topology.algebra.order.intermediate_value ⟷ Mathlib.Topology.Algebra.Order.IntermediateValue

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

@@ -116,7 +116,7 @@ theorem IsPreconnected.intermediate_value₂_eventually₁ {s : Set X} (hs : IsP
     {l : Filter X} (ha : a ∈ s) [NeBot l] (hl : l ≤ 𝓟 s) {f g : X → α} (hf : ContinuousOn f s)
     (hg : ContinuousOn g s) (ha' : f a ≤ g a) (he : g ≤ᶠ[l] f) : ∃ x ∈ s, f x = g x :=
   by
-  rw [continuousOn_iff_continuous_restrict] at hf hg 
+  rw [continuousOn_iff_continuous_restrict] at hf hg
   obtain ⟨b, h⟩ :=
     @intermediate_value_univ₂_eventually₁ _ _ _ _ _ _ (Subtype.preconnectedSpace hs) ⟨a, ha⟩ _
       (comap_coe_ne_bot_of_le_principal hl) _ _ hf hg ha' (he.comap _)
@@ -130,7 +130,7 @@ theorem IsPreconnected.intermediate_value₂_eventually₂ {s : Set X} (hs : IsP
     (hf : ContinuousOn f s) (hg : ContinuousOn g s) (he₁ : f ≤ᶠ[l₁] g) (he₂ : g ≤ᶠ[l₂] f) :
     ∃ x ∈ s, f x = g x :=
   by
-  rw [continuousOn_iff_continuous_restrict] at hf hg 
+  rw [continuousOn_iff_continuous_restrict] at hf hg
   obtain ⟨b, h⟩ :=
     @intermediate_value_univ₂_eventually₂ _ _ _ _ _ _ (Subtype.preconnectedSpace hs) _ _
       (comap_coe_ne_bot_of_le_principal hl₁) (comap_coe_ne_bot_of_le_principal hl₂) _ _ hf hg
@@ -509,7 +509,7 @@ theorem isPreconnected_Icc : IsPreconnected (Icc a b) :=
       cases le_total x y
       · exact isPreconnected_Icc_aux x y s t h hs ht hab hx hy
       · rw [inter_comm s t]
-        rw [union_comm s t] at hab 
+        rw [union_comm s t] at hab
         exact isPreconnected_Icc_aux y x t s h ht hs hab hy hx)
 #align is_preconnected_Icc isPreconnected_Icc
 -/

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Alistair Tucker
 -/
-import Mathbin.Order.CompleteLatticeIntervals
-import Mathbin.Topology.Order.Basic
+import Order.CompleteLatticeIntervals
+import Topology.Order.Basic
 
 #align_import topology.algebra.order.intermediate_value from "leanprover-community/mathlib"@"50832daea47b195a48b5b33b1c8b2162c48c3afc"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Alistair Tucker
-
-! This file was ported from Lean 3 source module topology.algebra.order.intermediate_value
-! leanprover-community/mathlib commit 50832daea47b195a48b5b33b1c8b2162c48c3afc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Order.CompleteLatticeIntervals
 import Mathbin.Topology.Order.Basic
 
+#align_import topology.algebra.order.intermediate_value from "leanprover-community/mathlib"@"50832daea47b195a48b5b33b1c8b2162c48c3afc"
+
 /-!
 # Intermediate Value Theorem
 

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

@@ -99,6 +99,7 @@ theorem intermediate_value_univ₂_eventually₂ [PreconnectedSpace X] {l₁ l
 #align intermediate_value_univ₂_eventually₂ intermediate_value_univ₂_eventually₂
 -/
 
+#print IsPreconnected.intermediate_value₂ /-
 /-- Intermediate value theorem for two functions: if `f` and `g` are two functions continuous
 on a preconnected set `s` and for some `a b ∈ s` we have `f a ≤ g a` and `g b ≤ f b`,
 then for some `x ∈ s` we have `f x = g x`. -/
@@ -111,7 +112,9 @@ theorem IsPreconnected.intermediate_value₂ {s : Set X} (hs : IsPreconnected s)
       hb'
   ⟨x, x.2, hx⟩
 #align is_preconnected.intermediate_value₂ IsPreconnected.intermediate_value₂
+-/
 
+#print IsPreconnected.intermediate_value₂_eventually₁ /-
 theorem IsPreconnected.intermediate_value₂_eventually₁ {s : Set X} (hs : IsPreconnected s) {a : X}
     {l : Filter X} (ha : a ∈ s) [NeBot l] (hl : l ≤ 𝓟 s) {f g : X → α} (hf : ContinuousOn f s)
     (hg : ContinuousOn g s) (ha' : f a ≤ g a) (he : g ≤ᶠ[l] f) : ∃ x ∈ s, f x = g x :=
@@ -122,7 +125,9 @@ theorem IsPreconnected.intermediate_value₂_eventually₁ {s : Set X} (hs : IsP
       (comap_coe_ne_bot_of_le_principal hl) _ _ hf hg ha' (he.comap _)
   exact ⟨b, b.prop, h⟩
 #align is_preconnected.intermediate_value₂_eventually₁ IsPreconnected.intermediate_value₂_eventually₁
+-/
 
+#print IsPreconnected.intermediate_value₂_eventually₂ /-
 theorem IsPreconnected.intermediate_value₂_eventually₂ {s : Set X} (hs : IsPreconnected s)
     {l₁ l₂ : Filter X} [NeBot l₁] [NeBot l₂] (hl₁ : l₁ ≤ 𝓟 s) (hl₂ : l₂ ≤ 𝓟 s) {f g : X → α}
     (hf : ContinuousOn f s) (hg : ContinuousOn g s) (he₁ : f ≤ᶠ[l₁] g) (he₂ : g ≤ᶠ[l₂] f) :
@@ -135,6 +140,7 @@ theorem IsPreconnected.intermediate_value₂_eventually₂ {s : Set X} (hs : IsP
       (he₁.comap _) (he₂.comap _)
   exact ⟨b, b.prop, h⟩
 #align is_preconnected.intermediate_value₂_eventually₂ IsPreconnected.intermediate_value₂_eventually₂
+-/
 
 #print IsPreconnected.intermediate_value /-
 /-- **Intermediate Value Theorem** for continuous functions on connected sets. -/
@@ -144,6 +150,7 @@ theorem IsPreconnected.intermediate_value {s : Set X} (hs : IsPreconnected s) {a
 #align is_preconnected.intermediate_value IsPreconnected.intermediate_value
 -/
 
+#print IsPreconnected.intermediate_value_Ico /-
 theorem IsPreconnected.intermediate_value_Ico {s : Set X} (hs : IsPreconnected s) {a : X}
     {l : Filter X} (ha : a ∈ s) [NeBot l] (hl : l ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s) {v : α}
     (ht : Tendsto f l (𝓝 v)) : Ico (f a) v ⊆ f '' s := fun y h =>
@@ -151,7 +158,9 @@ theorem IsPreconnected.intermediate_value_Ico {s : Set X} (hs : IsPreconnected s
     hs.intermediate_value₂_eventually₁ ha hl hf continuousOn_const h.1
       (eventually_ge_of_tendsto_gt h.2 ht)
 #align is_preconnected.intermediate_value_Ico IsPreconnected.intermediate_value_Ico
+-/
 
+#print IsPreconnected.intermediate_value_Ioc /-
 theorem IsPreconnected.intermediate_value_Ioc {s : Set X} (hs : IsPreconnected s) {a : X}
     {l : Filter X} (ha : a ∈ s) [NeBot l] (hl : l ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s) {v : α}
     (ht : Tendsto f l (𝓝 v)) : Ioc v (f a) ⊆ f '' s := fun y h =>
@@ -160,7 +169,9 @@ theorem IsPreconnected.intermediate_value_Ioc {s : Set X} (hs : IsPreconnected s
       hs.intermediate_value₂_eventually₁ ha hl continuousOn_const hf h.2
         (eventually_le_of_tendsto_lt h.1 ht)
 #align is_preconnected.intermediate_value_Ioc IsPreconnected.intermediate_value_Ioc
+-/
 
+#print IsPreconnected.intermediate_value_Ioo /-
 theorem IsPreconnected.intermediate_value_Ioo {s : Set X} (hs : IsPreconnected s) {l₁ l₂ : Filter X}
     [NeBot l₁] [NeBot l₂] (hl₁ : l₁ ≤ 𝓟 s) (hl₂ : l₂ ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s)
     {v₁ v₂ : α} (ht₁ : Tendsto f l₁ (𝓝 v₁)) (ht₂ : Tendsto f l₂ (𝓝 v₂)) : Ioo v₁ v₂ ⊆ f '' s :=
@@ -169,14 +180,18 @@ theorem IsPreconnected.intermediate_value_Ioo {s : Set X} (hs : IsPreconnected s
     hs.intermediate_value₂_eventually₂ hl₁ hl₂ hf continuousOn_const
       (eventually_le_of_tendsto_lt h.1 ht₁) (eventually_ge_of_tendsto_gt h.2 ht₂)
 #align is_preconnected.intermediate_value_Ioo IsPreconnected.intermediate_value_Ioo
+-/
 
+#print IsPreconnected.intermediate_value_Ici /-
 theorem IsPreconnected.intermediate_value_Ici {s : Set X} (hs : IsPreconnected s) {a : X}
     {l : Filter X} (ha : a ∈ s) [NeBot l] (hl : l ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s)
     (ht : Tendsto f l atTop) : Ici (f a) ⊆ f '' s := fun y h =>
   bex_def.1 <|
     hs.intermediate_value₂_eventually₁ ha hl hf continuousOn_const h (tendsto_atTop.1 ht y)
 #align is_preconnected.intermediate_value_Ici IsPreconnected.intermediate_value_Ici
+-/
 
+#print IsPreconnected.intermediate_value_Iic /-
 theorem IsPreconnected.intermediate_value_Iic {s : Set X} (hs : IsPreconnected s) {a : X}
     {l : Filter X} (ha : a ∈ s) [NeBot l] (hl : l ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s)
     (ht : Tendsto f l atBot) : Iic (f a) ⊆ f '' s := fun y h =>
@@ -184,7 +199,9 @@ theorem IsPreconnected.intermediate_value_Iic {s : Set X} (hs : IsPreconnected s
     (BEx.imp_right fun x _ => Eq.symm) <|
       hs.intermediate_value₂_eventually₁ ha hl continuousOn_const hf h (tendsto_atBot.1 ht y)
 #align is_preconnected.intermediate_value_Iic IsPreconnected.intermediate_value_Iic
+-/
 
+#print IsPreconnected.intermediate_value_Ioi /-
 theorem IsPreconnected.intermediate_value_Ioi {s : Set X} (hs : IsPreconnected s) {l₁ l₂ : Filter X}
     [NeBot l₁] [NeBot l₂] (hl₁ : l₁ ≤ 𝓟 s) (hl₂ : l₂ ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s)
     {v : α} (ht₁ : Tendsto f l₁ (𝓝 v)) (ht₂ : Tendsto f l₂ atTop) : Ioi v ⊆ f '' s := fun y h =>
@@ -192,7 +209,9 @@ theorem IsPreconnected.intermediate_value_Ioi {s : Set X} (hs : IsPreconnected s
     hs.intermediate_value₂_eventually₂ hl₁ hl₂ hf continuousOn_const
       (eventually_le_of_tendsto_lt h ht₁) (tendsto_atTop.1 ht₂ y)
 #align is_preconnected.intermediate_value_Ioi IsPreconnected.intermediate_value_Ioi
+-/
 
+#print IsPreconnected.intermediate_value_Iio /-
 theorem IsPreconnected.intermediate_value_Iio {s : Set X} (hs : IsPreconnected s) {l₁ l₂ : Filter X}
     [NeBot l₁] [NeBot l₂] (hl₁ : l₁ ≤ 𝓟 s) (hl₂ : l₂ ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s)
     {v : α} (ht₁ : Tendsto f l₁ atBot) (ht₂ : Tendsto f l₂ (𝓝 v)) : Iio v ⊆ f '' s := fun y h =>
@@ -200,7 +219,9 @@ theorem IsPreconnected.intermediate_value_Iio {s : Set X} (hs : IsPreconnected s
     hs.intermediate_value₂_eventually₂ hl₁ hl₂ hf continuousOn_const (tendsto_atBot.1 ht₁ y)
       (eventually_ge_of_tendsto_gt h ht₂)
 #align is_preconnected.intermediate_value_Iio IsPreconnected.intermediate_value_Iio
+-/
 
+#print IsPreconnected.intermediate_value_Iii /-
 theorem IsPreconnected.intermediate_value_Iii {s : Set X} (hs : IsPreconnected s) {l₁ l₂ : Filter X}
     [NeBot l₁] [NeBot l₂] (hl₁ : l₁ ≤ 𝓟 s) (hl₂ : l₂ ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s)
     (ht₁ : Tendsto f l₁ atBot) (ht₂ : Tendsto f l₂ atTop) : univ ⊆ f '' s := fun y h =>
@@ -208,6 +229,7 @@ theorem IsPreconnected.intermediate_value_Iii {s : Set X} (hs : IsPreconnected s
     hs.intermediate_value₂_eventually₂ hl₁ hl₂ hf continuousOn_const (tendsto_atBot.1 ht₁ y)
       (tendsto_atTop.1 ht₂ y)
 #align is_preconnected.intermediate_value_Iii IsPreconnected.intermediate_value_Iii
+-/
 
 #print intermediate_value_univ /-
 /-- **Intermediate Value Theorem** for continuous functions on connected spaces. -/
@@ -283,6 +305,7 @@ variable {α : Type u} {β : Type v} {γ : Type w} [ConditionallyCompleteLinearO
   [TopologicalSpace α] [OrderTopology α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β]
   [OrderTopology β] [Nonempty γ]
 
+#print IsConnected.Ioo_csInf_csSup_subset /-
 /-- A bounded connected subset of a conditionally complete linear order includes the open interval
 `(Inf s, Sup s)`. -/
 theorem IsConnected.Ioo_csInf_csSup_subset {s : Set α} (hs : IsConnected s) (hb : BddBelow s)
@@ -291,13 +314,17 @@ theorem IsConnected.Ioo_csInf_csSup_subset {s : Set α} (hs : IsConnected s) (hb
   let ⟨z, zs, hz⟩ := (lt_isLUB_iff (isLUB_csSup hs.Nonempty ha)).1 hx.2
   hs.Icc_subset ys zs ⟨le_of_lt hy, le_of_lt hz⟩
 #align is_connected.Ioo_cInf_cSup_subset IsConnected.Ioo_csInf_csSup_subset
+-/
 
+#print eq_Icc_csInf_csSup_of_connected_bdd_closed /-
 theorem eq_Icc_csInf_csSup_of_connected_bdd_closed {s : Set α} (hc : IsConnected s)
     (hb : BddBelow s) (ha : BddAbove s) (hcl : IsClosed s) : s = Icc (sInf s) (sSup s) :=
   Subset.antisymm (subset_Icc_csInf_csSup hb ha) <|
     hc.Icc_subset (hcl.csInf_mem hc.Nonempty hb) (hcl.csSup_mem hc.Nonempty ha)
 #align eq_Icc_cInf_cSup_of_connected_bdd_closed eq_Icc_csInf_csSup_of_connected_bdd_closed
+-/
 
+#print IsPreconnected.Ioi_csInf_subset /-
 theorem IsPreconnected.Ioi_csInf_subset {s : Set α} (hs : IsPreconnected s) (hb : BddBelow s)
     (ha : ¬BddAbove s) : Ioi (sInf s) ⊆ s :=
   by
@@ -307,12 +334,16 @@ theorem IsPreconnected.Ioi_csInf_subset {s : Set α} (hs : IsPreconnected s) (hb
   obtain ⟨z, zs, hz⟩ : ∃ z ∈ s, x < z := not_bddAbove_iff.1 ha x
   exact hs.Icc_subset ys zs ⟨le_of_lt hy, le_of_lt hz⟩
 #align is_preconnected.Ioi_cInf_subset IsPreconnected.Ioi_csInf_subset
+-/
 
+#print IsPreconnected.Iio_csSup_subset /-
 theorem IsPreconnected.Iio_csSup_subset {s : Set α} (hs : IsPreconnected s) (hb : ¬BddBelow s)
     (ha : BddAbove s) : Iio (sSup s) ⊆ s :=
   @IsPreconnected.Ioi_csInf_subset αᵒᵈ _ _ _ s hs ha hb
 #align is_preconnected.Iio_cSup_subset IsPreconnected.Iio_csSup_subset
+-/
 
+#print IsPreconnected.mem_intervals /-
 /-- A preconnected set in a conditionally complete linear order is either one of the intervals
 `[Inf s, Sup s]`, `[Inf s, Sup s)`, `(Inf s, Sup s]`, `(Inf s, Sup s)`, `[Inf s, +∞)`,
 `(Inf s, +∞)`, `(-∞, Sup s]`, `(-∞, Sup s)`, `(-∞, +∞)`, or `∅`. The converse statement requires
@@ -348,7 +379,9 @@ theorem IsPreconnected.mem_intervals {s : Set α} (hs : IsPreconnected s) :
   · iterate 8 apply Or.inr
     exact Or.inl (hs.eq_univ_of_unbounded hb ha)
 #align is_preconnected.mem_intervals IsPreconnected.mem_intervals
+-/
 
+#print setOf_isPreconnected_subset_of_ordered /-
 /-- A preconnected set is either one of the intervals `Icc`, `Ico`, `Ioc`, `Ioo`, `Ici`, `Ioi`,
 `Iic`, `Iio`, or `univ`, or `∅`. The converse statement requires `α` to be densely ordered. Though
 one can represent `∅` as `(Inf s, Inf s)`, we include it into the list of possible cases to improve
@@ -381,6 +414,7 @@ theorem setOf_isPreconnected_subset_of_ordered :
   · exact Or.inr <| Or.inr <| Or.inl hs
   · exact Or.inr <| Or.inr <| Or.inr hs
 #align set_of_is_preconnected_subset_of_ordered setOf_isPreconnected_subset_of_ordered
+-/
 
 /-!
 ### Intervals are connected
@@ -390,6 +424,7 @@ conditionally complete linear order is preconnected.
 -/
 
 
+#print IsClosed.mem_of_ge_of_forall_exists_gt /-
 /-- A "continuous induction principle" for a closed interval: if a set `s` meets `[a, b]`
 on a closed subset, contains `a`, and the set `s ∩ [a, b)` has no maximal point, then `b ∈ s`. -/
 theorem IsClosed.mem_of_ge_of_forall_exists_gt {a b : α} {s : Set α} (hs : IsClosed (s ∩ Icc a b))
@@ -406,7 +441,9 @@ theorem IsClosed.mem_of_ge_of_forall_exists_gt {a b : α} {s : Set α} (hs : IsC
   rcases hgt c ⟨c_mem.1, c_mem.2.1, hc⟩ with ⟨x, xs, cx, xb⟩
   exact not_lt_of_le (le_csSup Sbd ⟨xs, le_trans (le_csSup Sbd ha) (le_of_lt cx), xb⟩) cx
 #align is_closed.mem_of_ge_of_forall_exists_gt IsClosed.mem_of_ge_of_forall_exists_gt
+-/
 
+#print IsClosed.Icc_subset_of_forall_exists_gt /-
 /-- A "continuous induction principle" for a closed interval: if a set `s` meets `[a, b]`
 on a closed subset, contains `a`, and for any `a ≤ x < y ≤ b`, `x ∈ s`, the set `s ∩ (x, y]`
 is not empty, then `[a, b] ⊆ s`. -/
@@ -424,9 +461,11 @@ theorem IsClosed.Icc_subset_of_forall_exists_gt {a b : α} {s : Set α} (hs : Is
     IsClosed.mem_of_ge_of_forall_exists_gt this ha hy.1 fun x hx =>
       hgt x ⟨hx.1, Ico_subset_Ico_right hy.2 hx.2⟩ y hx.2.2
 #align is_closed.Icc_subset_of_forall_exists_gt IsClosed.Icc_subset_of_forall_exists_gt
+-/
 
 variable [DenselyOrdered α] {a b : α}
 
+#print IsClosed.Icc_subset_of_forall_mem_nhdsWithin /-
 /-- A "continuous induction principle" for a closed interval: if a set `s` meets `[a, b]`
 on a closed subset, contains `a`, and for any `x ∈ s ∩ [a, b)` the set `s` includes some open
 neighborhood of `x` within `(x, +∞)`, then `[a, b] ⊆ s`. -/
@@ -439,7 +478,9 @@ theorem IsClosed.Icc_subset_of_forall_mem_nhdsWithin {a b : α} {s : Set α}
     inter_mem (hgt x ⟨hxs, hxab⟩) (Ioc_mem_nhdsWithin_Ioi ⟨le_rfl, hyxb⟩)
   exact (nhdsWithin_Ioi_self_neBot' ⟨b, hxab.2⟩).nonempty_of_mem this
 #align is_closed.Icc_subset_of_forall_mem_nhds_within IsClosed.Icc_subset_of_forall_mem_nhdsWithin
+-/
 
+#print isPreconnected_Icc_aux /-
 theorem isPreconnected_Icc_aux (x y : α) (s t : Set α) (hxy : x ≤ y) (hs : IsClosed s)
     (ht : IsClosed t) (hab : Icc a b ⊆ s ∪ t) (hx : x ∈ Icc a b ∩ s) (hy : y ∈ Icc a b ∩ t) :
     (Icc a b ∩ (s ∩ t)).Nonempty :=
@@ -459,6 +500,7 @@ theorem isPreconnected_Icc_aux (x y : α) (s t : Set α) (hxy : x ≤ y) (hs : I
   have : Ioc z y ⊆ s ∪ t := fun w hw => hab (xyab ⟨le_trans hz.1 (le_of_lt hw.1), hw.2⟩)
   exact fun w ⟨wt, wzy⟩ => (this wzy).elim id fun h => (wt h).elim
 #align is_preconnected_Icc_aux isPreconnected_Icc_aux
+-/
 
