order.omega_complete_partial_order ⟷ Mathlib.Order.OmegaCompletePartialOrder

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

@@ -6,7 +6,7 @@ Authors: Simon Hudon
 import Control.Monad.Basic
 import Data.Part
 import Order.Hom.Order
-import Data.Nat.Order.Basic
+import Algebra.Order.Group.Nat
 import Tactic.Wlog
 
 #align_import order.omega_complete_partial_order from "leanprover-community/mathlib"@"92ca63f0fb391a9ca5f22d2409a6080e786d99f7"

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

@@ -187,7 +187,7 @@ open OmegaCompletePartialOrder
 
 section Prio
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:339:40: warning: unsupported option extends_priority -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:340:40: warning: unsupported option extends_priority -/
 set_option extends_priority 50
 
 #print OmegaCompletePartialOrder /-

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

@@ -378,7 +378,7 @@ theorem eq_of_chain {c : Chain (Part α)} {a b : α} (ha : some a ∈ c) (hb : s
   cases' ha with i ha; replace ha := ha.symm
   cases' hb with j hb; replace hb := hb.symm
   wlog h : i ≤ j; · exact (this j hb i ha (le_of_not_le h)).symm
-  rw [eq_some_iff] at ha hb 
+  rw [eq_some_iff] at ha hb
   have := c.monotone h _ ha; apply mem_unique this hb
 #align part.eq_of_chain Part.eq_of_chain
 -/
@@ -409,9 +409,9 @@ theorem ωSup_eq_none {c : Chain (Part α)} (h : ¬∃ a, some a ∈ c) : Part.
 #print Part.mem_chain_of_mem_ωSup /-
 theorem mem_chain_of_mem_ωSup {c : Chain (Part α)} {a : α} (h : a ∈ Part.ωSup c) : some a ∈ c :=
   by
-  simp [Part.ωSup] at h ; split_ifs at h 
+  simp [Part.ωSup] at h; split_ifs at h
   · have h' := Classical.choose_spec h_1
-    rw [← eq_some_iff] at h ; rw [← h]; exact h'
+    rw [← eq_some_iff] at h; rw [← h]; exact h'
   · rcases h with ⟨⟨⟩⟩
 #align part.mem_chain_of_mem_ωSup Part.mem_chain_of_mem_ωSup
 -/
@@ -438,7 +438,7 @@ theorem mem_ωSup (x : α) (c : Chain (Part α)) : x ∈ ωSup c ↔ some x ∈
   constructor
   · split_ifs; swap; rintro ⟨⟨⟩⟩
     intro h'; have hh := Classical.choose_spec h
-    simp at h' ; subst x; exact hh
+    simp at h'; subst x; exact hh
   · intro h
     have h' : ∃ a : α, some a ∈ c := ⟨_, h⟩
     rw [dif_pos h']; have hh := Classical.choose_spec h'
@@ -555,7 +555,7 @@ theorem sSup_continuous (s : Set <| α →o β) (hs : ∀ f ∈ s, Continuous f)
 #print CompleteLattice.iSup_continuous /-
 theorem iSup_continuous {ι : Sort _} {f : ι → α →o β} (h : ∀ i, Continuous (f i)) :
     Continuous (⨆ i, f i) :=
-  sSup_continuous _ <| Set.forall_range_iff.2 h
+  sSup_continuous _ <| Set.forall_mem_range.2 h
 #align complete_lattice.supr_continuous CompleteLattice.iSup_continuous
 -/
 
@@ -563,7 +563,7 @@ theorem iSup_continuous {ι : Sort _} {f : ι → α →o β} (h : ∀ i, Contin
 theorem sSup_continuous' (s : Set (α → β)) (hc : ∀ f ∈ s, Continuous' f) : Continuous' (sSup s) :=
   by
   lift s to Set (α →o β) using fun f hf => (hc f hf).to_monotone
-  simp only [Set.ball_image_iff, continuous'_coe] at hc 
+  simp only [Set.forall_mem_image, continuous'_coe] at hc
   rw [sSup_image]
   norm_cast
   exact supr_continuous fun f => supr_continuous fun hf => hc f hf
@@ -733,9 +733,9 @@ theorem ωSup_bind {β γ : Type v} (c : Chain α) (f : α →o Part β) (g : α
   simp only [ωSup_le_iff, Part.bind_le, chain.mem_map_iff, and_imp, OrderHom.bind_coe, exists_imp]
   constructor <;> intro h'''
   · intro b hb; apply ωSup_le _ _ _
-    rintro i y hy; simp only [Part.mem_ωSup] at hb 
+    rintro i y hy; simp only [Part.mem_ωSup] at hb
     rcases hb with ⟨j, hb⟩; replace hb := hb.symm
-    simp only [Part.eq_some_iff, chain.map_coe, Function.comp_apply, OrderHom.apply_coe] at hy hb 
+    simp only [Part.eq_some_iff, chain.map_coe, Function.comp_apply, OrderHom.apply_coe] at hy hb
     replace hb : b ∈ f (c (max i j)) := f.mono (c.mono (le_max_right i j)) _ hb
     replace hy : y ∈ g (c (max i j)) b := g.mono (c.mono (le_max_left i j)) _ _ hy
     apply h''' (max i j)
@@ -744,7 +744,7 @@ theorem ωSup_bind {β γ : Type v} (c : Chain α) (f : α →o Part β) (g : α
     exact ⟨_, hb, hy⟩
   · intro i; intro y hy
     simp only [exists_prop, Part.bind_eq_bind, Part.mem_bind_iff, chain.map_coe,
-      Function.comp_apply, OrderHom.bind_coe] at hy 
+      Function.comp_apply, OrderHom.bind_coe] at hy
     rcases hy with ⟨b, hb₀, hb₁⟩
     apply h''' b _
     · apply le_ωSup (c.map g) _ _ _ hb₁

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -235,7 +235,7 @@ theorem le_ωSup_of_le {c : Chain α} {x : α} (i : ℕ) (h : x ≤ c i) : x ≤
 #print OmegaCompletePartialOrder.ωSup_total /-
 theorem ωSup_total {c : Chain α} {x : α} (h : ∀ i, c i ≤ x ∨ x ≤ c i) : ωSup c ≤ x ∨ x ≤ ωSup c :=
   by_cases (fun this : ∀ i, c i ≤ x => Or.inl (ωSup_le _ _ this)) fun this : ¬∀ i, c i ≤ x =>
-    have : ∃ i, ¬c i ≤ x := by simp only [not_forall] at this ⊢ <;> assumption
+    have : ∃ i, ¬c i ≤ x := by simp only [Classical.not_forall] at this ⊢ <;> assumption
     let ⟨i, hx⟩ := this
     have : x ≤ c i := (h i).resolve_left hx
     Or.inr <| le_ωSup_of_le _ this

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

@@ -3,11 +3,11 @@ Copyright (c) 2020 Simon Hudon. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Simon Hudon
 -/
-import Mathbin.Control.Monad.Basic
-import Mathbin.Data.Part
-import Mathbin.Order.Hom.Order
-import Mathbin.Data.Nat.Order.Basic
-import Mathbin.Tactic.Wlog
+import Control.Monad.Basic
+import Data.Part
+import Order.Hom.Order
+import Data.Nat.Order.Basic
+import Tactic.Wlog
 
 #align_import order.omega_complete_partial_order from "leanprover-community/mathlib"@"92ca63f0fb391a9ca5f22d2409a6080e786d99f7"
 
@@ -187,7 +187,7 @@ open OmegaCompletePartialOrder
 
 section Prio
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:334:40: warning: unsupported option extends_priority -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:339:40: warning: unsupported option extends_priority -/
 set_option extends_priority 50
 
 #print OmegaCompletePartialOrder /-

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

@@ -537,8 +537,8 @@ instance (priority := 100) [CompleteLattice α] : OmegaCompletePartialOrder α
     where
   ωSup c := ⨆ i, c i
   ωSup_le := fun ⟨c, _⟩ s hs => by
-    simp only [iSup_le_iff, OrderHom.coe_fun_mk] at hs ⊢ <;> intro i <;> apply hs i
-  le_ωSup := fun ⟨c, _⟩ i => by simp only [OrderHom.coe_fun_mk] <;> apply le_iSup_of_le i <;> rfl
+    simp only [iSup_le_iff, OrderHom.coe_mk] at hs ⊢ <;> intro i <;> apply hs i
+  le_ωSup := fun ⟨c, _⟩ i => by simp only [OrderHom.coe_mk] <;> apply le_iSup_of_le i <;> rfl
 
 variable {α} {β : Type v} [OmegaCompletePartialOrder α] [CompleteLattice β]
 
@@ -784,31 +784,31 @@ theorem continuous (F : α →𝒄 β) (C : Chain α) : F (ωSup C) = ωSup (C.m
 #align omega_complete_partial_order.continuous_hom.continuous OmegaCompletePartialOrder.ContinuousHom.continuous
 -/
 
-#print OmegaCompletePartialOrder.ContinuousHom.ofFun /-
+#print OmegaCompletePartialOrder.ContinuousHom.copy /-
 /-- Construct a continuous function from a bare function, a continuous function, and a proof that
 they are equal. -/
 @[simps, reducible]
-def ofFun (f : α → β) (g : α →𝒄 β) (h : f = g) : α →𝒄 β := by
+def copy (f : α → β) (g : α →𝒄 β) (h : f = g) : α →𝒄 β := by
   refine' { toOrderHom := { toFun := f .. } .. } <;> subst h <;> rcases g with ⟨⟨⟩⟩ <;> assumption
-#align omega_complete_partial_order.continuous_hom.of_fun OmegaCompletePartialOrder.ContinuousHom.ofFun
+#align omega_complete_partial_order.continuous_hom.of_fun OmegaCompletePartialOrder.ContinuousHom.copy
 -/
 
-#print OmegaCompletePartialOrder.ContinuousHom.ofMono /-
+#print OmegaCompletePartialOrder.ContinuousHom.mk /-
 /-- Construct a continuous function from a monotone function with a proof of continuity. -/
 @[simps, reducible]
-def ofMono (f : α →o β) (h : ∀ c : Chain α, f (ωSup c) = ωSup (c.map f)) : α →𝒄 β
+def mk (f : α →o β) (h : ∀ c : Chain α, f (ωSup c) = ωSup (c.map f)) : α →𝒄 β
     where
   toFun := f
   monotone' := f.Monotone
   cont := h
-#align omega_complete_partial_order.continuous_hom.of_mono OmegaCompletePartialOrder.ContinuousHom.ofMono
+#align omega_complete_partial_order.continuous_hom.of_mono OmegaCompletePartialOrder.ContinuousHom.mk
 -/
 
 #print OmegaCompletePartialOrder.ContinuousHom.id /-
 /-- The identity as a continuous function. -/
 @[simps]
 def id : α →𝒄 α :=
-  ofMono OrderHom.id continuous_id
+  mk OrderHom.id continuous_id
 #align omega_complete_partial_order.continuous_hom.id OmegaCompletePartialOrder.ContinuousHom.id
 -/
 
@@ -816,7 +816,7 @@ def id : α →𝒄 α :=
 /-- The composition of continuous functions. -/
 @[simps]
 def comp (f : β →𝒄 γ) (g : α →𝒄 β) : α →𝒄 γ :=
-  ofMono (OrderHom.comp ↑f ↑g) (continuous_comp _ _ g.cont f.cont)
+  mk (OrderHom.comp ↑f ↑g) (continuous_comp _ _ g.cont f.cont)
 #align omega_complete_partial_order.continuous_hom.comp OmegaCompletePartialOrder.ContinuousHom.comp
 -/
 
@@ -852,15 +852,17 @@ theorem comp_assoc (f : γ →𝒄 φ) (g : β →𝒄 γ) (h : α →𝒄 β) :
 #align omega_complete_partial_order.continuous_hom.comp_assoc OmegaCompletePartialOrder.ContinuousHom.comp_assoc
 -/
 
+#print OmegaCompletePartialOrder.ContinuousHom.coe_apply /-
 @[simp]
 theorem coe_apply (a : α) (f : α →𝒄 β) : (f : α →o β) a = f a :=
   rfl
 #align omega_complete_partial_order.continuous_hom.coe_apply OmegaCompletePartialOrder.ContinuousHom.coe_apply
+-/
 
 #print OmegaCompletePartialOrder.ContinuousHom.const /-
 /-- `function.const` is a continuous function. -/
 def const (x : β) : α →𝒄 β :=
-  ofMono (OrderHom.const _ x) (continuous_const x)
+  mk (OrderHom.const _ x) (continuous_const x)
 #align omega_complete_partial_order.continuous_hom.const OmegaCompletePartialOrder.ContinuousHom.const
 -/
 
@@ -915,7 +917,7 @@ theorem forall_forall_merge' (c₀ : Chain (α →𝒄 β)) (c₁ : Chain α) (z
 of the functions in the `ω`-chain. -/
 @[simps]
 protected def ωSup (c : Chain (α →𝒄 β)) : α →𝒄 β :=
-  ContinuousHom.ofMono (ωSup <| c.map toMono)
+  ContinuousHom.mk (ωSup <| c.map toMono)
     (by
       intro c'
       apply eq_of_forall_ge_iff; intro z
@@ -987,7 +989,7 @@ def flip {α : Type _} (f : α → β →𝒄 γ) : β →𝒄 α → γ
 /-- `part.bind` as a continuous function. -/
 @[simps (config := { rhsMd := reducible })]
 noncomputable def bind {β γ : Type v} (f : α →𝒄 Part β) (g : α →𝒄 β → Part γ) : α →𝒄 Part γ :=
-  ofMono (OrderHom.bind ↑f ↑g) fun c =>
+  mk (OrderHom.bind ↑f ↑g) fun c =>
     by
     rw [OrderHom.bind, ← OrderHom.bind, ωSup_bind, ← f.continuous, ← g.continuous]
     rfl
@@ -998,7 +1000,7 @@ noncomputable def bind {β γ : Type v} (f : α →𝒄 Part β) (g : α →𝒄
 /-- `part.map` as a continuous function. -/
 @[simps (config := { rhsMd := reducible })]
 noncomputable def map {β γ : Type v} (f : β → γ) (g : α →𝒄 Part β) : α →𝒄 Part γ :=
-  ofFun (fun x => f <$> g x) (bind g (const (pure ∘ f))) <| by
+  copy (fun x => f <$> g x) (bind g (const (pure ∘ f))) <| by
     ext <;>
       simp only [map_eq_bind_pure_comp, bind_apply, OrderHom.bind_coe, const_apply,
         OrderHom.const_coe_coe, coe_apply]
@@ -1009,7 +1011,7 @@ noncomputable def map {β γ : Type v} (f : β → γ) (g : α →𝒄 Part β)
 /-- `part.seq` as a continuous function. -/
 @[simps (config := { rhsMd := reducible })]
 noncomputable def seq {β γ : Type v} (f : α →𝒄 Part (β → γ)) (g : α →𝒄 Part β) : α →𝒄 Part γ :=
-  ofFun (fun x => f x <*> g x) (bind f <| flip <| flip map g)
+  copy (fun x => f x <*> g x) (bind f <| flip <| flip map g)
     (by
       ext <;>
           simp only [seq_eq_bind_map, flip, Part.bind_eq_bind, map_apply, Part.mem_bind_iff,

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Simon Hudon. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Simon Hudon
-
-! This file was ported from Lean 3 source module order.omega_complete_partial_order
-! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Control.Monad.Basic
 import Mathbin.Data.Part
@@ -14,6 +9,8 @@ import Mathbin.Order.Hom.Order
 import Mathbin.Data.Nat.Order.Basic
 import Mathbin.Tactic.Wlog
 
+#align_import order.omega_complete_partial_order from "leanprover-community/mathlib"@"92ca63f0fb391a9ca5f22d2409a6080e786d99f7"
+
 /-!
 # Omega Complete Partial Orders
 

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

@@ -77,6 +77,7 @@ variable {β γ}
 
 variable {α} {α' : Type _} {β' : Type _} [Preorder α'] [Preorder β']
 
+#print OrderHom.bind /-
 /-- `part.bind` as a monotone function -/
 @[simps]
 def bind {β γ} (f : α →o Part β) (g : α →o β → Part γ) : α →o Part γ
@@ -88,6 +89,7 @@ def bind {β γ} (f : α →o Part β) (g : α →o β → Part γ) : α →o Pa
     intro b hb ha
     refine' ⟨b, f.monotone h _ hb, g.monotone h _ _ ha⟩
 #align order_hom.bind OrderHom.bind
+-/
 
 end OrderHom
 
@@ -159,9 +161,11 @@ theorem map_id : c.map OrderHom.id = c :=
 #align omega_complete_partial_order.chain.map_id OmegaCompletePartialOrder.Chain.map_id
 -/
 
+#print OmegaCompletePartialOrder.Chain.map_comp /-
 theorem map_comp : (c.map f).map g = c.map (g.comp f) :=
   rfl
 #align omega_complete_partial_order.chain.map_comp OmegaCompletePartialOrder.Chain.map_comp
+-/
 
 #print OmegaCompletePartialOrder.Chain.map_le_map /-
 @[mono]
@@ -170,11 +174,13 @@ theorem map_le_map {g : α →o β} (h : f ≤ g) : c.map f ≤ c.map g := fun i
 #align omega_complete_partial_order.chain.map_le_map OmegaCompletePartialOrder.Chain.map_le_map
 -/
 
+#print OmegaCompletePartialOrder.Chain.zip /-
 /-- `chain.zip` pairs up the elements of two chains that have the same index -/
 @[simps]
 def zip (c₀ : Chain α) (c₁ : Chain β) : Chain (α × β) :=
   OrderHom.prod c₀ c₁
 #align omega_complete_partial_order.chain.zip OmegaCompletePartialOrder.Chain.zip
+-/
 
 end Chain
 
@@ -333,11 +339,13 @@ theorem continuous_id : Continuous (@OrderHom.id α _) := by intro <;> rw [c.map
 #align omega_complete_partial_order.continuous_id OmegaCompletePartialOrder.continuous_id
 -/
 
+#print OmegaCompletePartialOrder.continuous_comp /-
 theorem continuous_comp (hfc : Continuous f) (hgc : Continuous g) : Continuous (g.comp f) :=
   by
   dsimp [Continuous] at *; intro
   rw [hfc, hgc, chain.map_comp]
 #align omega_complete_partial_order.continuous_comp OmegaCompletePartialOrder.continuous_comp
+-/
 
 #print OmegaCompletePartialOrder.id_continuous' /-
 theorem id_continuous' : Continuous' (@id α) :=
@@ -367,6 +375,7 @@ variable {α : Type u} {β : Type v} {γ : Type _}
 
 open OmegaCompletePartialOrder
 
+#print Part.eq_of_chain /-
 theorem eq_of_chain {c : Chain (Part α)} {a b : α} (ha : some a ∈ c) (hb : some b ∈ c) : a = b :=
   by
   cases' ha with i ha; replace ha := ha.symm
@@ -375,12 +384,16 @@ theorem eq_of_chain {c : Chain (Part α)} {a b : α} (ha : some a ∈ c) (hb : s
   rw [eq_some_iff] at ha hb 
   have := c.monotone h _ ha; apply mem_unique this hb
 #align part.eq_of_chain Part.eq_of_chain
+-/
 
