/
 theorem le_supᵢ_inf_supᵢ (f g : ι → α) : (⨆ i, f i ⊓ g i) ≤ (⨆ i, f i) ⊓ ⨆ i, g i :=
   le_inf (supᵢ_mono fun i => inf_le_left) (supᵢ_mono fun i => inf_le_right)
@@ -3781,9 +3781,9 @@ theorem le_supᵢ_inf_supᵢ (f g : ι → α) : (⨆ i, f i ⊓ g i) ≤ (⨆ i
 
 /- warning: infi_sup_infi_le -> infᵢ_sup_infᵢ_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (g : ι -> α), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{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} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => g i))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i) (g i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : CompleteLattice.{u1} α] (f : ι -> α) (g : ι -> α), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{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} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => g i))) (infᵢ.{u1, u2} α (CompleteSemilatticeInf.toHasInf.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_1)) ι (fun (i : ι) => Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (CompleteLattice.toLattice.{u1} α _inst_1))) (f i) (g i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (g : ι -> α), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => g i))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => HasSup.sup.{u2} α (SemilatticeSup.toHasSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f i) (g i)))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : CompleteLattice.{u2} α] (f : ι -> α) (g : ι -> α), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α _inst_1)))) (Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => f i)) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => g i))) (infᵢ.{u2, u1} α (CompleteLattice.toInfSet.{u2} α _inst_1) ι (fun (i : ι) => Sup.sup.{u2} α (SemilatticeSup.toSup.{u2} α (Lattice.toSemilatticeSup.{u2} α (CompleteLattice.toLattice.{u2} α _inst_1))) (f i) (g i)))
 Case conversion may be inaccurate. Consider using '#align infi_sup_infi_le infᵢ_sup_infᵢ_leₓ'. -/
 theorem infᵢ_sup_infᵢ_le (f g : ι → α) : ((⨅ i, f i) ⊔ ⨅ i, g i) ≤ ⨅ i, f i ⊔ g i :=
   @le_supᵢ_inf_supᵢ αᵒᵈ ι _ f g
@@ -3815,14 +3815,14 @@ end CompleteLattice
 