 #print isPreconnected_Icc /-
 /-- A closed interval in a densely ordered conditionally complete linear order is preconnected. -/
@@ -590,6 +632,7 @@ instance (priority := 100) ordered_connected_space : PreconnectedSpace α :=
 #align ordered_connected_space ordered_connected_space
 -/
 
+#print setOf_isPreconnected_eq_of_ordered /-
 /-- In a dense conditionally complete linear order, the set of preconnected sets is exactly
 the set of the intervals `Icc`, `Ico`, `Ioc`, `Ioo`, `Ici`, `Ioi`, `Iic`, `Iio`, `(-∞, +∞)`,
 or `∅`. Though one can represent `∅` as `(Inf s, Inf s)`, we include it into the list of
@@ -616,6 +659,7 @@ theorem setOf_isPreconnected_eq_of_ordered :
     isPreconnected_Ioi, isPreconnected_Iio, isPreconnected_Ici, isPreconnected_Iic,
     is_preconnected_univ, isPreconnected_empty]
 #align set_of_is_preconnected_eq_of_ordered setOf_isPreconnected_eq_of_ordered
+-/
 
 /-!
 ### Intermediate Value Theorem on an interval
@@ -627,26 +671,33 @@ continuous on an interval.
 
 variable {δ : Type _} [LinearOrder δ] [TopologicalSpace δ] [OrderClosedTopology δ]
 
+#print intermediate_value_Icc /-
 /-- **Intermediate Value Theorem** for continuous functions on closed intervals, case
 `f a ≤ t ≤ f b`.-/
 theorem intermediate_value_Icc {a b : α} (hab : a ≤ b) {f : α → δ} (hf : ContinuousOn f (Icc a b)) :
     Icc (f a) (f b) ⊆ f '' Icc a b :=
   isPreconnected_Icc.intermediate_value (left_mem_Icc.2 hab) (right_mem_Icc.2 hab) hf
 #align intermediate_value_Icc intermediate_value_Icc
+-/
 
+#print intermediate_value_Icc' /-
 /-- **Intermediate Value Theorem** for continuous functions on closed intervals, case
 `f a ≥ t ≥ f b`.-/
 theorem intermediate_value_Icc' {a b : α} (hab : a ≤ b) {f : α → δ}
     (hf : ContinuousOn f (Icc a b)) : Icc (f b) (f a) ⊆ f '' Icc a b :=
   isPreconnected_Icc.intermediate_value (right_mem_Icc.2 hab) (left_mem_Icc.2 hab) hf
 #align intermediate_value_Icc' intermediate_value_Icc'
+-/
 
+#print intermediate_value_uIcc /-
 /-- **Intermediate Value Theorem** for continuous functions on closed intervals, unordered case. -/
 theorem intermediate_value_uIcc {a b : α} {f : α → δ} (hf : ContinuousOn f (uIcc a b)) :
     uIcc (f a) (f b) ⊆ f '' uIcc a b := by
   cases le_total (f a) (f b) <;> simp [*, is_preconnected_uIcc.intermediate_value]
 #align intermediate_value_uIcc intermediate_value_uIcc
+-/
 
+#print intermediate_value_Ico /-
 theorem intermediate_value_Ico {a b : α} (hab : a ≤ b) {f : α → δ} (hf : ContinuousOn f (Icc a b)) :
     Ico (f a) (f b) ⊆ f '' Ico a b :=
   Or.elim (eq_or_lt_of_le hab) (fun he y h => absurd h.2 (not_lt_of_le (he ▸ h.1))) fun hlt =>
@@ -654,7 +705,9 @@ theorem intermediate_value_Ico {a b : α} (hab : a ≤ b) {f : α → δ} (hf :
       (right_nhdsWithin_Ico_neBot hlt) inf_le_right _ (hf.mono Ico_subset_Icc_self) _
       ((hf.ContinuousWithinAt ⟨hab, refl b⟩).mono Ico_subset_Icc_self)
 #align intermediate_value_Ico intermediate_value_Ico
+-/
 
+#print intermediate_value_Ico' /-
 theorem intermediate_value_Ico' {a b : α} (hab : a ≤ b) {f : α → δ}
     (hf : ContinuousOn f (Icc a b)) : Ioc (f b) (f a) ⊆ f '' Ico a b :=
   Or.elim (eq_or_lt_of_le hab) (fun he y h => absurd h.1 (not_lt_of_le (he ▸ h.2))) fun hlt =>
@@ -662,7 +715,9 @@ theorem intermediate_value_Ico' {a b : α} (hab : a ≤ b) {f : α → δ}
       (right_nhdsWithin_Ico_neBot hlt) inf_le_right _ (hf.mono Ico_subset_Icc_self) _
       ((hf.ContinuousWithinAt ⟨hab, refl b⟩).mono Ico_subset_Icc_self)
 #align intermediate_value_Ico' intermediate_value_Ico'
+-/
 
+#print intermediate_value_Ioc /-
 theorem intermediate_value_Ioc {a b : α} (hab : a ≤ b) {f : α → δ} (hf : ContinuousOn f (Icc a b)) :
     Ioc (f a) (f b) ⊆ f '' Ioc a b :=
   Or.elim (eq_or_lt_of_le hab) (fun he y h => absurd h.2 (not_le_of_lt (he ▸ h.1))) fun hlt =>
@@ -670,7 +725,9 @@ theorem intermediate_value_Ioc {a b : α} (hab : a ≤ b) {f : α → δ} (hf :
       (left_nhdsWithin_Ioc_neBot hlt) inf_le_right _ (hf.mono Ioc_subset_Icc_self) _
       ((hf.ContinuousWithinAt ⟨refl a, hab⟩).mono Ioc_subset_Icc_self)
 #align intermediate_value_Ioc intermediate_value_Ioc
+-/
 
+#print intermediate_value_Ioc' /-
 theorem intermediate_value_Ioc' {a b : α} (hab : a ≤ b) {f : α → δ}
     (hf : ContinuousOn f (Icc a b)) : Ico (f b) (f a) ⊆ f '' Ioc a b :=
   Or.elim (eq_or_lt_of_le hab) (fun he y h => absurd h.1 (not_le_of_lt (he ▸ h.2))) fun hlt =>
@@ -678,7 +735,9 @@ theorem intermediate_value_Ioc' {a b : α} (hab : a ≤ b) {f : α → δ}
       (left_nhdsWithin_Ioc_neBot hlt) inf_le_right _ (hf.mono Ioc_subset_Icc_self) _
       ((hf.ContinuousWithinAt ⟨refl a, hab⟩).mono Ioc_subset_Icc_self)
 #align intermediate_value_Ioc' intermediate_value_Ioc'
+-/
 
+#print intermediate_value_Ioo /-
 theorem intermediate_value_Ioo {a b : α} (hab : a ≤ b) {f : α → δ} (hf : ContinuousOn f (Icc a b)) :
     Ioo (f a) (f b) ⊆ f '' Ioo a b :=
   Or.elim (eq_or_lt_of_le hab) (fun he y h => absurd h.2 (not_lt_of_lt (he ▸ h.1))) fun hlt =>
@@ -688,7 +747,9 @@ theorem intermediate_value_Ioo {a b : α} (hab : a ≤ b) {f : α → δ} (hf :
       ((hf.ContinuousWithinAt ⟨refl a, hab⟩).mono Ioo_subset_Icc_self)
       ((hf.ContinuousWithinAt ⟨hab, refl b⟩).mono Ioo_subset_Icc_self)
 #align intermediate_value_Ioo intermediate_value_Ioo
+-/
 
+#print intermediate_value_Ioo' /-
 theorem intermediate_value_Ioo' {a b : α} (hab : a ≤ b) {f : α → δ}
     (hf : ContinuousOn f (Icc a b)) : Ioo (f b) (f a) ⊆ f '' Ioo a b :=
   Or.elim (eq_or_lt_of_le hab) (fun he y h => absurd h.1 (not_lt_of_lt (he ▸ h.2))) fun hlt =>
@@ -698,34 +759,44 @@ theorem intermediate_value_Ioo' {a b : α} (hab : a ≤ b) {f : α → δ}
       ((hf.ContinuousWithinAt ⟨hab, refl b⟩).mono Ioo_subset_Icc_self)
       ((hf.ContinuousWithinAt ⟨refl a, hab⟩).mono Ioo_subset_Icc_self)
 #align intermediate_value_Ioo' intermediate_value_Ioo'
+-/
 
+#print ContinuousOn.surjOn_Icc /-
 /-- **Intermediate value theorem**: if `f` is continuous on an order-connected set `s` and `a`,
 `b` are two points of this set, then `f` sends `s` to a superset of `Icc (f x) (f y)`. -/
 theorem ContinuousOn.surjOn_Icc {s : Set α} [hs : OrdConnected s] {f : α → δ}
     (hf : ContinuousOn f s) {a b : α} (ha : a ∈ s) (hb : b ∈ s) : SurjOn f s (Icc (f a) (f b)) :=
   hs.IsPreconnected.intermediate_value ha hb hf
 #align continuous_on.surj_on_Icc ContinuousOn.surjOn_Icc
+-/
 
+#print ContinuousOn.surjOn_uIcc /-
 /-- **Intermediate value theorem**: if `f` is continuous on an order-connected set `s` and `a`,
 `b` are two points of this set, then `f` sends `s` to a superset of `[f x, f y]`. -/
 theorem ContinuousOn.surjOn_uIcc {s : Set α} [hs : OrdConnected s] {f : α → δ}
     (hf : ContinuousOn f s) {a b : α} (ha : a ∈ s) (hb : b ∈ s) : SurjOn f s (uIcc (f a) (f b)) :=
   by cases' le_total (f a) (f b) with hab hab <;> simp [hf.surj_on_Icc, *]
 #align continuous_on.surj_on_uIcc ContinuousOn.surjOn_uIcc
+-/
 
+#print Continuous.surjective /-
 /-- A continuous function which tendsto `at_top` `at_top` and to `at_bot` `at_bot` is surjective. -/
 theorem Continuous.surjective {f : α → δ} (hf : Continuous f) (h_top : Tendsto f atTop atTop)
     (h_bot : Tendsto f atBot atBot) : Function.Surjective f := fun p =>
   mem_range_of_exists_le_of_exists_ge hf (h_bot.Eventually (eventually_le_atBot p)).exists
     (h_top.Eventually (eventually_ge_atTop p)).exists
 #align continuous.surjective Continuous.surjective
+-/
 
+#print Continuous.surjective' /-
 /-- A continuous function which tendsto `at_bot` `at_top` and to `at_top` `at_bot` is surjective. -/
 theorem Continuous.surjective' {f : α → δ} (hf : Continuous f) (h_top : Tendsto f atBot atTop)
     (h_bot : Tendsto f atTop atBot) : Function.Surjective f :=
   @Continuous.surjective αᵒᵈ _ _ _ _ _ _ _ _ _ hf h_top h_bot
 #align continuous.surjective' Continuous.surjective'
+-/
 
+#print ContinuousOn.surjOn_of_tendsto /-
 /-- If a function `f : α → β` is continuous on a nonempty interval `s`, its restriction to `s`
 tends to `at_bot : filter β` along `at_bot : filter ↥s` and tends to `at_top : filter β` along
 `at_top : filter ↥s`, then the restriction of `f` to `s` is surjective. We formulate the
@@ -736,7 +807,9 @@ theorem ContinuousOn.surjOn_of_tendsto {f : α → δ} {s : Set α} [OrdConnecte
   haveI := Classical.inhabited_of_nonempty hs.to_subtype
   surj_on_iff_surjective.2 <| (continuousOn_iff_continuous_restrict.1 hf).Surjective htop hbot
 #align continuous_on.surj_on_of_tendsto ContinuousOn.surjOn_of_tendsto
+-/
 
+#print ContinuousOn.surjOn_of_tendsto' /-
 /-- If a function `f : α → β` is continuous on a nonempty interval `s`, its restriction to `s`
 tends to `at_top : filter β` along `at_bot : filter ↥s` and tends to `at_bot : filter β` along
 `at_top : filter ↥s`, then the restriction of `f` to `s` is surjective. We formulate the
@@ -746,4 +819,5 @@ theorem ContinuousOn.surjOn_of_tendsto' {f : α → δ} {s : Set α} [OrdConnect
     (htop : Tendsto (fun x : s => f x) atTop atBot) : SurjOn f s univ :=
   @ContinuousOn.surjOn_of_tendsto α _ _ _ _ δᵒᵈ _ _ _ _ _ _ hs hf hbot htop
 #align continuous_on.surj_on_of_tendsto' ContinuousOn.surjOn_of_tendsto'
+-/
 

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

@@ -72,7 +72,7 @@ on a preconnected space and `f a ≤ g a` and `g b ≤ f b`, then for some `x` w
 theorem intermediate_value_univ₂ [PreconnectedSpace X] {a b : X} {f g : X → α} (hf : Continuous f)
     (hg : Continuous g) (ha : f a ≤ g a) (hb : g b ≤ f b) : ∃ x, f x = g x :=
   by
-  obtain ⟨x, h, hfg, hgf⟩ : (univ ∩ { x | f x ≤ g x ∧ g x ≤ f x }).Nonempty
+  obtain ⟨x, h, hfg, hgf⟩ : (univ ∩ {x | f x ≤ g x ∧ g x ≤ f x}).Nonempty
   exact
     isPreconnected_closed_iff.1 PreconnectedSpace.isPreconnected_univ _ _ (isClosed_le hf hg)
       (isClosed_le hg hf) (fun x hx => le_total _ _) ⟨a, trivial, ha⟩ ⟨b, trivial, hb⟩
@@ -335,14 +335,14 @@ theorem IsPreconnected.mem_intervals {s : Set α} (hs : IsPreconnected s) :
     · exact Or.inr <| Or.inr <| Or.inr <| Or.inl hs
   · refine' Or.inr <| Or.inr <| Or.inr <| Or.inr _
     cases'
-      mem_Ici_Ioi_of_subset_of_subset (hs.Ioi_cInf_subset hb ha) fun x hx => csInf_le hb hx with
-      hs hs
+      mem_Ici_Ioi_of_subset_of_subset (hs.Ioi_cInf_subset hb ha) fun x hx => csInf_le hb hx with hs
+      hs
     · exact Or.inl hs
     · exact Or.inr (Or.inl hs)
   · iterate 6 apply Or.inr
     cases'
-      mem_Iic_Iio_of_subset_of_subset (hs.Iio_cSup_subset hb ha) fun x hx => le_csSup ha hx with
-      hs hs
+      mem_Iic_Iio_of_subset_of_subset (hs.Iio_cSup_subset hb ha) fun x hx => le_csSup ha hx with hs
+      hs
     · exact Or.inl hs
     · exact Or.inr (Or.inl hs)
   · iterate 8 apply Or.inr
@@ -354,7 +354,7 @@ theorem IsPreconnected.mem_intervals {s : Set α} (hs : IsPreconnected s) :
 one can represent `∅` as `(Inf s, Inf s)`, we include it into the list of possible cases to improve
 readability. -/
 theorem setOf_isPreconnected_subset_of_ordered :
-    { s : Set α | IsPreconnected s } ⊆-- bounded intervals
+    {s : Set α | IsPreconnected s} ⊆-- bounded intervals
                 range
                 (uncurry Icc) ∪
               range (uncurry Ico) ∪
@@ -595,7 +595,7 @@ the set of the intervals `Icc`, `Ico`, `Ioc`, `Ioo`, `Ici`, `Ioi`, `Iic`, `Iio`,
 or `∅`. Though one can represent `∅` as `(Inf s, Inf s)`, we include it into the list of
 possible cases to improve readability. -/
 theorem setOf_isPreconnected_eq_of_ordered :
-    { s : Set α | IsPreconnected s } =-- bounded intervals
+    {s : Set α | IsPreconnected s} =-- bounded intervals
                 range
                 (uncurry Icc) ∪
               range (uncurry Ico) ∪

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

@@ -116,7 +116,7 @@ theorem IsPreconnected.intermediate_value₂_eventually₁ {s : Set X} (hs : IsP
     {l : Filter X} (ha : a ∈ s) [NeBot l] (hl : l ≤ 𝓟 s) {f g : X → α} (hf : ContinuousOn f s)
     (hg : ContinuousOn g s) (ha' : f a ≤ g a) (he : g ≤ᶠ[l] f) : ∃ x ∈ s, f x = g x :=
   by
-  rw [continuousOn_iff_continuous_restrict] at hf hg
+  rw [continuousOn_iff_continuous_restrict] at hf hg 
   obtain ⟨b, h⟩ :=
     @intermediate_value_univ₂_eventually₁ _ _ _ _ _ _ (Subtype.preconnectedSpace hs) ⟨a, ha⟩ _
       (comap_coe_ne_bot_of_le_principal hl) _ _ hf hg ha' (he.comap _)
@@ -128,7 +128,7 @@ theorem IsPreconnected.intermediate_value₂_eventually₂ {s : Set X} (hs : IsP
     (hf : ContinuousOn f s) (hg : ContinuousOn g s) (he₁ : f ≤ᶠ[l₁] g) (he₂ : g ≤ᶠ[l₂] f) :
     ∃ x ∈ s, f x = g x :=
   by
-  rw [continuousOn_iff_continuous_restrict] at hf hg
+  rw [continuousOn_iff_continuous_restrict] at hf hg 
   obtain ⟨b, h⟩ :=
     @intermediate_value_univ₂_eventually₂ _ _ _ _ _ _ (Subtype.preconnectedSpace hs) _ _
       (comap_coe_ne_bot_of_le_principal hl₁) (comap_coe_ne_bot_of_le_principal hl₂) _ _ hf hg
@@ -470,7 +470,7 @@ theorem isPreconnected_Icc : IsPreconnected (Icc a b) :=
       cases le_total x y
       · exact isPreconnected_Icc_aux x y s t h hs ht hab hx hy
       · rw [inter_comm s t]
-        rw [union_comm s t] at hab
+        rw [union_comm s t] at hab 
         exact isPreconnected_Icc_aux y x t s h ht hs hab hy hx)
 #align is_preconnected_Icc isPreconnected_Icc
 -/

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

@@ -47,7 +47,7 @@ intermediate value theorem, connected space, connected set
 
 open Filter OrderDual TopologicalSpace Function Set
 
-open Topology Filter
+open scoped Topology Filter
 
 universe u v w
 
@@ -66,6 +66,7 @@ section
 variable {X : Type u} {α : Type v} [TopologicalSpace X] [LinearOrder α] [TopologicalSpace α]
   [OrderClosedTopology α]
 
+#print intermediate_value_univ₂ /-
 /-- Intermediate value theorem for two functions: if `f` and `g` are two continuous functions
 on a preconnected space and `f a ≤ g a` and `g b ≤ f b`, then for some `x` we have `f x = g x`. -/
 theorem intermediate_value_univ₂ [PreconnectedSpace X] {a b : X} {f g : X → α} (hf : Continuous f)
@@ -77,14 +78,18 @@ theorem intermediate_value_univ₂ [PreconnectedSpace X] {a b : X} {f g : X →
       (isClosed_le hg hf) (fun x hx => le_total _ _) ⟨a, trivial, ha⟩ ⟨b, trivial, hb⟩
   exact ⟨x, le_antisymm hfg hgf⟩
 #align intermediate_value_univ₂ intermediate_value_univ₂
+-/
 
+#print intermediate_value_univ₂_eventually₁ /-
 theorem intermediate_value_univ₂_eventually₁ [PreconnectedSpace X] {a : X} {l : Filter X} [NeBot l]
     {f g : X → α} (hf : Continuous f) (hg : Continuous g) (ha : f a ≤ g a) (he : g ≤ᶠ[l] f) :
     ∃ x, f x = g x :=
   let ⟨c, hc⟩ := he.Frequently.exists
   intermediate_value_univ₂ hf hg ha hc
 #align intermediate_value_univ₂_eventually₁ intermediate_value_univ₂_eventually₁
+-/
 
+#print intermediate_value_univ₂_eventually₂ /-
 theorem intermediate_value_univ₂_eventually₂ [PreconnectedSpace X] {l₁ l₂ : Filter X} [NeBot l₁]
     [NeBot l₂] {f g : X → α} (hf : Continuous f) (hg : Continuous g) (he₁ : f ≤ᶠ[l₁] g)
     (he₂ : g ≤ᶠ[l₂] f) : ∃ x, f x = g x :=
@@ -92,6 +97,7 @@ theorem intermediate_value_univ₂_eventually₂ [PreconnectedSpace X] {l₁ l
   let ⟨c₂, hc₂⟩ := he₂.Frequently.exists
   intermediate_value_univ₂ hf hg hc₁ hc₂
 #align intermediate_value_univ₂_eventually₂ intermediate_value_univ₂_eventually₂
+-/
 
 /-- Intermediate value theorem for two functions: if `f` and `g` are two functions continuous
 on a preconnected set `s` and for some `a b ∈ s` we have `f a ≤ g a` and `g b ≤ f b`,
@@ -210,6 +216,7 @@ theorem intermediate_value_univ [PreconnectedSpace X] (a b : X) {f : X → α} (
 #align intermediate_value_univ intermediate_value_univ
 -/
 