+#print Part.ωSup /-
 /-- The (noncomputable) `ωSup` definition for the `ω`-CPO structure on `part α`. -/
 protected noncomputable def ωSup (c : Chain (Part α)) : Part α :=
   if h : ∃ a, some a ∈ c then some (Classical.choose h) else none
 #align part.ωSup Part.ωSup
+-/
 
+#print Part.ωSup_eq_some /-
 theorem ωSup_eq_some {c : Chain (Part α)} {a : α} (h : some a ∈ c) : Part.ωSup c = some a :=
   have : ∃ a, some a ∈ c := ⟨a, h⟩
   have a' : some (Classical.choose this) ∈ c := Classical.choose_spec this
@@ -388,11 +401,15 @@ theorem ωSup_eq_some {c : Chain (Part α)} {a : α} (h : some a ∈ c) : Part.
     Part.ωSup c = some (Classical.choose this) := dif_pos this
     _ = some a := congr_arg _ (eq_of_chain a' h)
 #align part.ωSup_eq_some Part.ωSup_eq_some
+-/
 
+#print Part.ωSup_eq_none /-
 theorem ωSup_eq_none {c : Chain (Part α)} (h : ¬∃ a, some a ∈ c) : Part.ωSup c = none :=
   dif_neg h
 #align part.ωSup_eq_none Part.ωSup_eq_none
+-/
 
+#print Part.mem_chain_of_mem_ωSup /-
 theorem mem_chain_of_mem_ωSup {c : Chain (Part α)} {a : α} (h : a ∈ Part.ωSup c) : some a ∈ c :=
   by
   simp [Part.ωSup] at h ; split_ifs at h 
@@ -400,6 +417,7 @@ theorem mem_chain_of_mem_ωSup {c : Chain (Part α)} {a : α} (h : a ∈ Part.ω
     rw [← eq_some_iff] at h ; rw [← h]; exact h'
   · rcases h with ⟨⟨⟩⟩
 #align part.mem_chain_of_mem_ωSup Part.mem_chain_of_mem_ωSup
+-/
 
 #print Part.omegaCompletePartialOrder /-
 noncomputable instance omegaCompletePartialOrder : OmegaCompletePartialOrder (Part α)
@@ -416,6 +434,7 @@ noncomputable instance omegaCompletePartialOrder : OmegaCompletePartialOrder (Pa
 
 section Inst
 
+#print Part.mem_ωSup /-
 theorem mem_ωSup (x : α) (c : Chain (Part α)) : x ∈ ωSup c ↔ some x ∈ c :=
   by
   simp [OmegaCompletePartialOrder.ωSup, Part.ωSup]
@@ -428,6 +447,7 @@ theorem mem_ωSup (x : α) (c : Chain (Part α)) : x ∈ ωSup c ↔ some x ∈
     rw [dif_pos h']; have hh := Classical.choose_spec h'
     rw [eq_of_chain hh h]; simp
 #align part.mem_ωSup Part.mem_ωSup
+-/
 
 end Inst
 
@@ -451,10 +471,12 @@ variable [∀ x, OmegaCompletePartialOrder <| β x]
 
 variable [OmegaCompletePartialOrder γ]
 
+#print Pi.OmegaCompletePartialOrder.flip₁_continuous' /-
 theorem flip₁_continuous' (f : ∀ x : α, γ → β x) (a : α) (hf : Continuous' fun x y => f y x) :
     Continuous' (f a) :=
   Continuous.of_bundled _ (fun x y h => hf.to_monotone h a) fun c => congr_fun (hf.to_bundled _ c) a
 #align pi.omega_complete_partial_order.flip₁_continuous' Pi.OmegaCompletePartialOrder.flip₁_continuous'
+-/
 
 #print Pi.OmegaCompletePartialOrder.flip₂_continuous' /-
 theorem flip₂_continuous' (f : γ → ∀ x, β x) (hf : ∀ x, Continuous' fun g => f g x) :
@@ -480,11 +502,13 @@ variable [OmegaCompletePartialOrder β]
 
 variable [OmegaCompletePartialOrder γ]
 
+#print Prod.ωSup /-
 /-- The supremum of a chain in the product `ω`-CPO. -/
 @[simps]
 protected def ωSup (c : Chain (α × β)) : α × β :=
   (ωSup (c.map OrderHom.fst), ωSup (c.map OrderHom.snd))
 #align prod.ωSup Prod.ωSup
+-/
 
 @[simps ωSup_fst ωSup_snd]
 instance : OmegaCompletePartialOrder (α × β)
@@ -493,11 +517,13 @@ instance : OmegaCompletePartialOrder (α × β)
   ωSup_le := fun c ⟨x, x'⟩ h => ⟨ωSup_le _ _ fun i => (h i).1, ωSup_le _ _ fun i => (h i).2⟩
   le_ωSup c i := ⟨le_ωSup (c.map OrderHom.fst) i, le_ωSup (c.map OrderHom.snd) i⟩
 
+#print Prod.ωSup_zip /-
 theorem ωSup_zip (c₀ : Chain α) (c₁ : Chain β) : ωSup (c₀.zip c₁) = (ωSup c₀, ωSup c₁) :=
   by
   apply eq_of_forall_ge_iff; rintro ⟨z₁, z₂⟩
   simp [ωSup_le_iff, forall_and]
 #align prod.ωSup_zip Prod.ωSup_zip
+-/
 
 end Prod
 
@@ -519,6 +545,7 @@ instance (priority := 100) [CompleteLattice α] : OmegaCompletePartialOrder α
 
 variable {α} {β : Type v} [OmegaCompletePartialOrder α] [CompleteLattice β]
 
+#print CompleteLattice.sSup_continuous /-
 theorem sSup_continuous (s : Set <| α →o β) (hs : ∀ f ∈ s, Continuous f) : Continuous (sSup s) :=
   by
   intro c; apply eq_of_forall_ge_iff; intro z
@@ -526,12 +553,16 @@ theorem sSup_continuous (s : Set <| α →o β) (hs : ∀ f ∈ s, Continuous f)
     simpa (config := { contextual := true }) [ωSup_le_iff, hs _ _ _]
   exact ⟨fun H n f hf => H f hf n, fun H f hf n => H n f hf⟩
 #align complete_lattice.Sup_continuous CompleteLattice.sSup_continuous
+-/
 
+#print CompleteLattice.iSup_continuous /-
 theorem iSup_continuous {ι : Sort _} {f : ι → α →o β} (h : ∀ i, Continuous (f i)) :
     Continuous (⨆ i, f i) :=
   sSup_continuous _ <| Set.forall_range_iff.2 h
 #align complete_lattice.supr_continuous CompleteLattice.iSup_continuous
+-/
 
+#print CompleteLattice.sSup_continuous' /-
 theorem sSup_continuous' (s : Set (α → β)) (hc : ∀ f ∈ s, Continuous' f) : Continuous' (sSup s) :=
   by
   lift s to Set (α →o β) using fun f hf => (hc f hf).to_monotone
@@ -540,25 +571,32 @@ theorem sSup_continuous' (s : Set (α → β)) (hc : ∀ f ∈ s, Continuous' f)
   norm_cast
   exact supr_continuous fun f => supr_continuous fun hf => hc f hf
 #align complete_lattice.Sup_continuous' CompleteLattice.sSup_continuous'
+-/
 
+#print CompleteLattice.sup_continuous /-
 theorem sup_continuous {f g : α →o β} (hf : Continuous f) (hg : Continuous g) :
     Continuous (f ⊔ g) := by
   rw [← sSup_pair]; apply Sup_continuous
   rintro f (rfl | rfl | _) <;> assumption
 #align complete_lattice.sup_continuous CompleteLattice.sup_continuous
+-/
 
+#print CompleteLattice.top_continuous /-
 theorem top_continuous : Continuous (⊤ : α →o β) :=
   by
   intro c; apply eq_of_forall_ge_iff; intro z
   simp only [ωSup_le_iff, forall_const, chain.map_coe, (· ∘ ·), Function.const, OrderHom.hasTop_top,
     OrderHom.const_coe_coe]
 #align complete_lattice.top_continuous CompleteLattice.top_continuous
+-/
 
+#print CompleteLattice.bot_continuous /-
 theorem bot_continuous : Continuous (⊥ : α →o β) :=
   by
   rw [← sSup_empty]
   exact Sup_continuous _ fun f hf => hf.elim
 #align complete_lattice.bot_continuous CompleteLattice.bot_continuous
+-/
 
 end CompleteLattice
 
@@ -566,6 +604,7 @@ namespace CompleteLattice
 
 variable {α β : Type _} [OmegaCompletePartialOrder α] [CompleteLinearOrder β]
 
+#print CompleteLattice.inf_continuous /-
 theorem inf_continuous (f g : α →o β) (hf : Continuous f) (hg : Continuous g) :
     Continuous (f ⊓ g) := by
   refine' fun c => eq_of_forall_ge_iff fun z => _
@@ -576,11 +615,14 @@ theorem inf_continuous (f g : α →o β) (hf : Continuous f) (hg : Continuous g
       (h (max i j)).imp (le_trans <| f.mono <| c.mono <| le_max_left _ _)
         (le_trans <| g.mono <| c.mono <| le_max_right _ _)⟩
 #align complete_lattice.inf_continuous CompleteLattice.inf_continuous
+-/
 
+#print CompleteLattice.inf_continuous' /-
 theorem inf_continuous' {f g : α → β} (hf : Continuous' f) (hg : Continuous' g) :
     Continuous' (f ⊓ g) :=
   ⟨_, inf_continuous _ _ hf.snd hg.snd⟩
 #align complete_lattice.inf_continuous' CompleteLattice.inf_continuous'
+-/
 
 end CompleteLattice
 
@@ -630,7 +672,6 @@ structure ContinuousHom extends OrderHom α β where
 
 attribute [nolint doc_blame] continuous_hom.to_order_hom
 
--- mathport name: «expr →𝒄 »
 infixr:25 " →𝒄 " => ContinuousHom
 
 -- Input: \r\MIc
@@ -687,6 +728,7 @@ theorem ite_continuous' {p : Prop} [hp : Decidable p] (f g : α → β) (hf : Co
 #align omega_complete_partial_order.continuous_hom.ite_continuous' OmegaCompletePartialOrder.ContinuousHom.ite_continuous'
 -/
 
+#print OmegaCompletePartialOrder.ContinuousHom.ωSup_bind /-
 theorem ωSup_bind {β γ : Type v} (c : Chain α) (f : α →o Part β) (g : α →o β → Part γ) :
     ωSup (c.map (f.bind g)) = ωSup (c.map f) >>= ωSup (c.map g) :=
   by
@@ -711,19 +753,25 @@ theorem ωSup_bind {β γ : Type v} (c : Chain α) (f : α →o Part β) (g : α
     · apply le_ωSup (c.map g) _ _ _ hb₁
     · apply le_ωSup (c.map f) i _ hb₀
 #align omega_complete_partial_order.continuous_hom.ωSup_bind OmegaCompletePartialOrder.ContinuousHom.ωSup_bind
+-/
 
+#print OmegaCompletePartialOrder.ContinuousHom.bind_continuous' /-
 theorem bind_continuous' {β γ : Type v} (f : α → Part β) (g : α → β → Part γ) :
     Continuous' f → Continuous' g → Continuous' fun x => f x >>= g x
   | ⟨hf, hf'⟩, ⟨hg, hg'⟩ =>
     Continuous.of_bundled' (OrderHom.bind ⟨f, hf⟩ ⟨g, hg⟩)
       (by intro c <;> rw [ωSup_bind, ← hf', ← hg'] <;> rfl)
 #align omega_complete_partial_order.continuous_hom.bind_continuous' OmegaCompletePartialOrder.ContinuousHom.bind_continuous'
+-/
 
+#print OmegaCompletePartialOrder.ContinuousHom.map_continuous' /-
 theorem map_continuous' {β γ : Type v} (f : β → γ) (g : α → Part β) (hg : Continuous' g) :
     Continuous' fun x => f <$> g x := by
   simp only [map_eq_bind_pure_comp] <;> apply bind_continuous' _ _ hg <;> apply const_continuous'
 #align omega_complete_partial_order.continuous_hom.map_continuous' OmegaCompletePartialOrder.ContinuousHom.map_continuous'
+-/
 
+#print OmegaCompletePartialOrder.ContinuousHom.seq_continuous' /-
 theorem seq_continuous' {β γ : Type v} (f : α → Part (β → γ)) (g : α → Part β) (hf : Continuous' f)
     (hg : Continuous' g) : Continuous' fun x => f x <*> g x := by
   simp only [seq_eq_bind_map] <;> apply bind_continuous' _ _ hf <;>
@@ -731,6 +779,7 @@ theorem seq_continuous' {β γ : Type v} (f : α → Part (β → γ)) (g : α 
       intro <;>
     apply map_continuous' _ _ hg
 #align omega_complete_partial_order.continuous_hom.seq_continuous' OmegaCompletePartialOrder.ContinuousHom.seq_continuous'
+-/
 
 #print OmegaCompletePartialOrder.ContinuousHom.continuous /-
 theorem continuous (F : α →𝒄 β) (C : Chain α) : F (ωSup C) = ωSup (C.map F) :=
@@ -787,18 +836,24 @@ protected theorem coe_inj (f g : α →𝒄 β) (h : (f : α → β) = g) : f =
 #align omega_complete_partial_order.continuous_hom.coe_inj OmegaCompletePartialOrder.ContinuousHom.coe_inj
 -/
 
+#print OmegaCompletePartialOrder.ContinuousHom.comp_id /-
 @[simp]
 theorem comp_id (f : β →𝒄 γ) : f.comp id = f := by ext <;> rfl
 #align omega_complete_partial_order.continuous_hom.comp_id OmegaCompletePartialOrder.ContinuousHom.comp_id
+-/
 
+#print OmegaCompletePartialOrder.ContinuousHom.id_comp /-
 @[simp]
 theorem id_comp (f : β →𝒄 γ) : id.comp f = f := by ext <;> rfl
 #align omega_complete_partial_order.continuous_hom.id_comp OmegaCompletePartialOrder.ContinuousHom.id_comp
+-/
 
+#print OmegaCompletePartialOrder.ContinuousHom.comp_assoc /-
 @[simp]
 theorem comp_assoc (f : γ →𝒄 φ) (g : β →𝒄 γ) (h : α →𝒄 β) : f.comp (g.comp h) = (f.comp g).comp h :=
   by ext <;> rfl
 #align omega_complete_partial_order.continuous_hom.comp_assoc OmegaCompletePartialOrder.ContinuousHom.comp_assoc
+-/
 
 @[simp]
 theorem coe_apply (a : α) (f : α →𝒄 β) : (f : α →o β) a = f a :=
@@ -880,6 +935,7 @@ instance : OmegaCompletePartialOrder (α →𝒄 β) :=
 
 namespace Prod
 
+#print OmegaCompletePartialOrder.ContinuousHom.Prod.apply /-
 /-- The application of continuous functions as a continuous function.  -/
 @[simps]
 def apply : (α →𝒄 β) × α →𝒄 β where
@@ -903,6 +959,7 @@ def apply : (α →𝒄 β) × α →𝒄 β where
       apply le_ωSup_of_le i
       rfl
 #align omega_complete_partial_order.continuous_hom.prod.apply OmegaCompletePartialOrder.ContinuousHom.Prod.apply
+-/
 
 end Prod
 
@@ -912,9 +969,11 @@ theorem ωSup_def (c : Chain (α →𝒄 β)) (x : α) : ωSup c x = ContinuousH
 #align omega_complete_partial_order.continuous_hom.ωSup_def OmegaCompletePartialOrder.ContinuousHom.ωSup_def
 -/
 
+#print OmegaCompletePartialOrder.ContinuousHom.ωSup_apply_ωSup /-
 theorem ωSup_apply_ωSup (c₀ : Chain (α →𝒄 β)) (c₁ : Chain α) :
     ωSup c₀ (ωSup c₁) = Prod.apply (ωSup (c₀.zip c₁)) := by simp [prod.apply_apply, Prod.ωSup_zip]
 #align omega_complete_partial_order.continuous_hom.ωSup_apply_ωSup OmegaCompletePartialOrder.ContinuousHom.ωSup_apply_ωSup
+-/
 
 #print OmegaCompletePartialOrder.ContinuousHom.flip /-
 /-- A family of continuous functions yields a continuous family of functions. -/

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

@@ -387,7 +387,6 @@ theorem ωSup_eq_some {c : Chain (Part α)} {a : α} (h : some a ∈ c) : Part.
   calc
     Part.ωSup c = some (Classical.choose this) := dif_pos this
     _ = some a := congr_arg _ (eq_of_chain a' h)
-    
 #align part.ωSup_eq_some Part.ωSup_eq_some
 
 theorem ωSup_eq_none {c : Chain (Part α)} (h : ¬∃ a, some a ∈ c) : Part.ωSup c = none :=

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

@@ -396,7 +396,7 @@ theorem ωSup_eq_none {c : Chain (Part α)} (h : ¬∃ a, some a ∈ c) : Part.
 
 theorem mem_chain_of_mem_ωSup {c : Chain (Part α)} {a : α} (h : a ∈ Part.ωSup c) : some a ∈ c :=
   by
-  simp [Part.ωSup] at h ; split_ifs  at h 
+  simp [Part.ωSup] at h ; split_ifs at h 
   · have h' := Classical.choose_spec h_1
     rw [← eq_some_iff] at h ; rw [← h]; exact h'
   · rcases h with ⟨⟨⟩⟩

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

@@ -232,7 +232,7 @@ theorem le_ωSup_of_le {c : Chain α} {x : α} (i : ℕ) (h : x ≤ c i) : x ≤
 #print OmegaCompletePartialOrder.ωSup_total /-
 theorem ωSup_total {c : Chain α} {x : α} (h : ∀ i, c i ≤ x ∨ x ≤ c i) : ωSup c ≤ x ∨ x ≤ ωSup c :=
   by_cases (fun this : ∀ i, c i ≤ x => Or.inl (ωSup_le _ _ this)) fun this : ¬∀ i, c i ≤ x =>
-    have : ∃ i, ¬c i ≤ x := by simp only [not_forall] at this⊢ <;> assumption
+    have : ∃ i, ¬c i ≤ x := by simp only [not_forall] at this ⊢ <;> assumption
     let ⟨i, hx⟩ := this
     have : x ≤ c i := (h i).resolve_left hx
     Or.inr <| le_ωSup_of_le _ this
@@ -372,7 +372,7 @@ theorem eq_of_chain {c : Chain (Part α)} {a b : α} (ha : some a ∈ c) (hb : s
   cases' ha with i ha; replace ha := ha.symm
   cases' hb with j hb; replace hb := hb.symm
   wlog h : i ≤ j; · exact (this j hb i ha (le_of_not_le h)).symm
-  rw [eq_some_iff] at ha hb
+  rw [eq_some_iff] at ha hb 
   have := c.monotone h _ ha; apply mem_unique this hb
 #align part.eq_of_chain Part.eq_of_chain
 
@@ -396,9 +396,9 @@ theorem ωSup_eq_none {c : Chain (Part α)} (h : ¬∃ a, some a ∈ c) : Part.
 