 /- warning: function.injective.complete_lattice -> Function.Injective.completeLattice is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : HasSup.{u1} α] [_inst_2 : HasInf.{u1} α] [_inst_3 : SupSet.{u1} α] [_inst_4 : InfSet.{u1} α] [_inst_5 : Top.{u1} α] [_inst_6 : Bot.{u1} α] [_inst_7 : CompleteLattice.{u2} β] (f : α -> β), (Function.Injective.{succ u1, succ u2} α β f) -> (forall (a : α) (b : α), Eq.{succ u2} β (f (HasSup.sup.{u1} α _inst_1 a b)) (HasSup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (CompleteLattice.toLattice.{u2} β _inst_7))) (f a) (f b))) -> (forall (a : α) (b : α), Eq.{succ u2} β (f (HasInf.inf.{u1} α _inst_2 a b)) (HasInf.inf.{u2} β (SemilatticeInf.toHasInf.{u2} β (Lattice.toSemilatticeInf.{u2} β (CompleteLattice.toLattice.{u2} β _inst_7))) (f a) (f b))) -> (forall (s : Set.{u1} α), Eq.{succ u2} β (f (SupSet.supₛ.{u1} α _inst_3 s)) (supᵢ.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_7)) α (fun (a : α) => supᵢ.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_7)) (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) => f a)))) -> (forall (s : Set.{u1} α), Eq.{succ u2} β (f (InfSet.infₛ.{u1} α _inst_4 s)) (infᵢ.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_7)) α (fun (a : α) => infᵢ.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_7)) (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) => f a)))) -> (Eq.{succ u2} β (f (Top.top.{u1} α _inst_5)) (Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β _inst_7))) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α _inst_6)) (Bot.bot.{u2} β (CompleteLattice.toHasBot.{u2} β _inst_7))) -> (CompleteLattice.{u1} α)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Sup.{u1} α] [_inst_2 : Inf.{u1} α] [_inst_3 : SupSet.{u1} α] [_inst_4 : InfSet.{u1} α] [_inst_5 : Top.{u1} α] [_inst_6 : Bot.{u1} α] [_inst_7 : CompleteLattice.{u2} β] (f : α -> β), (Function.Injective.{succ u1, succ u2} α β f) -> (forall (a : α) (b : α), Eq.{succ u2} β (f (Sup.sup.{u1} α _inst_1 a b)) (Sup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (CompleteLattice.toLattice.{u2} β _inst_7))) (f a) (f b))) -> (forall (a : α) (b : α), Eq.{succ u2} β (f (Inf.inf.{u1} α _inst_2 a b)) (Inf.inf.{u2} β (SemilatticeInf.toHasInf.{u2} β (Lattice.toSemilatticeInf.{u2} β (CompleteLattice.toLattice.{u2} β _inst_7))) (f a) (f b))) -> (forall (s : Set.{u1} α), Eq.{succ u2} β (f (SupSet.supₛ.{u1} α _inst_3 s)) (supᵢ.{u2, succ u1} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_7)) α (fun (a : α) => supᵢ.{u2, 0} β (CompleteSemilatticeSup.toHasSup.{u2} β (CompleteLattice.toCompleteSemilatticeSup.{u2} β _inst_7)) (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) => f a)))) -> (forall (s : Set.{u1} α), Eq.{succ u2} β (f (InfSet.infₛ.{u1} α _inst_4 s)) (infᵢ.{u2, succ u1} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_7)) α (fun (a : α) => infᵢ.{u2, 0} β (CompleteSemilatticeInf.toHasInf.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_7)) (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) => f a)))) -> (Eq.{succ u2} β (f (Top.top.{u1} α _inst_5)) (Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β _inst_7))) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α _inst_6)) (Bot.bot.{u2} β (CompleteLattice.toHasBot.{u2} β _inst_7))) -> (CompleteLattice.{u1} α)