+#print mem_range_of_exists_le_of_exists_ge /-
 /-- **Intermediate Value Theorem** for continuous functions on connected spaces. -/
 theorem mem_range_of_exists_le_of_exists_ge [PreconnectedSpace X] {c : α} {f : X → α}
     (hf : Continuous f) (h₁ : ∃ a, f a ≤ c) (h₂ : ∃ b, c ≤ f b) : c ∈ range f :=
@@ -217,6 +224,7 @@ theorem mem_range_of_exists_le_of_exists_ge [PreconnectedSpace X] {c : α} {f :
   let ⟨b, hb⟩ := h₂
   intermediate_value_univ a b hf ⟨ha, hb⟩
 #align mem_range_of_exists_le_of_exists_ge mem_range_of_exists_le_of_exists_ge
+-/
 
 /-!
 ### (Pre)connected sets in a linear order
@@ -452,6 +460,7 @@ theorem isPreconnected_Icc_aux (x y : α) (s t : Set α) (hxy : x ≤ y) (hs : I
   exact fun w ⟨wt, wzy⟩ => (this wzy).elim id fun h => (wt h).elim
 #align is_preconnected_Icc_aux isPreconnected_Icc_aux
 
+#print isPreconnected_Icc /-
 /-- A closed interval in a densely ordered conditionally complete linear order is preconnected. -/
 theorem isPreconnected_Icc : IsPreconnected (Icc a b) :=
   isPreconnected_closed_iff.2
@@ -464,83 +473,122 @@ theorem isPreconnected_Icc : IsPreconnected (Icc a b) :=
         rw [union_comm s t] at hab
         exact isPreconnected_Icc_aux y x t s h ht hs hab hy hx)
 #align is_preconnected_Icc isPreconnected_Icc
+-/
 
+#print isPreconnected_uIcc /-
 theorem isPreconnected_uIcc : IsPreconnected (uIcc a b) :=
   isPreconnected_Icc
 #align is_preconnected_uIcc isPreconnected_uIcc
+-/
 
+#print Set.OrdConnected.isPreconnected /-
 theorem Set.OrdConnected.isPreconnected {s : Set α} (h : s.OrdConnected) : IsPreconnected s :=
   isPreconnected_of_forall_pair fun x hx y hy =>
     ⟨uIcc x y, h.uIcc_subset hx hy, left_mem_uIcc, right_mem_uIcc, isPreconnected_uIcc⟩
 #align set.ord_connected.is_preconnected Set.OrdConnected.isPreconnected
+-/
 
+#print isPreconnected_iff_ordConnected /-
 theorem isPreconnected_iff_ordConnected {s : Set α} : IsPreconnected s ↔ OrdConnected s :=
   ⟨IsPreconnected.ordConnected, Set.OrdConnected.isPreconnected⟩
 #align is_preconnected_iff_ord_connected isPreconnected_iff_ordConnected
+-/
 
+#print isPreconnected_Ici /-
 theorem isPreconnected_Ici : IsPreconnected (Ici a) :=
   ordConnected_Ici.IsPreconnected
 #align is_preconnected_Ici isPreconnected_Ici
+-/
 
+#print isPreconnected_Iic /-
 theorem isPreconnected_Iic : IsPreconnected (Iic a) :=
   ordConnected_Iic.IsPreconnected
 #align is_preconnected_Iic isPreconnected_Iic
+-/
 
+#print isPreconnected_Iio /-
 theorem isPreconnected_Iio : IsPreconnected (Iio a) :=
   ordConnected_Iio.IsPreconnected
 #align is_preconnected_Iio isPreconnected_Iio
+-/
 
+#print isPreconnected_Ioi /-
 theorem isPreconnected_Ioi : IsPreconnected (Ioi a) :=
   ordConnected_Ioi.IsPreconnected
 #align is_preconnected_Ioi isPreconnected_Ioi
+-/
 
+#print isPreconnected_Ioo /-
 theorem isPreconnected_Ioo : IsPreconnected (Ioo a b) :=
   ordConnected_Ioo.IsPreconnected
 #align is_preconnected_Ioo isPreconnected_Ioo
+-/
 
+#print isPreconnected_Ioc /-
 theorem isPreconnected_Ioc : IsPreconnected (Ioc a b) :=
   ordConnected_Ioc.IsPreconnected
 #align is_preconnected_Ioc isPreconnected_Ioc
+-/
 
+#print isPreconnected_Ico /-
 theorem isPreconnected_Ico : IsPreconnected (Ico a b) :=
   ordConnected_Ico.IsPreconnected
 #align is_preconnected_Ico isPreconnected_Ico
+-/
 
+#print isConnected_Ici /-
 theorem isConnected_Ici : IsConnected (Ici a) :=
   ⟨nonempty_Ici, isPreconnected_Ici⟩
 #align is_connected_Ici isConnected_Ici
+-/
 
+#print isConnected_Iic /-
 theorem isConnected_Iic : IsConnected (Iic a) :=
   ⟨nonempty_Iic, isPreconnected_Iic⟩
 #align is_connected_Iic isConnected_Iic
+-/
 
+#print isConnected_Ioi /-
 theorem isConnected_Ioi [NoMaxOrder α] : IsConnected (Ioi a) :=
   ⟨nonempty_Ioi, isPreconnected_Ioi⟩
 #align is_connected_Ioi isConnected_Ioi
+-/
 
+#print isConnected_Iio /-
 theorem isConnected_Iio [NoMinOrder α] : IsConnected (Iio a) :=
   ⟨nonempty_Iio, isPreconnected_Iio⟩
 #align is_connected_Iio isConnected_Iio
+-/
 
+#print isConnected_Icc /-
 theorem isConnected_Icc (h : a ≤ b) : IsConnected (Icc a b) :=
   ⟨nonempty_Icc.2 h, isPreconnected_Icc⟩
 #align is_connected_Icc isConnected_Icc
+-/
 
+#print isConnected_Ioo /-
 theorem isConnected_Ioo (h : a < b) : IsConnected (Ioo a b) :=
   ⟨nonempty_Ioo.2 h, isPreconnected_Ioo⟩
 #align is_connected_Ioo isConnected_Ioo
+-/
 
+#print isConnected_Ioc /-
 theorem isConnected_Ioc (h : a < b) : IsConnected (Ioc a b) :=
   ⟨nonempty_Ioc.2 h, isPreconnected_Ioc⟩
 #align is_connected_Ioc isConnected_Ioc
+-/
 
+#print isConnected_Ico /-
 theorem isConnected_Ico (h : a < b) : IsConnected (Ico a b) :=
   ⟨nonempty_Ico.2 h, isPreconnected_Ico⟩
 #align is_connected_Ico isConnected_Ico
+-/
 
+#print ordered_connected_space /-
 instance (priority := 100) ordered_connected_space : PreconnectedSpace α :=
   ⟨ordConnected_univ.IsPreconnected⟩
 #align ordered_connected_space ordered_connected_space
+-/
 
 /-- In a dense conditionally complete linear order, the set of preconnected sets is exactly
 the set of the intervals `Icc`, `Ico`, `Ioc`, `Ioo`, `Ici`, `Ioi`, `Iic`, `Iio`, `(-∞, +∞)`,

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

@@ -66,12 +66,6 @@ section
 variable {X : Type u} {α : Type v} [TopologicalSpace X] [LinearOrder α] [TopologicalSpace α]
   [OrderClosedTopology α]
 
-/- warning: intermediate_value_univ₂ -> intermediate_value_univ₂ is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] [_inst_5 : PreconnectedSpace.{u1} X _inst_1] {a : X} {b : X} {f : X -> α} {g : X -> α}, (Continuous.{u1, u2} X α _inst_1 _inst_3 f) -> (Continuous.{u1, u2} X α _inst_1 _inst_3 g) -> (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) (f a) (g a)) -> (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) (g b) (f b)) -> (Exists.{succ u1} X (fun (x : X) => Eq.{succ u2} α (f x) (g x)))
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-Case conversion may be inaccurate. Consider using '#align intermediate_value_univ₂ intermediate_value_univ₂ₓ'. -/
 /-- Intermediate value theorem for two functions: if `f` and `g` are two continuous functions
 on a preconnected space and `f a ≤ g a` and `g b ≤ f b`, then for some `x` we have `f x = g x`. -/
 theorem intermediate_value_univ₂ [PreconnectedSpace X] {a b : X} {f g : X → α} (hf : Continuous f)
@@ -84,12 +78,6 @@ theorem intermediate_value_univ₂ [PreconnectedSpace X] {a b : X} {f g : X →
   exact ⟨x, le_antisymm hfg hgf⟩
 #align intermediate_value_univ₂ intermediate_value_univ₂
 
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-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] [_inst_5 : PreconnectedSpace.{u1} X _inst_1] {a : X} {l : Filter.{u1} X} [_inst_6 : Filter.NeBot.{u1} X l] {f : X -> α} {g : X -> α}, (Continuous.{u1, u2} X α _inst_1 _inst_3 f) -> (Continuous.{u1, u2} X α _inst_1 _inst_3 g) -> (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) (f a) (g a)) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l g f) -> (Exists.{succ u1} X (fun (x : X) => Eq.{succ u2} α (f x) (g x)))
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-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] [_inst_5 : PreconnectedSpace.{u1} X _inst_1] {a : X} {l : Filter.{u1} X} [_inst_6 : Filter.NeBot.{u1} X l] {f : X -> α} {g : X -> α}, (Continuous.{u1, u2} X α _inst_1 _inst_3 f) -> (Continuous.{u1, u2} X α _inst_1 _inst_3 g) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (f a) (g a)) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) l g f) -> (Exists.{succ u1} X (fun (x : X) => Eq.{succ u2} α (f x) (g x)))
-Case conversion may be inaccurate. Consider using '#align intermediate_value_univ₂_eventually₁ intermediate_value_univ₂_eventually₁ₓ'. -/
 theorem intermediate_value_univ₂_eventually₁ [PreconnectedSpace X] {a : X} {l : Filter X} [NeBot l]
     {f g : X → α} (hf : Continuous f) (hg : Continuous g) (ha : f a ≤ g a) (he : g ≤ᶠ[l] f) :
     ∃ x, f x = g x :=
@@ -97,12 +85,6 @@ theorem intermediate_value_univ₂_eventually₁ [PreconnectedSpace X] {a : X} {
   intermediate_value_univ₂ hf hg ha hc
 #align intermediate_value_univ₂_eventually₁ intermediate_value_univ₂_eventually₁
 
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-Case conversion may be inaccurate. Consider using '#align intermediate_value_univ₂_eventually₂ intermediate_value_univ₂_eventually₂ₓ'. -/
 theorem intermediate_value_univ₂_eventually₂ [PreconnectedSpace X] {l₁ l₂ : Filter X} [NeBot l₁]
     [NeBot l₂] {f g : X → α} (hf : Continuous f) (hg : Continuous g) (he₁ : f ≤ᶠ[l₁] g)
     (he₂ : g ≤ᶠ[l₂] f) : ∃ x, f x = g x :=
@@ -111,12 +93,6 @@ theorem intermediate_value_univ₂_eventually₂ [PreconnectedSpace X] {l₁ l
   intermediate_value_univ₂ hf hg hc₁ hc₂
 #align intermediate_value_univ₂_eventually₂ intermediate_value_univ₂_eventually₂
 
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-Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value₂ IsPreconnected.intermediate_value₂ₓ'. -/
 /-- Intermediate value theorem for two functions: if `f` and `g` are two functions continuous
 on a preconnected set `s` and for some `a b ∈ s` we have `f a ≤ g a` and `g b ≤ f b`,
 then for some `x ∈ s` we have `f x = g x`. -/
@@ -130,12 +106,6 @@ theorem IsPreconnected.intermediate_value₂ {s : Set X} (hs : IsPreconnected s)
   ⟨x, x.2, hx⟩
 #align is_preconnected.intermediate_value₂ IsPreconnected.intermediate_value₂
 
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-Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value₂_eventually₁ IsPreconnected.intermediate_value₂_eventually₁ₓ'. -/
 theorem IsPreconnected.intermediate_value₂_eventually₁ {s : Set X} (hs : IsPreconnected s) {a : X}
     {l : Filter X} (ha : a ∈ s) [NeBot l] (hl : l ≤ 𝓟 s) {f g : X → α} (hf : ContinuousOn f s)
     (hg : ContinuousOn g s) (ha' : f a ≤ g a) (he : g ≤ᶠ[l] f) : ∃ x ∈ s, f x = g x :=
@@ -147,9 +117,6 @@ theorem IsPreconnected.intermediate_value₂_eventually₁ {s : Set X} (hs : IsP
   exact ⟨b, b.prop, h⟩
 #align is_preconnected.intermediate_value₂_eventually₁ IsPreconnected.intermediate_value₂_eventually₁
 
-/- warning: is_preconnected.intermediate_value₂_eventually₂ -> IsPreconnected.intermediate_value₂_eventually₂ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value₂_eventually₂ IsPreconnected.intermediate_value₂_eventually₂ₓ'. -/
 theorem IsPreconnected.intermediate_value₂_eventually₂ {s : Set X} (hs : IsPreconnected s)
     {l₁ l₂ : Filter X} [NeBot l₁] [NeBot l₂] (hl₁ : l₁ ≤ 𝓟 s) (hl₂ : l₂ ≤ 𝓟 s) {f g : X → α}
     (hf : ContinuousOn f s) (hg : ContinuousOn g s) (he₁ : f ≤ᶠ[l₁] g) (he₂ : g ≤ᶠ[l₂] f) :
@@ -171,12 +138,6 @@ theorem IsPreconnected.intermediate_value {s : Set X} (hs : IsPreconnected s) {a
 #align is_preconnected.intermediate_value IsPreconnected.intermediate_value
 -/
 
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-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v : α}, (Filter.Tendsto.{u1, u2} X α f l (nhds.{u2} α _inst_3 v)) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) (Set.Ico.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) (f a) v) (Set.image.{u1, u2} X α f s))))))
-Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Ico IsPreconnected.intermediate_value_Icoₓ'. -/
 theorem IsPreconnected.intermediate_value_Ico {s : Set X} (hs : IsPreconnected s) {a : X}
     {l : Filter X} (ha : a ∈ s) [NeBot l] (hl : l ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s) {v : α}
     (ht : Tendsto f l (𝓝 v)) : Ico (f a) v ⊆ f '' s := fun y h =>
@@ -185,12 +146,6 @@ theorem IsPreconnected.intermediate_value_Ico {s : Set X} (hs : IsPreconnected s
       (eventually_ge_of_tendsto_gt h.2 ht)
 #align is_preconnected.intermediate_value_Ico IsPreconnected.intermediate_value_Ico
 
-/- warning: is_preconnected.intermediate_value_Ioc -> IsPreconnected.intermediate_value_Ioc is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Ioc IsPreconnected.intermediate_value_Iocₓ'. -/
 theorem IsPreconnected.intermediate_value_Ioc {s : Set X} (hs : IsPreconnected s) {a : X}
     {l : Filter X} (ha : a ∈ s) [NeBot l] (hl : l ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s) {v : α}
     (ht : Tendsto f l (𝓝 v)) : Ioc v (f a) ⊆ f '' s := fun y h =>
@@ -200,9 +155,6 @@ theorem IsPreconnected.intermediate_value_Ioc {s : Set X} (hs : IsPreconnected s
         (eventually_le_of_tendsto_lt h.1 ht)
 #align is_preconnected.intermediate_value_Ioc IsPreconnected.intermediate_value_Ioc
 
-/- warning: is_preconnected.intermediate_value_Ioo -> IsPreconnected.intermediate_value_Ioo is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Ioo IsPreconnected.intermediate_value_Iooₓ'. -/
 theorem IsPreconnected.intermediate_value_Ioo {s : Set X} (hs : IsPreconnected s) {l₁ l₂ : Filter X}
     [NeBot l₁] [NeBot l₂] (hl₁ : l₁ ≤ 𝓟 s) (hl₂ : l₂ ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s)
     {v₁ v₂ : α} (ht₁ : Tendsto f l₁ (𝓝 v₁)) (ht₂ : Tendsto f l₂ (𝓝 v₂)) : Ioo v₁ v₂ ⊆ f '' s :=
@@ -212,12 +164,6 @@ theorem IsPreconnected.intermediate_value_Ioo {s : Set X} (hs : IsPreconnected s
       (eventually_le_of_tendsto_lt h.1 ht₁) (eventually_ge_of_tendsto_gt h.2 ht₂)
 #align is_preconnected.intermediate_value_Ioo IsPreconnected.intermediate_value_Ioo
 
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-Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Ici IsPreconnected.intermediate_value_Iciₓ'. -/
 theorem IsPreconnected.intermediate_value_Ici {s : Set X} (hs : IsPreconnected s) {a : X}
     {l : Filter X} (ha : a ∈ s) [NeBot l] (hl : l ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s)
     (ht : Tendsto f l atTop) : Ici (f a) ⊆ f '' s := fun y h =>
@@ -225,12 +171,6 @@ theorem IsPreconnected.intermediate_value_Ici {s : Set X} (hs : IsPreconnected s
     hs.intermediate_value₂_eventually₁ ha hl hf continuousOn_const h (tendsto_atTop.1 ht y)
 #align is_preconnected.intermediate_value_Ici IsPreconnected.intermediate_value_Ici
 
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-Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Iic IsPreconnected.intermediate_value_Iicₓ'. -/
 theorem IsPreconnected.intermediate_value_Iic {s : Set X} (hs : IsPreconnected s) {a : X}
     {l : Filter X} (ha : a ∈ s) [NeBot l] (hl : l ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s)
     (ht : Tendsto f l atBot) : Iic (f a) ⊆ f '' s := fun y h =>
@@ -239,12 +179,6 @@ theorem IsPreconnected.intermediate_value_Iic {s : Set X} (hs : IsPreconnected s
       hs.intermediate_value₂_eventually₁ ha hl continuousOn_const hf h (tendsto_atBot.1 ht y)
 #align is_preconnected.intermediate_value_Iic IsPreconnected.intermediate_value_Iic
 
-/- warning: is_preconnected.intermediate_value_Ioi -> IsPreconnected.intermediate_value_Ioi is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Ioi IsPreconnected.intermediate_value_Ioiₓ'. -/
 theorem IsPreconnected.intermediate_value_Ioi {s : Set X} (hs : IsPreconnected s) {l₁ l₂ : Filter X}
     [NeBot l₁] [NeBot l₂] (hl₁ : l₁ ≤ 𝓟 s) (hl₂ : l₂ ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s)
     {v : α} (ht₁ : Tendsto f l₁ (𝓝 v)) (ht₂ : Tendsto f l₂ atTop) : Ioi v ⊆ f '' s := fun y h =>
@@ -253,12 +187,6 @@ theorem IsPreconnected.intermediate_value_Ioi {s : Set X} (hs : IsPreconnected s
       (eventually_le_of_tendsto_lt h ht₁) (tendsto_atTop.1 ht₂ y)
 #align is_preconnected.intermediate_value_Ioi IsPreconnected.intermediate_value_Ioi
 
-/- warning: is_preconnected.intermediate_value_Iio -> IsPreconnected.intermediate_value_Iio is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v : α}, (Filter.Tendsto.{u1, u2} X α f l₁ (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))))) -> (Filter.Tendsto.{u1, u2} X α f l₂ (nhds.{u2} α _inst_3 v)) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))) v) (Set.image.{u1, u2} X α f s)))))
-but is expected to have type
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v : α}, (Filter.Tendsto.{u1, u2} X α f l₁ (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))) -> (Filter.Tendsto.{u1, u2} X α f l₂ (nhds.{u2} α _inst_3 v)) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) v) (Set.image.{u1, u2} X α f s)))))
-Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Iio IsPreconnected.intermediate_value_Iioₓ'. -/
 theorem IsPreconnected.intermediate_value_Iio {s : Set X} (hs : IsPreconnected s) {l₁ l₂ : Filter X}
     [NeBot l₁] [NeBot l₂] (hl₁ : l₁ ≤ 𝓟 s) (hl₂ : l₂ ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s)
     {v : α} (ht₁ : Tendsto f l₁ atBot) (ht₂ : Tendsto f l₂ (𝓝 v)) : Iio v ⊆ f '' s := fun y h =>
@@ -267,12 +195,6 @@ theorem IsPreconnected.intermediate_value_Iio {s : Set X} (hs : IsPreconnected s
       (eventually_ge_of_tendsto_gt h ht₂)
 #align is_preconnected.intermediate_value_Iio IsPreconnected.intermediate_value_Iio
 
-/- warning: is_preconnected.intermediate_value_Iii -> IsPreconnected.intermediate_value_Iii is a dubious translation:
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-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (Filter.Tendsto.{u1, u2} X α f l₁ (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))))) -> (Filter.Tendsto.{u1, u2} X α f l₂ (Filter.atTop.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))))) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.univ.{u2} α) (Set.image.{u1, u2} X α f s))))
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-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (Filter.Tendsto.{u1, u2} X α f l₁ (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))) -> (Filter.Tendsto.{u1, u2} X α f l₂ (Filter.atTop.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) (Set.univ.{u2} α) (Set.image.{u1, u2} X α f s))))
-Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Iii IsPreconnected.intermediate_value_Iiiₓ'. -/
 theorem IsPreconnected.intermediate_value_Iii {s : Set X} (hs : IsPreconnected s) {l₁ l₂ : Filter X}
     [NeBot l₁] [NeBot l₂] (hl₁ : l₁ ≤ 𝓟 s) (hl₂ : l₂ ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s)
     (ht₁ : Tendsto f l₁ atBot) (ht₂ : Tendsto f l₂ atTop) : univ ⊆ f '' s := fun y h =>
@@ -288,12 +210,6 @@ theorem intermediate_value_univ [PreconnectedSpace X] (a b : X) {f : X → α} (
 #align intermediate_value_univ intermediate_value_univ
 -/
 