 theorem mem_chain_of_mem_ωSup {c : Chain (Part α)} {a : α} (h : a ∈ Part.ωSup c) : some a ∈ c :=
   by
-  simp [Part.ωSup] at h; split_ifs  at h
+  simp [Part.ωSup] at h ; split_ifs  at h 
   · have h' := Classical.choose_spec h_1
-    rw [← eq_some_iff] at h; rw [← h]; exact h'
+    rw [← eq_some_iff] at h ; rw [← h]; exact h'
   · rcases h with ⟨⟨⟩⟩
 #align part.mem_chain_of_mem_ωSup Part.mem_chain_of_mem_ωSup
 
@@ -407,7 +407,7 @@ noncomputable instance omegaCompletePartialOrder : OmegaCompletePartialOrder (Pa
     where
   ωSup := Part.ωSup
   le_ωSup c i := by
-    intro x hx; rw [← eq_some_iff] at hx⊢
+    intro x hx; rw [← eq_some_iff] at hx ⊢
     rw [ωSup_eq_some, ← hx]; rw [← hx]; exact ⟨i, rfl⟩
   ωSup_le := by
     rintro c x hx a ha; replace ha := mem_chain_of_mem_ωSup ha
@@ -423,7 +423,7 @@ theorem mem_ωSup (x : α) (c : Chain (Part α)) : x ∈ ωSup c ↔ some x ∈
   constructor
   · split_ifs; swap; rintro ⟨⟨⟩⟩
     intro h'; have hh := Classical.choose_spec h
-    simp at h'; subst x; exact hh
+    simp at h' ; subst x; exact hh
   · intro h
     have h' : ∃ a : α, some a ∈ c := ⟨_, h⟩
     rw [dif_pos h']; have hh := Classical.choose_spec h'
@@ -515,7 +515,7 @@ instance (priority := 100) [CompleteLattice α] : OmegaCompletePartialOrder α
     where
   ωSup c := ⨆ i, c i
   ωSup_le := fun ⟨c, _⟩ s hs => by
-    simp only [iSup_le_iff, OrderHom.coe_fun_mk] at hs⊢ <;> intro i <;> apply hs i
+    simp only [iSup_le_iff, OrderHom.coe_fun_mk] at hs ⊢ <;> intro i <;> apply hs i
   le_ωSup := fun ⟨c, _⟩ i => by simp only [OrderHom.coe_fun_mk] <;> apply le_iSup_of_le i <;> rfl
 
 variable {α} {β : Type v} [OmegaCompletePartialOrder α] [CompleteLattice β]
@@ -536,7 +536,7 @@ theorem iSup_continuous {ι : Sort _} {f : ι → α →o β} (h : ∀ i, Contin
 theorem sSup_continuous' (s : Set (α → β)) (hc : ∀ f ∈ s, Continuous' f) : Continuous' (sSup s) :=
   by
   lift s to Set (α →o β) using fun f hf => (hc f hf).to_monotone
-  simp only [Set.ball_image_iff, continuous'_coe] at hc
+  simp only [Set.ball_image_iff, continuous'_coe] at hc 
   rw [sSup_image]
   norm_cast
   exact supr_continuous fun f => supr_continuous fun hf => hc f hf
@@ -695,9 +695,9 @@ theorem ωSup_bind {β γ : Type v} (c : Chain α) (f : α →o Part β) (g : α
   simp only [ωSup_le_iff, Part.bind_le, chain.mem_map_iff, and_imp, OrderHom.bind_coe, exists_imp]
   constructor <;> intro h'''
   · intro b hb; apply ωSup_le _ _ _
-    rintro i y hy; simp only [Part.mem_ωSup] at hb
+    rintro i y hy; simp only [Part.mem_ωSup] at hb 
     rcases hb with ⟨j, hb⟩; replace hb := hb.symm
-    simp only [Part.eq_some_iff, chain.map_coe, Function.comp_apply, OrderHom.apply_coe] at hy hb
+    simp only [Part.eq_some_iff, chain.map_coe, Function.comp_apply, OrderHom.apply_coe] at hy hb 
     replace hb : b ∈ f (c (max i j)) := f.mono (c.mono (le_max_right i j)) _ hb
     replace hy : y ∈ g (c (max i j)) b := g.mono (c.mono (le_max_left i j)) _ _ hy
     apply h''' (max i j)
@@ -706,7 +706,7 @@ theorem ωSup_bind {β γ : Type v} (c : Chain α) (f : α →o Part β) (g : α
     exact ⟨_, hb, hy⟩
   · intro i; intro y hy
     simp only [exists_prop, Part.bind_eq_bind, Part.mem_bind_iff, chain.map_coe,
-      Function.comp_apply, OrderHom.bind_coe] at hy
+      Function.comp_apply, OrderHom.bind_coe] at hy 
     rcases hy with ⟨b, hb₀, hb₁⟩
     apply h''' b _
     · apply le_ωSup (c.map g) _ _ _ hb₁
@@ -744,7 +744,7 @@ theorem continuous (F : α →𝒄 β) (C : Chain α) : F (ωSup C) = ωSup (C.m
 they are equal. -/
 @[simps, reducible]
 def ofFun (f : α → β) (g : α →𝒄 β) (h : f = g) : α →𝒄 β := by
-  refine' { toOrderHom := { toFun := f.. }.. } <;> subst h <;> rcases g with ⟨⟨⟩⟩ <;> assumption
+  refine' { toOrderHom := { toFun := f .. } .. } <;> subst h <;> rcases g with ⟨⟨⟩⟩ <;> assumption
 #align omega_complete_partial_order.continuous_hom.of_fun OmegaCompletePartialOrder.ContinuousHom.ofFun
 -/
 
@@ -885,7 +885,7 @@ namespace Prod
 @[simps]
 def apply : (α →𝒄 β) × α →𝒄 β where
   toFun f := f.1 f.2
-  monotone' x y h := by dsimp; trans y.fst x.snd <;> [apply h.1;apply y.1.Monotone h.2]
+  monotone' x y h := by dsimp; trans y.fst x.snd <;> [apply h.1; apply y.1.Monotone h.2]
   cont := by
     intro c
     apply le_antisymm

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

@@ -65,7 +65,7 @@ universe u v
 
 attribute [-simp] Part.bind_eq_bind Part.map_eq_map
 
-open Classical
+open scoped Classical
 
 namespace OrderHom
 
@@ -163,10 +163,12 @@ theorem map_comp : (c.map f).map g = c.map (g.comp f) :=
   rfl
 #align omega_complete_partial_order.chain.map_comp OmegaCompletePartialOrder.Chain.map_comp
 
+#print OmegaCompletePartialOrder.Chain.map_le_map /-
 @[mono]
 theorem map_le_map {g : α →o β} (h : f ≤ g) : c.map f ≤ c.map g := fun i => by
   simp [mem_map_iff] <;> intros <;> exists i <;> apply h
 #align omega_complete_partial_order.chain.map_le_map OmegaCompletePartialOrder.Chain.map_le_map
+-/
 
 /-- `chain.zip` pairs up the elements of two chains that have the same index -/
 @[simps]
@@ -207,6 +209,7 @@ variable {α : Type u} {β : Type v} {γ : Type _}
 
 variable [OmegaCompletePartialOrder α]
 
+#print OmegaCompletePartialOrder.lift /-
 /-- Transfer a `omega_complete_partial_order` on `β` to a `omega_complete_partial_order` on `α`
 using a strictly monotone function `f : β →o α`, a definition of ωSup and a proof that `f` is
 continuous with regard to the provided `ωSup` and the ωCPO on `α`. -/
@@ -218,11 +221,15 @@ protected def lift [PartialOrder β] (f : β →o α) (ωSup₀ : Chain β → 
   ωSup_le c x hx := h _ _ (by rw [h'] <;> apply ωSup_le <;> intro <;> apply f.monotone (hx i))
   le_ωSup c i := h _ _ (by rw [h'] <;> apply le_ωSup (c.map f))
 #align omega_complete_partial_order.lift OmegaCompletePartialOrder.lift
+-/
 
+#print OmegaCompletePartialOrder.le_ωSup_of_le /-
 theorem le_ωSup_of_le {c : Chain α} {x : α} (i : ℕ) (h : x ≤ c i) : x ≤ ωSup c :=
   le_trans h (le_ωSup c _)
 #align omega_complete_partial_order.le_ωSup_of_le OmegaCompletePartialOrder.le_ωSup_of_le
+-/
 
+#print OmegaCompletePartialOrder.ωSup_total /-
 theorem ωSup_total {c : Chain α} {x : α} (h : ∀ i, c i ≤ x ∨ x ≤ c i) : ωSup c ≤ x ∨ x ≤ ωSup c :=
   by_cases (fun this : ∀ i, c i ≤ x => Or.inl (ωSup_le _ _ this)) fun this : ¬∀ i, c i ≤ x =>
     have : ∃ i, ¬c i ≤ x := by simp only [not_forall] at this⊢ <;> assumption
@@ -230,12 +237,16 @@ theorem ωSup_total {c : Chain α} {x : α} (h : ∀ i, c i ≤ x ∨ x ≤ c i)
     have : x ≤ c i := (h i).resolve_left hx
     Or.inr <| le_ωSup_of_le _ this
 #align omega_complete_partial_order.ωSup_total OmegaCompletePartialOrder.ωSup_total
+-/
 
+#print OmegaCompletePartialOrder.ωSup_le_ωSup_of_le /-
 @[mono]
 theorem ωSup_le_ωSup_of_le {c₀ c₁ : Chain α} (h : c₀ ≤ c₁) : ωSup c₀ ≤ ωSup c₁ :=
   ωSup_le _ _ fun i => Exists.rec_on (h i) fun j h => le_trans h (le_ωSup _ _)
 #align omega_complete_partial_order.ωSup_le_ωSup_of_le OmegaCompletePartialOrder.ωSup_le_ωSup_of_le
+-/
 
+#print OmegaCompletePartialOrder.ωSup_le_iff /-
 theorem ωSup_le_iff (c : Chain α) (x : α) : ωSup c ≤ x ↔ ∀ i, c i ≤ x :=
   by
   constructor <;> intros
@@ -243,6 +254,7 @@ theorem ωSup_le_iff (c : Chain α) (x : α) : ωSup c ≤ x ↔ ∀ i, c i ≤
     exact le_ωSup _ _; assumption
   exact ωSup_le _ _ ‹_›
 #align omega_complete_partial_order.ωSup_le_iff OmegaCompletePartialOrder.ωSup_le_iff
+-/
 
 #print OmegaCompletePartialOrder.subtype /-
 /-- A subset `p : α → Prop` of the type closed under `ωSup` induces an
@@ -445,11 +457,13 @@ theorem flip₁_continuous' (f : ∀ x : α, γ → β x) (a : α) (hf : Continu
   Continuous.of_bundled _ (fun x y h => hf.to_monotone h a) fun c => congr_fun (hf.to_bundled _ c) a
 #align pi.omega_complete_partial_order.flip₁_continuous' Pi.OmegaCompletePartialOrder.flip₁_continuous'
 
+#print Pi.OmegaCompletePartialOrder.flip₂_continuous' /-
 theorem flip₂_continuous' (f : γ → ∀ x, β x) (hf : ∀ x, Continuous' fun g => f g x) :
     Continuous' f :=
   Continuous.of_bundled _ (fun x y h a => (hf a).to_monotone h)
     (by intro c <;> ext a <;> apply (hf a).to_bundled _ c)
 #align pi.omega_complete_partial_order.flip₂_continuous' Pi.OmegaCompletePartialOrder.flip₂_continuous'
+-/
 
 end OmegaCompletePartialOrder
 
@@ -661,10 +675,12 @@ protected theorem monotone (f : α →𝒄 β) : Monotone f :=
 #align omega_complete_partial_order.continuous_hom.monotone OmegaCompletePartialOrder.ContinuousHom.monotone
 -/
 
+#print OmegaCompletePartialOrder.ContinuousHom.apply_mono /-
 @[mono]
 theorem apply_mono {f g : α →𝒄 β} {x y : α} (h₁ : f ≤ g) (h₂ : x ≤ y) : f x ≤ g y :=
   OrderHom.apply_mono (show (f : α →o β) ≤ g from h₁) h₂
 #align omega_complete_partial_order.continuous_hom.apply_mono OmegaCompletePartialOrder.ContinuousHom.apply_mono
+-/
 
 #print OmegaCompletePartialOrder.ContinuousHom.ite_continuous' /-
 theorem ite_continuous' {p : Prop} [hp : Decidable p] (f g : α → β) (hf : Continuous' f)
@@ -816,6 +832,7 @@ def toMono : (α →𝒄 β) →o α →o β where
 #align omega_complete_partial_order.continuous_hom.to_mono OmegaCompletePartialOrder.ContinuousHom.toMono
 -/
 
+#print OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge /-
 /-- When proving that a chain of applications is below a bound `z`, it suffices to consider the
 functions and values being selected from the same index in the chains.
 
@@ -832,12 +849,15 @@ theorem forall_forall_merge (c₀ : Chain (α →𝒄 β)) (c₁ : Chain α) (z
     · apply (c₀ i).Monotone; apply c₁.monotone; apply le_max_right
     · apply c₀.monotone; apply le_max_left
 #align omega_complete_partial_order.continuous_hom.forall_forall_merge OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge
+-/
 
+#print OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge' /-
 @[simp]
 theorem forall_forall_merge' (c₀ : Chain (α →𝒄 β)) (c₁ : Chain α) (z : β) :
     (∀ j i : ℕ, (c₀ i) (c₁ j) ≤ z) ↔ ∀ i : ℕ, (c₀ i) (c₁ i) ≤ z := by
   rw [forall_swap, forall_forall_merge]
 #align omega_complete_partial_order.continuous_hom.forall_forall_merge' OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge'
+-/
 
 #print OmegaCompletePartialOrder.ContinuousHom.ωSup /-
 /-- The `ωSup` operator for continuous functions, which takes the pointwise countable supremum
@@ -887,14 +907,17 @@ def apply : (α →𝒄 β) × α →𝒄 β where
 
 end Prod
 
+#print OmegaCompletePartialOrder.ContinuousHom.ωSup_def /-
 theorem ωSup_def (c : Chain (α →𝒄 β)) (x : α) : ωSup c x = ContinuousHom.ωSup c x :=
   rfl
 #align omega_complete_partial_order.continuous_hom.ωSup_def OmegaCompletePartialOrder.ContinuousHom.ωSup_def
+-/
 
 theorem ωSup_apply_ωSup (c₀ : Chain (α →𝒄 β)) (c₁ : Chain α) :
     ωSup c₀ (ωSup c₁) = Prod.apply (ωSup (c₀.zip c₁)) := by simp [prod.apply_apply, Prod.ωSup_zip]
 #align omega_complete_partial_order.continuous_hom.ωSup_apply_ωSup OmegaCompletePartialOrder.ContinuousHom.ωSup_apply_ωSup
 
+#print OmegaCompletePartialOrder.ContinuousHom.flip /-
 /-- A family of continuous functions yields a continuous family of functions. -/
 @[simps]
 def flip {α : Type _} (f : α → β →𝒄 γ) : β →𝒄 α → γ
@@ -903,7 +926,9 @@ def flip {α : Type _} (f : α → β →𝒄 γ) : β →𝒄 α → γ
   monotone' x y h a := (f a).Monotone h
   cont := by intro <;> ext <;> change f x _ = _ <;> rw [(f x).Continuous] <;> rfl
 #align omega_complete_partial_order.continuous_hom.flip OmegaCompletePartialOrder.ContinuousHom.flip
+-/
 
+#print OmegaCompletePartialOrder.ContinuousHom.bind /-
 /-- `part.bind` as a continuous function. -/
 @[simps (config := { rhsMd := reducible })]
 noncomputable def bind {β γ : Type v} (f : α →𝒄 Part β) (g : α →𝒄 β → Part γ) : α →𝒄 Part γ :=
@@ -912,6 +937,7 @@ noncomputable def bind {β γ : Type v} (f : α →𝒄 Part β) (g : α →𝒄
     rw [OrderHom.bind, ← OrderHom.bind, ωSup_bind, ← f.continuous, ← g.continuous]
     rfl
 #align omega_complete_partial_order.continuous_hom.bind OmegaCompletePartialOrder.ContinuousHom.bind
+-/
 
 #print OmegaCompletePartialOrder.ContinuousHom.map /-
 /-- `part.map` as a continuous function. -/

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

@@ -77,12 +77,6 @@ variable {β γ}
 
 variable {α} {α' : Type _} {β' : Type _} [Preorder α'] [Preorder β']
 
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 /-- `part.bind` as a monotone function -/
 @[simps]
 def bind {β γ} (f : α →o Part β) (g : α →o β → Part γ) : α →o Part γ
@@ -165,33 +159,15 @@ theorem map_id : c.map OrderHom.id = c :=
 #align omega_complete_partial_order.chain.map_id OmegaCompletePartialOrder.Chain.map_id
 -/
 
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 theorem map_comp : (c.map f).map g = c.map (g.comp f) :=
   rfl
 #align omega_complete_partial_order.chain.map_comp OmegaCompletePartialOrder.Chain.map_comp
 
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 @[mono]
 theorem map_le_map {g : α →o β} (h : f ≤ g) : c.map f ≤ c.map g := fun i => by
   simp [mem_map_iff] <;> intros <;> exists i <;> apply h
 #align omega_complete_partial_order.chain.map_le_map OmegaCompletePartialOrder.Chain.map_le_map
 
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 /-- `chain.zip` pairs up the elements of two chains that have the same index -/
 @[simps]
 def zip (c₀ : Chain α) (c₁ : Chain β) : Chain (α × β) :=
@@ -231,12 +207,6 @@ variable {α : Type u} {β : Type v} {γ : Type _}
 
 variable [OmegaCompletePartialOrder α]
 
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 /-- Transfer a `omega_complete_partial_order` on `β` to a `omega_complete_partial_order` on `α`
 using a strictly monotone function `f : β →o α`, a definition of ωSup and a proof that `f` is
 continuous with regard to the provided `ωSup` and the ωCPO on `α`. -/
@@ -249,22 +219,10 @@ protected def lift [PartialOrder β] (f : β →o α) (ωSup₀ : Chain β → 
   le_ωSup c i := h _ _ (by rw [h'] <;> apply le_ωSup (c.map f))
 #align omega_complete_partial_order.lift OmegaCompletePartialOrder.lift
 
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 theorem le_ωSup_of_le {c : Chain α} {x : α} (i : ℕ) (h : x ≤ c i) : x ≤ ωSup c :=
   le_trans h (le_ωSup c _)
 #align omega_complete_partial_order.le_ωSup_of_le OmegaCompletePartialOrder.le_ωSup_of_le
 
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 theorem ωSup_total {c : Chain α} {x : α} (h : ∀ i, c i ≤ x ∨ x ≤ c i) : ωSup c ≤ x ∨ x ≤ ωSup c :=
   by_cases (fun this : ∀ i, c i ≤ x => Or.inl (ωSup_le _ _ this)) fun this : ¬∀ i, c i ≤ x =>
     have : ∃ i, ¬c i ≤ x := by simp only [not_forall] at this⊢ <;> assumption
@@ -273,23 +231,11 @@ theorem ωSup_total {c : Chain α} {x : α} (h : ∀ i, c i ≤ x ∨ x ≤ c i)
     Or.inr <| le_ωSup_of_le _ this
 #align omega_complete_partial_order.ωSup_total OmegaCompletePartialOrder.ωSup_total
 
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-Case conversion may be inaccurate. Consider using '#align omega_complete_partial_order.ωSup_le_ωSup_of_le OmegaCompletePartialOrder.ωSup_le_ωSup_of_leₓ'. -/
 @[mono]
 theorem ωSup_le_ωSup_of_le {c₀ c₁ : Chain α} (h : c₀ ≤ c₁) : ωSup c₀ ≤ ωSup c₁ :=
   ωSup_le _ _ fun i => Exists.rec_on (h i) fun j h => le_trans h (le_ωSup _ _)
 #align omega_complete_partial_order.ωSup_le_ωSup_of_le OmegaCompletePartialOrder.ωSup_le_ωSup_of_le
 
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 theorem ωSup_le_iff (c : Chain α) (x : α) : ωSup c ≤ x ↔ ∀ i, c i ≤ x :=
   by
   constructor <;> intros
@@ -375,12 +321,6 @@ theorem continuous_id : Continuous (@OrderHom.id α _) := by intro <;> rw [c.map
 #align omega_complete_partial_order.continuous_id OmegaCompletePartialOrder.continuous_id
 -/
 
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 theorem continuous_comp (hfc : Continuous f) (hgc : Continuous g) : Continuous (g.comp f) :=
   by
   dsimp [Continuous] at *; intro
@@ -415,12 +355,6 @@ variable {α : Type u} {β : Type v} {γ : Type _}
 
 open OmegaCompletePartialOrder
 
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-Case conversion may be inaccurate. Consider using '#align part.eq_of_chain Part.eq_of_chainₓ'. -/
 theorem eq_of_chain {c : Chain (Part α)} {a b : α} (ha : some a ∈ c) (hb : some b ∈ c) : a = b :=
   by
   cases' ha with i ha; replace ha := ha.symm
@@ -430,23 +364,11 @@ theorem eq_of_chain {c : Chain (Part α)} {a b : α} (ha : some a ∈ c) (hb : s
   have := c.monotone h _ ha; apply mem_unique this hb
 #align part.eq_of_chain Part.eq_of_chain
 
-/- warning: part.ωSup -> Part.ωSup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align part.ωSup Part.ωSupₓ'. -/
 /-- The (noncomputable) `ωSup` definition for the `ω`-CPO structure on `part α`. -/
 protected noncomputable def ωSup (c : Chain (Part α)) : Part α :=
   if h : ∃ a, some a ∈ c then some (Classical.choose h) else none
 #align part.ωSup Part.ωSup
 
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-Case conversion may be inaccurate. Consider using '#align part.ωSup_eq_some Part.ωSup_eq_someₓ'. -/
 theorem ωSup_eq_some {c : Chain (Part α)} {a : α} (h : some a ∈ c) : Part.ωSup c = some a :=
   have : ∃ a, some a ∈ c := ⟨a, h⟩
   have a' : some (Classical.choose this) ∈ c := Classical.choose_spec this
@@ -456,22 +378,10 @@ theorem ωSup_eq_some {c : Chain (Part α)} {a : α} (h : some a ∈ c) : Part.
     