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : HasSup.{u1} α] [_inst_2 : HasInf.{u1} α] [_inst_3 : SupSet.{u1} α] [_inst_4 : InfSet.{u1} α] [_inst_5 : Top.{u1} α] [_inst_6 : Bot.{u1} α] [_inst_7 : CompleteLattice.{u2} β] (f : α -> β), (Function.Injective.{succ u1, succ u2} α β f) -> (forall (a : α) (b : α), Eq.{succ u2} β (f (HasSup.sup.{u1} α _inst_1 a b)) (HasSup.sup.{u2} β (SemilatticeSup.toHasSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (CompleteLattice.toLattice.{u2} β _inst_7))) (f a) (f b))) -> (forall (a : α) (b : α), Eq.{succ u2} β (f (HasInf.inf.{u1} α _inst_2 a b)) (HasInf.inf.{u2} β (Lattice.toHasInf.{u2} β (CompleteLattice.toLattice.{u2} β _inst_7)) (f a) (f b))) -> (forall (s : Set.{u1} α), Eq.{succ u2} β (f (SupSet.supₛ.{u1} α _inst_3 s)) (supᵢ.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_7) α (fun (a : α) => supᵢ.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_7) (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) => f a)))) -> (forall (s : Set.{u1} α), Eq.{succ u2} β (f (InfSet.infₛ.{u1} α _inst_4 s)) (infᵢ.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_7) α (fun (a : α) => infᵢ.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_7) (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) => f a)))) -> (Eq.{succ u2} β (f (Top.top.{u1} α _inst_5)) (Top.top.{u2} β (CompleteLattice.toTop.{u2} β _inst_7))) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α _inst_6)) (Bot.bot.{u2} β (CompleteLattice.toBot.{u2} β _inst_7))) -> (CompleteLattice.{u1} α)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Sup.{u1} α] [_inst_2 : Inf.{u1} α] [_inst_3 : SupSet.{u1} α] [_inst_4 : InfSet.{u1} α] [_inst_5 : Top.{u1} α] [_inst_6 : Bot.{u1} α] [_inst_7 : CompleteLattice.{u2} β] (f : α -> β), (Function.Injective.{succ u1, succ u2} α β f) -> (forall (a : α) (b : α), Eq.{succ u2} β (f (Sup.sup.{u1} α _inst_1 a b)) (Sup.sup.{u2} β (SemilatticeSup.toSup.{u2} β (Lattice.toSemilatticeSup.{u2} β (CompleteLattice.toLattice.{u2} β _inst_7))) (f a) (f b))) -> (forall (a : α) (b : α), Eq.{succ u2} β (f (Inf.inf.{u1} α _inst_2 a b)) (Inf.inf.{u2} β (Lattice.toInf.{u2} β (CompleteLattice.toLattice.{u2} β _inst_7)) (f a) (f b))) -> (forall (s : Set.{u1} α), Eq.{succ u2} β (f (SupSet.supₛ.{u1} α _inst_3 s)) (supᵢ.{u2, succ u1} β (CompleteLattice.toSupSet.{u2} β _inst_7) α (fun (a : α) => supᵢ.{u2, 0} β (CompleteLattice.toSupSet.{u2} β _inst_7) (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) => f a)))) -> (forall (s : Set.{u1} α), Eq.{succ u2} β (f (InfSet.infₛ.{u1} α _inst_4 s)) (infᵢ.{u2, succ u1} β (CompleteLattice.toInfSet.{u2} β _inst_7) α (fun (a : α) => infᵢ.{u2, 0} β (CompleteLattice.toInfSet.{u2} β _inst_7) (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) => f a)))) -> (Eq.{succ u2} β (f (Top.top.{u1} α _inst_5)) (Top.top.{u2} β (CompleteLattice.toTop.{u2} β _inst_7))) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α _inst_6)) (Bot.bot.{u2} β (CompleteLattice.toBot.{u2} β _inst_7))) -> (CompleteLattice.{u1} α)
 Case conversion may be inaccurate. Consider using '#align function.injective.complete_lattice Function.Injective.completeLatticeₓ'. -/
 -- See note [reducible non-instances]
 /-- Pullback a `complete_lattice` along an injection. -/
 @[reducible]
-protected def Function.Injective.completeLattice [HasSup α] [HasInf α] [SupSet α] [InfSet α] [Top α]
+protected def Function.Injective.completeLattice [Sup α] [Inf α] [SupSet α] [InfSet α] [Top α]
     [Bot α] [CompleteLattice β] (f : α → β) (hf : Function.Injective f)
     (map_sup : ∀ a b, f (a ⊔ b) = f a ⊔ f b) (map_inf : ∀ a b, f (a ⊓ b) = f a ⊓ f b)
     (map_Sup : ∀ s, f (supₛ s) = ⨆ a ∈ s, f a) (map_Inf : ∀ s, f (infₛ s) = ⨅ a ∈ s, f a)