-/- warning: mem_range_of_exists_le_of_exists_ge -> mem_range_of_exists_le_of_exists_ge is a dubious translation:
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-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] [_inst_5 : PreconnectedSpace.{u1} X _inst_1] {c : α} {f : X -> α}, (Continuous.{u1, u2} X α _inst_1 _inst_3 f) -> (Exists.{succ u1} X (fun (a : X) => LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) (f a) c)) -> (Exists.{succ u1} X (fun (b : X) => LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) c (f b))) -> (Membership.Mem.{u2, u2} α (Set.{u2} α) (Set.hasMem.{u2} α) c (Set.range.{u2, succ u1} α X f))
-but is expected to have type
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] [_inst_5 : PreconnectedSpace.{u1} X _inst_1] {c : α} {f : X -> α}, (Continuous.{u1, u2} X α _inst_1 _inst_3 f) -> (Exists.{succ u1} X (fun (a : X) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (f a) c)) -> (Exists.{succ u1} X (fun (b : X) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) c (f b))) -> (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) c (Set.range.{u2, succ u1} α X f))
-Case conversion may be inaccurate. Consider using '#align mem_range_of_exists_le_of_exists_ge mem_range_of_exists_le_of_exists_geₓ'. -/
 /-- **Intermediate Value Theorem** for continuous functions on connected spaces. -/
 theorem mem_range_of_exists_le_of_exists_ge [PreconnectedSpace X] {c : α} {f : X → α}
     (hf : Continuous f) (h₁ : ∃ a, f a ≤ c) (h₂ : ∃ b, c ≤ f b) : c ∈ range f :=
@@ -359,12 +275,6 @@ variable {α : Type u} {β : Type v} {γ : Type w} [ConditionallyCompleteLinearO
   [TopologicalSpace α] [OrderTopology α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β]
   [OrderTopology β] [Nonempty γ]
 
-/- warning: is_connected.Ioo_cInf_cSup_subset -> IsConnected.Ioo_csInf_csSup_subset is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsConnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsConnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
-Case conversion may be inaccurate. Consider using '#align is_connected.Ioo_cInf_cSup_subset IsConnected.Ioo_csInf_csSup_subsetₓ'. -/
 /-- A bounded connected subset of a conditionally complete linear order includes the open interval
 `(Inf s, Sup s)`. -/
 theorem IsConnected.Ioo_csInf_csSup_subset {s : Set α} (hs : IsConnected s) (hb : BddBelow s)
@@ -374,24 +284,12 @@ theorem IsConnected.Ioo_csInf_csSup_subset {s : Set α} (hs : IsConnected s) (hb
   hs.Icc_subset ys zs ⟨le_of_lt hy, le_of_lt hz⟩
 #align is_connected.Ioo_cInf_cSup_subset IsConnected.Ioo_csInf_csSup_subset
 
-/- warning: eq_Icc_cInf_cSup_of_connected_bdd_closed -> eq_Icc_csInf_csSup_of_connected_bdd_closed is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsConnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (IsClosed.{u1} α _inst_2 s) -> (Eq.{succ u1} (Set.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsConnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (IsClosed.{u1} α _inst_2 s) -> (Eq.{succ u1} (Set.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)))
-Case conversion may be inaccurate. Consider using '#align eq_Icc_cInf_cSup_of_connected_bdd_closed eq_Icc_csInf_csSup_of_connected_bdd_closedₓ'. -/
 theorem eq_Icc_csInf_csSup_of_connected_bdd_closed {s : Set α} (hc : IsConnected s)
     (hb : BddBelow s) (ha : BddAbove s) (hcl : IsClosed s) : s = Icc (sInf s) (sSup s) :=
   Subset.antisymm (subset_Icc_csInf_csSup hb ha) <|
     hc.Icc_subset (hcl.csInf_mem hc.Nonempty hb) (hcl.csSup_mem hc.Nonempty ha)
 #align eq_Icc_cInf_cSup_of_connected_bdd_closed eq_Icc_csInf_csSup_of_connected_bdd_closed
 
-/- warning: is_preconnected.Ioi_cInf_subset -> IsPreconnected.Ioi_csInf_subset is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsPreconnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Not (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
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-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsPreconnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Not (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
-Case conversion may be inaccurate. Consider using '#align is_preconnected.Ioi_cInf_subset IsPreconnected.Ioi_csInf_subsetₓ'. -/
 theorem IsPreconnected.Ioi_csInf_subset {s : Set α} (hs : IsPreconnected s) (hb : BddBelow s)
     (ha : ¬BddAbove s) : Ioi (sInf s) ⊆ s :=
   by
@@ -402,20 +300,11 @@ theorem IsPreconnected.Ioi_csInf_subset {s : Set α} (hs : IsPreconnected s) (hb
   exact hs.Icc_subset ys zs ⟨le_of_lt hy, le_of_lt hz⟩
 #align is_preconnected.Ioi_cInf_subset IsPreconnected.Ioi_csInf_subset
 
-/- warning: is_preconnected.Iio_cSup_subset -> IsPreconnected.Iio_csSup_subset is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsPreconnected.{u1} α _inst_2 s) -> (Not (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
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-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsPreconnected.{u1} α _inst_2 s) -> (Not (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
-Case conversion may be inaccurate. Consider using '#align is_preconnected.Iio_cSup_subset IsPreconnected.Iio_csSup_subsetₓ'. -/
 theorem IsPreconnected.Iio_csSup_subset {s : Set α} (hs : IsPreconnected s) (hb : ¬BddBelow s)
     (ha : BddAbove s) : Iio (sSup s) ⊆ s :=
   @IsPreconnected.Ioi_csInf_subset αᵒᵈ _ _ _ s hs ha hb
 #align is_preconnected.Iio_cSup_subset IsPreconnected.Iio_csSup_subset
 
-/- warning: is_preconnected.mem_intervals -> IsPreconnected.mem_intervals is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_preconnected.mem_intervals IsPreconnected.mem_intervalsₓ'. -/
 /-- A preconnected set in a conditionally complete linear order is either one of the intervals
 `[Inf s, Sup s]`, `[Inf s, Sup s)`, `(Inf s, Sup s]`, `(Inf s, Sup s)`, `[Inf s, +∞)`,
 `(Inf s, +∞)`, `(-∞, Sup s]`, `(-∞, Sup s)`, `(-∞, +∞)`, or `∅`. The converse statement requires
@@ -452,12 +341,6 @@ theorem IsPreconnected.mem_intervals {s : Set α} (hs : IsPreconnected s) :
     exact Or.inl (hs.eq_univ_of_unbounded hb ha)
 #align is_preconnected.mem_intervals IsPreconnected.mem_intervals
 
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-Case conversion may be inaccurate. Consider using '#align set_of_is_preconnected_subset_of_ordered setOf_isPreconnected_subset_of_orderedₓ'. -/
 /-- A preconnected set is either one of the intervals `Icc`, `Ico`, `Ioc`, `Ioo`, `Ici`, `Ioi`,
 `Iic`, `Iio`, or `univ`, or `∅`. The converse statement requires `α` to be densely ordered. Though
 one can represent `∅` as `(Inf s, Inf s)`, we include it into the list of possible cases to improve
@@ -499,12 +382,6 @@ conditionally complete linear order is preconnected.
 -/
 
 
-/- warning: is_closed.mem_of_ge_of_forall_exists_gt -> IsClosed.mem_of_ge_of_forall_exists_gt is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {a : α} {b : α} {s : Set.{u1} α}, (IsClosed.{u1} α _inst_2 (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) x b)))) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s)
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-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {a : α} {b : α} {s : Set.{u1} α}, (IsClosed.{u1} α _inst_2 (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) x b)))) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s)
-Case conversion may be inaccurate. Consider using '#align is_closed.mem_of_ge_of_forall_exists_gt IsClosed.mem_of_ge_of_forall_exists_gtₓ'. -/
 /-- A "continuous induction principle" for a closed interval: if a set `s` meets `[a, b]`
 on a closed subset, contains `a`, and the set `s ∩ [a, b)` has no maximal point, then `b ∈ s`. -/
 theorem IsClosed.mem_of_ge_of_forall_exists_gt {a b : α} {s : Set α} (hs : IsClosed (s ∩ Icc a b))
@@ -522,12 +399,6 @@ theorem IsClosed.mem_of_ge_of_forall_exists_gt {a b : α} {s : Set α} (hs : IsC
   exact not_lt_of_le (le_csSup Sbd ⟨xs, le_trans (le_csSup Sbd ha) (le_of_lt cx), xb⟩) cx
 #align is_closed.mem_of_ge_of_forall_exists_gt IsClosed.mem_of_ge_of_forall_exists_gt
 
-/- warning: is_closed.Icc_subset_of_forall_exists_gt -> IsClosed.Icc_subset_of_forall_exists_gt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {a : α} {b : α} {s : Set.{u1} α}, (IsClosed.{u1} α _inst_2 (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) x)) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) x y))))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {a : α} {b : α} {s : Set.{u1} α}, (IsClosed.{u1} α _inst_2 (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) x)) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) x y))))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) s)
-Case conversion may be inaccurate. Consider using '#align is_closed.Icc_subset_of_forall_exists_gt IsClosed.Icc_subset_of_forall_exists_gtₓ'. -/
 /-- A "continuous induction principle" for a closed interval: if a set `s` meets `[a, b]`
 on a closed subset, contains `a`, and for any `a ≤ x < y ≤ b`, `x ∈ s`, the set `s ∩ (x, y]`
 is not empty, then `[a, b] ⊆ s`. -/
@@ -548,12 +419,6 @@ theorem IsClosed.Icc_subset_of_forall_exists_gt {a b : α} {s : Set α} (hs : Is
 
 variable [DenselyOrdered α] {a b : α}
 
-/- warning: is_closed.Icc_subset_of_forall_mem_nhds_within -> IsClosed.Icc_subset_of_forall_mem_nhdsWithin is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α} {s : Set.{u1} α}, (IsClosed.{u1} α _inst_2 (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_2 x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) x)))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α} {s : Set.{u1} α}, (IsClosed.{u1} α _inst_2 (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_2 x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) x)))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) s)
-Case conversion may be inaccurate. Consider using '#align is_closed.Icc_subset_of_forall_mem_nhds_within IsClosed.Icc_subset_of_forall_mem_nhdsWithinₓ'. -/
 /-- A "continuous induction principle" for a closed interval: if a set `s` meets `[a, b]`
 on a closed subset, contains `a`, and for any `x ∈ s ∩ [a, b)` the set `s` includes some open
 neighborhood of `x` within `(x, +∞)`, then `[a, b] ⊆ s`. -/
@@ -567,12 +432,6 @@ theorem IsClosed.Icc_subset_of_forall_mem_nhdsWithin {a b : α} {s : Set α}
   exact (nhdsWithin_Ioi_self_neBot' ⟨b, hxab.2⟩).nonempty_of_mem this
 #align is_closed.Icc_subset_of_forall_mem_nhds_within IsClosed.Icc_subset_of_forall_mem_nhdsWithin
 
-/- warning: is_preconnected_Icc_aux -> isPreconnected_Icc_aux is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α} (x : α) (y : α) (s : Set.{u1} α) (t : Set.{u1} α), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x y) -> (IsClosed.{u1} α _inst_2 s) -> (IsClosed.{u1} α _inst_2 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) s)) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) t)) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α} (x : α) (y : α) (s : Set.{u1} α) (t : Set.{u1} α), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x y) -> (IsClosed.{u1} α _inst_2 s) -> (IsClosed.{u1} α _inst_2 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) s)) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) t)) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)))
-Case conversion may be inaccurate. Consider using '#align is_preconnected_Icc_aux isPreconnected_Icc_auxₓ'. -/
 theorem isPreconnected_Icc_aux (x y : α) (s t : Set α) (hxy : x ≤ y) (hs : IsClosed s)
     (ht : IsClosed t) (hab : Icc a b ⊆ s ∪ t) (hx : x ∈ Icc a b ∩ s) (hy : y ∈ Icc a b ∩ t) :
     (Icc a b ∩ (s ∩ t)).Nonempty :=
@@ -593,12 +452,6 @@ theorem isPreconnected_Icc_aux (x y : α) (s t : Set α) (hxy : x ≤ y) (hs : I
   exact fun w ⟨wt, wzy⟩ => (this wzy).elim id fun h => (wt h).elim
 #align is_preconnected_Icc_aux isPreconnected_Icc_aux
 
-/- warning: is_preconnected_Icc -> isPreconnected_Icc is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)
-Case conversion may be inaccurate. Consider using '#align is_preconnected_Icc isPreconnected_Iccₓ'. -/
 /-- A closed interval in a densely ordered conditionally complete linear order is preconnected. -/
 theorem isPreconnected_Icc : IsPreconnected (Icc a b) :=
   isPreconnected_closed_iff.2
@@ -612,203 +465,83 @@ theorem isPreconnected_Icc : IsPreconnected (Icc a b) :=
         exact isPreconnected_Icc_aux y x t s h ht hs hab hy hx)
 #align is_preconnected_Icc isPreconnected_Icc
 
-/- warning: is_preconnected_uIcc -> isPreconnected_uIcc is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.uIcc.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) a b)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.uIcc.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) a b)
-Case conversion may be inaccurate. Consider using '#align is_preconnected_uIcc isPreconnected_uIccₓ'. -/
 theorem isPreconnected_uIcc : IsPreconnected (uIcc a b) :=
   isPreconnected_Icc
 #align is_preconnected_uIcc isPreconnected_uIcc
 
-/- warning: set.ord_connected.is_preconnected -> Set.OrdConnected.isPreconnected is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {s : Set.{u1} α}, (Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (IsPreconnected.{u1} α _inst_2 s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {s : Set.{u1} α}, (Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (IsPreconnected.{u1} α _inst_2 s)
-Case conversion may be inaccurate. Consider using '#align set.ord_connected.is_preconnected Set.OrdConnected.isPreconnectedₓ'. -/
 theorem Set.OrdConnected.isPreconnected {s : Set α} (h : s.OrdConnected) : IsPreconnected s :=
   isPreconnected_of_forall_pair fun x hx y hy =>
     ⟨uIcc x y, h.uIcc_subset hx hy, left_mem_uIcc, right_mem_uIcc, isPreconnected_uIcc⟩
 #align set.ord_connected.is_preconnected Set.OrdConnected.isPreconnected
 
-/- warning: is_preconnected_iff_ord_connected -> isPreconnected_iff_ordConnected is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {s : Set.{u1} α}, Iff (IsPreconnected.{u1} α _inst_2 s) (Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {s : Set.{u1} α}, Iff (IsPreconnected.{u1} α _inst_2 s) (Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)
-Case conversion may be inaccurate. Consider using '#align is_preconnected_iff_ord_connected isPreconnected_iff_ordConnectedₓ'. -/
 theorem isPreconnected_iff_ordConnected {s : Set α} : IsPreconnected s ↔ OrdConnected s :=
   ⟨IsPreconnected.ordConnected, Set.OrdConnected.isPreconnected⟩
 #align is_preconnected_iff_ord_connected isPreconnected_iff_ordConnected
 
-/- warning: is_preconnected_Ici -> isPreconnected_Ici is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsPreconnected.{u1} α _inst_2 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsPreconnected.{u1} α _inst_2 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
-Case conversion may be inaccurate. Consider using '#align is_preconnected_Ici isPreconnected_Iciₓ'. -/
 theorem isPreconnected_Ici : IsPreconnected (Ici a) :=
   ordConnected_Ici.IsPreconnected
 #align is_preconnected_Ici isPreconnected_Ici
 
-/- warning: is_preconnected_Iic -> isPreconnected_Iic is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsPreconnected.{u1} α _inst_2 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsPreconnected.{u1} α _inst_2 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
-Case conversion may be inaccurate. Consider using '#align is_preconnected_Iic isPreconnected_Iicₓ'. -/
 theorem isPreconnected_Iic : IsPreconnected (Iic a) :=
   ordConnected_Iic.IsPreconnected
 #align is_preconnected_Iic isPreconnected_Iic
 
-/- warning: is_preconnected_Iio -> isPreconnected_Iio is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsPreconnected.{u1} α _inst_2 (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsPreconnected.{u1} α _inst_2 (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
-Case conversion may be inaccurate. Consider using '#align is_preconnected_Iio isPreconnected_Iioₓ'. -/
 theorem isPreconnected_Iio : IsPreconnected (Iio a) :=
   ordConnected_Iio.IsPreconnected
 #align is_preconnected_Iio isPreconnected_Iio
 
-/- warning: is_preconnected_Ioi -> isPreconnected_Ioi is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsPreconnected.{u1} α _inst_2 (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsPreconnected.{u1} α _inst_2 (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
-Case conversion may be inaccurate. Consider using '#align is_preconnected_Ioi isPreconnected_Ioiₓ'. -/
 theorem isPreconnected_Ioi : IsPreconnected (Ioi a) :=
   ordConnected_Ioi.IsPreconnected
 #align is_preconnected_Ioi isPreconnected_Ioi
 
-/- warning: is_preconnected_Ioo -> isPreconnected_Ioo is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)
-Case conversion may be inaccurate. Consider using '#align is_preconnected_Ioo isPreconnected_Iooₓ'. -/
 theorem isPreconnected_Ioo : IsPreconnected (Ioo a b) :=
   ordConnected_Ioo.IsPreconnected
 #align is_preconnected_Ioo isPreconnected_Ioo
 
-/- warning: is_preconnected_Ioc -> isPreconnected_Ioc is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)
-Case conversion may be inaccurate. Consider using '#align is_preconnected_Ioc isPreconnected_Iocₓ'. -/
 theorem isPreconnected_Ioc : IsPreconnected (Ioc a b) :=
   ordConnected_Ioc.IsPreconnected
 #align is_preconnected_Ioc isPreconnected_Ioc
 
-/- warning: is_preconnected_Ico -> isPreconnected_Ico is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)
-Case conversion may be inaccurate. Consider using '#align is_preconnected_Ico isPreconnected_Icoₓ'. -/
 theorem isPreconnected_Ico : IsPreconnected (Ico a b) :=
   ordConnected_Ico.IsPreconnected
 #align is_preconnected_Ico isPreconnected_Ico
 
-/- warning: is_connected_Ici -> isConnected_Ici is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsConnected.{u1} α _inst_2 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsConnected.{u1} α _inst_2 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
-Case conversion may be inaccurate. Consider using '#align is_connected_Ici isConnected_Iciₓ'. -/
 theorem isConnected_Ici : IsConnected (Ici a) :=
   ⟨nonempty_Ici, isPreconnected_Ici⟩
 #align is_connected_Ici isConnected_Ici
 
-/- warning: is_connected_Iic -> isConnected_Iic is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsConnected.{u1} α _inst_2 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsConnected.{u1} α _inst_2 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
-Case conversion may be inaccurate. Consider using '#align is_connected_Iic isConnected_Iicₓ'. -/
 theorem isConnected_Iic : IsConnected (Iic a) :=
   ⟨nonempty_Iic, isPreconnected_Iic⟩
 #align is_connected_Iic isConnected_Iic
 
-/- warning: is_connected_Ioi -> isConnected_Ioi is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} [_inst_9 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], IsConnected.{u1} α _inst_2 (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} [_inst_9 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], IsConnected.{u1} α _inst_2 (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
-Case conversion may be inaccurate. Consider using '#align is_connected_Ioi isConnected_Ioiₓ'. -/
 theorem isConnected_Ioi [NoMaxOrder α] : IsConnected (Ioi a) :=
   ⟨nonempty_Ioi, isPreconnected_Ioi⟩
 #align is_connected_Ioi isConnected_Ioi
 
-/- warning: is_connected_Iio -> isConnected_Iio is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} [_inst_9 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], IsConnected.{u1} α _inst_2 (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} [_inst_9 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], IsConnected.{u1} α _inst_2 (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
-Case conversion may be inaccurate. Consider using '#align is_connected_Iio isConnected_Iioₓ'. -/
 theorem isConnected_Iio [NoMinOrder α] : IsConnected (Iio a) :=
   ⟨nonempty_Iio, isPreconnected_Iio⟩
 #align is_connected_Iio isConnected_Iio
 
-/- warning: is_connected_Icc -> isConnected_Icc is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (IsConnected.{u1} α _inst_2 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (IsConnected.{u1} α _inst_2 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))
-Case conversion may be inaccurate. Consider using '#align is_connected_Icc isConnected_Iccₓ'. -/
 theorem isConnected_Icc (h : a ≤ b) : IsConnected (Icc a b) :=
   ⟨nonempty_Icc.2 h, isPreconnected_Icc⟩
 #align is_connected_Icc isConnected_Icc
 
-/- warning: is_connected_Ioo -> isConnected_Ioo is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (IsConnected.{u1} α _inst_2 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))
-Case conversion may be inaccurate. Consider using '#align is_connected_Ioo isConnected_Iooₓ'. -/
 theorem isConnected_Ioo (h : a < b) : IsConnected (Ioo a b) :=
   ⟨nonempty_Ioo.2 h, isPreconnected_Ioo⟩
 #align is_connected_Ioo isConnected_Ioo
 
-/- warning: is_connected_Ioc -> isConnected_Ioc is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (IsConnected.{u1} α _inst_2 (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (IsConnected.{u1} α _inst_2 (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))
-Case conversion may be inaccurate. Consider using '#align is_connected_Ioc isConnected_Iocₓ'. -/
 theorem isConnected_Ioc (h : a < b) : IsConnected (Ioc a b) :=
   ⟨nonempty_Ioc.2 h, isPreconnected_Ioc⟩
 #align is_connected_Ioc isConnected_Ioc
 