 #align part.ωSup_eq_some Part.ωSup_eq_some
 
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 theorem ωSup_eq_none {c : Chain (Part α)} (h : ¬∃ a, some a ∈ c) : Part.ωSup c = none :=
   dif_neg h
 #align part.ωSup_eq_none Part.ωSup_eq_none
 
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-Case conversion may be inaccurate. Consider using '#align part.mem_chain_of_mem_ωSup Part.mem_chain_of_mem_ωSupₓ'. -/
 theorem mem_chain_of_mem_ωSup {c : Chain (Part α)} {a : α} (h : a ∈ Part.ωSup c) : some a ∈ c :=
   by
   simp [Part.ωSup] at h; split_ifs  at h
@@ -495,12 +405,6 @@ noncomputable instance omegaCompletePartialOrder : OmegaCompletePartialOrder (Pa
 
 section Inst
 
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-Case conversion may be inaccurate. Consider using '#align part.mem_ωSup Part.mem_ωSupₓ'. -/
 theorem mem_ωSup (x : α) (c : Chain (Part α)) : x ∈ ωSup c ↔ some x ∈ c :=
   by
   simp [OmegaCompletePartialOrder.ωSup, Part.ωSup]
@@ -536,23 +440,11 @@ variable [∀ x, OmegaCompletePartialOrder <| β x]
 
 variable [OmegaCompletePartialOrder γ]
 
-/- warning: pi.omega_complete_partial_order.flip₁_continuous' -> Pi.OmegaCompletePartialOrder.flip₁_continuous' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align pi.omega_complete_partial_order.flip₁_continuous' Pi.OmegaCompletePartialOrder.flip₁_continuous'ₓ'. -/
 theorem flip₁_continuous' (f : ∀ x : α, γ → β x) (a : α) (hf : Continuous' fun x y => f y x) :
     Continuous' (f a) :=
   Continuous.of_bundled _ (fun x y h => hf.to_monotone h a) fun c => congr_fun (hf.to_bundled _ c) a
 #align pi.omega_complete_partial_order.flip₁_continuous' Pi.OmegaCompletePartialOrder.flip₁_continuous'
 
-/- warning: pi.omega_complete_partial_order.flip₂_continuous' -> Pi.OmegaCompletePartialOrder.flip₂_continuous' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align pi.omega_complete_partial_order.flip₂_continuous' Pi.OmegaCompletePartialOrder.flip₂_continuous'ₓ'. -/
 theorem flip₂_continuous' (f : γ → ∀ x, β x) (hf : ∀ x, Continuous' fun g => f g x) :
     Continuous' f :=
   Continuous.of_bundled _ (fun x y h a => (hf a).to_monotone h)
@@ -575,12 +467,6 @@ variable [OmegaCompletePartialOrder β]
 
 variable [OmegaCompletePartialOrder γ]
 
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-Case conversion may be inaccurate. Consider using '#align prod.ωSup Prod.ωSupₓ'. -/
 /-- The supremum of a chain in the product `ω`-CPO. -/
 @[simps]
 protected def ωSup (c : Chain (α × β)) : α × β :=
@@ -594,12 +480,6 @@ instance : OmegaCompletePartialOrder (α × β)
   ωSup_le := fun c ⟨x, x'⟩ h => ⟨ωSup_le _ _ fun i => (h i).1, ωSup_le _ _ fun i => (h i).2⟩
   le_ωSup c i := ⟨le_ωSup (c.map OrderHom.fst) i, le_ωSup (c.map OrderHom.snd) i⟩
 
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 theorem ωSup_zip (c₀ : Chain α) (c₁ : Chain β) : ωSup (c₀.zip c₁) = (ωSup c₀, ωSup c₁) :=
   by
   apply eq_of_forall_ge_iff; rintro ⟨z₁, z₂⟩
@@ -626,12 +506,6 @@ instance (priority := 100) [CompleteLattice α] : OmegaCompletePartialOrder α
 
 variable {α} {β : Type v} [OmegaCompletePartialOrder α] [CompleteLattice β]
 
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 theorem sSup_continuous (s : Set <| α →o β) (hs : ∀ f ∈ s, Continuous f) : Continuous (sSup s) :=
   by
   intro c; apply eq_of_forall_ge_iff; intro z
@@ -640,23 +514,11 @@ theorem sSup_continuous (s : Set <| α →o β) (hs : ∀ f ∈ s, Continuous f)
   exact ⟨fun H n f hf => H f hf n, fun H f hf n => H n f hf⟩
 #align complete_lattice.Sup_continuous CompleteLattice.sSup_continuous
 
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 theorem iSup_continuous {ι : Sort _} {f : ι → α →o β} (h : ∀ i, Continuous (f i)) :
     Continuous (⨆ i, f i) :=
   sSup_continuous _ <| Set.forall_range_iff.2 h
 #align complete_lattice.supr_continuous CompleteLattice.iSup_continuous
 
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 theorem sSup_continuous' (s : Set (α → β)) (hc : ∀ f ∈ s, Continuous' f) : Continuous' (sSup s) :=
   by
   lift s to Set (α →o β) using fun f hf => (hc f hf).to_monotone
@@ -666,24 +528,12 @@ theorem sSup_continuous' (s : Set (α → β)) (hc : ∀ f ∈ s, Continuous' f)
   exact supr_continuous fun f => supr_continuous fun hf => hc f hf
 #align complete_lattice.Sup_continuous' CompleteLattice.sSup_continuous'
 
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 theorem sup_continuous {f g : α →o β} (hf : Continuous f) (hg : Continuous g) :
     Continuous (f ⊔ g) := by
   rw [← sSup_pair]; apply Sup_continuous
   rintro f (rfl | rfl | _) <;> assumption
 #align complete_lattice.sup_continuous CompleteLattice.sup_continuous
 
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 theorem top_continuous : Continuous (⊤ : α →o β) :=
   by
   intro c; apply eq_of_forall_ge_iff; intro z
@@ -691,12 +541,6 @@ theorem top_continuous : Continuous (⊤ : α →o β) :=
     OrderHom.const_coe_coe]
 #align complete_lattice.top_continuous CompleteLattice.top_continuous
 
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 theorem bot_continuous : Continuous (⊥ : α →o β) :=
   by
   rw [← sSup_empty]
@@ -709,12 +553,6 @@ namespace CompleteLattice
 
 variable {α β : Type _} [OmegaCompletePartialOrder α] [CompleteLinearOrder β]
 
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 theorem inf_continuous (f g : α →o β) (hf : Continuous f) (hg : Continuous g) :
     Continuous (f ⊓ g) := by
   refine' fun c => eq_of_forall_ge_iff fun z => _
@@ -726,12 +564,6 @@ theorem inf_continuous (f g : α →o β) (hf : Continuous f) (hg : Continuous g
         (le_trans <| g.mono <| c.mono <| le_max_right _ _)⟩
 #align complete_lattice.inf_continuous CompleteLattice.inf_continuous
 
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 theorem inf_continuous' {f g : α → β} (hf : Continuous' f) (hg : Continuous' g) :
     Continuous' (f ⊓ g) :=
   ⟨_, inf_continuous _ _ hf.snd hg.snd⟩
@@ -829,12 +661,6 @@ protected theorem monotone (f : α →𝒄 β) : Monotone f :=
 #align omega_complete_partial_order.continuous_hom.monotone OmegaCompletePartialOrder.ContinuousHom.monotone
 -/
 
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 @[mono]
 theorem apply_mono {f g : α →𝒄 β} {x y : α} (h₁ : f ≤ g) (h₂ : x ≤ y) : f x ≤ g y :=
   OrderHom.apply_mono (show (f : α →o β) ≤ g from h₁) h₂
@@ -846,12 +672,6 @@ theorem ite_continuous' {p : Prop} [hp : Decidable p] (f g : α → β) (hf : Co
 #align omega_complete_partial_order.continuous_hom.ite_continuous' OmegaCompletePartialOrder.ContinuousHom.ite_continuous'
 -/
 
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 theorem ωSup_bind {β γ : Type v} (c : Chain α) (f : α →o Part β) (g : α →o β → Part γ) :
     ωSup (c.map (f.bind g)) = ωSup (c.map f) >>= ωSup (c.map g) :=
   by
@@ -877,12 +697,6 @@ theorem ωSup_bind {β γ : Type v} (c : Chain α) (f : α →o Part β) (g : α
     · apply le_ωSup (c.map f) i _ hb₀
 #align omega_complete_partial_order.continuous_hom.ωSup_bind OmegaCompletePartialOrder.ContinuousHom.ωSup_bind
 
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 theorem bind_continuous' {β γ : Type v} (f : α → Part β) (g : α → β → Part γ) :
     Continuous' f → Continuous' g → Continuous' fun x => f x >>= g x
   | ⟨hf, hf'⟩, ⟨hg, hg'⟩ =>
@@ -890,23 +704,11 @@ theorem bind_continuous' {β γ : Type v} (f : α → Part β) (g : α → β 
       (by intro c <;> rw [ωSup_bind, ← hf', ← hg'] <;> rfl)
 #align omega_complete_partial_order.continuous_hom.bind_continuous' OmegaCompletePartialOrder.ContinuousHom.bind_continuous'
 
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 theorem map_continuous' {β γ : Type v} (f : β → γ) (g : α → Part β) (hg : Continuous' g) :
     Continuous' fun x => f <$> g x := by
   simp only [map_eq_bind_pure_comp] <;> apply bind_continuous' _ _ hg <;> apply const_continuous'
 #align omega_complete_partial_order.continuous_hom.map_continuous' OmegaCompletePartialOrder.ContinuousHom.map_continuous'
 
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 theorem seq_continuous' {β γ : Type v} (f : α → Part (β → γ)) (g : α → Part β) (hf : Continuous' f)
     (hg : Continuous' g) : Continuous' fun x => f x <*> g x := by
   simp only [seq_eq_bind_map] <;> apply bind_continuous' _ _ hf <;>
@@ -970,32 +772,14 @@ protected theorem coe_inj (f g : α →𝒄 β) (h : (f : α → β) = g) : f =
 #align omega_complete_partial_order.continuous_hom.coe_inj OmegaCompletePartialOrder.ContinuousHom.coe_inj
 -/
 
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 @[simp]
 theorem comp_id (f : β →𝒄 γ) : f.comp id = f := by ext <;> rfl
 #align omega_complete_partial_order.continuous_hom.comp_id OmegaCompletePartialOrder.ContinuousHom.comp_id
 
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 @[simp]
 theorem id_comp (f : β →𝒄 γ) : id.comp f = f := by ext <;> rfl
 #align omega_complete_partial_order.continuous_hom.id_comp OmegaCompletePartialOrder.ContinuousHom.id_comp
 
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 @[simp]
 theorem comp_assoc (f : γ →𝒄 φ) (g : β →𝒄 γ) (h : α →𝒄 β) : f.comp (g.comp h) = (f.comp g).comp h :=
   by ext <;> rfl
@@ -1032,12 +816,6 @@ def toMono : (α →𝒄 β) →o α →o β where
 #align omega_complete_partial_order.continuous_hom.to_mono OmegaCompletePartialOrder.ContinuousHom.toMono
 -/
 
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 /-- When proving that a chain of applications is below a bound `z`, it suffices to consider the
 functions and values being selected from the same index in the chains.
 
@@ -1055,12 +833,6 @@ theorem forall_forall_merge (c₀ : Chain (α →𝒄 β)) (c₁ : Chain α) (z
     · apply c₀.monotone; apply le_max_left
 #align omega_complete_partial_order.continuous_hom.forall_forall_merge OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge
 
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 @[simp]
 theorem forall_forall_merge' (c₀ : Chain (α →𝒄 β)) (c₁ : Chain α) (z : β) :
     (∀ j i : ℕ, (c₀ i) (c₁ j) ≤ z) ↔ ∀ i : ℕ, (c₀ i) (c₁ i) ≤ z := by
@@ -1089,12 +861,6 @@ instance : OmegaCompletePartialOrder (α →𝒄 β) :=
 
 namespace Prod
 
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 /-- The application of continuous functions as a continuous function.  -/
 @[simps]
 def apply : (α →𝒄 β) × α →𝒄 β where
@@ -1121,32 +887,14 @@ def apply : (α →𝒄 β) × α →𝒄 β where
 
 end Prod
 
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 theorem ωSup_def (c : Chain (α →𝒄 β)) (x : α) : ωSup c x = ContinuousHom.ωSup c x :=
   rfl
 #align omega_complete_partial_order.continuous_hom.ωSup_def OmegaCompletePartialOrder.ContinuousHom.ωSup_def
 
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 theorem ωSup_apply_ωSup (c₀ : Chain (α →𝒄 β)) (c₁ : Chain α) :
     ωSup c₀ (ωSup c₁) = Prod.apply (ωSup (c₀.zip c₁)) := by simp [prod.apply_apply, Prod.ωSup_zip]
 #align omega_complete_partial_order.continuous_hom.ωSup_apply_ωSup OmegaCompletePartialOrder.ContinuousHom.ωSup_apply_ωSup
 
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-  forall {β : Type.{u1}} {γ : Type.{u2}} [_inst_2 : OmegaCompletePartialOrder.{u1} β] [_inst_3 : OmegaCompletePartialOrder.{u2} γ] {α : Type.{u3}}, (α -> (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} β γ _inst_2 _inst_3)) -> (OmegaCompletePartialOrder.ContinuousHom.{u1, max u3 u2} β (α -> γ) _inst_2 (Pi.omegaCompletePartialOrder.{u3, u2} α (fun (ᾰ : α) => γ) (fun (a : α) => _inst_3)))
-but is expected to have type
-  forall {β : Type.{u1}} {γ : Type.{u2}} [_inst_2 : OmegaCompletePartialOrder.{u1} β] [_inst_3 : OmegaCompletePartialOrder.{u2} γ] {α : Type.{u3}}, (α -> (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} β γ _inst_2 _inst_3)) -> (OmegaCompletePartialOrder.ContinuousHom.{u1, max u2 u3} β (α -> γ) _inst_2 (Pi.instOmegaCompletePartialOrderForAll.{u3, u2} α (fun (ᾰ : α) => γ) (fun (a : α) => _inst_3)))
-Case conversion may be inaccurate. Consider using '#align omega_complete_partial_order.continuous_hom.flip OmegaCompletePartialOrder.ContinuousHom.flipₓ'. -/
 /-- A family of continuous functions yields a continuous family of functions. -/
 @[simps]
 def flip {α : Type _} (f : α → β →𝒄 γ) : β →𝒄 α → γ
@@ -1156,12 +904,6 @@ def flip {α : Type _} (f : α → β →𝒄 γ) : β →𝒄 α → γ
   cont := by intro <;> ext <;> change f x _ = _ <;> rw [(f x).Continuous] <;> rfl
 #align omega_complete_partial_order.continuous_hom.flip OmegaCompletePartialOrder.ContinuousHom.flip
 
-/- warning: omega_complete_partial_order.continuous_hom.bind -> OmegaCompletePartialOrder.ContinuousHom.bind is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] {β : Type.{u2}} {γ : Type.{u2}}, (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α (Part.{u2} β) _inst_1 (Part.omegaCompletePartialOrder.{u2} β)) -> (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α (β -> (Part.{u2} γ)) _inst_1 (Pi.omegaCompletePartialOrder.{u2, u2} β (fun (ᾰ : β) => Part.{u2} γ) (fun (a : β) => Part.omegaCompletePartialOrder.{u2} γ))) -> (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α (Part.{u2} γ) _inst_1 (Part.omegaCompletePartialOrder.{u2} γ))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] {β : Type.{u2}} {γ : Type.{u2}}, (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α (Part.{u2} β) _inst_1 (Part.omegaCompletePartialOrder.{u2} β)) -> (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α (β -> (Part.{u2} γ)) _inst_1 (Pi.instOmegaCompletePartialOrderForAll.{u2, u2} β (fun (ᾰ : β) => Part.{u2} γ) (fun (a : β) => Part.omegaCompletePartialOrder.{u2} γ))) -> (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α (Part.{u2} γ) _inst_1 (Part.omegaCompletePartialOrder.{u2} γ))
-Case conversion may be inaccurate. Consider using '#align omega_complete_partial_order.continuous_hom.bind OmegaCompletePartialOrder.ContinuousHom.bindₓ'. -/
 /-- `part.bind` as a continuous function. -/
 @[simps (config := { rhsMd := reducible })]
 noncomputable def bind {β γ : Type v} (f : α →𝒄 Part β) (g : α →𝒄 β → Part γ) : α →𝒄 Part γ :=