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

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.

@@ -1518,11 +1518,11 @@ theorem iInf_sigma {p : β → Type*} {f : Sigma p → α} : ⨅ x, f x = ⨅ (i
 
 lemma iSup_sigma' {κ : β → Type*} (f : ∀ i, κ i → α) :
     (⨆ i, ⨆ j, f i j) = ⨆ x : Σ i, κ i, f x.1 x.2 :=
-(iSup_sigma (f := λ x ↦ f x.1 x.2)).symm
+(iSup_sigma (f := fun x ↦ f x.1 x.2)).symm
 
 lemma iInf_sigma' {κ : β → Type*} (f : ∀ i, κ i → α) :
     (⨅ i, ⨅ j, f i j) = ⨅ x : Σ i, κ i, f x.1 x.2 :=
-(iInf_sigma (f := λ x ↦ f x.1 x.2)).symm
+(iInf_sigma (f := fun x ↦ f x.1 x.2)).symm
 
 theorem iSup_prod {f : β × γ → α} : ⨆ x, f x = ⨆ (i) (j), f (i, j) :=
   eq_of_forall_ge_iff fun c => by simp only [iSup_le_iff, Prod.forall]
@@ -1533,10 +1533,10 @@ theorem iInf_prod {f : β × γ → α} : ⨅ x, f x = ⨅ (i) (j), f (i, j) :=
 #align infi_prod iInf_prod
 
 lemma iSup_prod' (f : β → γ → α) : (⨆ i, ⨆ j, f i j) = ⨆ x : β × γ, f x.1 x.2 :=
-(iSup_prod (f := λ x ↦ f x.1 x.2)).symm
+(iSup_prod (f := fun x ↦ f x.1 x.2)).symm
 
 lemma iInf_prod' (f : β → γ → α) : (⨅ i, ⨅ j, f i j) = ⨅ x : β × γ, f x.1 x.2 :=
-(iInf_prod (f := λ x ↦ f x.1 x.2)).symm
+(iInf_prod (f := fun x ↦ f x.1 x.2)).symm
 
 theorem biSup_prod {f : β × γ → α} {s : Set β} {t : Set γ} :
     ⨆ x ∈ s ×ˢ t, f x = ⨆ (a ∈ s) (b ∈ t), f (a, b) := by

... or reduce its scope (the full removal is not as obvious).

@@ -45,8 +45,6 @@ In lemma names,
 * `⨅ i, f i` : `iInf f`, the infimum of the range of `f`.
 -/
 
-set_option autoImplicit true
-
 open Function OrderDual Set
 
 variable {α β β₂ γ : Type*} {ι ι' : Sort*} {κ : ι → Sort*} {κ' : ι' → Sort*}
@@ -1972,6 +1970,8 @@ protected def Function.Injective.completeLattice [Sup α] [Inf α] [SupSet α] [
 
 namespace ULift
 
+universe v
+
 instance supSet [SupSet α] : SupSet (ULift.{v} α) where sSup s := ULift.up (sSup <| ULift.up ⁻¹' s)
 
 theorem down_sSup [SupSet α] (s : Set (ULift.{v} α)) : (sSup s).down = sSup (ULift.up ⁻¹' s) := rfl

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

@@ -339,18 +339,18 @@ namespace OrderDual
 
 variable (α)
 
-instance completeLattice [CompleteLattice α] : CompleteLattice αᵒᵈ where
-  __ := OrderDual.lattice α
+instance instCompleteLattice [CompleteLattice α] : CompleteLattice αᵒᵈ where
+  __ := OrderDual.instLattice α
   __ := OrderDual.supSet α
   __ := OrderDual.infSet α
-  __ := OrderDual.boundedOrder α
+  __ := OrderDual.instBoundedOrder α
   le_sSup := @CompleteLattice.sInf_le α _
   sSup_le := @CompleteLattice.le_sInf α _
   sInf_le := @CompleteLattice.le_sSup α _
   le_sInf := @CompleteLattice.sSup_le α _
 
 instance [CompleteLinearOrder α] : CompleteLinearOrder αᵒᵈ where
-  __ := OrderDual.completeLattice α
+  __ := OrderDual.instCompleteLattice α
   __ := OrderDual.instLinearOrder α
 
 end OrderDual
@@ -1691,21 +1691,21 @@ end CompleteLinearOrder
 -/
 
 
-instance Prop.completeLattice : CompleteLattice Prop where
-  __ := Prop.boundedOrder
-  __ := Prop.distribLattice
+instance Prop.instCompleteLattice : CompleteLattice Prop where
+  __ := Prop.instBoundedOrder
+  __ := Prop.instDistribLattice
   sSup s := ∃ a ∈ s, a
   le_sSup _ a h p := ⟨a, h, p⟩
   sSup_le _ _ h := fun ⟨b, h', p⟩ => h b h' p
   sInf s := ∀ a, a ∈ s → a
   sInf_le _ a h p := p a h
   le_sInf _ _ h p b hb := h b hb p
-#align Prop.complete_lattice Prop.completeLattice
+#align Prop.complete_lattice Prop.instCompleteLattice
 