-/- warning: is_connected_Ico -> isConnected_Ico is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (IsConnected.{u1} α _inst_2 (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (IsConnected.{u1} α _inst_2 (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))
-Case conversion may be inaccurate. Consider using '#align is_connected_Ico isConnected_Icoₓ'. -/
 theorem isConnected_Ico (h : a < b) : IsConnected (Ico a b) :=
   ⟨nonempty_Ico.2 h, isPreconnected_Ico⟩
 #align is_connected_Ico isConnected_Ico
 
-/- warning: ordered_connected_space -> ordered_connected_space is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], PreconnectedSpace.{u1} α _inst_2
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], PreconnectedSpace.{u1} α _inst_2
-Case conversion may be inaccurate. Consider using '#align ordered_connected_space ordered_connected_spaceₓ'. -/
 instance (priority := 100) ordered_connected_space : PreconnectedSpace α :=
   ⟨ordConnected_univ.IsPreconnected⟩
 #align ordered_connected_space ordered_connected_space
 
-/- warning: set_of_is_preconnected_eq_of_ordered -> setOf_isPreconnected_eq_of_ordered is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], Eq.{succ u1} (Set.{u1} (Set.{u1} α)) (setOf.{u1} (Set.{u1} α) (fun (s : Set.{u1} α) => IsPreconnected.{u1} α _inst_2 s)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))))) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))))) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))))) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.univ.{u1} α) (Singleton.singleton.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasSingleton.{u1} (Set.{u1} α)) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], Eq.{succ u1} (Set.{u1} (Set.{u1} α)) (setOf.{u1} (Set.{u1} α) (fun (s : Set.{u1} α) => IsPreconnected.{u1} α _inst_2 s)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.instUnionSet.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.instUnionSet.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.instUnionSet.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.instUnionSet.{u1} (Set.{u1} α)) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))))) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))))) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))))) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.instUnionSet.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.instUnionSet.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.instUnionSet.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.instUnionSet.{u1} (Set.{u1} α)) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.univ.{u1} α) (Singleton.singleton.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instSingletonSet.{u1} (Set.{u1} α)) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))))))
-Case conversion may be inaccurate. Consider using '#align set_of_is_preconnected_eq_of_ordered setOf_isPreconnected_eq_of_orderedₓ'. -/
 /-- In a dense conditionally complete linear order, the set of preconnected sets is exactly
 the set of the intervals `Icc`, `Ico`, `Ioc`, `Ioo`, `Ici`, `Ioi`, `Iic`, `Iio`, `(-∞, +∞)`,
 or `∅`. Though one can represent `∅` as `(Inf s, Inf s)`, we include it into the list of
@@ -846,12 +579,6 @@ continuous on an interval.
 
 variable {δ : Type _} [LinearOrder δ] [TopologicalSpace δ] [OrderClosedTopology δ]
 
-/- warning: intermediate_value_Icc -> intermediate_value_Icc is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Icc.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f a) (f b)) (Set.image.{u1, u2} α δ f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.Icc.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f a) (f b)) (Set.image.{u2, u1} α δ f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b))))
-Case conversion may be inaccurate. Consider using '#align intermediate_value_Icc intermediate_value_Iccₓ'. -/
 /-- **Intermediate Value Theorem** for continuous functions on closed intervals, case
 `f a ≤ t ≤ f b`.-/
 theorem intermediate_value_Icc {a b : α} (hab : a ≤ b) {f : α → δ} (hf : ContinuousOn f (Icc a b)) :
@@ -859,12 +586,6 @@ theorem intermediate_value_Icc {a b : α} (hab : a ≤ b) {f : α → δ} (hf :
   isPreconnected_Icc.intermediate_value (left_mem_Icc.2 hab) (right_mem_Icc.2 hab) hf
 #align intermediate_value_Icc intermediate_value_Icc
 
-/- warning: intermediate_value_Icc' -> intermediate_value_Icc' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Icc.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f b) (f a)) (Set.image.{u1, u2} α δ f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.Icc.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f b) (f a)) (Set.image.{u2, u1} α δ f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b))))
-Case conversion may be inaccurate. Consider using '#align intermediate_value_Icc' intermediate_value_Icc'ₓ'. -/
 /-- **Intermediate Value Theorem** for continuous functions on closed intervals, case
 `f a ≥ t ≥ f b`.-/
 theorem intermediate_value_Icc' {a b : α} (hab : a ≤ b) {f : α → δ}
@@ -872,24 +593,12 @@ theorem intermediate_value_Icc' {a b : α} (hab : a ≤ b) {f : α → δ}
   isPreconnected_Icc.intermediate_value (right_mem_Icc.2 hab) (left_mem_Icc.2 hab) hf
 #align intermediate_value_Icc' intermediate_value_Icc'
 
-/- warning: intermediate_value_uIcc -> intermediate_value_uIcc is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α} {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.uIcc.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.uIcc.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9) (f a) (f b)) (Set.image.{u1, u2} α δ f (Set.uIcc.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) a b)))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α} {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.uIcc.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.uIcc.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)) (f a) (f b)) (Set.image.{u2, u1} α δ f (Set.uIcc.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)) a b)))
-Case conversion may be inaccurate. Consider using '#align intermediate_value_uIcc intermediate_value_uIccₓ'. -/
 /-- **Intermediate Value Theorem** for continuous functions on closed intervals, unordered case. -/
 theorem intermediate_value_uIcc {a b : α} {f : α → δ} (hf : ContinuousOn f (uIcc a b)) :
     uIcc (f a) (f b) ⊆ f '' uIcc a b := by
   cases le_total (f a) (f b) <;> simp [*, is_preconnected_uIcc.intermediate_value]
 #align intermediate_value_uIcc intermediate_value_uIcc
 
-/- warning: intermediate_value_Ico -> intermediate_value_Ico is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ico.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f a) (f b)) (Set.image.{u1, u2} α δ f (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.Ico.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f a) (f b)) (Set.image.{u2, u1} α δ f (Set.Ico.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b))))
-Case conversion may be inaccurate. Consider using '#align intermediate_value_Ico intermediate_value_Icoₓ'. -/
 theorem intermediate_value_Ico {a b : α} (hab : a ≤ b) {f : α → δ} (hf : ContinuousOn f (Icc a b)) :
     Ico (f a) (f b) ⊆ f '' Ico a b :=
   Or.elim (eq_or_lt_of_le hab) (fun he y h => absurd h.2 (not_lt_of_le (he ▸ h.1))) fun hlt =>
@@ -898,12 +607,6 @@ theorem intermediate_value_Ico {a b : α} (hab : a ≤ b) {f : α → δ} (hf :
       ((hf.ContinuousWithinAt ⟨hab, refl b⟩).mono Ico_subset_Icc_self)
 #align intermediate_value_Ico intermediate_value_Ico
 
-/- warning: intermediate_value_Ico' -> intermediate_value_Ico' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ioc.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f b) (f a)) (Set.image.{u1, u2} α δ f (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.Ioc.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f b) (f a)) (Set.image.{u2, u1} α δ f (Set.Ico.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b))))
-Case conversion may be inaccurate. Consider using '#align intermediate_value_Ico' intermediate_value_Ico'ₓ'. -/
 theorem intermediate_value_Ico' {a b : α} (hab : a ≤ b) {f : α → δ}
     (hf : ContinuousOn f (Icc a b)) : Ioc (f b) (f a) ⊆ f '' Ico a b :=
   Or.elim (eq_or_lt_of_le hab) (fun he y h => absurd h.1 (not_lt_of_le (he ▸ h.2))) fun hlt =>
@@ -912,12 +615,6 @@ theorem intermediate_value_Ico' {a b : α} (hab : a ≤ b) {f : α → δ}
       ((hf.ContinuousWithinAt ⟨hab, refl b⟩).mono Ico_subset_Icc_self)
 #align intermediate_value_Ico' intermediate_value_Ico'
 
-/- warning: intermediate_value_Ioc -> intermediate_value_Ioc is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ioc.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f a) (f b)) (Set.image.{u1, u2} α δ f (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.Ioc.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f a) (f b)) (Set.image.{u2, u1} α δ f (Set.Ioc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b))))
-Case conversion may be inaccurate. Consider using '#align intermediate_value_Ioc intermediate_value_Iocₓ'. -/
 theorem intermediate_value_Ioc {a b : α} (hab : a ≤ b) {f : α → δ} (hf : ContinuousOn f (Icc a b)) :
     Ioc (f a) (f b) ⊆ f '' Ioc a b :=
   Or.elim (eq_or_lt_of_le hab) (fun he y h => absurd h.2 (not_le_of_lt (he ▸ h.1))) fun hlt =>
@@ -926,12 +623,6 @@ theorem intermediate_value_Ioc {a b : α} (hab : a ≤ b) {f : α → δ} (hf :
       ((hf.ContinuousWithinAt ⟨refl a, hab⟩).mono Ioc_subset_Icc_self)
 #align intermediate_value_Ioc intermediate_value_Ioc
 
-/- warning: intermediate_value_Ioc' -> intermediate_value_Ioc' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ico.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f b) (f a)) (Set.image.{u1, u2} α δ f (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.Ico.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f b) (f a)) (Set.image.{u2, u1} α δ f (Set.Ioc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b))))
-Case conversion may be inaccurate. Consider using '#align intermediate_value_Ioc' intermediate_value_Ioc'ₓ'. -/
 theorem intermediate_value_Ioc' {a b : α} (hab : a ≤ b) {f : α → δ}
     (hf : ContinuousOn f (Icc a b)) : Ico (f b) (f a) ⊆ f '' Ioc a b :=
   Or.elim (eq_or_lt_of_le hab) (fun he y h => absurd h.1 (not_le_of_lt (he ▸ h.2))) fun hlt =>
@@ -940,12 +631,6 @@ theorem intermediate_value_Ioc' {a b : α} (hab : a ≤ b) {f : α → δ}
       ((hf.ContinuousWithinAt ⟨refl a, hab⟩).mono Ioc_subset_Icc_self)
 #align intermediate_value_Ioc' intermediate_value_Ioc'
 
-/- warning: intermediate_value_Ioo -> intermediate_value_Ioo is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ioo.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f a) (f b)) (Set.image.{u1, u2} α δ f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.Ioo.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f a) (f b)) (Set.image.{u2, u1} α δ f (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b))))
-Case conversion may be inaccurate. Consider using '#align intermediate_value_Ioo intermediate_value_Iooₓ'. -/
 theorem intermediate_value_Ioo {a b : α} (hab : a ≤ b) {f : α → δ} (hf : ContinuousOn f (Icc a b)) :
     Ioo (f a) (f b) ⊆ f '' Ioo a b :=
   Or.elim (eq_or_lt_of_le hab) (fun he y h => absurd h.2 (not_lt_of_lt (he ▸ h.1))) fun hlt =>
@@ -956,12 +641,6 @@ theorem intermediate_value_Ioo {a b : α} (hab : a ≤ b) {f : α → δ} (hf :
       ((hf.ContinuousWithinAt ⟨hab, refl b⟩).mono Ioo_subset_Icc_self)
 #align intermediate_value_Ioo intermediate_value_Ioo
 
-/- warning: intermediate_value_Ioo' -> intermediate_value_Ioo' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ioo.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f b) (f a)) (Set.image.{u1, u2} α δ f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.Ioo.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f b) (f a)) (Set.image.{u2, u1} α δ f (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b))))
-Case conversion may be inaccurate. Consider using '#align intermediate_value_Ioo' intermediate_value_Ioo'ₓ'. -/
 theorem intermediate_value_Ioo' {a b : α} (hab : a ≤ b) {f : α → δ}
     (hf : ContinuousOn f (Icc a b)) : Ioo (f b) (f a) ⊆ f '' Ioo a b :=
   Or.elim (eq_or_lt_of_le hab) (fun he y h => absurd h.1 (not_lt_of_lt (he ▸ h.2))) fun hlt =>
@@ -972,12 +651,6 @@ theorem intermediate_value_Ioo' {a b : α} (hab : a ≤ b) {f : α → δ}
       ((hf.ContinuousWithinAt ⟨refl a, hab⟩).mono Ioo_subset_Icc_self)
 #align intermediate_value_Ioo' intermediate_value_Ioo'
 
-/- warning: continuous_on.surj_on_Icc -> ContinuousOn.surjOn_Icc is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {s : Set.{u1} α} [hs : Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s] {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f s) -> (forall {a : α} {b : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (Set.SurjOn.{u1, u2} α δ f s (Set.Icc.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f a) (f b))))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {s : Set.{u2} α} [hs : Set.OrdConnected.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) s] {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f s) -> (forall {a : α} {b : α}, (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a s) -> (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) b s) -> (Set.SurjOn.{u2, u1} α δ f s (Set.Icc.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f a) (f b))))
-Case conversion may be inaccurate. Consider using '#align continuous_on.surj_on_Icc ContinuousOn.surjOn_Iccₓ'. -/
 /-- **Intermediate value theorem**: if `f` is continuous on an order-connected set `s` and `a`,
 `b` are two points of this set, then `f` sends `s` to a superset of `Icc (f x) (f y)`. -/
 theorem ContinuousOn.surjOn_Icc {s : Set α} [hs : OrdConnected s] {f : α → δ}
@@ -985,12 +658,6 @@ theorem ContinuousOn.surjOn_Icc {s : Set α} [hs : OrdConnected s] {f : α → 
   hs.IsPreconnected.intermediate_value ha hb hf
 #align continuous_on.surj_on_Icc ContinuousOn.surjOn_Icc
 
-/- warning: continuous_on.surj_on_uIcc -> ContinuousOn.surjOn_uIcc is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {s : Set.{u1} α} [hs : Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s] {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f s) -> (forall {a : α} {b : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (Set.SurjOn.{u1, u2} α δ f s (Set.uIcc.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9) (f a) (f b))))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {s : Set.{u2} α} [hs : Set.OrdConnected.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) s] {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f s) -> (forall {a : α} {b : α}, (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a s) -> (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) b s) -> (Set.SurjOn.{u2, u1} α δ f s (Set.uIcc.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)) (f a) (f b))))
-Case conversion may be inaccurate. Consider using '#align continuous_on.surj_on_uIcc ContinuousOn.surjOn_uIccₓ'. -/
 /-- **Intermediate value theorem**: if `f` is continuous on an order-connected set `s` and `a`,
 `b` are two points of this set, then `f` sends `s` to a superset of `[f x, f y]`. -/
 theorem ContinuousOn.surjOn_uIcc {s : Set α} [hs : OrdConnected s] {f : α → δ}
@@ -998,12 +665,6 @@ theorem ContinuousOn.surjOn_uIcc {s : Set α} [hs : OrdConnected s] {f : α →
   by cases' le_total (f a) (f b) with hab hab <;> simp [hf.surj_on_Icc, *]
 #align continuous_on.surj_on_uIcc ContinuousOn.surjOn_uIcc
 
-/- warning: continuous.surjective -> Continuous.surjective is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {f : α -> δ}, (Continuous.{u1, u2} α δ _inst_2 _inst_10 f) -> (Filter.Tendsto.{u1, u2} α δ f (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (Filter.atTop.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Filter.Tendsto.{u1, u2} α δ f (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (Filter.atBot.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Function.Surjective.{succ u1, succ u2} α δ f)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {f : α -> δ}, (Continuous.{u2, u1} α δ _inst_2 _inst_10 f) -> (Filter.Tendsto.{u2, u1} α δ f (Filter.atTop.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) (Filter.atTop.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))))) -> (Filter.Tendsto.{u2, u1} α δ f (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) (Filter.atBot.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))))) -> (Function.Surjective.{succ u2, succ u1} α δ f)
-Case conversion may be inaccurate. Consider using '#align continuous.surjective Continuous.surjectiveₓ'. -/
 /-- A continuous function which tendsto `at_top` `at_top` and to `at_bot` `at_bot` is surjective. -/
 theorem Continuous.surjective {f : α → δ} (hf : Continuous f) (h_top : Tendsto f atTop atTop)
     (h_bot : Tendsto f atBot atBot) : Function.Surjective f := fun p =>
@@ -1011,21 +672,12 @@ theorem Continuous.surjective {f : α → δ} (hf : Continuous f) (h_top : Tends
     (h_top.Eventually (eventually_ge_atTop p)).exists
 #align continuous.surjective Continuous.surjective
 
-/- warning: continuous.surjective' -> Continuous.surjective' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {f : α -> δ}, (Continuous.{u1, u2} α δ _inst_2 _inst_10 f) -> (Filter.Tendsto.{u1, u2} α δ f (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (Filter.atTop.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Filter.Tendsto.{u1, u2} α δ f (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (Filter.atBot.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Function.Surjective.{succ u1, succ u2} α δ f)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {f : α -> δ}, (Continuous.{u2, u1} α δ _inst_2 _inst_10 f) -> (Filter.Tendsto.{u2, u1} α δ f (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) (Filter.atTop.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))))) -> (Filter.Tendsto.{u2, u1} α δ f (Filter.atTop.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) (Filter.atBot.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))))) -> (Function.Surjective.{succ u2, succ u1} α δ f)
-Case conversion may be inaccurate. Consider using '#align continuous.surjective' Continuous.surjective'ₓ'. -/
 /-- A continuous function which tendsto `at_bot` `at_top` and to `at_top` `at_bot` is surjective. -/
 theorem Continuous.surjective' {f : α → δ} (hf : Continuous f) (h_top : Tendsto f atBot atTop)
     (h_bot : Tendsto f atTop atBot) : Function.Surjective f :=
   @Continuous.surjective αᵒᵈ _ _ _ _ _ _ _ _ _ hf h_top h_bot
 #align continuous.surjective' Continuous.surjective'
 
-/- warning: continuous_on.surj_on_of_tendsto -> ContinuousOn.surjOn_of_tendsto is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_on.surj_on_of_tendsto ContinuousOn.surjOn_of_tendstoₓ'. -/
 /-- If a function `f : α → β` is continuous on a nonempty interval `s`, its restriction to `s`
 tends to `at_bot : filter β` along `at_bot : filter ↥s` and tends to `at_top : filter β` along
 `at_top : filter ↥s`, then the restriction of `f` to `s` is surjective. We formulate the
@@ -1037,9 +689,6 @@ theorem ContinuousOn.surjOn_of_tendsto {f : α → δ} {s : Set α} [OrdConnecte
   surj_on_iff_surjective.2 <| (continuousOn_iff_continuous_restrict.1 hf).Surjective htop hbot
 #align continuous_on.surj_on_of_tendsto ContinuousOn.surjOn_of_tendsto
 
-/- warning: continuous_on.surj_on_of_tendsto' -> ContinuousOn.surjOn_of_tendsto' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_on.surj_on_of_tendsto' ContinuousOn.surjOn_of_tendsto'ₓ'. -/
 /-- If a function `f : α → β` is continuous on a nonempty interval `s`, its restriction to `s`
 tends to `at_top : filter β` along `at_bot : filter ↥s` and tends to `at_bot : filter β` along
 `at_top : filter ↥s`, then the restriction of `f` to `s` is surjective. We formulate the

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

@@ -511,14 +511,12 @@ theorem IsClosed.mem_of_ge_of_forall_exists_gt {a b : α} {s : Set α} (hs : IsC
     (ha : a ∈ s) (hab : a ≤ b) (hgt : ∀ x ∈ s ∩ Ico a b, (s ∩ Ioc x b).Nonempty) : b ∈ s :=
   by
   let S := s ∩ Icc a b
-  replace ha : a ∈ S
-  exact ⟨ha, left_mem_Icc.2 hab⟩
+  replace ha : a ∈ S; exact ⟨ha, left_mem_Icc.2 hab⟩
   have Sbd : BddAbove S := ⟨b, fun z hz => hz.2.2⟩
   let c := Sup (s ∩ Icc a b)
   have c_mem : c ∈ S := hs.cSup_mem ⟨_, ha⟩ Sbd
   have c_le : c ≤ b := csSup_le ⟨_, ha⟩ fun x hx => hx.2.2
-  cases' eq_or_lt_of_le c_le with hc hc
-  exact hc ▸ c_mem.1
+  cases' eq_or_lt_of_le c_le with hc hc; exact hc ▸ c_mem.1
   exfalso
   rcases hgt c ⟨c_mem.1, c_mem.2.1, hc⟩ with ⟨x, xs, cx, xb⟩
   exact not_lt_of_le (le_csSup Sbd ⟨xs, le_trans (le_csSup Sbd ha) (le_of_lt cx), xb⟩) cx
@@ -539,10 +537,7 @@ theorem IsClosed.Icc_subset_of_forall_exists_gt {a b : α} {s : Set α} (hs : Is
   intro y hy
   have : IsClosed (s ∩ Icc a y) :=
     by
-    suffices s ∩ Icc a y = s ∩ Icc a b ∩ Icc a y
-      by
-      rw [this]
-      exact IsClosed.inter hs isClosed_Icc
+    suffices s ∩ Icc a y = s ∩ Icc a b ∩ Icc a y by rw [this]; exact IsClosed.inter hs isClosed_Icc
     rw [inter_assoc]
     congr
     exact (inter_eq_self_of_subset_right <| Icc_subset_Icc_right hy.2).symm

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

@@ -148,10 +148,7 @@ theorem IsPreconnected.intermediate_value₂_eventually₁ {s : Set X} (hs : IsP
 #align is_preconnected.intermediate_value₂_eventually₁ IsPreconnected.intermediate_value₂_eventually₁
 