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

@@ -154,10 +154,7 @@ theorem exists_of_mem_map {b : β} : b ∈ c.map f → ∃ a, a ∈ c ∧ f a =
 
 #print OmegaCompletePartialOrder.Chain.mem_map_iff /-
 theorem mem_map_iff {b : β} : b ∈ c.map f ↔ ∃ a, a ∈ c ∧ f a = b :=
-  ⟨exists_of_mem_map _, fun h => by
-    rcases h with ⟨w, h, h'⟩
-    subst b
-    apply mem_map c _ h⟩
+  ⟨exists_of_mem_map _, fun h => by rcases h with ⟨w, h, h'⟩; subst b; apply mem_map c _ h⟩
 #align omega_complete_partial_order.chain.mem_map_iff OmegaCompletePartialOrder.Chain.mem_map_iff
 -/
 
@@ -297,8 +294,7 @@ theorem ωSup_le_iff (c : Chain α) (x : α) : ωSup c ≤ x ↔ ∀ i, c i ≤
   by
   constructor <;> intros
   · trans ωSup c
-    exact le_ωSup _ _
-    assumption
+    exact le_ωSup _ _; assumption
   exact ωSup_le _ _ ‹_›
 #align omega_complete_partial_order.ωSup_le_iff OmegaCompletePartialOrder.ωSup_le_iff
 
@@ -480,9 +476,7 @@ theorem mem_chain_of_mem_ωSup {c : Chain (Part α)} {a : α} (h : a ∈ Part.ω
   by
   simp [Part.ωSup] at h; split_ifs  at h
   · have h' := Classical.choose_spec h_1
-    rw [← eq_some_iff] at h
-    rw [← h]
-    exact h'
+    rw [← eq_some_iff] at h; rw [← h]; exact h'
   · rcases h with ⟨⟨⟩⟩
 #align part.mem_chain_of_mem_ωSup Part.mem_chain_of_mem_ωSup
 
@@ -491,18 +485,11 @@ noncomputable instance omegaCompletePartialOrder : OmegaCompletePartialOrder (Pa
     where
   ωSup := Part.ωSup
   le_ωSup c i := by
-    intro x hx
-    rw [← eq_some_iff] at hx⊢
-    rw [ωSup_eq_some, ← hx]
-    rw [← hx]
-    exact ⟨i, rfl⟩
+    intro x hx; rw [← eq_some_iff] at hx⊢
+    rw [ωSup_eq_some, ← hx]; rw [← hx]; exact ⟨i, rfl⟩
   ωSup_le := by
-    rintro c x hx a ha
-    replace ha := mem_chain_of_mem_ωSup ha
-    cases' ha with i ha
-    apply hx i
-    rw [← ha]
-    apply mem_some
+    rintro c x hx a ha; replace ha := mem_chain_of_mem_ωSup ha
+    cases' ha with i ha; apply hx i; rw [← ha]; apply mem_some
 #align part.omega_complete_partial_order Part.omegaCompletePartialOrder
 -/
 
@@ -518,20 +505,13 @@ theorem mem_ωSup (x : α) (c : Chain (Part α)) : x ∈ ωSup c ↔ some x ∈
   by
   simp [OmegaCompletePartialOrder.ωSup, Part.ωSup]
   constructor
-  · split_ifs
-    swap
-    rintro ⟨⟨⟩⟩
-    intro h'
-    have hh := Classical.choose_spec h
-    simp at h'
-    subst x
-    exact hh
+  · split_ifs; swap; rintro ⟨⟨⟩⟩
+    intro h'; have hh := Classical.choose_spec h
+    simp at h'; subst x; exact hh
   · intro h
     have h' : ∃ a : α, some a ∈ c := ⟨_, h⟩
-    rw [dif_pos h']
-    have hh := Classical.choose_spec h'
-    rw [eq_of_chain hh h]
-    simp
+    rw [dif_pos h']; have hh := Classical.choose_spec h'
+    rw [eq_of_chain hh h]; simp
 #align part.mem_ωSup Part.mem_ωSup
 
 end Inst
@@ -547,10 +527,7 @@ open OmegaCompletePartialOrder OmegaCompletePartialOrder.Chain
 instance [∀ a, OmegaCompletePartialOrder (β a)] : OmegaCompletePartialOrder (∀ a, β a)
     where
   ωSup c a := ωSup (c.map (Pi.evalOrderHom a))
-  ωSup_le c f hf a :=
-    ωSup_le _ _ <| by
-      rintro i
-      apply hf
+  ωSup_le c f hf a := ωSup_le _ _ <| by rintro i; apply hf
   le_ωSup c i x := le_ωSup_of_le _ <| le_rfl
 
 namespace OmegaCompletePartialOrder
@@ -657,9 +634,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align complete_lattice.Sup_continuous CompleteLattice.sSup_continuousₓ'. -/
 theorem sSup_continuous (s : Set <| α →o β) (hs : ∀ f ∈ s, Continuous f) : Continuous (sSup s) :=
   by
-  intro c
-  apply eq_of_forall_ge_iff
-  intro z
+  intro c; apply eq_of_forall_ge_iff; intro z
   suffices (∀ f ∈ s, ∀ (n), (f : _) (c n) ≤ z) ↔ ∀ (n), ∀ f ∈ s, (f : _) (c n) ≤ z by
     simpa (config := { contextual := true }) [ωSup_le_iff, hs _ _ _]
   exact ⟨fun H n f hf => H f hf n, fun H f hf n => H n f hf⟩
@@ -883,12 +858,9 @@ theorem ωSup_bind {β γ : Type v} (c : Chain α) (f : α →o Part β) (g : α
   apply eq_of_forall_ge_iff; intro x
   simp only [ωSup_le_iff, Part.bind_le, chain.mem_map_iff, and_imp, OrderHom.bind_coe, exists_imp]
   constructor <;> intro h'''
-  · intro b hb
-    apply ωSup_le _ _ _
-    rintro i y hy
-    simp only [Part.mem_ωSup] at hb
-    rcases hb with ⟨j, hb⟩
-    replace hb := hb.symm
+  · intro b hb; apply ωSup_le _ _ _
+    rintro i y hy; simp only [Part.mem_ωSup] at hb
+    rcases hb with ⟨j, hb⟩; replace hb := hb.symm
     simp only [Part.eq_some_iff, chain.map_coe, Function.comp_apply, OrderHom.apply_coe] at hy hb
     replace hb : b ∈ f (c (max i j)) := f.mono (c.mono (le_max_right i j)) _ hb
     replace hy : y ∈ g (c (max i j)) b := g.mono (c.mono (le_max_left i j)) _ _ hy
@@ -896,8 +868,7 @@ theorem ωSup_bind {β γ : Type v} (c : Chain α) (f : α →o Part β) (g : α
     simp only [exists_prop, Part.bind_eq_bind, Part.mem_bind_iff, chain.map_coe,
       Function.comp_apply, OrderHom.bind_coe]
     exact ⟨_, hb, hy⟩
-  · intro i
-    intro y hy
+  · intro i; intro y hy
     simp only [exists_prop, Part.bind_eq_bind, Part.mem_bind_iff, chain.map_coe,
       Function.comp_apply, OrderHom.bind_coe] at hy
     rcases hy with ⟨b, hb₀, hb₁⟩
@@ -1080,11 +1051,8 @@ theorem forall_forall_merge (c₀ : Chain (α →𝒄 β)) (c₁ : Chain α) (z
   · apply h
   · apply le_trans _ (h (max i j))
     trans c₀ i (c₁ (max i j))
-    · apply (c₀ i).Monotone
-      apply c₁.monotone
-      apply le_max_right
-    · apply c₀.monotone
-      apply le_max_left
+    · apply (c₀ i).Monotone; apply c₁.monotone; apply le_max_right
+    · apply c₀.monotone; apply le_max_left
 #align omega_complete_partial_order.continuous_hom.forall_forall_merge OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge
 
 /- warning: omega_complete_partial_order.continuous_hom.forall_forall_merge' -> OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge' is a dubious translation:
@@ -1131,24 +1099,19 @@ Case conversion may be inaccurate. Consider using '#align omega_complete_partial
 @[simps]
 def apply : (α →𝒄 β) × α →𝒄 β where
   toFun f := f.1 f.2
-  monotone' x y h := by
-    dsimp
-    trans y.fst x.snd <;> [apply h.1;apply y.1.Monotone h.2]
+  monotone' x y h := by dsimp; trans y.fst x.snd <;> [apply h.1;apply y.1.Monotone h.2]
   cont := by
     intro c
     apply le_antisymm
-    · apply ωSup_le
-      intro i
+    · apply ωSup_le; intro i
       dsimp
       rw [(c _).fst.Continuous]
-      apply ωSup_le
-      intro j
+      apply ωSup_le; intro j
       apply le_ωSup_of_le (max i j)
       apply apply_mono
       exact monotone_fst (OrderHom.mono _ (le_max_left _ _))
       exact monotone_snd (OrderHom.mono _ (le_max_right _ _))
-    · apply ωSup_le
-      intro i
+    · apply ωSup_le; intro i
       apply le_ωSup_of_le i
       dsimp
       apply OrderHom.mono _

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -1133,7 +1133,7 @@ def apply : (α →𝒄 β) × α →𝒄 β where
   toFun f := f.1 f.2
   monotone' x y h := by
     dsimp
-    trans y.fst x.snd <;> [apply h.1, apply y.1.Monotone h.2]
+    trans y.fst x.snd <;> [apply h.1;apply y.1.Monotone h.2]
   cont := by
     intro c
     apply le_antisymm

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

@@ -178,12 +178,16 @@ theorem map_comp : (c.map f).map g = c.map (g.comp f) :=
   rfl
 #align omega_complete_partial_order.chain.map_comp OmegaCompletePartialOrder.Chain.map_comp
 
-#print OmegaCompletePartialOrder.Chain.map_le_map /-
+/- warning: omega_complete_partial_order.chain.map_le_map -> OmegaCompletePartialOrder.Chain.map_le_map is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (c : OmegaCompletePartialOrder.Chain.{u1} α _inst_1) {f : OrderHom.{u1, u2} α β _inst_1 _inst_2} {g : OrderHom.{u1, u2} α β _inst_1 _inst_2}, (LE.le.{max u1 u2} (OrderHom.{u1, u2} α β _inst_1 _inst_2) (Preorder.toHasLe.{max u1 u2} (OrderHom.{u1, u2} α β _inst_1 _inst_2) (OrderHom.preorder.{u1, u2} α β _inst_1 _inst_2)) f g) -> (LE.le.{u2} (OmegaCompletePartialOrder.Chain.{u2} β _inst_2) (OmegaCompletePartialOrder.Chain.hasLe.{u2} β _inst_2) (OmegaCompletePartialOrder.Chain.map.{u1, u2} α β _inst_1 _inst_2 c f) (OmegaCompletePartialOrder.Chain.map.{u1, u2} α β _inst_1 _inst_2 c g))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : Preorder.{u2} β] (c : OmegaCompletePartialOrder.Chain.{u1} α _inst_1) {f : OrderHom.{u1, u2} α β _inst_1 _inst_2} {g : OrderHom.{u1, u2} α β _inst_1 _inst_2}, (LE.le.{max u1 u2} (OrderHom.{u1, u2} α β _inst_1 _inst_2) (Preorder.toLE.{max u1 u2} (OrderHom.{u1, u2} α β _inst_1 _inst_2) (OrderHom.instPreorderOrderHom.{u1, u2} α β _inst_1 _inst_2)) f g) -> (LE.le.{u2} (OmegaCompletePartialOrder.Chain.{u2} β _inst_2) (OmegaCompletePartialOrder.Chain.instLEChain.{u2} β _inst_2) (OmegaCompletePartialOrder.Chain.map.{u1, u2} α β _inst_1 _inst_2 c f) (OmegaCompletePartialOrder.Chain.map.{u1, u2} α β _inst_1 _inst_2 c g))
+Case conversion may be inaccurate. Consider using '#align omega_complete_partial_order.chain.map_le_map OmegaCompletePartialOrder.Chain.map_le_mapₓ'. -/
 @[mono]
 theorem map_le_map {g : α →o β} (h : f ≤ g) : c.map f ≤ c.map g := fun i => by
   simp [mem_map_iff] <;> intros <;> exists i <;> apply h
 #align omega_complete_partial_order.chain.map_le_map OmegaCompletePartialOrder.Chain.map_le_map
--/
 
 /- warning: omega_complete_partial_order.chain.zip -> OmegaCompletePartialOrder.Chain.zip is a dubious translation:
 lean 3 declaration is
@@ -230,7 +234,12 @@ variable {α : Type u} {β : Type v} {γ : Type _}
 
 variable [OmegaCompletePartialOrder α]
 
-#print OmegaCompletePartialOrder.lift /-
+/- warning: omega_complete_partial_order.lift -> OmegaCompletePartialOrder.lift is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] (f : OrderHom.{u2, u1} β α (PartialOrder.toPreorder.{u2} β _inst_2) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (ωSup₀ : (OmegaCompletePartialOrder.Chain.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) -> β), (forall (x : β) (y : β), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderHom.{u2, u1} β α (PartialOrder.toPreorder.{u2} β _inst_2) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (fun (_x : OrderHom.{u2, u1} β α (PartialOrder.toPreorder.{u2} β _inst_2) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) => β -> α) (OrderHom.hasCoeToFun.{u2, u1} β α (PartialOrder.toPreorder.{u2} β _inst_2) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) f x) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderHom.{u2, u1} β α (PartialOrder.toPreorder.{u2} β _inst_2) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (fun (_x : OrderHom.{u2, u1} β α (PartialOrder.toPreorder.{u2} β _inst_2) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) => β -> α) (OrderHom.hasCoeToFun.{u2, u1} β α (PartialOrder.toPreorder.{u2} β _inst_2) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) f y)) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) x y)) -> (forall (c : OmegaCompletePartialOrder.Chain.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)), Eq.{succ u1} α (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (OrderHom.{u2, u1} β α (PartialOrder.toPreorder.{u2} β _inst_2) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (fun (_x : OrderHom.{u2, u1} β α (PartialOrder.toPreorder.{u2} β _inst_2) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) => β -> α) (OrderHom.hasCoeToFun.{u2, u1} β α (PartialOrder.toPreorder.{u2} β _inst_2) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) f (ωSup₀ c)) (OmegaCompletePartialOrder.ωSup.{u1} α _inst_1 (OmegaCompletePartialOrder.Chain.map.{u2, u1} β α (PartialOrder.toPreorder.{u2} β _inst_2) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) c f))) -> (OmegaCompletePartialOrder.{u2} β)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : PartialOrder.{u2} β] (f : OrderHom.{u2, u1} β α (PartialOrder.toPreorder.{u2} β _inst_2) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (ωSup₀ : (OmegaCompletePartialOrder.Chain.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) -> β), (forall (x : β) (y : β), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (OrderHom.toFun.{u2, u1} β α (PartialOrder.toPreorder.{u2} β _inst_2) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) f x) (OrderHom.toFun.{u2, u1} β α (PartialOrder.toPreorder.{u2} β _inst_2) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) f y)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)) x y)) -> (forall (c : OmegaCompletePartialOrder.Chain.{u2} β (PartialOrder.toPreorder.{u2} β _inst_2)), Eq.{succ u1} α (OrderHom.toFun.{u2, u1} β α (PartialOrder.toPreorder.{u2} β _inst_2) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) f (ωSup₀ c)) (OmegaCompletePartialOrder.ωSup.{u1} α _inst_1 (OmegaCompletePartialOrder.Chain.map.{u2, u1} β α (PartialOrder.toPreorder.{u2} β _inst_2) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) c f))) -> (OmegaCompletePartialOrder.{u2} β)
+Case conversion may be inaccurate. Consider using '#align omega_complete_partial_order.lift OmegaCompletePartialOrder.liftₓ'. -/
 /-- Transfer a `omega_complete_partial_order` on `β` to a `omega_complete_partial_order` on `α`
 using a strictly monotone function `f : β →o α`, a definition of ωSup and a proof that `f` is
 continuous with regard to the provided `ωSup` and the ωCPO on `α`. -/
@@ -242,15 +251,23 @@ protected def lift [PartialOrder β] (f : β →o α) (ωSup₀ : Chain β → 
   ωSup_le c x hx := h _ _ (by rw [h'] <;> apply ωSup_le <;> intro <;> apply f.monotone (hx i))
   le_ωSup c i := h _ _ (by rw [h'] <;> apply le_ωSup (c.map f))
 #align omega_complete_partial_order.lift OmegaCompletePartialOrder.lift
--/
 
-#print OmegaCompletePartialOrder.le_ωSup_of_le /-
+/- warning: omega_complete_partial_order.le_ωSup_of_le -> OmegaCompletePartialOrder.le_ωSup_of_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] {c : OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))} {x : α} (i : Nat), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) x (coeFn.{succ u1, succ u1} (OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (fun (_x : OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) => Nat -> α) (OmegaCompletePartialOrder.Chain.hasCoeToFun.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) c i)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) x (OmegaCompletePartialOrder.ωSup.{u1} α _inst_1 c))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] {c : OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))} {x : α} (i : Nat), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) x (OrderHom.toFun.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) c i)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) x (OmegaCompletePartialOrder.ωSup.{u1} α _inst_1 c))
+Case conversion may be inaccurate. Consider using '#align omega_complete_partial_order.le_ωSup_of_le OmegaCompletePartialOrder.le_ωSup_of_leₓ'. -/
 theorem le_ωSup_of_le {c : Chain α} {x : α} (i : ℕ) (h : x ≤ c i) : x ≤ ωSup c :=
   le_trans h (le_ωSup c _)
 #align omega_complete_partial_order.le_ωSup_of_le OmegaCompletePartialOrder.le_ωSup_of_le
--/
 
-#print OmegaCompletePartialOrder.ωSup_total /-
+/- warning: omega_complete_partial_order.ωSup_total -> OmegaCompletePartialOrder.ωSup_total is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] {c : OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))} {x : α}, (forall (i : Nat), Or (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (fun (_x : OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) => Nat -> α) (OmegaCompletePartialOrder.Chain.hasCoeToFun.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) c i) x) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) x (coeFn.{succ u1, succ u1} (OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (fun (_x : OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) => Nat -> α) (OmegaCompletePartialOrder.Chain.hasCoeToFun.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) c i))) -> (Or (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (OmegaCompletePartialOrder.ωSup.{u1} α _inst_1 c) x) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) x (OmegaCompletePartialOrder.ωSup.{u1} α _inst_1 c)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] {c : OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))} {x : α}, (forall (i : Nat), Or (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (OrderHom.toFun.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) c i) x) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) x (OrderHom.toFun.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) c i))) -> (Or (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (OmegaCompletePartialOrder.ωSup.{u1} α _inst_1 c) x) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) x (OmegaCompletePartialOrder.ωSup.{u1} α _inst_1 c)))
+Case conversion may be inaccurate. Consider using '#align omega_complete_partial_order.ωSup_total OmegaCompletePartialOrder.ωSup_totalₓ'. -/
 theorem ωSup_total {c : Chain α} {x : α} (h : ∀ i, c i ≤ x ∨ x ≤ c i) : ωSup c ≤ x ∨ x ≤ ωSup c :=
   by_cases (fun this : ∀ i, c i ≤ x => Or.inl (ωSup_le _ _ this)) fun this : ¬∀ i, c i ≤ x =>
     have : ∃ i, ¬c i ≤ x := by simp only [not_forall] at this⊢ <;> assumption
@@ -258,16 +275,24 @@ theorem ωSup_total {c : Chain α} {x : α} (h : ∀ i, c i ≤ x ∨ x ≤ c i)
     have : x ≤ c i := (h i).resolve_left hx
     Or.inr <| le_ωSup_of_le _ this
 #align omega_complete_partial_order.ωSup_total OmegaCompletePartialOrder.ωSup_total
--/
 