-noncomputable instance Prop.completeLinearOrder : CompleteLinearOrder Prop where
-  __ := Prop.completeLattice
+noncomputable instance Prop.instCompleteLinearOrder : CompleteLinearOrder Prop where
+  __ := Prop.instCompleteLattice
   __ := Prop.linearOrder
-#align Prop.complete_linear_order Prop.completeLinearOrder
+#align Prop.complete_linear_order Prop.instCompleteLinearOrder
 
 @[simp]
 theorem sSup_Prop_eq {s : Set Prop} : sSup s = ∃ p ∈ s, p :=
@@ -1736,14 +1736,14 @@ instance Pi.infSet {α : Type*} {β : α → Type*} [∀ i, InfSet (β i)] : Inf
   ⟨fun s i => ⨅ f : s, (f : ∀ i, β i) i⟩
 #align pi.has_Inf Pi.infSet
 
-instance Pi.completeLattice {α : Type*} {β : α → Type*} [∀ i, CompleteLattice (β i)] :
+instance Pi.instCompleteLattice {α : Type*} {β : α → Type*} [∀ i, CompleteLattice (β i)] :
     CompleteLattice (∀ i, β i) where
-  __ := Pi.boundedOrder; __ := Pi.lattice
+  __ := Pi.instBoundedOrder; __ := Pi.instLattice
   le_sSup s f hf := fun i => le_iSup (fun f : s => (f : ∀ i, β i) i) ⟨f, hf⟩
   sInf_le s f hf := fun i => iInf_le (fun f : s => (f : ∀ i, β i) i) ⟨f, hf⟩
   sSup_le _ _ hf := fun i => iSup_le fun g => hf g g.2 i
   le_sInf _ _ hf := fun i => le_iInf fun g => hf g g.2 i
-#align pi.complete_lattice Pi.completeLattice
+#align pi.complete_lattice Pi.instCompleteLattice
 
 theorem sSup_apply {α : Type*} {β : α → Type*} [∀ i, SupSet (β i)] {s : Set (∀ a, β a)} {a : α} :
     (sSup s) a = ⨆ f : s, (f : ∀ a, β a) a :=
@@ -1880,9 +1880,9 @@ theorem iSup_mk [SupSet α] [SupSet β] (f : ι → α) (g : ι → β) :
 
 variable (α β)
 
-instance completeLattice [CompleteLattice α] [CompleteLattice β] : CompleteLattice (α × β) where
-  __ := Prod.lattice α β
-  __ := Prod.boundedOrder α β
+instance instCompleteLattice [CompleteLattice α] [CompleteLattice β] : CompleteLattice (α × β) where
+  __ := Prod.instLattice α β
+  __ := Prod.instBoundedOrder α β
   __ := Prod.supSet α β
   __ := Prod.infSet α β
   le_sSup _ _ hab := ⟨le_sSup <| mem_image_of_mem _ hab, le_sSup <| mem_image_of_mem _ hab⟩
@@ -1994,7 +1994,7 @@ theorem down_iInf [InfSet α] (f : ι → ULift.{v} α) : (⨅ i, f i).down = 
 theorem up_iInf [InfSet α] (f : ι → α) : up (⨅ i, f i) = ⨅ i, up (f i) :=
   congr_arg ULift.up <| (down_iInf _).symm
 
-instance completeLattice [CompleteLattice α] : CompleteLattice (ULift.{v} α) :=
+instance instCompleteLattice [CompleteLattice α] : CompleteLattice (ULift.{v} α) :=
   ULift.down_injective.completeLattice _ down_sup down_inf
     (fun s => by rw [sSup_eq_iSup', down_iSup, iSup_subtype''])
     (fun s => by rw [sInf_eq_iInf', down_iInf, iInf_subtype'']) down_top down_bot