 /- warning: is_preconnected.intermediate_value₂_eventually₂ -> IsPreconnected.intermediate_value₂_eventually₂ is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l₁ f g) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l₂ g f) -> (Exists.{succ u1} X (fun (x : X) => Exists.{0} (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) (fun (H : Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) => Eq.{succ u2} α (f x) (g x))))))
-but is expected to have type
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) l₁ f g) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) l₂ g f) -> (Exists.{succ u1} X (fun (x : X) => And (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x s) (Eq.{succ u2} α (f x) (g x))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value₂_eventually₂ IsPreconnected.intermediate_value₂_eventually₂ₓ'. -/
 theorem IsPreconnected.intermediate_value₂_eventually₂ {s : Set X} (hs : IsPreconnected s)
     {l₁ l₂ : Filter X} [NeBot l₁] [NeBot l₂] (hl₁ : l₁ ≤ 𝓟 s) (hl₂ : l₂ ≤ 𝓟 s) {f g : X → α}
@@ -204,10 +201,7 @@ theorem IsPreconnected.intermediate_value_Ioc {s : Set X} (hs : IsPreconnected s
 #align is_preconnected.intermediate_value_Ioc IsPreconnected.intermediate_value_Ioc
 
 /- warning: is_preconnected.intermediate_value_Ioo -> IsPreconnected.intermediate_value_Ioo is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Ioo IsPreconnected.intermediate_value_Iooₓ'. -/
 theorem IsPreconnected.intermediate_value_Ioo {s : Set X} (hs : IsPreconnected s) {l₁ l₂ : Filter X}
     [NeBot l₁] [NeBot l₂] (hl₁ : l₁ ≤ 𝓟 s) (hl₂ : l₂ ≤ 𝓟 s) {f : X → α} (hf : ContinuousOn f s)
@@ -420,10 +414,7 @@ theorem IsPreconnected.Iio_csSup_subset {s : Set α} (hs : IsPreconnected s) (hb
 #align is_preconnected.Iio_cSup_subset IsPreconnected.Iio_csSup_subset
 
 /- warning: is_preconnected.mem_intervals -> IsPreconnected.mem_intervals is a dubious translation:
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(ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α 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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_preconnected.mem_intervals IsPreconnected.mem_intervalsₓ'. -/
 /-- A preconnected set in a conditionally complete linear order is either one of the intervals
 `[Inf s, Sup s]`, `[Inf s, Sup s)`, `(Inf s, Sup s]`, `(Inf s, Sup s)`, `[Inf s, +∞)`,
@@ -1038,10 +1029,7 @@ theorem Continuous.surjective' {f : α → δ} (hf : Continuous f) (h_top : Tend
 #align continuous.surjective' Continuous.surjective'
 
 /- warning: continuous_on.surj_on_of_tendsto -> ContinuousOn.surjOn_of_tendsto is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align continuous_on.surj_on_of_tendsto ContinuousOn.surjOn_of_tendstoₓ'. -/
 /-- If a function `f : α → β` is continuous on a nonempty interval `s`, its restriction to `s`
 tends to `at_bot : filter β` along `at_bot : filter ↥s` and tends to `at_top : filter β` along
@@ -1055,10 +1043,7 @@ theorem ContinuousOn.surjOn_of_tendsto {f : α → δ} {s : Set α} [OrdConnecte
 #align continuous_on.surj_on_of_tendsto ContinuousOn.surjOn_of_tendsto
 
 /- warning: continuous_on.surj_on_of_tendsto' -> ContinuousOn.surjOn_of_tendsto' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align continuous_on.surj_on_of_tendsto' ContinuousOn.surjOn_of_tendsto'ₓ'. -/
 /-- If a function `f : α → β` is continuous on a nonempty interval `s`, its restriction to `s`
 tends to `at_top : filter β` along `at_bot : filter ↥s` and tends to `at_bot : filter β` along

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

@@ -66,7 +66,12 @@ section
 variable {X : Type u} {α : Type v} [TopologicalSpace X] [LinearOrder α] [TopologicalSpace α]
   [OrderClosedTopology α]
 
-#print intermediate_value_univ₂ /-
+/- warning: intermediate_value_univ₂ -> intermediate_value_univ₂ is a dubious translation:
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+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] [_inst_5 : PreconnectedSpace.{u1} X _inst_1] {a : X} {b : X} {f : X -> α} {g : X -> α}, (Continuous.{u1, u2} X α _inst_1 _inst_3 f) -> (Continuous.{u1, u2} X α _inst_1 _inst_3 g) -> (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) (f a) (g a)) -> (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) (g b) (f b)) -> (Exists.{succ u1} X (fun (x : X) => Eq.{succ u2} α (f x) (g x)))
+but is expected to have type
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] [_inst_5 : PreconnectedSpace.{u1} X _inst_1] {a : X} {b : X} {f : X -> α} {g : X -> α}, (Continuous.{u1, u2} X α _inst_1 _inst_3 f) -> (Continuous.{u1, u2} X α _inst_1 _inst_3 g) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (f a) (g a)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (g b) (f b)) -> (Exists.{succ u1} X (fun (x : X) => Eq.{succ u2} α (f x) (g x)))
+Case conversion may be inaccurate. Consider using '#align intermediate_value_univ₂ intermediate_value_univ₂ₓ'. -/
 /-- Intermediate value theorem for two functions: if `f` and `g` are two continuous functions
 on a preconnected space and `f a ≤ g a` and `g b ≤ f b`, then for some `x` we have `f x = g x`. -/
 theorem intermediate_value_univ₂ [PreconnectedSpace X] {a b : X} {f g : X → α} (hf : Continuous f)
@@ -78,18 +83,26 @@ theorem intermediate_value_univ₂ [PreconnectedSpace X] {a b : X} {f g : X →
       (isClosed_le hg hf) (fun x hx => le_total _ _) ⟨a, trivial, ha⟩ ⟨b, trivial, hb⟩
   exact ⟨x, le_antisymm hfg hgf⟩
 #align intermediate_value_univ₂ intermediate_value_univ₂
--/
 
-#print intermediate_value_univ₂_eventually₁ /-
+/- warning: intermediate_value_univ₂_eventually₁ -> intermediate_value_univ₂_eventually₁ is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] [_inst_5 : PreconnectedSpace.{u1} X _inst_1] {a : X} {l : Filter.{u1} X} [_inst_6 : Filter.NeBot.{u1} X l] {f : X -> α} {g : X -> α}, (Continuous.{u1, u2} X α _inst_1 _inst_3 f) -> (Continuous.{u1, u2} X α _inst_1 _inst_3 g) -> (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) (f a) (g a)) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l g f) -> (Exists.{succ u1} X (fun (x : X) => Eq.{succ u2} α (f x) (g x)))
+but is expected to have type
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] [_inst_5 : PreconnectedSpace.{u1} X _inst_1] {a : X} {l : Filter.{u1} X} [_inst_6 : Filter.NeBot.{u1} X l] {f : X -> α} {g : X -> α}, (Continuous.{u1, u2} X α _inst_1 _inst_3 f) -> (Continuous.{u1, u2} X α _inst_1 _inst_3 g) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (f a) (g a)) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) l g f) -> (Exists.{succ u1} X (fun (x : X) => Eq.{succ u2} α (f x) (g x)))
+Case conversion may be inaccurate. Consider using '#align intermediate_value_univ₂_eventually₁ intermediate_value_univ₂_eventually₁ₓ'. -/
 theorem intermediate_value_univ₂_eventually₁ [PreconnectedSpace X] {a : X} {l : Filter X} [NeBot l]
     {f g : X → α} (hf : Continuous f) (hg : Continuous g) (ha : f a ≤ g a) (he : g ≤ᶠ[l] f) :
     ∃ x, f x = g x :=
   let ⟨c, hc⟩ := he.Frequently.exists
   intermediate_value_univ₂ hf hg ha hc
 #align intermediate_value_univ₂_eventually₁ intermediate_value_univ₂_eventually₁
--/
 
-#print intermediate_value_univ₂_eventually₂ /-
+/- warning: intermediate_value_univ₂_eventually₂ -> intermediate_value_univ₂_eventually₂ is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] [_inst_5 : PreconnectedSpace.{u1} X _inst_1] {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_6 : Filter.NeBot.{u1} X l₁] [_inst_7 : Filter.NeBot.{u1} X l₂] {f : X -> α} {g : X -> α}, (Continuous.{u1, u2} X α _inst_1 _inst_3 f) -> (Continuous.{u1, u2} X α _inst_1 _inst_3 g) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l₁ f g) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l₂ g f) -> (Exists.{succ u1} X (fun (x : X) => Eq.{succ u2} α (f x) (g x)))
+but is expected to have type
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] [_inst_5 : PreconnectedSpace.{u1} X _inst_1] {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_6 : Filter.NeBot.{u1} X l₁] [_inst_7 : Filter.NeBot.{u1} X l₂] {f : X -> α} {g : X -> α}, (Continuous.{u1, u2} X α _inst_1 _inst_3 f) -> (Continuous.{u1, u2} X α _inst_1 _inst_3 g) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) l₁ f g) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) l₂ g f) -> (Exists.{succ u1} X (fun (x : X) => Eq.{succ u2} α (f x) (g x)))
+Case conversion may be inaccurate. Consider using '#align intermediate_value_univ₂_eventually₂ intermediate_value_univ₂_eventually₂ₓ'. -/
 theorem intermediate_value_univ₂_eventually₂ [PreconnectedSpace X] {l₁ l₂ : Filter X} [NeBot l₁]
     [NeBot l₂] {f g : X → α} (hf : Continuous f) (hg : Continuous g) (he₁ : f ≤ᶠ[l₁] g)
     (he₂ : g ≤ᶠ[l₂] f) : ∃ x, f x = g x :=
@@ -97,11 +110,10 @@ theorem intermediate_value_univ₂_eventually₂ [PreconnectedSpace X] {l₁ l
   let ⟨c₂, hc₂⟩ := he₂.Frequently.exists
   intermediate_value_univ₂ hf hg hc₁ hc₂
 #align intermediate_value_univ₂_eventually₂ intermediate_value_univ₂_eventually₂
--/
 
 /- warning: is_preconnected.intermediate_value₂ -> IsPreconnected.intermediate_value₂ is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {b : X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) b s) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) (f a) (g a)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) (g b) (f b)) -> (Exists.{succ u1} X (fun (x : X) => Exists.{0} (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) (fun (H : Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) => Eq.{succ u2} α (f x) (g x))))))
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {b : X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) b s) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) (f a) (g a)) -> (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) (g b) (f b)) -> (Exists.{succ u1} X (fun (x : X) => Exists.{0} (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) (fun (H : Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) => Eq.{succ u2} α (f x) (g x))))))
 but is expected to have type
   forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {b : X}, (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) a s) -> (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) b s) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (f a) (g a)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (g b) (f b)) -> (Exists.{succ u1} X (fun (x : X) => And (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x s) (Eq.{succ u2} α (f x) (g x))))))
 Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value₂ IsPreconnected.intermediate_value₂ₓ'. -/
@@ -120,7 +132,7 @@ theorem IsPreconnected.intermediate_value₂ {s : Set X} (hs : IsPreconnected s)
 
 /- warning: is_preconnected.intermediate_value₂_eventually₁ -> IsPreconnected.intermediate_value₂_eventually₁ is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) (f a) (g a)) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l g f) -> (Exists.{succ u1} X (fun (x : X) => Exists.{0} (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) (fun (H : Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) => Eq.{succ u2} α (f x) (g x)))))))
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) (f a) (g a)) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l g f) -> (Exists.{succ u1} X (fun (x : X) => Exists.{0} (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) (fun (H : Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) => Eq.{succ u2} α (f x) (g x)))))))
 but is expected to have type
   forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (f a) (g a)) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) l g f) -> (Exists.{succ u1} X (fun (x : X) => And (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x s) (Eq.{succ u2} α (f x) (g x)))))))
 Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value₂_eventually₁ IsPreconnected.intermediate_value₂_eventually₁ₓ'. -/
@@ -137,7 +149,7 @@ theorem IsPreconnected.intermediate_value₂_eventually₁ {s : Set X} (hs : IsP
 
 /- warning: is_preconnected.intermediate_value₂_eventually₂ -> IsPreconnected.intermediate_value₂_eventually₂ is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l₁ f g) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l₂ g f) -> (Exists.{succ u1} X (fun (x : X) => Exists.{0} (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) (fun (H : Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) => Eq.{succ u2} α (f x) (g x))))))
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l₁ f g) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l₂ g f) -> (Exists.{succ u1} X (fun (x : X) => Exists.{0} (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) (fun (H : Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) => Eq.{succ u2} α (f x) (g x))))))
 but is expected to have type
   forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) l₁ f g) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) l₂ g f) -> (Exists.{succ u1} X (fun (x : X) => And (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x s) (Eq.{succ u2} α (f x) (g x))))))
 Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value₂_eventually₂ IsPreconnected.intermediate_value₂_eventually₂ₓ'. -/
@@ -164,7 +176,7 @@ theorem IsPreconnected.intermediate_value {s : Set X} (hs : IsPreconnected s) {a
 
 /- warning: is_preconnected.intermediate_value_Ico -> IsPreconnected.intermediate_value_Ico is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v : α}, (Filter.Tendsto.{u1, u2} X α f l (nhds.{u2} α _inst_3 v)) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.Ico.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))) (f a) v) (Set.image.{u1, u2} X α f s))))))
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v : α}, (Filter.Tendsto.{u1, u2} X α f l (nhds.{u2} α _inst_3 v)) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.Ico.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))) (f a) v) (Set.image.{u1, u2} X α f s))))))
 but is expected to have type
   forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v : α}, (Filter.Tendsto.{u1, u2} X α f l (nhds.{u2} α _inst_3 v)) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) (Set.Ico.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) (f a) v) (Set.image.{u1, u2} X α f s))))))
 Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Ico IsPreconnected.intermediate_value_Icoₓ'. -/
@@ -178,7 +190,7 @@ theorem IsPreconnected.intermediate_value_Ico {s : Set X} (hs : IsPreconnected s
 
 /- warning: is_preconnected.intermediate_value_Ioc -> IsPreconnected.intermediate_value_Ioc is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v : α}, (Filter.Tendsto.{u1, u2} X α f l (nhds.{u2} α _inst_3 v)) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.Ioc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))) v (f a)) (Set.image.{u1, u2} X α f s))))))
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v : α}, (Filter.Tendsto.{u1, u2} X α f l (nhds.{u2} α _inst_3 v)) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.Ioc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))) v (f a)) (Set.image.{u1, u2} X α f s))))))
 but is expected to have type
   forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v : α}, (Filter.Tendsto.{u1, u2} X α f l (nhds.{u2} α _inst_3 v)) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) (Set.Ioc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) v (f a)) (Set.image.{u1, u2} X α f s))))))
 Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Ioc IsPreconnected.intermediate_value_Iocₓ'. -/
@@ -193,7 +205,7 @@ theorem IsPreconnected.intermediate_value_Ioc {s : Set X} (hs : IsPreconnected s
 
 /- warning: is_preconnected.intermediate_value_Ioo -> IsPreconnected.intermediate_value_Ioo is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v₁ : α} {v₂ : α}, (Filter.Tendsto.{u1, u2} X α f l₁ (nhds.{u2} α _inst_3 v₁)) -> (Filter.Tendsto.{u1, u2} X α f l₂ (nhds.{u2} α _inst_3 v₂)) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))) v₁ v₂) (Set.image.{u1, u2} X α f s)))))
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v₁ : α} {v₂ : α}, (Filter.Tendsto.{u1, u2} X α f l₁ (nhds.{u2} α _inst_3 v₁)) -> (Filter.Tendsto.{u1, u2} X α f l₂ (nhds.{u2} α _inst_3 v₂)) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))) v₁ v₂) (Set.image.{u1, u2} X α f s)))))
 but is expected to have type
   forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v₁ : α} {v₂ : α}, (Filter.Tendsto.{u1, u2} X α f l₁ (nhds.{u2} α _inst_3 v₁)) -> (Filter.Tendsto.{u1, u2} X α f l₂ (nhds.{u2} α _inst_3 v₂)) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) v₁ v₂) (Set.image.{u1, u2} X α f s)))))
 Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Ioo IsPreconnected.intermediate_value_Iooₓ'. -/
@@ -208,7 +220,7 @@ theorem IsPreconnected.intermediate_value_Ioo {s : Set X} (hs : IsPreconnected s
 
 /- warning: is_preconnected.intermediate_value_Ici -> IsPreconnected.intermediate_value_Ici is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (Filter.Tendsto.{u1, u2} X α f l (Filter.atTop.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))))) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.Ici.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))) (f a)) (Set.image.{u1, u2} X α f s)))))
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (Filter.Tendsto.{u1, u2} X α f l (Filter.atTop.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))))) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.Ici.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))) (f a)) (Set.image.{u1, u2} X α f s)))))
 but is expected to have type
   forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (Filter.Tendsto.{u1, u2} X α f l (Filter.atTop.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) (Set.Ici.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) (f a)) (Set.image.{u1, u2} X α f s)))))
 Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Ici IsPreconnected.intermediate_value_Iciₓ'. -/
@@ -221,7 +233,7 @@ theorem IsPreconnected.intermediate_value_Ici {s : Set X} (hs : IsPreconnected s
 
 /- warning: is_preconnected.intermediate_value_Iic -> IsPreconnected.intermediate_value_Iic is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (Filter.Tendsto.{u1, u2} X α f l (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))))) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.Iic.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))) (f a)) (Set.image.{u1, u2} X α f s)))))
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (Filter.Tendsto.{u1, u2} X α f l (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))))) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.Iic.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))) (f a)) (Set.image.{u1, u2} X α f s)))))
 but is expected to have type
   forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (Filter.Tendsto.{u1, u2} X α f l (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) (Set.Iic.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) (f a)) (Set.image.{u1, u2} X α f s)))))
 Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Iic IsPreconnected.intermediate_value_Iicₓ'. -/
@@ -235,7 +247,7 @@ theorem IsPreconnected.intermediate_value_Iic {s : Set X} (hs : IsPreconnected s
 
 /- warning: is_preconnected.intermediate_value_Ioi -> IsPreconnected.intermediate_value_Ioi is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v : α}, (Filter.Tendsto.{u1, u2} X α f l₁ (nhds.{u2} α _inst_3 v)) -> (Filter.Tendsto.{u1, u2} X α f l₂ (Filter.atTop.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))))) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.Ioi.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))) v) (Set.image.{u1, u2} X α f s)))))
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v : α}, (Filter.Tendsto.{u1, u2} X α f l₁ (nhds.{u2} α _inst_3 v)) -> (Filter.Tendsto.{u1, u2} X α f l₂ (Filter.atTop.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))))) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.Ioi.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))) v) (Set.image.{u1, u2} X α f s)))))
 but is expected to have type
   forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v : α}, (Filter.Tendsto.{u1, u2} X α f l₁ (nhds.{u2} α _inst_3 v)) -> (Filter.Tendsto.{u1, u2} X α f l₂ (Filter.atTop.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) (Set.Ioi.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) v) (Set.image.{u1, u2} X α f s)))))
 Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Ioi IsPreconnected.intermediate_value_Ioiₓ'. -/
@@ -249,7 +261,7 @@ theorem IsPreconnected.intermediate_value_Ioi {s : Set X} (hs : IsPreconnected s
 
 /- warning: is_preconnected.intermediate_value_Iio -> IsPreconnected.intermediate_value_Iio is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v : α}, (Filter.Tendsto.{u1, u2} X α f l₁ (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))))) -> (Filter.Tendsto.{u1, u2} X α f l₂ (nhds.{u2} α _inst_3 v)) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))) v) (Set.image.{u1, u2} X α f s)))))
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v : α}, (Filter.Tendsto.{u1, u2} X α f l₁ (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))))) -> (Filter.Tendsto.{u1, u2} X α f l₂ (nhds.{u2} α _inst_3 v)) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))) v) (Set.image.{u1, u2} X α f s)))))
 but is expected to have type
   forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (forall {v : α}, (Filter.Tendsto.{u1, u2} X α f l₁ (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))) -> (Filter.Tendsto.{u1, u2} X α f l₂ (nhds.{u2} α _inst_3 v)) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))) v) (Set.image.{u1, u2} X α f s)))))
 Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Iio IsPreconnected.intermediate_value_Iioₓ'. -/
@@ -263,7 +275,7 @@ theorem IsPreconnected.intermediate_value_Iio {s : Set X} (hs : IsPreconnected s
 
 /- warning: is_preconnected.intermediate_value_Iii -> IsPreconnected.intermediate_value_Iii is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (Filter.Tendsto.{u1, u2} X α f l₁ (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))))) -> (Filter.Tendsto.{u1, u2} X α f l₂ (Filter.atTop.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))))) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.univ.{u2} α) (Set.image.{u1, u2} X α f s))))
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toHasLe.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (Filter.Tendsto.{u1, u2} X α f l₁ (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))))) -> (Filter.Tendsto.{u1, u2} X α f l₂ (Filter.atTop.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2)))))) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.hasSubset.{u2} α) (Set.univ.{u2} α) (Set.image.{u1, u2} X α f s))))
 but is expected to have type
   forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (Filter.Tendsto.{u1, u2} X α f l₁ (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))) -> (Filter.Tendsto.{u1, u2} X α f l₂ (Filter.atTop.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2))))))) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) (Set.univ.{u2} α) (Set.image.{u1, u2} X α f s))))
 Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value_Iii IsPreconnected.intermediate_value_Iiiₓ'. -/
@@ -282,7 +294,12 @@ theorem intermediate_value_univ [PreconnectedSpace X] (a b : X) {f : X → α} (
 #align intermediate_value_univ intermediate_value_univ
 -/
 
-#print mem_range_of_exists_le_of_exists_ge /-
+/- warning: mem_range_of_exists_le_of_exists_ge -> mem_range_of_exists_le_of_exists_ge is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] [_inst_5 : PreconnectedSpace.{u1} X _inst_1] {c : α} {f : X -> α}, (Continuous.{u1, u2} X α _inst_1 _inst_3 f) -> (Exists.{succ u1} X (fun (a : X) => LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) (f a) c)) -> (Exists.{succ u1} X (fun (b : X) => LE.le.{u2} α (Preorder.toHasLe.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) c (f b))) -> (Membership.Mem.{u2, u2} α (Set.{u2} α) (Set.hasMem.{u2} α) c (Set.range.{u2, succ u1} α X f))
+but is expected to have type
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] [_inst_5 : PreconnectedSpace.{u1} X _inst_1] {c : α} {f : X -> α}, (Continuous.{u1, u2} X α _inst_1 _inst_3 f) -> (Exists.{succ u1} X (fun (a : X) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (f a) c)) -> (Exists.{succ u1} X (fun (b : X) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) c (f b))) -> (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) c (Set.range.{u2, succ u1} α X f))
+Case conversion may be inaccurate. Consider using '#align mem_range_of_exists_le_of_exists_ge mem_range_of_exists_le_of_exists_geₓ'. -/
 /-- **Intermediate Value Theorem** for continuous functions on connected spaces. -/
 theorem mem_range_of_exists_le_of_exists_ge [PreconnectedSpace X] {c : α} {f : X → α}
     (hf : Continuous f) (h₁ : ∃ a, f a ≤ c) (h₂ : ∃ b, c ≤ f b) : c ∈ range f :=
@@ -290,7 +307,6 @@ theorem mem_range_of_exists_le_of_exists_ge [PreconnectedSpace X] {c : α} {f :
   let ⟨b, hb⟩ := h₂
   intermediate_value_univ a b hf ⟨ha, hb⟩
 #align mem_range_of_exists_le_of_exists_ge mem_range_of_exists_le_of_exists_ge
--/
 
 /-!
 ### (Pre)connected sets in a linear order
@@ -494,7 +510,7 @@ conditionally complete linear order is preconnected.
 