-#print OmegaCompletePartialOrder.ωSup_le_ωSup_of_le /-
+/- warning: omega_complete_partial_order.ωSup_le_ωSup_of_le -> OmegaCompletePartialOrder.ωSup_le_ωSup_of_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] {c₀ : OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))} {c₁ : OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))}, (LE.le.{u1} (OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (OmegaCompletePartialOrder.Chain.hasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) c₀ c₁) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (OmegaCompletePartialOrder.ωSup.{u1} α _inst_1 c₀) (OmegaCompletePartialOrder.ωSup.{u1} α _inst_1 c₁))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] {c₀ : OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))} {c₁ : OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))}, (LE.le.{u1} (OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (OmegaCompletePartialOrder.Chain.instLEChain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) c₀ c₁) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (OmegaCompletePartialOrder.ωSup.{u1} α _inst_1 c₀) (OmegaCompletePartialOrder.ωSup.{u1} α _inst_1 c₁))
+Case conversion may be inaccurate. Consider using '#align omega_complete_partial_order.ωSup_le_ωSup_of_le OmegaCompletePartialOrder.ωSup_le_ωSup_of_leₓ'. -/
 @[mono]
 theorem ωSup_le_ωSup_of_le {c₀ c₁ : Chain α} (h : c₀ ≤ c₁) : ωSup c₀ ≤ ωSup c₁ :=
   ωSup_le _ _ fun i => Exists.rec_on (h i) fun j h => le_trans h (le_ωSup _ _)
 #align omega_complete_partial_order.ωSup_le_ωSup_of_le OmegaCompletePartialOrder.ωSup_le_ωSup_of_le
--/
 
-#print OmegaCompletePartialOrder.ωSup_le_iff /-
+/- warning: omega_complete_partial_order.ωSup_le_iff -> OmegaCompletePartialOrder.ωSup_le_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] (c : OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (x : α), Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (OmegaCompletePartialOrder.ωSup.{u1} α _inst_1 c) x) (forall (i : Nat), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (coeFn.{succ u1, succ u1} (OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (fun (_x : OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) => Nat -> α) (OmegaCompletePartialOrder.Chain.hasCoeToFun.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) c i) x)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] (c : OmegaCompletePartialOrder.Chain.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (x : α), Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (OmegaCompletePartialOrder.ωSup.{u1} α _inst_1 c) x) (forall (i : Nat), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1))) (OrderHom.toFun.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) c i) x)
+Case conversion may be inaccurate. Consider using '#align omega_complete_partial_order.ωSup_le_iff OmegaCompletePartialOrder.ωSup_le_iffₓ'. -/
 theorem ωSup_le_iff (c : Chain α) (x : α) : ωSup c ≤ x ↔ ∀ i, c i ≤ x :=
   by
   constructor <;> intros
@@ -276,7 +301,6 @@ theorem ωSup_le_iff (c : Chain α) (x : α) : ωSup c ≤ x ↔ ∀ i, c i ≤
     assumption
   exact ωSup_le _ _ ‹_›
 #align omega_complete_partial_order.ωSup_le_iff OmegaCompletePartialOrder.ωSup_le_iff
--/
 
 #print OmegaCompletePartialOrder.subtype /-
 /-- A subset `p : α → Prop` of the type closed under `ωSup` induces an
@@ -546,13 +570,17 @@ theorem flip₁_continuous' (f : ∀ x : α, γ → β x) (a : α) (hf : Continu
   Continuous.of_bundled _ (fun x y h => hf.to_monotone h a) fun c => congr_fun (hf.to_bundled _ c) a
 #align pi.omega_complete_partial_order.flip₁_continuous' Pi.OmegaCompletePartialOrder.flip₁_continuous'
 
-#print Pi.OmegaCompletePartialOrder.flip₂_continuous' /-
+/- warning: pi.omega_complete_partial_order.flip₂_continuous' -> Pi.OmegaCompletePartialOrder.flip₂_continuous' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : α -> Type.{u2}} {γ : Type.{u3}} [_inst_1 : forall (x : α), OmegaCompletePartialOrder.{u2} (β x)] [_inst_2 : OmegaCompletePartialOrder.{u3} γ] (f : γ -> (forall (x : α), β x)), (forall (x : α), OmegaCompletePartialOrder.Continuous'.{u3, u2} γ (β x) _inst_2 (_inst_1 x) (fun (g : γ) => f g x)) -> (OmegaCompletePartialOrder.Continuous'.{u3, max u1 u2} γ (forall (x : α), β x) _inst_2 (Pi.omegaCompletePartialOrder.{u1, u2} α (fun (x : α) => β x) (fun (a : α) => _inst_1 a)) f)
+but is expected to have type
+  forall {α : Type.{u1}} {β : α -> Type.{u2}} {γ : Type.{u3}} [_inst_1 : forall (x : α), OmegaCompletePartialOrder.{u2} (β x)] [_inst_2 : OmegaCompletePartialOrder.{u3} γ] (f : γ -> (forall (x : α), β x)), (forall (x : α), OmegaCompletePartialOrder.Continuous'.{u3, u2} γ (β x) _inst_2 (_inst_1 x) (fun (g : γ) => f g x)) -> (OmegaCompletePartialOrder.Continuous'.{u3, max u1 u2} γ (forall (x : α), β x) _inst_2 (Pi.instOmegaCompletePartialOrderForAll.{u1, u2} α (fun (x : α) => β x) (fun (a : α) => _inst_1 a)) f)
+Case conversion may be inaccurate. Consider using '#align pi.omega_complete_partial_order.flip₂_continuous' Pi.OmegaCompletePartialOrder.flip₂_continuous'ₓ'. -/
 theorem flip₂_continuous' (f : γ → ∀ x, β x) (hf : ∀ x, Continuous' fun g => f g x) :
     Continuous' f :=
   Continuous.of_bundled _ (fun x y h a => (hf a).to_monotone h)
     (by intro c <;> ext a <;> apply (hf a).to_bundled _ c)
 #align pi.omega_complete_partial_order.flip₂_continuous' Pi.OmegaCompletePartialOrder.flip₂_continuous'
--/
 
 end OmegaCompletePartialOrder
 
@@ -677,7 +705,7 @@ theorem sup_continuous {f g : α →o β} (hf : Continuous f) (hg : Continuous g
 
 /- warning: complete_lattice.top_continuous -> CompleteLattice.top_continuous is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLattice.{u2} β], OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) (Top.top.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (OrderHom.hasTop.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) (BoundedOrder.toOrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (CompleteLattice.toBoundedOrder.{u2} β _inst_2))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLattice.{u2} β], OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) (Top.top.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (OrderHom.hasTop.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) (BoundedOrder.toOrderTop.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (CompleteLattice.toBoundedOrder.{u2} β _inst_2))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLattice.{u2} β], OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2) (Top.top.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2)))) (OrderHom.instTopOrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2))) (BoundedOrder.toOrderTop.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2)))) (CompleteLattice.toBoundedOrder.{u2} β _inst_2))))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.top_continuous CompleteLattice.top_continuousₓ'. -/
@@ -690,7 +718,7 @@ theorem top_continuous : Continuous (⊤ : α →o β) :=
 
 /- warning: complete_lattice.bot_continuous -> CompleteLattice.bot_continuous is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLattice.{u2} β], OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) (Bot.bot.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (OrderHom.hasBot.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) (BoundedOrder.toOrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (CompleteLattice.toBoundedOrder.{u2} β _inst_2))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLattice.{u2} β], OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) (Bot.bot.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (OrderHom.hasBot.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))) (BoundedOrder.toOrderBot.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (CompleteLattice.toBoundedOrder.{u2} β _inst_2))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLattice.{u2} β], OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2) (Bot.bot.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2)))) (OrderHom.instBotOrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2))) (BoundedOrder.toOrderBot.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2)))) (CompleteLattice.toBoundedOrder.{u2} β _inst_2))))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.bot_continuous CompleteLattice.bot_continuousₓ'. -/
@@ -826,12 +854,16 @@ protected theorem monotone (f : α →𝒄 β) : Monotone f :=
 #align omega_complete_partial_order.continuous_hom.monotone OmegaCompletePartialOrder.ContinuousHom.monotone
 -/
 
-#print OmegaCompletePartialOrder.ContinuousHom.apply_mono /-
+/- warning: omega_complete_partial_order.continuous_hom.apply_mono -> OmegaCompletePartialOrder.ContinuousHom.apply_mono is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align omega_complete_partial_order.continuous_hom.apply_mono OmegaCompletePartialOrder.ContinuousHom.apply_monoₓ'. -/
 @[mono]
 theorem apply_mono {f g : α →𝒄 β} {x y : α} (h₁ : f ≤ g) (h₂ : x ≤ y) : f x ≤ g y :=
   OrderHom.apply_mono (show (f : α →o β) ≤ g from h₁) h₂
 #align omega_complete_partial_order.continuous_hom.apply_mono OmegaCompletePartialOrder.ContinuousHom.apply_mono
--/
 
 #print OmegaCompletePartialOrder.ContinuousHom.ite_continuous' /-
 theorem ite_continuous' {p : Prop} [hp : Decidable p] (f g : α → β) (hf : Continuous' f)
@@ -1029,7 +1061,12 @@ def toMono : (α →𝒄 β) →o α →o β where
 #align omega_complete_partial_order.continuous_hom.to_mono OmegaCompletePartialOrder.ContinuousHom.toMono
 -/
 
-#print OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge /-
+/- warning: omega_complete_partial_order.continuous_hom.forall_forall_merge -> OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align omega_complete_partial_order.continuous_hom.forall_forall_merge OmegaCompletePartialOrder.ContinuousHom.forall_forall_mergeₓ'. -/
 /-- When proving that a chain of applications is below a bound `z`, it suffices to consider the
 functions and values being selected from the same index in the chains.
 
@@ -1049,15 +1086,18 @@ theorem forall_forall_merge (c₀ : Chain (α →𝒄 β)) (c₁ : Chain α) (z
     · apply c₀.monotone
       apply le_max_left
 #align omega_complete_partial_order.continuous_hom.forall_forall_merge OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge
--/
 
-#print OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge' /-
+/- warning: omega_complete_partial_order.continuous_hom.forall_forall_merge' -> OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align omega_complete_partial_order.continuous_hom.forall_forall_merge' OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge'ₓ'. -/
 @[simp]
 theorem forall_forall_merge' (c₀ : Chain (α →𝒄 β)) (c₁ : Chain α) (z : β) :
     (∀ j i : ℕ, (c₀ i) (c₁ j) ≤ z) ↔ ∀ i : ℕ, (c₀ i) (c₁ i) ≤ z := by
   rw [forall_swap, forall_forall_merge]
 #align omega_complete_partial_order.continuous_hom.forall_forall_merge' OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge'
--/
 
 #print OmegaCompletePartialOrder.ContinuousHom.ωSup /-
 /-- The `ωSup` operator for continuous functions, which takes the pointwise countable supremum
@@ -1118,11 +1158,15 @@ def apply : (α →𝒄 β) × α →𝒄 β where
 
 end Prod
 
-#print OmegaCompletePartialOrder.ContinuousHom.ωSup_def /-
+/- warning: omega_complete_partial_order.continuous_hom.ωSup_def -> OmegaCompletePartialOrder.ContinuousHom.ωSup_def is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : OmegaCompletePartialOrder.{u2} β] (c : OmegaCompletePartialOrder.Chain.{max u1 u2} (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α β _inst_1 _inst_2) (PartialOrder.toPreorder.{max u1 u2} (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α β _inst_1 _inst_2) (OmegaCompletePartialOrder.ContinuousHom.partialOrder.{u1, u2} α β _inst_1 _inst_2))) (x : α), Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α β _inst_1 _inst_2) (fun (_x : OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α β _inst_1 _inst_2) => α -> β) (OmegaCompletePartialOrder.ContinuousHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) (OmegaCompletePartialOrder.ωSup.{max u1 u2} (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α β _inst_1 _inst_2) (OmegaCompletePartialOrder.ContinuousHom.omegaCompletePartialOrder.{u1, u2} α β _inst_1 _inst_2) c) x) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α β _inst_1 _inst_2) (fun (_x : OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α β _inst_1 _inst_2) => α -> β) (OmegaCompletePartialOrder.ContinuousHom.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) (OmegaCompletePartialOrder.ContinuousHom.ωSup.{u1, u2} α β _inst_1 _inst_2 c) x)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : OmegaCompletePartialOrder.{u2} β] (c : OmegaCompletePartialOrder.Chain.{max u2 u1} (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α β _inst_1 _inst_2) (PartialOrder.toPreorder.{max u1 u2} (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α β _inst_1 _inst_2) (OmegaCompletePartialOrder.instPartialOrderContinuousHom.{u1, u2} α β _inst_1 _inst_2))) (x : α), Eq.{succ u2} β (OrderHom.toFun.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β _inst_2)) (OmegaCompletePartialOrder.ContinuousHom.toOrderHom.{u1, u2} α β _inst_1 _inst_2 (OmegaCompletePartialOrder.ωSup.{max u1 u2} (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α β _inst_1 _inst_2) (OmegaCompletePartialOrder.ContinuousHom.instOmegaCompletePartialOrderContinuousHom.{u1, u2} α β _inst_1 _inst_2) c)) x) (OrderHom.toFun.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β _inst_2)) (OmegaCompletePartialOrder.ContinuousHom.toOrderHom.{u1, u2} α β _inst_1 _inst_2 (OmegaCompletePartialOrder.ContinuousHom.ωSup.{u1, u2} α β _inst_1 _inst_2 c)) x)
+Case conversion may be inaccurate. Consider using '#align omega_complete_partial_order.continuous_hom.ωSup_def OmegaCompletePartialOrder.ContinuousHom.ωSup_defₓ'. -/
 theorem ωSup_def (c : Chain (α →𝒄 β)) (x : α) : ωSup c x = ContinuousHom.ωSup c x :=
   rfl
 #align omega_complete_partial_order.continuous_hom.ωSup_def OmegaCompletePartialOrder.ContinuousHom.ωSup_def
--/
 
 /- warning: omega_complete_partial_order.continuous_hom.ωSup_apply_ωSup -> OmegaCompletePartialOrder.ContinuousHom.ωSup_apply_ωSup is a dubious translation:
 lean 3 declaration is
@@ -1134,7 +1178,12 @@ theorem ωSup_apply_ωSup (c₀ : Chain (α →𝒄 β)) (c₁ : Chain α) :
     ωSup c₀ (ωSup c₁) = Prod.apply (ωSup (c₀.zip c₁)) := by simp [prod.apply_apply, Prod.ωSup_zip]
 #align omega_complete_partial_order.continuous_hom.ωSup_apply_ωSup OmegaCompletePartialOrder.ContinuousHom.ωSup_apply_ωSup
 
-#print OmegaCompletePartialOrder.ContinuousHom.flip /-
+/- warning: omega_complete_partial_order.continuous_hom.flip -> OmegaCompletePartialOrder.ContinuousHom.flip is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {γ : Type.{u2}} [_inst_2 : OmegaCompletePartialOrder.{u1} β] [_inst_3 : OmegaCompletePartialOrder.{u2} γ] {α : Type.{u3}}, (α -> (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} β γ _inst_2 _inst_3)) -> (OmegaCompletePartialOrder.ContinuousHom.{u1, max u3 u2} β (α -> γ) _inst_2 (Pi.omegaCompletePartialOrder.{u3, u2} α (fun (ᾰ : α) => γ) (fun (a : α) => _inst_3)))
+but is expected to have type
+  forall {β : Type.{u1}} {γ : Type.{u2}} [_inst_2 : OmegaCompletePartialOrder.{u1} β] [_inst_3 : OmegaCompletePartialOrder.{u2} γ] {α : Type.{u3}}, (α -> (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} β γ _inst_2 _inst_3)) -> (OmegaCompletePartialOrder.ContinuousHom.{u1, max u2 u3} β (α -> γ) _inst_2 (Pi.instOmegaCompletePartialOrderForAll.{u3, u2} α (fun (ᾰ : α) => γ) (fun (a : α) => _inst_3)))
+Case conversion may be inaccurate. Consider using '#align omega_complete_partial_order.continuous_hom.flip OmegaCompletePartialOrder.ContinuousHom.flipₓ'. -/
 /-- A family of continuous functions yields a continuous family of functions. -/
 @[simps]
 def flip {α : Type _} (f : α → β →𝒄 γ) : β →𝒄 α → γ
@@ -1143,9 +1192,13 @@ def flip {α : Type _} (f : α → β →𝒄 γ) : β →𝒄 α → γ
   monotone' x y h a := (f a).Monotone h
   cont := by intro <;> ext <;> change f x _ = _ <;> rw [(f x).Continuous] <;> rfl
 #align omega_complete_partial_order.continuous_hom.flip OmegaCompletePartialOrder.ContinuousHom.flip
--/
 
-#print OmegaCompletePartialOrder.ContinuousHom.bind /-
+/- warning: omega_complete_partial_order.continuous_hom.bind -> OmegaCompletePartialOrder.ContinuousHom.bind is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] {β : Type.{u2}} {γ : Type.{u2}}, (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α (Part.{u2} β) _inst_1 (Part.omegaCompletePartialOrder.{u2} β)) -> (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α (β -> (Part.{u2} γ)) _inst_1 (Pi.omegaCompletePartialOrder.{u2, u2} β (fun (ᾰ : β) => Part.{u2} γ) (fun (a : β) => Part.omegaCompletePartialOrder.{u2} γ))) -> (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α (Part.{u2} γ) _inst_1 (Part.omegaCompletePartialOrder.{u2} γ))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] {β : Type.{u2}} {γ : Type.{u2}}, (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α (Part.{u2} β) _inst_1 (Part.omegaCompletePartialOrder.{u2} β)) -> (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α (β -> (Part.{u2} γ)) _inst_1 (Pi.instOmegaCompletePartialOrderForAll.{u2, u2} β (fun (ᾰ : β) => Part.{u2} γ) (fun (a : β) => Part.omegaCompletePartialOrder.{u2} γ))) -> (OmegaCompletePartialOrder.ContinuousHom.{u1, u2} α (Part.{u2} γ) _inst_1 (Part.omegaCompletePartialOrder.{u2} γ))
+Case conversion may be inaccurate. Consider using '#align omega_complete_partial_order.continuous_hom.bind OmegaCompletePartialOrder.ContinuousHom.bindₓ'. -/
 /-- `part.bind` as a continuous function. -/
 @[simps (config := { rhsMd := reducible })]
 noncomputable def bind {β γ : Type v} (f : α →𝒄 Part β) (g : α →𝒄 β → Part γ) : α →𝒄 Part γ :=
@@ -1154,7 +1207,6 @@ noncomputable def bind {β γ : Type v} (f : α →𝒄 Part β) (g : α →𝒄
     rw [OrderHom.bind, ← OrderHom.bind, ωSup_bind, ← f.continuous, ← g.continuous]
     rfl
 #align omega_complete_partial_order.continuous_hom.bind OmegaCompletePartialOrder.ContinuousHom.bind
--/
 