 /- warning: is_closed.mem_of_ge_of_forall_exists_gt -> IsClosed.mem_of_ge_of_forall_exists_gt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {a : α} {b : α} {s : Set.{u1} α}, (IsClosed.{u1} α _inst_2 (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) x b)))) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {a : α} {b : α} {s : Set.{u1} α}, (IsClosed.{u1} α _inst_2 (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) x b)))) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {a : α} {b : α} {s : Set.{u1} α}, (IsClosed.{u1} α _inst_2 (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) x b)))) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s)
 Case conversion may be inaccurate. Consider using '#align is_closed.mem_of_ge_of_forall_exists_gt IsClosed.mem_of_ge_of_forall_exists_gtₓ'. -/
@@ -548,7 +564,7 @@ variable [DenselyOrdered α] {a b : α}
 
 /- warning: is_closed.Icc_subset_of_forall_mem_nhds_within -> IsClosed.Icc_subset_of_forall_mem_nhdsWithin is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α} {s : Set.{u1} α}, (IsClosed.{u1} α _inst_2 (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_2 x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) x)))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) s)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α} {s : Set.{u1} α}, (IsClosed.{u1} α _inst_2 (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_2 x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) x)))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) s)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α} {s : Set.{u1} α}, (IsClosed.{u1} α _inst_2 (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_2 x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) x)))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) s)
 Case conversion may be inaccurate. Consider using '#align is_closed.Icc_subset_of_forall_mem_nhds_within IsClosed.Icc_subset_of_forall_mem_nhdsWithinₓ'. -/
@@ -567,7 +583,7 @@ theorem IsClosed.Icc_subset_of_forall_mem_nhdsWithin {a b : α} {s : Set α}
 
 /- warning: is_preconnected_Icc_aux -> isPreconnected_Icc_aux is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α} (x : α) (y : α) (s : Set.{u1} α) (t : Set.{u1} α), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x y) -> (IsClosed.{u1} α _inst_2 s) -> (IsClosed.{u1} α _inst_2 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) s)) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) t)) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α} (x : α) (y : α) (s : Set.{u1} α) (t : Set.{u1} α), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x y) -> (IsClosed.{u1} α _inst_2 s) -> (IsClosed.{u1} α _inst_2 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) s)) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) t)) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α} (x : α) (y : α) (s : Set.{u1} α) (t : Set.{u1} α), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x y) -> (IsClosed.{u1} α _inst_2 s) -> (IsClosed.{u1} α _inst_2 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) s)) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) t)) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)))
 Case conversion may be inaccurate. Consider using '#align is_preconnected_Icc_aux isPreconnected_Icc_auxₓ'. -/
@@ -591,7 +607,12 @@ theorem isPreconnected_Icc_aux (x y : α) (s t : Set α) (hxy : x ≤ y) (hs : I
   exact fun w ⟨wt, wzy⟩ => (this wzy).elim id fun h => (wt h).elim
 #align is_preconnected_Icc_aux isPreconnected_Icc_aux
 
-#print isPreconnected_Icc /-
+/- warning: is_preconnected_Icc -> isPreconnected_Icc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)
+Case conversion may be inaccurate. Consider using '#align is_preconnected_Icc isPreconnected_Iccₓ'. -/
 /-- A closed interval in a densely ordered conditionally complete linear order is preconnected. -/
 theorem isPreconnected_Icc : IsPreconnected (Icc a b) :=
   isPreconnected_closed_iff.2
@@ -604,126 +625,201 @@ theorem isPreconnected_Icc : IsPreconnected (Icc a b) :=
         rw [union_comm s t] at hab
         exact isPreconnected_Icc_aux y x t s h ht hs hab hy hx)
 #align is_preconnected_Icc isPreconnected_Icc
--/
 
-#print isPreconnected_uIcc /-
+/- warning: is_preconnected_uIcc -> isPreconnected_uIcc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.uIcc.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) a b)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.uIcc.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) a b)
+Case conversion may be inaccurate. Consider using '#align is_preconnected_uIcc isPreconnected_uIccₓ'. -/
 theorem isPreconnected_uIcc : IsPreconnected (uIcc a b) :=
   isPreconnected_Icc
 #align is_preconnected_uIcc isPreconnected_uIcc
--/
 
-#print Set.OrdConnected.isPreconnected /-
+/- warning: set.ord_connected.is_preconnected -> Set.OrdConnected.isPreconnected is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {s : Set.{u1} α}, (Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (IsPreconnected.{u1} α _inst_2 s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {s : Set.{u1} α}, (Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (IsPreconnected.{u1} α _inst_2 s)
+Case conversion may be inaccurate. Consider using '#align set.ord_connected.is_preconnected Set.OrdConnected.isPreconnectedₓ'. -/
 theorem Set.OrdConnected.isPreconnected {s : Set α} (h : s.OrdConnected) : IsPreconnected s :=
   isPreconnected_of_forall_pair fun x hx y hy =>
     ⟨uIcc x y, h.uIcc_subset hx hy, left_mem_uIcc, right_mem_uIcc, isPreconnected_uIcc⟩
 #align set.ord_connected.is_preconnected Set.OrdConnected.isPreconnected
--/
 
-#print isPreconnected_iff_ordConnected /-
+/- warning: is_preconnected_iff_ord_connected -> isPreconnected_iff_ordConnected is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {s : Set.{u1} α}, Iff (IsPreconnected.{u1} α _inst_2 s) (Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {s : Set.{u1} α}, Iff (IsPreconnected.{u1} α _inst_2 s) (Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)
+Case conversion may be inaccurate. Consider using '#align is_preconnected_iff_ord_connected isPreconnected_iff_ordConnectedₓ'. -/
 theorem isPreconnected_iff_ordConnected {s : Set α} : IsPreconnected s ↔ OrdConnected s :=
   ⟨IsPreconnected.ordConnected, Set.OrdConnected.isPreconnected⟩
 #align is_preconnected_iff_ord_connected isPreconnected_iff_ordConnected
--/
 
-#print isPreconnected_Ici /-
+/- warning: is_preconnected_Ici -> isPreconnected_Ici is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsPreconnected.{u1} α _inst_2 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsPreconnected.{u1} α _inst_2 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
+Case conversion may be inaccurate. Consider using '#align is_preconnected_Ici isPreconnected_Iciₓ'. -/
 theorem isPreconnected_Ici : IsPreconnected (Ici a) :=
   ordConnected_Ici.IsPreconnected
 #align is_preconnected_Ici isPreconnected_Ici
--/
 
-#print isPreconnected_Iic /-
+/- warning: is_preconnected_Iic -> isPreconnected_Iic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsPreconnected.{u1} α _inst_2 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsPreconnected.{u1} α _inst_2 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
+Case conversion may be inaccurate. Consider using '#align is_preconnected_Iic isPreconnected_Iicₓ'. -/
 theorem isPreconnected_Iic : IsPreconnected (Iic a) :=
   ordConnected_Iic.IsPreconnected
 #align is_preconnected_Iic isPreconnected_Iic
--/
 
-#print isPreconnected_Iio /-
+/- warning: is_preconnected_Iio -> isPreconnected_Iio is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsPreconnected.{u1} α _inst_2 (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsPreconnected.{u1} α _inst_2 (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
+Case conversion may be inaccurate. Consider using '#align is_preconnected_Iio isPreconnected_Iioₓ'. -/
 theorem isPreconnected_Iio : IsPreconnected (Iio a) :=
   ordConnected_Iio.IsPreconnected
 #align is_preconnected_Iio isPreconnected_Iio
--/
 
-#print isPreconnected_Ioi /-
+/- warning: is_preconnected_Ioi -> isPreconnected_Ioi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsPreconnected.{u1} α _inst_2 (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsPreconnected.{u1} α _inst_2 (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
+Case conversion may be inaccurate. Consider using '#align is_preconnected_Ioi isPreconnected_Ioiₓ'. -/
 theorem isPreconnected_Ioi : IsPreconnected (Ioi a) :=
   ordConnected_Ioi.IsPreconnected
 #align is_preconnected_Ioi isPreconnected_Ioi
--/
 
-#print isPreconnected_Ioo /-
+/- warning: is_preconnected_Ioo -> isPreconnected_Ioo is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)
+Case conversion may be inaccurate. Consider using '#align is_preconnected_Ioo isPreconnected_Iooₓ'. -/
 theorem isPreconnected_Ioo : IsPreconnected (Ioo a b) :=
   ordConnected_Ioo.IsPreconnected
 #align is_preconnected_Ioo isPreconnected_Ioo
--/
 
-#print isPreconnected_Ioc /-
+/- warning: is_preconnected_Ioc -> isPreconnected_Ioc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)
+Case conversion may be inaccurate. Consider using '#align is_preconnected_Ioc isPreconnected_Iocₓ'. -/
 theorem isPreconnected_Ioc : IsPreconnected (Ioc a b) :=
   ordConnected_Ioc.IsPreconnected
 #align is_preconnected_Ioc isPreconnected_Ioc
--/
 
-#print isPreconnected_Ico /-
+/- warning: is_preconnected_Ico -> isPreconnected_Ico is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, IsPreconnected.{u1} α _inst_2 (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)
+Case conversion may be inaccurate. Consider using '#align is_preconnected_Ico isPreconnected_Icoₓ'. -/
 theorem isPreconnected_Ico : IsPreconnected (Ico a b) :=
   ordConnected_Ico.IsPreconnected
 #align is_preconnected_Ico isPreconnected_Ico
--/
 
-#print isConnected_Ici /-
+/- warning: is_connected_Ici -> isConnected_Ici is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsConnected.{u1} α _inst_2 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsConnected.{u1} α _inst_2 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
+Case conversion may be inaccurate. Consider using '#align is_connected_Ici isConnected_Iciₓ'. -/
 theorem isConnected_Ici : IsConnected (Ici a) :=
   ⟨nonempty_Ici, isPreconnected_Ici⟩
 #align is_connected_Ici isConnected_Ici
--/
 
-#print isConnected_Iic /-
+/- warning: is_connected_Iic -> isConnected_Iic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsConnected.{u1} α _inst_2 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α}, IsConnected.{u1} α _inst_2 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
+Case conversion may be inaccurate. Consider using '#align is_connected_Iic isConnected_Iicₓ'. -/
 theorem isConnected_Iic : IsConnected (Iic a) :=
   ⟨nonempty_Iic, isPreconnected_Iic⟩
 #align is_connected_Iic isConnected_Iic
--/
 
-#print isConnected_Ioi /-
+/- warning: is_connected_Ioi -> isConnected_Ioi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} [_inst_9 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], IsConnected.{u1} α _inst_2 (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} [_inst_9 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], IsConnected.{u1} α _inst_2 (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
+Case conversion may be inaccurate. Consider using '#align is_connected_Ioi isConnected_Ioiₓ'. -/
 theorem isConnected_Ioi [NoMaxOrder α] : IsConnected (Ioi a) :=
   ⟨nonempty_Ioi, isPreconnected_Ioi⟩
 #align is_connected_Ioi isConnected_Ioi
--/
 
-#print isConnected_Iio /-
+/- warning: is_connected_Iio -> isConnected_Iio is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} [_inst_9 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], IsConnected.{u1} α _inst_2 (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} [_inst_9 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], IsConnected.{u1} α _inst_2 (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a)
+Case conversion may be inaccurate. Consider using '#align is_connected_Iio isConnected_Iioₓ'. -/
 theorem isConnected_Iio [NoMinOrder α] : IsConnected (Iio a) :=
   ⟨nonempty_Iio, isPreconnected_Iio⟩
 #align is_connected_Iio isConnected_Iio
--/
 
-#print isConnected_Icc /-
+/- warning: is_connected_Icc -> isConnected_Icc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (IsConnected.{u1} α _inst_2 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (IsConnected.{u1} α _inst_2 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))
+Case conversion may be inaccurate. Consider using '#align is_connected_Icc isConnected_Iccₓ'. -/
 theorem isConnected_Icc (h : a ≤ b) : IsConnected (Icc a b) :=
   ⟨nonempty_Icc.2 h, isPreconnected_Icc⟩
 #align is_connected_Icc isConnected_Icc
--/
 
-#print isConnected_Ioo /-
+/- warning: is_connected_Ioo -> isConnected_Ioo is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (IsConnected.{u1} α _inst_2 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (IsConnected.{u1} α _inst_2 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))
+Case conversion may be inaccurate. Consider using '#align is_connected_Ioo isConnected_Iooₓ'. -/
 theorem isConnected_Ioo (h : a < b) : IsConnected (Ioo a b) :=
   ⟨nonempty_Ioo.2 h, isPreconnected_Ioo⟩
 #align is_connected_Ioo isConnected_Ioo
--/
 
-#print isConnected_Ioc /-
+/- warning: is_connected_Ioc -> isConnected_Ioc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (IsConnected.{u1} α _inst_2 (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (IsConnected.{u1} α _inst_2 (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))
+Case conversion may be inaccurate. Consider using '#align is_connected_Ioc isConnected_Iocₓ'. -/
 theorem isConnected_Ioc (h : a < b) : IsConnected (Ioc a b) :=
   ⟨nonempty_Ioc.2 h, isPreconnected_Ioc⟩
 #align is_connected_Ioc isConnected_Ioc
--/
 
-#print isConnected_Ico /-
+/- warning: is_connected_Ico -> isConnected_Ico is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (IsConnected.{u1} α _inst_2 (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (IsConnected.{u1} α _inst_2 (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))
+Case conversion may be inaccurate. Consider using '#align is_connected_Ico isConnected_Icoₓ'. -/
 theorem isConnected_Ico (h : a < b) : IsConnected (Ico a b) :=
   ⟨nonempty_Ico.2 h, isPreconnected_Ico⟩
 #align is_connected_Ico isConnected_Ico
--/
 
-#print ordered_connected_space /-
+/- warning: ordered_connected_space -> ordered_connected_space is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], PreconnectedSpace.{u1} α _inst_2
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], PreconnectedSpace.{u1} α _inst_2
+Case conversion may be inaccurate. Consider using '#align ordered_connected_space ordered_connected_spaceₓ'. -/
 instance (priority := 100) ordered_connected_space : PreconnectedSpace α :=
   ⟨ordConnected_univ.IsPreconnected⟩
 #align ordered_connected_space ordered_connected_space
--/
 
 /- warning: set_of_is_preconnected_eq_of_ordered -> setOf_isPreconnected_eq_of_ordered is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], Eq.{succ u1} (Set.{u1} (Set.{u1} α)) (setOf.{u1} (Set.{u1} α) (fun (s : Set.{u1} α) => IsPreconnected.{u1} α _inst_2 s)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))))) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))))) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))))) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.univ.{u1} α) (Singleton.singleton.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasSingleton.{u1} (Set.{u1} α)) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], Eq.{succ u1} (Set.{u1} (Set.{u1} α)) (setOf.{u1} (Set.{u1} α) (fun (s : Set.{u1} α) => IsPreconnected.{u1} α _inst_2 s)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))))) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))))) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))))) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.hasUnion.{u1} (Set.{u1} α)) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.univ.{u1} α) (Singleton.singleton.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasSingleton.{u1} (Set.{u1} α)) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))], Eq.{succ u1} (Set.{u1} (Set.{u1} α)) (setOf.{u1} (Set.{u1} α) (fun (s : Set.{u1} α) => IsPreconnected.{u1} α _inst_2 s)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.instUnionSet.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.instUnionSet.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.instUnionSet.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.instUnionSet.{u1} (Set.{u1} α)) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))))) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))))) (Set.range.{u1, succ u1} (Set.{u1} α) (Prod.{u1, u1} α α) (Function.uncurry.{u1, u1, u1} α α (Set.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))))) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.instUnionSet.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.instUnionSet.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.instUnionSet.{u1} (Set.{u1} α)) (Union.union.{u1} (Set.{u1} (Set.{u1} α)) (Set.instUnionSet.{u1} (Set.{u1} α)) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Set.range.{u1, succ u1} (Set.{u1} α) α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.univ.{u1} α) (Singleton.singleton.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instSingletonSet.{u1} (Set.{u1} α)) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))))))
 Case conversion may be inaccurate. Consider using '#align set_of_is_preconnected_eq_of_ordered setOf_isPreconnected_eq_of_orderedₓ'. -/
@@ -766,7 +862,7 @@ variable {δ : Type _} [LinearOrder δ] [TopologicalSpace δ] [OrderClosedTopolo
 
 /- warning: intermediate_value_Icc -> intermediate_value_Icc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Icc.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f a) (f b)) (Set.image.{u1, u2} α δ f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Icc.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f a) (f b)) (Set.image.{u1, u2} α δ f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.Icc.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f a) (f b)) (Set.image.{u2, u1} α δ f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b))))
 Case conversion may be inaccurate. Consider using '#align intermediate_value_Icc intermediate_value_Iccₓ'. -/
@@ -779,7 +875,7 @@ theorem intermediate_value_Icc {a b : α} (hab : a ≤ b) {f : α → δ} (hf :
 
 /- warning: intermediate_value_Icc' -> intermediate_value_Icc' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Icc.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f b) (f a)) (Set.image.{u1, u2} α δ f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Icc.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f b) (f a)) (Set.image.{u1, u2} α δ f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.Icc.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f b) (f a)) (Set.image.{u2, u1} α δ f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b))))
 Case conversion may be inaccurate. Consider using '#align intermediate_value_Icc' intermediate_value_Icc'ₓ'. -/
@@ -792,7 +888,7 @@ theorem intermediate_value_Icc' {a b : α} (hab : a ≤ b) {f : α → δ}
 
 /- warning: intermediate_value_uIcc -> intermediate_value_uIcc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α} {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.uIcc.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.uIcc.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9) (f a) (f b)) (Set.image.{u1, u2} α δ f (Set.uIcc.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) a b)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α} {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.uIcc.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.uIcc.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9) (f a) (f b)) (Set.image.{u1, u2} α δ f (Set.uIcc.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) a b)))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α} {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.uIcc.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.uIcc.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)) (f a) (f b)) (Set.image.{u2, u1} α δ f (Set.uIcc.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)) a b)))
 Case conversion may be inaccurate. Consider using '#align intermediate_value_uIcc intermediate_value_uIccₓ'. -/
@@ -804,7 +900,7 @@ theorem intermediate_value_uIcc {a b : α} {f : α → δ} (hf : ContinuousOn f
 
 /- warning: intermediate_value_Ico -> intermediate_value_Ico is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ico.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f a) (f b)) (Set.image.{u1, u2} α δ f (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ico.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f a) (f b)) (Set.image.{u1, u2} α δ f (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.Ico.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f a) (f b)) (Set.image.{u2, u1} α δ f (Set.Ico.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b))))
 Case conversion may be inaccurate. Consider using '#align intermediate_value_Ico intermediate_value_Icoₓ'. -/
@@ -818,7 +914,7 @@ theorem intermediate_value_Ico {a b : α} (hab : a ≤ b) {f : α → δ} (hf :
 
 /- warning: intermediate_value_Ico' -> intermediate_value_Ico' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ioc.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f b) (f a)) (Set.image.{u1, u2} α δ f (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ioc.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f b) (f a)) (Set.image.{u1, u2} α δ f (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.Ioc.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f b) (f a)) (Set.image.{u2, u1} α δ f (Set.Ico.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b))))
 Case conversion may be inaccurate. Consider using '#align intermediate_value_Ico' intermediate_value_Ico'ₓ'. -/
@@ -832,7 +928,7 @@ theorem intermediate_value_Ico' {a b : α} (hab : a ≤ b) {f : α → δ}
 
 /- warning: intermediate_value_Ioc -> intermediate_value_Ioc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ioc.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f a) (f b)) (Set.image.{u1, u2} α δ f (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ioc.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f a) (f b)) (Set.image.{u1, u2} α δ f (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.Ioc.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f a) (f b)) (Set.image.{u2, u1} α δ f (Set.Ioc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b))))
 Case conversion may be inaccurate. Consider using '#align intermediate_value_Ioc intermediate_value_Iocₓ'. -/
@@ -846,7 +942,7 @@ theorem intermediate_value_Ioc {a b : α} (hab : a ≤ b) {f : α → δ} (hf :
 