 #print OmegaCompletePartialOrder.ContinuousHom.map /-
 /-- `part.map` as a continuous function. -/

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

@@ -616,18 +616,18 @@ instance (priority := 100) [CompleteLattice α] : OmegaCompletePartialOrder α
     where
   ωSup c := ⨆ i, c i
   ωSup_le := fun ⟨c, _⟩ s hs => by
-    simp only [supᵢ_le_iff, OrderHom.coe_fun_mk] at hs⊢ <;> intro i <;> apply hs i
-  le_ωSup := fun ⟨c, _⟩ i => by simp only [OrderHom.coe_fun_mk] <;> apply le_supᵢ_of_le i <;> rfl
+    simp only [iSup_le_iff, OrderHom.coe_fun_mk] at hs⊢ <;> intro i <;> apply hs i
+  le_ωSup := fun ⟨c, _⟩ i => by simp only [OrderHom.coe_fun_mk] <;> apply le_iSup_of_le i <;> rfl
 
 variable {α} {β : Type v} [OmegaCompletePartialOrder α] [CompleteLattice β]
 
-/- warning: complete_lattice.Sup_continuous -> CompleteLattice.supₛ_continuous is a dubious translation:
+/- warning: complete_lattice.Sup_continuous -> CompleteLattice.sSup_continuous is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (s : Set.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))), (forall (f : OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2)))), (Membership.Mem.{max u1 u2, max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2)))) (Set.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (Set.hasMem.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) f s) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) f)) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) (SupSet.supₛ.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2)))) (OrderHom.hasSup.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) _inst_2) s))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (s : Set.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))), (forall (f : OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2)))), (Membership.Mem.{max u1 u2, max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2)))) (Set.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) (Set.hasMem.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))) f s) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) f)) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) (SupSet.sSup.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2)))) (OrderHom.hasSup.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) _inst_2) s))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (s : Set.{max u2 u1} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2))))), (forall (f : OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2)))), (Membership.mem.{max u1 u2, max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2)))) (Set.{max u2 u1} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2))))) (Set.instMembershipSet.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2))))) f s) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2) f)) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2) (SupSet.supₛ.{max u2 u1} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2)))) (OrderHom.instSupSetOrderHomToPreorderToPartialOrderToCompleteSemilatticeInf.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) _inst_2) s))
-Case conversion may be inaccurate. Consider using '#align complete_lattice.Sup_continuous CompleteLattice.supₛ_continuousₓ'. -/
-theorem supₛ_continuous (s : Set <| α →o β) (hs : ∀ f ∈ s, Continuous f) : Continuous (supₛ s) :=
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLattice.{u2} β] (s : Set.{max u2 u1} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2))))), (forall (f : OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2)))), (Membership.mem.{max u1 u2, max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2)))) (Set.{max u2 u1} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2))))) (Set.instMembershipSet.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2))))) f s) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2) f)) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2) (SupSet.sSup.{max u2 u1} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2)))) (OrderHom.instSupSetOrderHomToPreorderToPartialOrderToCompleteSemilatticeInf.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) _inst_2) s))
+Case conversion may be inaccurate. Consider using '#align complete_lattice.Sup_continuous CompleteLattice.sSup_continuousₓ'. -/
+theorem sSup_continuous (s : Set <| α →o β) (hs : ∀ f ∈ s, Continuous f) : Continuous (sSup s) :=
   by
   intro c
   apply eq_of_forall_ge_iff
@@ -635,33 +635,33 @@ theorem supₛ_continuous (s : Set <| α →o β) (hs : ∀ f ∈ s, Continuous
   suffices (∀ f ∈ s, ∀ (n), (f : _) (c n) ≤ z) ↔ ∀ (n), ∀ f ∈ s, (f : _) (c n) ≤ z by
     simpa (config := { contextual := true }) [ωSup_le_iff, hs _ _ _]
   exact ⟨fun H n f hf => H f hf n, fun H f hf n => H n f hf⟩
-#align complete_lattice.Sup_continuous CompleteLattice.supₛ_continuous
+#align complete_lattice.Sup_continuous CompleteLattice.sSup_continuous
 
-/- warning: complete_lattice.supr_continuous -> CompleteLattice.supᵢ_continuous is a dubious translation:
+/- warning: complete_lattice.supr_continuous -> CompleteLattice.iSup_continuous is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {ι : Sort.{u3}} {f : ι -> (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))}, (forall (i : ι), OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) (f i)) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) (supᵢ.{max u1 u2, u3} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2)))) (OrderHom.hasSup.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) _inst_2) ι (fun (i : ι) => f i)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {ι : Sort.{u3}} {f : ι -> (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2))))}, (forall (i : ι), OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) (f i)) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) (iSup.{max u1 u2, u3} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2)))) (OrderHom.hasSup.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) _inst_2) ι (fun (i : ι) => f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : OmegaCompletePartialOrder.{u2} α] [_inst_2 : CompleteLattice.{u3} β] {ι : Sort.{u1}} {f : ι -> (OrderHom.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (OmegaCompletePartialOrder.toPartialOrder.{u2} α _inst_1)) (PartialOrder.toPreorder.{u3} β (OmegaCompletePartialOrder.toPartialOrder.{u3} β (CompleteLattice.instOmegaCompletePartialOrder.{u3} β _inst_2))))}, (forall (i : ι), OmegaCompletePartialOrder.Continuous.{u2, u3} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u3} β _inst_2) (f i)) -> (OmegaCompletePartialOrder.Continuous.{u2, u3} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u3} β _inst_2) (supᵢ.{max u3 u2, u1} (OrderHom.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (OmegaCompletePartialOrder.toPartialOrder.{u2} α _inst_1)) (PartialOrder.toPreorder.{u3} β (OmegaCompletePartialOrder.toPartialOrder.{u3} β (CompleteLattice.instOmegaCompletePartialOrder.{u3} β _inst_2)))) (OrderHom.instSupSetOrderHomToPreorderToPartialOrderToCompleteSemilatticeInf.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (OmegaCompletePartialOrder.toPartialOrder.{u2} α _inst_1)) _inst_2) ι (fun (i : ι) => f i)))
-Case conversion may be inaccurate. Consider using '#align complete_lattice.supr_continuous CompleteLattice.supᵢ_continuousₓ'. -/
-theorem supᵢ_continuous {ι : Sort _} {f : ι → α →o β} (h : ∀ i, Continuous (f i)) :
+  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : OmegaCompletePartialOrder.{u2} α] [_inst_2 : CompleteLattice.{u3} β] {ι : Sort.{u1}} {f : ι -> (OrderHom.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (OmegaCompletePartialOrder.toPartialOrder.{u2} α _inst_1)) (PartialOrder.toPreorder.{u3} β (OmegaCompletePartialOrder.toPartialOrder.{u3} β (CompleteLattice.instOmegaCompletePartialOrder.{u3} β _inst_2))))}, (forall (i : ι), OmegaCompletePartialOrder.Continuous.{u2, u3} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u3} β _inst_2) (f i)) -> (OmegaCompletePartialOrder.Continuous.{u2, u3} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u3} β _inst_2) (iSup.{max u3 u2, u1} (OrderHom.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (OmegaCompletePartialOrder.toPartialOrder.{u2} α _inst_1)) (PartialOrder.toPreorder.{u3} β (OmegaCompletePartialOrder.toPartialOrder.{u3} β (CompleteLattice.instOmegaCompletePartialOrder.{u3} β _inst_2)))) (OrderHom.instSupSetOrderHomToPreorderToPartialOrderToCompleteSemilatticeInf.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (OmegaCompletePartialOrder.toPartialOrder.{u2} α _inst_1)) _inst_2) ι (fun (i : ι) => f i)))
+Case conversion may be inaccurate. Consider using '#align complete_lattice.supr_continuous CompleteLattice.iSup_continuousₓ'. -/
+theorem iSup_continuous {ι : Sort _} {f : ι → α →o β} (h : ∀ i, Continuous (f i)) :
     Continuous (⨆ i, f i) :=
-  supₛ_continuous _ <| Set.forall_range_iff.2 h
-#align complete_lattice.supr_continuous CompleteLattice.supᵢ_continuous
+  sSup_continuous _ <| Set.forall_range_iff.2 h
+#align complete_lattice.supr_continuous CompleteLattice.iSup_continuous
 
-/- warning: complete_lattice.Sup_continuous' -> CompleteLattice.supₛ_continuous' is a dubious translation:
+/- warning: complete_lattice.Sup_continuous' -> CompleteLattice.sSup_continuous' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{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) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) f)) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{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 : OmegaCompletePartialOrder.{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) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) f)) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{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.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{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.instMembershipSet.{max u1 u2} (α -> β)) f s) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2) f)) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2) (SupSet.supₛ.{max u2 u1} (α -> β) (Pi.supSet.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => CompleteLattice.toSupSet.{u2} β _inst_2)) s))
-Case conversion may be inaccurate. Consider using '#align complete_lattice.Sup_continuous' CompleteLattice.supₛ_continuous'ₓ'. -/
-theorem supₛ_continuous' (s : Set (α → β)) (hc : ∀ f ∈ s, Continuous' f) : Continuous' (supₛ s) :=
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{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.instMembershipSet.{max u1 u2} (α -> β)) f s) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2) f)) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2) (SupSet.sSup.{max u2 u1} (α -> β) (Pi.supSet.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => CompleteLattice.toSupSet.{u2} β _inst_2)) s))
+Case conversion may be inaccurate. Consider using '#align complete_lattice.Sup_continuous' CompleteLattice.sSup_continuous'ₓ'. -/
+theorem sSup_continuous' (s : Set (α → β)) (hc : ∀ f ∈ s, Continuous' f) : Continuous' (sSup s) :=
   by
   lift s to Set (α →o β) using fun f hf => (hc f hf).to_monotone
   simp only [Set.ball_image_iff, continuous'_coe] at hc
-  rw [supₛ_image]
+  rw [sSup_image]
   norm_cast
   exact supr_continuous fun f => supr_continuous fun hf => hc f hf
-#align complete_lattice.Sup_continuous' CompleteLattice.supₛ_continuous'
+#align complete_lattice.Sup_continuous' CompleteLattice.sSup_continuous'
 
 /- warning: complete_lattice.sup_continuous -> CompleteLattice.sup_continuous is a dubious translation:
 lean 3 declaration is
@@ -671,7 +671,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align complete_lattice.sup_continuous CompleteLattice.sup_continuousₓ'. -/
 theorem sup_continuous {f g : α →o β} (hf : Continuous f) (hg : Continuous g) :
     Continuous (f ⊔ g) := by
-  rw [← supₛ_pair]; apply Sup_continuous
+  rw [← sSup_pair]; apply Sup_continuous
   rintro f (rfl | rfl | _) <;> assumption
 #align complete_lattice.sup_continuous CompleteLattice.sup_continuous
 
@@ -696,7 +696,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align complete_lattice.bot_continuous CompleteLattice.bot_continuousₓ'. -/
 theorem bot_continuous : Continuous (⊥ : α →o β) :=
   by
-  rw [← supₛ_empty]
+  rw [← sSup_empty]
   exact Sup_continuous _ fun f hf => hf.elim
 #align complete_lattice.bot_continuous CompleteLattice.bot_continuous
 

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

@@ -902,7 +902,7 @@ theorem map_continuous' {β γ : Type v} (f : β → γ) (g : α → Part β) (h
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] {β : Type.{u2}} {γ : Type.{u2}} (f : α -> (Part.{u2} (β -> γ))) (g : α -> (Part.{u2} β)), (OmegaCompletePartialOrder.Continuous'.{u1, u2} α (Part.{u2} (β -> γ)) _inst_1 (Part.omegaCompletePartialOrder.{u2} (β -> γ)) f) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α (Part.{u2} β) _inst_1 (Part.omegaCompletePartialOrder.{u2} β) g) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α (Part.{u2} γ) _inst_1 (Part.omegaCompletePartialOrder.{u2} γ) (fun (x : α) => Seq.seq.{u2, u2} Part.{u2} (Applicative.toHasSeq.{u2, u2} Part.{u2} (Monad.toApplicative.{u2, u2} Part.{u2} Part.monad.{u2})) β γ (f x) (g x)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] {β : Type.{u2}} {γ : Type.{u2}} (f : α -> (Part.{u2} (β -> γ))) (g : α -> (Part.{u2} β)), (OmegaCompletePartialOrder.Continuous'.{u1, u2} α (Part.{u2} (β -> γ)) _inst_1 (Part.omegaCompletePartialOrder.{u2} (β -> γ)) f) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α (Part.{u2} β) _inst_1 (Part.omegaCompletePartialOrder.{u2} β) g) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α (Part.{u2} γ) _inst_1 (Part.omegaCompletePartialOrder.{u2} γ) (fun (x : α) => Seq.seq.{u2, u2} Part.{u2} (Applicative.toSeq.{u2, u2} Part.{u2} (Monad.toApplicative.{u2, u2} Part.{u2} Part.instMonadPart.{u2})) β γ (f x) (fun (x._@.Mathlib.Order.OmegaCompletePartialOrder._hyg.6415 : Unit) => g x)))
+  forall {α : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] {β : Type.{u2}} {γ : Type.{u2}} (f : α -> (Part.{u2} (β -> γ))) (g : α -> (Part.{u2} β)), (OmegaCompletePartialOrder.Continuous'.{u1, u2} α (Part.{u2} (β -> γ)) _inst_1 (Part.omegaCompletePartialOrder.{u2} (β -> γ)) f) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α (Part.{u2} β) _inst_1 (Part.omegaCompletePartialOrder.{u2} β) g) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α (Part.{u2} γ) _inst_1 (Part.omegaCompletePartialOrder.{u2} γ) (fun (x : α) => Seq.seq.{u2, u2} Part.{u2} (Applicative.toSeq.{u2, u2} Part.{u2} (Monad.toApplicative.{u2, u2} Part.{u2} Part.instMonadPart.{u2})) β γ (f x) (fun (x._@.Mathlib.Order.OmegaCompletePartialOrder._hyg.6462 : Unit) => g x)))
 Case conversion may be inaccurate. Consider using '#align omega_complete_partial_order.continuous_hom.seq_continuous' OmegaCompletePartialOrder.ContinuousHom.seq_continuous'ₓ'. -/
 theorem seq_continuous' {β γ : Type v} (f : α → Part (β → γ)) (g : α → Part β) (hf : Continuous' f)
     (hg : Continuous' g) : Continuous' fun x => f x <*> g x := by

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

@@ -665,9 +665,9 @@ theorem supₛ_continuous' (s : Set (α → β)) (hc : ∀ f ∈ s, Continuous'
 
 /- warning: complete_lattice.sup_continuous -> CompleteLattice.sup_continuous is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))} {g : OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))}, (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) f) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) g) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) (HasSup.sup.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2)))) (OrderHom.hasSup.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (Lattice.toSemilatticeSup.{u2} β (CompleteLattice.toLattice.{u2} β _inst_2))) f g))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))} {g : OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))}, (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) f) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) g) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2) (Sup.sup.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.omegaCompletePartialOrder.{u2} β _inst_2)))) (OrderHom.hasSup.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (Lattice.toSemilatticeSup.{u2} β (CompleteLattice.toLattice.{u2} β _inst_2))) f g))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2)))} {g : OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2)))}, (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2) f) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2) g) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2) (HasSup.sup.{max u2 u1} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2)))) (OrderHom.instHasSupOrderHomToPreorderToPartialOrder.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (Lattice.toSemilatticeSup.{u2} β (CompleteLattice.toLattice.{u2} β _inst_2))) f g))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLattice.{u2} β] {f : OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2)))} {g : OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2)))}, (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2) f) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2) g) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2) (Sup.sup.{max u2 u1} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.instOmegaCompletePartialOrder.{u2} β _inst_2)))) (OrderHom.instSupOrderHomToPreorderToPartialOrder.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (Lattice.toSemilatticeSup.{u2} β (CompleteLattice.toLattice.{u2} β _inst_2))) f g))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.sup_continuous CompleteLattice.sup_continuousₓ'. -/
 theorem sup_continuous {f g : α →o β} (hf : Continuous f) (hg : Continuous g) :
     Continuous (f ⊔ g) := by
@@ -708,9 +708,9 @@ variable {α β : Type _} [OmegaCompletePartialOrder α] [CompleteLinearOrder β
 
 /- warning: complete_lattice.inf_continuous -> CompleteLattice.inf_continuous is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLinearOrder.{u2} β] (f : OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2))))) (g : OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2))))), (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2)) f) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2)) g) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2)) (HasInf.inf.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.omegaCompletePartialOrder.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2))))) (OrderHom.hasInf.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (Lattice.toSemilatticeInf.{u2} β (CompleteLattice.toLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2)))) f g))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLinearOrder.{u2} β] (f : OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2))))) (g : OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2))))), (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2)) f) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2)) g) -> (OmegaCompletePartialOrder.Continuous.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2)) (Inf.inf.{max u1 u2} (OrderHom.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (PartialOrder.toPreorder.{u2} β (OmegaCompletePartialOrder.toPartialOrder.{u2} β (CompleteLattice.omegaCompletePartialOrder.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2))))) (OrderHom.hasInf.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (OmegaCompletePartialOrder.toPartialOrder.{u1} α _inst_1)) (Lattice.toSemilatticeInf.{u2} β (CompleteLattice.toLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2)))) f g))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u2} α] [_inst_2 : CompleteLinearOrder.{u1} β] (f : OrderHom.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (OmegaCompletePartialOrder.toPartialOrder.{u2} α _inst_1)) (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2))))) (g : OrderHom.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (OmegaCompletePartialOrder.toPartialOrder.{u2} α _inst_1)) (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2))))), (OmegaCompletePartialOrder.Continuous.{u2, u1} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2)) f) -> (OmegaCompletePartialOrder.Continuous.{u2, u1} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2)) g) -> (OmegaCompletePartialOrder.Continuous.{u2, u1} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2)) (HasInf.inf.{max u1 u2} (OrderHom.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (OmegaCompletePartialOrder.toPartialOrder.{u2} α _inst_1)) (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2))))) (OrderHom.instHasInfOrderHomToPreorderToPartialOrder.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (OmegaCompletePartialOrder.toPartialOrder.{u2} α _inst_1)) (Lattice.toSemilatticeInf.{u1} β (CompleteLattice.toLattice.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2)))) f g))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u2} α] [_inst_2 : CompleteLinearOrder.{u1} β] (f : OrderHom.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (OmegaCompletePartialOrder.toPartialOrder.{u2} α _inst_1)) (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2))))) (g : OrderHom.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (OmegaCompletePartialOrder.toPartialOrder.{u2} α _inst_1)) (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2))))), (OmegaCompletePartialOrder.Continuous.{u2, u1} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2)) f) -> (OmegaCompletePartialOrder.Continuous.{u2, u1} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2)) g) -> (OmegaCompletePartialOrder.Continuous.{u2, u1} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2)) (Inf.inf.{max u1 u2} (OrderHom.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (OmegaCompletePartialOrder.toPartialOrder.{u2} α _inst_1)) (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2))))) (OrderHom.instInfOrderHomToPreorderToPartialOrder.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (OmegaCompletePartialOrder.toPartialOrder.{u2} α _inst_1)) (Lattice.toSemilatticeInf.{u1} β (CompleteLattice.toLattice.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2)))) f g))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.inf_continuous CompleteLattice.inf_continuousₓ'. -/
 theorem inf_continuous (f g : α →o β) (hf : Continuous f) (hg : Continuous g) :
     Continuous (f ⊓ g) := by
@@ -725,9 +725,9 @@ theorem inf_continuous (f g : α →o β) (hf : Continuous f) (hg : Continuous g
 
 /- warning: complete_lattice.inf_continuous' -> CompleteLattice.inf_continuous' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLinearOrder.{u2} β] {f : α -> β} {g : α -> β}, (OmegaCompletePartialOrder.Continuous'.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2)) f) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2)) g) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2)) (HasInf.inf.{max u1 u2} (α -> β) (Pi.hasInf.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => SemilatticeInf.toHasInf.{u2} β (Lattice.toSemilatticeInf.{u2} β (CompleteLattice.toLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2))))) f g))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : OmegaCompletePartialOrder.{u1} α] [_inst_2 : CompleteLinearOrder.{u2} β] {f : α -> β} {g : α -> β}, (OmegaCompletePartialOrder.Continuous'.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2)) f) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2)) g) -> (OmegaCompletePartialOrder.Continuous'.{u1, u2} α β _inst_1 (CompleteLattice.omegaCompletePartialOrder.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2)) (Inf.inf.{max u1 u2} (α -> β) (Pi.hasInf.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => SemilatticeInf.toHasInf.{u2} β (Lattice.toSemilatticeInf.{u2} β (CompleteLattice.toLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_2))))) f g))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u2} α] [_inst_2 : CompleteLinearOrder.{u1} β] {f : α -> β} {g : α -> β}, (OmegaCompletePartialOrder.Continuous'.{u2, u1} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2)) f) -> (OmegaCompletePartialOrder.Continuous'.{u2, u1} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2)) g) -> (OmegaCompletePartialOrder.Continuous'.{u2, u1} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2)) (HasInf.inf.{max u1 u2} (α -> β) (Pi.instHasInfForAll.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => Lattice.toHasInf.{u1} β (CompleteLattice.toLattice.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2)))) f g))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : OmegaCompletePartialOrder.{u2} α] [_inst_2 : CompleteLinearOrder.{u1} β] {f : α -> β} {g : α -> β}, (OmegaCompletePartialOrder.Continuous'.{u2, u1} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2)) f) -> (OmegaCompletePartialOrder.Continuous'.{u2, u1} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2)) g) -> (OmegaCompletePartialOrder.Continuous'.{u2, u1} α β _inst_1 (CompleteLattice.instOmegaCompletePartialOrder.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2)) (Inf.inf.{max u1 u2} (α -> β) (Pi.instInfForAll.{u2, u1} α (fun (ᾰ : α) => β) (fun (i : α) => Lattice.toInf.{u1} β (CompleteLattice.toLattice.{u1} β (CompleteLinearOrder.toCompleteLattice.{u1} β _inst_2)))) f g))
 Case conversion may be inaccurate. Consider using '#align complete_lattice.inf_continuous' CompleteLattice.inf_continuous'ₓ'. -/
 theorem inf_continuous' {f g : α → β} (hf : Continuous' f) (hg : Continuous' g) :
     Continuous' (f ⊓ g) :=

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

A PR accompanying #12339.

Zulip discussion

@@ -232,8 +232,8 @@ theorem ωSup_le_ωSup_of_le {c₀ c₁ : Chain α} (h : c₀ ≤ c₁) : ωSup
 theorem ωSup_le_iff (c : Chain α) (x : α) : ωSup c ≤ x ↔ ∀ i, c i ≤ x := by
   constructor <;> intros
   · trans ωSup c
-    exact le_ωSup _ _
-    assumption
+    · exact le_ωSup _ _
+    · assumption
   exact ωSup_le _ _ ‹_›
 #align omega_complete_partial_order.ωSup_le_iff OmegaCompletePartialOrder.ωSup_le_iff
 
@@ -295,9 +295,9 @@ lemma isLUB_of_scottContinuous {c : Chain α} {f : α → β} (hf : ScottContinu
 
 lemma ScottContinuous.continuous' {f : α → β} (hf : ScottContinuous f) : Continuous' f := by
   constructor
-  intro c
-  rw [← (ωSup_eq_of_isLUB (isLUB_of_scottContinuous hf))]
-  simp only [OrderHom.coe_mk]
+  · intro c
+    rw [← (ωSup_eq_of_isLUB (isLUB_of_scottContinuous hf))]
+    simp only [OrderHom.coe_mk]
 
 theorem Continuous'.to_monotone {f : α → β} (hf : Continuous' f) : Monotone f :=
   hf.fst
@@ -417,7 +417,7 @@ theorem mem_ωSup (x : α) (c : Chain (Part α)) : x ∈ ωSup c ↔ some x ∈
   constructor
   · split_ifs with h
     swap
-    rintro ⟨⟨⟩⟩
+    · rintro ⟨⟨⟩⟩
     intro h'
     have hh := Classical.choose_spec h
     simp only [mem_some_iff] at h'
@@ -857,8 +857,8 @@ def apply : (α →𝒄 β) × α →𝒄 β where
       intro j
       apply le_ωSup_of_le (max i j)
       apply apply_mono
-      exact monotone_fst (OrderHom.mono _ (le_max_left _ _))
-      exact monotone_snd (OrderHom.mono _ (le_max_right _ _))
+      · exact monotone_fst (OrderHom.mono _ (le_max_left _ _))
+      · exact monotone_snd (OrderHom.mono _ (le_max_right _ _))
     · apply ωSup_le
       intro i
       apply le_ωSup_of_le i

Scatter the content of Data.Nat.Basic across:

• Data.Nat.Defs for the lemmas having no dependencies
• Algebra.Group.Nat for the monoid instances and the few miscellaneous lemmas needing them.
• Algebra.Ring.Nat for the semiring instance and the few miscellaneous lemmas following it.

Similarly, scatter

• Data.Int.Basic across Data.Int.Defs, Algebra.Group.Int, Algebra.Ring.Int
• Data.Nat.Order.Basic across Data.Nat.Defs, Algebra.Order.Group.Nat, Algebra.Order.Ring.Nat
• Data.Int.Order.Basic across Data.Int.Defs, Algebra.Order.Group.Int, Algebra.Order.Ring.Int

Also move a few lemmas from Data.Nat.Order.Lemmas to Data.Nat.Defs.

Before

After

@@ -7,7 +7,7 @@ import Mathlib.Control.Monad.Basic
 import Mathlib.Data.Part
 import Mathlib.Order.Chain
 import Mathlib.Order.Hom.Order
-import Mathlib.Data.Nat.Order.Basic
+import Mathlib.Algebra.Order.Ring.Nat
 
 #align_import order.omega_complete_partial_order from "leanprover-community/mathlib"@"92ca63f0fb391a9ca5f22d2409a6080e786d99f7"
 

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -194,7 +194,6 @@ class OmegaCompletePartialOrder (α : Type*) extends PartialOrder α where
 namespace OmegaCompletePartialOrder
 
 variable {α : Type u} {β : Type v} {γ : Type*}
-
 variable [OmegaCompletePartialOrder α]
 
 /-- Transfer an `OmegaCompletePartialOrder` on `β` to an `OmegaCompletePartialOrder` on `α`
@@ -584,7 +583,6 @@ end CompleteLattice
 namespace OmegaCompletePartialOrder
 
 variable {α : Type u} {α' : Type*} {β : Type v} {β' : Type*} {γ : Type*} {φ : Type*}
-
 variable [OmegaCompletePartialOrder α] [OmegaCompletePartialOrder β]
 variable [OmegaCompletePartialOrder γ] [OmegaCompletePartialOrder φ]
 variable [OmegaCompletePartialOrder α'] [OmegaCompletePartialOrder β']

More tactics that are not used, found using the linter at #11308.

The PR consists of tactic removals, whitespace changes and replacing a porting note by an explanation.

@@ -154,7 +154,7 @@ theorem map_comp : (c.map f).map g = c.map (g.comp f) :=
 
 @[mono]
 theorem map_le_map {g : α →o β} (h : f ≤ g) : c.map f ≤ c.map g :=
-  fun i => by simp [mem_map_iff]; intros; exists i; apply h
+  fun i => by simp [mem_map_iff]; exists i; apply h
 #align omega_complete_partial_order.chain.map_le_map OmegaCompletePartialOrder.Chain.map_le_map
 
 /-- `OmegaCompletePartialOrder.Chain.zip` pairs up the elements of two chains

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

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

@@ -529,16 +529,16 @@ theorem sSup_continuous (s : Set <| α →o β) (hs : ∀ f ∈ s, Continuous f)
 
 theorem iSup_continuous {ι : Sort*} {f : ι → α →o β} (h : ∀ i, Continuous (f i)) :
     Continuous (⨆ i, f i) :=
-  sSup_continuous _ <| Set.forall_range_iff.2 h
+  sSup_continuous _ <| Set.forall_mem_range.2 h
 #align complete_lattice.supr_continuous CompleteLattice.iSup_continuous
 
 theorem sSup_continuous' (s : Set (α → β)) (hc : ∀ f ∈ s, Continuous' f) :
     Continuous' (sSup s) := by
   lift s to Set (α →o β) using fun f hf => (hc f hf).to_monotone
-  simp only [Set.ball_image_iff, continuous'_coe] at hc
+  simp only [Set.forall_mem_image, continuous'_coe] at hc
   rw [sSup_image]
   norm_cast
-  exact iSup_continuous fun f => iSup_continuous fun hf => hc f hf
+  exact iSup_continuous fun f ↦ iSup_continuous fun hf ↦ hc hf
 #align complete_lattice.Sup_continuous' CompleteLattice.sSup_continuous'
 
 theorem sup_continuous {f g : α →o β} (hf : Continuous f) (hg : Continuous g) :

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -60,7 +60,7 @@ universe u v
 -- Porting note: can this really be a good idea?
 attribute [-simp] Part.bind_eq_bind Part.map_eq_map
 
-open Classical
+open scoped Classical
 
 namespace OrderHom
 

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -57,7 +57,7 @@ supremum helps define the meaning of recursive procedures.
 
 universe u v
 
--- porting note: can this really be a good idea?
+-- Porting note: can this really be a good idea?
 attribute [-simp] Part.bind_eq_bind Part.map_eq_map
 
 open Classical
@@ -174,7 +174,7 @@ end OmegaCompletePartialOrder
 
 open OmegaCompletePartialOrder
 
--- porting note: removed "set_option extends_priority 50"
+-- Porting note: removed "set_option extends_priority 50"
 
 /-- An omega-complete partial order is a partial order with a supremum
 operation on increasing sequences indexed by natural numbers (which we
@@ -361,7 +361,7 @@ theorem eq_of_chain {c : Chain (Part α)} {a b : α} (ha : some a ∈ c) (hb : s
   rcases le_total i j with hij | hji
   · have := c.monotone hij _ ha; apply mem_unique this hb
   · have := c.monotone hji _ hb; apply Eq.symm; apply mem_unique this ha
-  --Porting note: Old proof
+  -- Porting note: Old proof
   -- wlog h : i ≤ j := le_total i j using a b i j, b a j i
   -- rw [eq_some_iff] at ha hb
   -- have := c.monotone h _ ha; apply mem_unique this hb
@@ -891,7 +891,7 @@ def flip {α : Type*} (f : α → β →𝒄 γ) : β →𝒄 α → γ where
 #align omega_complete_partial_order.continuous_hom.flip_apply OmegaCompletePartialOrder.ContinuousHom.flip_apply
 
 /-- `Part.bind` as a continuous function. -/
-@[simps! apply] --Porting note: removed `(config := { rhsMd := reducible })`
+@[simps! apply] -- Porting note: removed `(config := { rhsMd := reducible })`
 noncomputable def bind {β γ : Type v} (f : α →𝒄 Part β) (g : α →𝒄 β → Part γ) : α →𝒄 Part γ :=
   .mk (OrderHom.bind f g.toOrderHom) fun c => by
     rw [ωSup_bind, ← f.continuous, g.toOrderHom_eq_coe, ← g.continuous]
@@ -900,7 +900,7 @@ noncomputable def bind {β γ : Type v} (f : α →𝒄 Part β) (g : α →𝒄
 #align omega_complete_partial_order.continuous_hom.bind_apply OmegaCompletePartialOrder.ContinuousHom.bind_apply
 
 /-- `Part.map` as a continuous function. -/
-@[simps! apply] --Porting note: removed `(config := { rhsMd := reducible })`
+@[simps! apply] -- Porting note: removed `(config := { rhsMd := reducible })`
 noncomputable def map {β γ : Type v} (f : β → γ) (g : α →𝒄 Part β) : α →𝒄 Part γ :=
   .copy (fun x => f <$> g x) (bind g (const (pure ∘ f))) <| by
     ext1
@@ -910,7 +910,7 @@ noncomputable def map {β γ : Type v} (f : β → γ) (g : α →𝒄 Part β)
 #align omega_complete_partial_order.continuous_hom.map_apply OmegaCompletePartialOrder.ContinuousHom.map_apply
 
 /-- `Part.seq` as a continuous function. -/
-@[simps! apply] --Porting note: removed `(config := { rhsMd := reducible })`
+@[simps! apply] -- Porting note: removed `(config := { rhsMd := reducible })`
 noncomputable def seq {β γ : Type v} (f : α →𝒄 Part (β → γ)) (g : α →𝒄 Part β) : α →𝒄 Part γ :=
   .copy (fun x => f x <*> g x) (bind f <| flip <| _root_.flip map g) <| by
       ext

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -75,7 +75,7 @@ def bind {β γ} (f : α →o Part β) (g : α →o β → Part γ) : α →o Pa
     intro x y h a
     simp only [and_imp, exists_prop, Part.bind_eq_bind, Part.mem_bind_iff, exists_imp]
     intro b hb ha
-    refine' ⟨b, f.monotone h _ hb, g.monotone h _ _ ha⟩
+    exact ⟨b, f.monotone h _ hb, g.monotone h _ _ ha⟩
 #align order_hom.bind OrderHom.bind
 #align order_hom.bind_coe OrderHom.bind_coe
 

Remove unnecessary "rw"s.

@@ -399,7 +399,7 @@ noncomputable instance omegaCompletePartialOrder :
   le_ωSup c i := by
     intro x hx
     rw [← eq_some_iff] at hx ⊢
-    rw [ωSup_eq_some, ← hx]
+    rw [ωSup_eq_some]
     rw [← hx]
     exact ⟨i, rfl⟩
   ωSup_le := by

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

simp not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -95,6 +95,7 @@ namespace Chain
 variable {α : Type u} {β : Type v} {γ : Type*}
 variable [Preorder α] [Preorder β] [Preorder γ]
 
+instance : FunLike (Chain α) ℕ α := inferInstanceAs <| FunLike (ℕ →o α) ℕ α
 instance : OrderHomClass (Chain α) ℕ α := inferInstanceAs <| OrderHomClass (ℕ →o α) ℕ α
 instance : CoeFun (Chain α) fun _ => ℕ → α := ⟨DFunLike.coe⟩
 
@@ -622,9 +623,11 @@ attribute [nolint docBlame] ContinuousHom.toOrderHom
 
 @[inherit_doc] infixr:25 " →𝒄 " => ContinuousHom -- Input: \r\MIc
 
-instance : OrderHomClass (α →𝒄 β) α β where
+instance : FunLike (α →𝒄 β) α β where
   coe f := f.toFun
   coe_injective' := by rintro ⟨⟩ ⟨⟩ h; congr; exact DFunLike.ext' h
+
+instance : OrderHomClass (α →𝒄 β) α β where
   map_rel f _ _ h := f.mono h
 
 -- Porting note: removed to avoid conflict with the generic instance

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

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

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

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

@@ -96,7 +96,7 @@ variable {α : Type u} {β : Type v} {γ : Type*}
 variable [Preorder α] [Preorder β] [Preorder γ]
 
 instance : OrderHomClass (Chain α) ℕ α := inferInstanceAs <| OrderHomClass (ℕ →o α) ℕ α
-instance : CoeFun (Chain α) fun _ => ℕ → α := ⟨FunLike.coe⟩
+instance : CoeFun (Chain α) fun _ => ℕ → α := ⟨DFunLike.coe⟩
 
 instance [Inhabited α] : Inhabited (Chain α) :=
   ⟨⟨default, fun _ _ _ => le_rfl⟩⟩
@@ -624,7 +624,7 @@ attribute [nolint docBlame] ContinuousHom.toOrderHom
 
 instance : OrderHomClass (α →𝒄 β) α β where
   coe f := f.toFun
-  coe_injective' := by rintro ⟨⟩ ⟨⟩ h; congr; exact FunLike.ext' h
+  coe_injective' := by rintro ⟨⟩ ⟨⟩ h; congr; exact DFunLike.ext' h
   map_rel f _ _ h := f.mono h
 
 -- Porting note: removed to avoid conflict with the generic instance
@@ -643,7 +643,7 @@ theorem toOrderHom_eq_coe (f : α →𝒄 β) : f.1 = f := rfl
 @[simp] theorem coe_mk (f : α →o β) (hf : Continuous f) : ⇑(mk f hf) = f := rfl
 @[simp] theorem coe_toOrderHom (f : α →𝒄 β) : ⇑f.1 = f := rfl
 
-/-- See Note [custom simps projection]. We specify this explicitly because we don't have a FunLike
+/-- See Note [custom simps projection]. We specify this explicitly because we don't have a DFunLike
 instance.
 -/
 def Simps.apply (h : α →𝒄 β) : α → β :=
@@ -652,7 +652,7 @@ def Simps.apply (h : α →𝒄 β) : α → β :=
 initialize_simps_projections ContinuousHom (toFun → apply)
 
 theorem congr_fun {f g : α →𝒄 β} (h : f = g) (x : α) : f x = g x :=
-  FunLike.congr_fun h x
+  DFunLike.congr_fun h x
 #align omega_complete_partial_order.continuous_hom.congr_fun OmegaCompletePartialOrder.ContinuousHom.congr_fun
 
 theorem congr_arg (f : α →𝒄 β) {x y : α} (h : x = y) : f x = f y :=
@@ -752,11 +752,11 @@ def comp (f : β →𝒄 γ) (g : α →𝒄 β) : α →𝒄 γ := ⟨.comp f.1
 #align omega_complete_partial_order.continuous_hom.comp_apply OmegaCompletePartialOrder.ContinuousHom.comp_apply
 
 @[ext]
-protected theorem ext (f g : α →𝒄 β) (h : ∀ x, f x = g x) : f = g := FunLike.ext f g h
+protected theorem ext (f g : α →𝒄 β) (h : ∀ x, f x = g x) : f = g := DFunLike.ext f g h
 #align omega_complete_partial_order.continuous_hom.ext OmegaCompletePartialOrder.ContinuousHom.ext
 
 protected theorem coe_inj (f g : α →𝒄 β) (h : (f : α → β) = g) : f = g :=
-  FunLike.ext' h
+  DFunLike.ext' h
 #align omega_complete_partial_order.continuous_hom.coe_inj OmegaCompletePartialOrder.ContinuousHom.coe_inj
 
 @[simp]