 /- warning: intermediate_value_Ioc' -> intermediate_value_Ioc' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ico.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f b) (f a)) (Set.image.{u1, u2} α δ f (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ico.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f b) (f a)) (Set.image.{u1, u2} α δ f (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.Ico.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f b) (f a)) (Set.image.{u2, u1} α δ f (Set.Ioc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b))))
 Case conversion may be inaccurate. Consider using '#align intermediate_value_Ioc' intermediate_value_Ioc'ₓ'. -/
@@ -860,7 +956,7 @@ theorem intermediate_value_Ioc' {a b : α} (hab : a ≤ b) {f : α → δ}
 
 /- warning: intermediate_value_Ioo -> intermediate_value_Ioo is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ioo.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f a) (f b)) (Set.image.{u1, u2} α δ f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ioo.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f a) (f b)) (Set.image.{u1, u2} α δ f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.Ioo.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f a) (f b)) (Set.image.{u2, u1} α δ f (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b))))
 Case conversion may be inaccurate. Consider using '#align intermediate_value_Ioo intermediate_value_Iooₓ'. -/
@@ -876,7 +972,7 @@ theorem intermediate_value_Ioo {a b : α} (hab : a ≤ b) {f : α → δ} (hf :
 
 /- warning: intermediate_value_Ioo' -> intermediate_value_Ioo' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ioo.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f b) (f a)) (Set.image.{u1, u2} α δ f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b)) -> (HasSubset.Subset.{u2} (Set.{u2} δ) (Set.hasSubset.{u2} δ) (Set.Ioo.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f b) (f a)) (Set.image.{u1, u2} α δ f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) a b))))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {a : α} {b : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) a b) -> (forall {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f (Set.Icc.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b)) -> (HasSubset.Subset.{u1} (Set.{u1} δ) (Set.instHasSubsetSet.{u1} δ) (Set.Ioo.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f b) (f a)) (Set.image.{u2, u1} α δ f (Set.Ioo.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) a b))))
 Case conversion may be inaccurate. Consider using '#align intermediate_value_Ioo' intermediate_value_Ioo'ₓ'. -/
@@ -892,7 +988,7 @@ theorem intermediate_value_Ioo' {a b : α} (hab : a ≤ b) {f : α → δ}
 
 /- warning: continuous_on.surj_on_Icc -> ContinuousOn.surjOn_Icc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {s : Set.{u1} α} [hs : Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s] {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f s) -> (forall {a : α} {b : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (Set.SurjOn.{u1, u2} α δ f s (Set.Icc.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f a) (f b))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {s : Set.{u1} α} [hs : Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s] {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f s) -> (forall {a : α} {b : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (Set.SurjOn.{u1, u2} α δ f s (Set.Icc.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))) (f a) (f b))))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {s : Set.{u2} α} [hs : Set.OrdConnected.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) s] {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f s) -> (forall {a : α} {b : α}, (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a s) -> (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) b s) -> (Set.SurjOn.{u2, u1} α δ f s (Set.Icc.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))) (f a) (f b))))
 Case conversion may be inaccurate. Consider using '#align continuous_on.surj_on_Icc ContinuousOn.surjOn_Iccₓ'. -/
@@ -905,7 +1001,7 @@ theorem ContinuousOn.surjOn_Icc {s : Set α} [hs : OrdConnected s] {f : α → 
 
 /- warning: continuous_on.surj_on_uIcc -> ContinuousOn.surjOn_uIcc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {s : Set.{u1} α} [hs : Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s] {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f s) -> (forall {a : α} {b : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (Set.SurjOn.{u1, u2} α δ f s (Set.uIcc.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9) (f a) (f b))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {s : Set.{u1} α} [hs : Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s] {f : α -> δ}, (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f s) -> (forall {a : α} {b : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (Set.SurjOn.{u1, u2} α δ f s (Set.uIcc.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9) (f a) (f b))))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {s : Set.{u2} α} [hs : Set.OrdConnected.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) s] {f : α -> δ}, (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f s) -> (forall {a : α} {b : α}, (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a s) -> (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) b s) -> (Set.SurjOn.{u2, u1} α δ f s (Set.uIcc.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)) (f a) (f b))))
 Case conversion may be inaccurate. Consider using '#align continuous_on.surj_on_uIcc ContinuousOn.surjOn_uIccₓ'. -/
@@ -918,7 +1014,7 @@ theorem ContinuousOn.surjOn_uIcc {s : Set α} [hs : OrdConnected s] {f : α →
 
 /- warning: continuous.surjective -> Continuous.surjective is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {f : α -> δ}, (Continuous.{u1, u2} α δ _inst_2 _inst_10 f) -> (Filter.Tendsto.{u1, u2} α δ f (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (Filter.atTop.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Filter.Tendsto.{u1, u2} α δ f (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (Filter.atBot.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Function.Surjective.{succ u1, succ u2} α δ f)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {f : α -> δ}, (Continuous.{u1, u2} α δ _inst_2 _inst_10 f) -> (Filter.Tendsto.{u1, u2} α δ f (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (Filter.atTop.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Filter.Tendsto.{u1, u2} α δ f (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (Filter.atBot.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Function.Surjective.{succ u1, succ u2} α δ f)
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {f : α -> δ}, (Continuous.{u2, u1} α δ _inst_2 _inst_10 f) -> (Filter.Tendsto.{u2, u1} α δ f (Filter.atTop.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) (Filter.atTop.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))))) -> (Filter.Tendsto.{u2, u1} α δ f (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) (Filter.atBot.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))))) -> (Function.Surjective.{succ u2, succ u1} α δ f)
 Case conversion may be inaccurate. Consider using '#align continuous.surjective Continuous.surjectiveₓ'. -/
@@ -931,7 +1027,7 @@ theorem Continuous.surjective {f : α → δ} (hf : Continuous f) (h_top : Tends
 
 /- warning: continuous.surjective' -> Continuous.surjective' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {f : α -> δ}, (Continuous.{u1, u2} α δ _inst_2 _inst_10 f) -> (Filter.Tendsto.{u1, u2} α δ f (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (Filter.atTop.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Filter.Tendsto.{u1, u2} α δ f (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (Filter.atBot.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Function.Surjective.{succ u1, succ u2} α δ f)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {f : α -> δ}, (Continuous.{u1, u2} α δ _inst_2 _inst_10 f) -> (Filter.Tendsto.{u1, u2} α δ f (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (Filter.atTop.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Filter.Tendsto.{u1, u2} α δ f (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (Filter.atBot.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Function.Surjective.{succ u1, succ u2} α δ f)
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {f : α -> δ}, (Continuous.{u2, u1} α δ _inst_2 _inst_10 f) -> (Filter.Tendsto.{u2, u1} α δ f (Filter.atBot.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) (Filter.atTop.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))))) -> (Filter.Tendsto.{u2, u1} α δ f (Filter.atTop.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))) (Filter.atBot.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))))) -> (Function.Surjective.{succ u2, succ u1} α δ f)
 Case conversion may be inaccurate. Consider using '#align continuous.surjective' Continuous.surjective'ₓ'. -/
@@ -943,7 +1039,7 @@ theorem Continuous.surjective' {f : α → δ} (hf : Continuous f) (h_top : Tend
 
 /- warning: continuous_on.surj_on_of_tendsto -> ContinuousOn.surjOn_of_tendsto is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {f : α -> δ} {s : Set.{u1} α} [_inst_12 : Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s], (Set.Nonempty.{u1} α s) -> (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f s) -> (Filter.Tendsto.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) δ (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x)) (Filter.atBot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))) (Filter.atBot.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Filter.Tendsto.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) δ (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x)) (Filter.atTop.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))) (Filter.atTop.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Set.SurjOn.{u1, u2} α δ f s (Set.univ.{u2} δ))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {f : α -> δ} {s : Set.{u1} α} [_inst_12 : Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s], (Set.Nonempty.{u1} α s) -> (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f s) -> (Filter.Tendsto.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) δ (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x)) (Filter.atBot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))) (Filter.atBot.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Filter.Tendsto.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) δ (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x)) (Filter.atTop.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))) (Filter.atTop.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Set.SurjOn.{u1, u2} α δ f s (Set.univ.{u2} δ))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {f : α -> δ} {s : Set.{u2} α} [_inst_12 : Set.OrdConnected.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) s], (Set.Nonempty.{u2} α s) -> (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f s) -> (Filter.Tendsto.{u2, u1} (Set.Elem.{u2} α s) δ (fun (x : Set.Elem.{u2} α s) => f (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (Filter.atBot.{u2} (Set.Elem.{u2} α s) (Subtype.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s))) (Filter.atBot.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))))) -> (Filter.Tendsto.{u2, u1} (Set.Elem.{u2} α s) δ (fun (x : Set.Elem.{u2} α s) => f (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (Filter.atTop.{u2} (Set.Elem.{u2} α s) (Subtype.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s))) (Filter.atTop.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))))) -> (Set.SurjOn.{u2, u1} α δ f s (Set.univ.{u1} δ))
 Case conversion may be inaccurate. Consider using '#align continuous_on.surj_on_of_tendsto ContinuousOn.surjOn_of_tendstoₓ'. -/
@@ -960,7 +1056,7 @@ theorem ContinuousOn.surjOn_of_tendsto {f : α → δ} {s : Set α} [OrdConnecte
 
 /- warning: continuous_on.surj_on_of_tendsto' -> ContinuousOn.surjOn_of_tendsto' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {f : α -> δ} {s : Set.{u1} α} [_inst_12 : Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s], (Set.Nonempty.{u1} α s) -> (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f s) -> (Filter.Tendsto.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) δ (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x)) (Filter.atBot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))) (Filter.atTop.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Filter.Tendsto.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) δ (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x)) (Filter.atTop.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))) (Filter.atBot.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Set.SurjOn.{u1, u2} α δ f s (Set.univ.{u2} δ))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))] {δ : Type.{u2}} [_inst_9 : LinearOrder.{u2} δ] [_inst_10 : TopologicalSpace.{u2} δ] [_inst_11 : OrderClosedTopology.{u2} δ _inst_10 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9))))] {f : α -> δ} {s : Set.{u1} α} [_inst_12 : Set.OrdConnected.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s], (Set.Nonempty.{u1} α s) -> (ContinuousOn.{u1, u2} α δ _inst_2 _inst_10 f s) -> (Filter.Tendsto.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) δ (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x)) (Filter.atBot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))) (Filter.atTop.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Filter.Tendsto.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) δ (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => f ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x)) (Filter.atTop.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))) (Filter.atBot.{u2} δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (LinearOrder.toLattice.{u2} δ _inst_9)))))) -> (Set.SurjOn.{u1, u2} α δ f s (Set.univ.{u2} δ))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1)))))] [_inst_8 : DenselyOrdered.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))))] {δ : Type.{u1}} [_inst_9 : LinearOrder.{u1} δ] [_inst_10 : TopologicalSpace.{u1} δ] [_inst_11 : OrderClosedTopology.{u1} δ _inst_10 (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9)))))] {f : α -> δ} {s : Set.{u2} α} [_inst_12 : Set.OrdConnected.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) s], (Set.Nonempty.{u2} α s) -> (ContinuousOn.{u2, u1} α δ _inst_2 _inst_10 f s) -> (Filter.Tendsto.{u2, u1} (Set.Elem.{u2} α s) δ (fun (x : Set.Elem.{u2} α s) => f (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (Filter.atBot.{u2} (Set.Elem.{u2} α s) (Subtype.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s))) (Filter.atTop.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))))) -> (Filter.Tendsto.{u2, u1} (Set.Elem.{u2} α s) δ (fun (x : Set.Elem.{u2} α s) => f (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (Filter.atTop.{u2} (Set.Elem.{u2} α s) (Subtype.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α _inst_1))))) (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s))) (Filter.atBot.{u1} δ (PartialOrder.toPreorder.{u1} δ (SemilatticeInf.toPartialOrder.{u1} δ (Lattice.toSemilatticeInf.{u1} δ (DistribLattice.toLattice.{u1} δ (instDistribLattice.{u1} δ _inst_9))))))) -> (Set.SurjOn.{u2, u1} α δ f s (Set.univ.{u1} δ))
 Case conversion may be inaccurate. Consider using '#align continuous_on.surj_on_of_tendsto' ContinuousOn.surjOn_of_tendsto'ₓ'. -/

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

@@ -349,65 +349,65 @@ variable {α : Type u} {β : Type v} {γ : Type w} [ConditionallyCompleteLinearO
   [TopologicalSpace α] [OrderTopology α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β]
   [OrderTopology β] [Nonempty γ]
 
-/- warning: is_connected.Ioo_cInf_cSup_subset -> IsConnected.Ioo_cinfₛ_csupₛ_subset is a dubious translation:
+/- warning: is_connected.Ioo_cInf_cSup_subset -> IsConnected.Ioo_csInf_csSup_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsConnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsConnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsConnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
-Case conversion may be inaccurate. Consider using '#align is_connected.Ioo_cInf_cSup_subset IsConnected.Ioo_cinfₛ_csupₛ_subsetₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsConnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
+Case conversion may be inaccurate. Consider using '#align is_connected.Ioo_cInf_cSup_subset IsConnected.Ioo_csInf_csSup_subsetₓ'. -/
 /-- A bounded connected subset of a conditionally complete linear order includes the open interval
 `(Inf s, Sup s)`. -/
-theorem IsConnected.Ioo_cinfₛ_csupₛ_subset {s : Set α} (hs : IsConnected s) (hb : BddBelow s)
-    (ha : BddAbove s) : Ioo (infₛ s) (supₛ s) ⊆ s := fun x hx =>
-  let ⟨y, ys, hy⟩ := (isGLB_lt_iff (isGLB_cinfₛ hs.Nonempty hb)).1 hx.1
-  let ⟨z, zs, hz⟩ := (lt_isLUB_iff (isLUB_csupₛ hs.Nonempty ha)).1 hx.2
+theorem IsConnected.Ioo_csInf_csSup_subset {s : Set α} (hs : IsConnected s) (hb : BddBelow s)
+    (ha : BddAbove s) : Ioo (sInf s) (sSup s) ⊆ s := fun x hx =>
+  let ⟨y, ys, hy⟩ := (isGLB_lt_iff (isGLB_csInf hs.Nonempty hb)).1 hx.1
+  let ⟨z, zs, hz⟩ := (lt_isLUB_iff (isLUB_csSup hs.Nonempty ha)).1 hx.2
   hs.Icc_subset ys zs ⟨le_of_lt hy, le_of_lt hz⟩
-#align is_connected.Ioo_cInf_cSup_subset IsConnected.Ioo_cinfₛ_csupₛ_subset
+#align is_connected.Ioo_cInf_cSup_subset IsConnected.Ioo_csInf_csSup_subset
 
-/- warning: eq_Icc_cInf_cSup_of_connected_bdd_closed -> eq_Icc_cinfₛ_csupₛ_of_connected_bdd_closed is a dubious translation:
+/- warning: eq_Icc_cInf_cSup_of_connected_bdd_closed -> eq_Icc_csInf_csSup_of_connected_bdd_closed is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsConnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (IsClosed.{u1} α _inst_2 s) -> (Eq.{succ u1} (Set.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsConnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (IsClosed.{u1} α _inst_2 s) -> (Eq.{succ u1} (Set.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsConnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (IsClosed.{u1} α _inst_2 s) -> (Eq.{succ u1} (Set.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)))
-Case conversion may be inaccurate. Consider using '#align eq_Icc_cInf_cSup_of_connected_bdd_closed eq_Icc_cinfₛ_csupₛ_of_connected_bdd_closedₓ'. -/
-theorem eq_Icc_cinfₛ_csupₛ_of_connected_bdd_closed {s : Set α} (hc : IsConnected s)
-    (hb : BddBelow s) (ha : BddAbove s) (hcl : IsClosed s) : s = Icc (infₛ s) (supₛ s) :=
-  Subset.antisymm (subset_Icc_cinfₛ_csupₛ hb ha) <|
-    hc.Icc_subset (hcl.cinfₛ_mem hc.Nonempty hb) (hcl.csupₛ_mem hc.Nonempty ha)
-#align eq_Icc_cInf_cSup_of_connected_bdd_closed eq_Icc_cinfₛ_csupₛ_of_connected_bdd_closed
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsConnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (IsClosed.{u1} α _inst_2 s) -> (Eq.{succ u1} (Set.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)))
+Case conversion may be inaccurate. Consider using '#align eq_Icc_cInf_cSup_of_connected_bdd_closed eq_Icc_csInf_csSup_of_connected_bdd_closedₓ'. -/
+theorem eq_Icc_csInf_csSup_of_connected_bdd_closed {s : Set α} (hc : IsConnected s)
+    (hb : BddBelow s) (ha : BddAbove s) (hcl : IsClosed s) : s = Icc (sInf s) (sSup s) :=
+  Subset.antisymm (subset_Icc_csInf_csSup hb ha) <|
+    hc.Icc_subset (hcl.csInf_mem hc.Nonempty hb) (hcl.csSup_mem hc.Nonempty ha)
+#align eq_Icc_cInf_cSup_of_connected_bdd_closed eq_Icc_csInf_csSup_of_connected_bdd_closed
 
-/- warning: is_preconnected.Ioi_cInf_subset -> IsPreconnected.Ioi_cinfₛ_subset is a dubious translation:
+/- warning: is_preconnected.Ioi_cInf_subset -> IsPreconnected.Ioi_csInf_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsPreconnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Not (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsPreconnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Not (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsPreconnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Not (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
-Case conversion may be inaccurate. Consider using '#align is_preconnected.Ioi_cInf_subset IsPreconnected.Ioi_cinfₛ_subsetₓ'. -/
-theorem IsPreconnected.Ioi_cinfₛ_subset {s : Set α} (hs : IsPreconnected s) (hb : BddBelow s)
-    (ha : ¬BddAbove s) : Ioi (infₛ s) ⊆ s :=
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsPreconnected.{u1} α _inst_2 s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Not (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
+Case conversion may be inaccurate. Consider using '#align is_preconnected.Ioi_cInf_subset IsPreconnected.Ioi_csInf_subsetₓ'. -/
+theorem IsPreconnected.Ioi_csInf_subset {s : Set α} (hs : IsPreconnected s) (hb : BddBelow s)
+    (ha : ¬BddAbove s) : Ioi (sInf s) ⊆ s :=
   by
   have sne : s.nonempty := @nonempty_of_not_bddAbove α _ s ⟨Inf ∅⟩ ha
   intro x hx
-  obtain ⟨y, ys, hy⟩ : ∃ y ∈ s, y < x := (isGLB_lt_iff (isGLB_cinfₛ sne hb)).1 hx
+  obtain ⟨y, ys, hy⟩ : ∃ y ∈ s, y < x := (isGLB_lt_iff (isGLB_csInf sne hb)).1 hx
   obtain ⟨z, zs, hz⟩ : ∃ z ∈ s, x < z := not_bddAbove_iff.1 ha x
   exact hs.Icc_subset ys zs ⟨le_of_lt hy, le_of_lt hz⟩
-#align is_preconnected.Ioi_cInf_subset IsPreconnected.Ioi_cinfₛ_subset
+#align is_preconnected.Ioi_cInf_subset IsPreconnected.Ioi_csInf_subset
 
-/- warning: is_preconnected.Iio_cSup_subset -> IsPreconnected.Iio_csupₛ_subset is a dubious translation:
+/- warning: is_preconnected.Iio_cSup_subset -> IsPreconnected.Iio_csSup_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsPreconnected.{u1} α _inst_2 s) -> (Not (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsPreconnected.{u1} α _inst_2 s) -> (Not (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsPreconnected.{u1} α _inst_2 s) -> (Not (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
-Case conversion may be inaccurate. Consider using '#align is_preconnected.Iio_cSup_subset IsPreconnected.Iio_csupₛ_subsetₓ'. -/
-theorem IsPreconnected.Iio_csupₛ_subset {s : Set α} (hs : IsPreconnected s) (hb : ¬BddBelow s)
-    (ha : BddAbove s) : Iio (supₛ s) ⊆ s :=
-  @IsPreconnected.Ioi_cinfₛ_subset αᵒᵈ _ _ _ s hs ha hb
-#align is_preconnected.Iio_cSup_subset IsPreconnected.Iio_csupₛ_subset
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsPreconnected.{u1} α _inst_2 s) -> (Not (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) s)
+Case conversion may be inaccurate. Consider using '#align is_preconnected.Iio_cSup_subset IsPreconnected.Iio_csSup_subsetₓ'. -/
+theorem IsPreconnected.Iio_csSup_subset {s : Set α} (hs : IsPreconnected s) (hb : ¬BddBelow s)
+    (ha : BddAbove s) : Iio (sSup s) ⊆ s :=
+  @IsPreconnected.Ioi_csInf_subset αᵒᵈ _ _ _ s hs ha hb
+#align is_preconnected.Iio_cSup_subset IsPreconnected.Iio_csSup_subset
 
 /- warning: is_preconnected.mem_intervals -> IsPreconnected.mem_intervals is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsPreconnected.{u1} α _inst_2 s) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) s (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.univ.{u1} α) (Singleton.singleton.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasSingleton.{u1} (Set.{u1} α)) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α)))))))))))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsPreconnected.{u1} α _inst_2 s) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) s (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasInsert.{u1} (Set.{u1} α)) (Set.univ.{u1} α) (Singleton.singleton.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasSingleton.{u1} (Set.{u1} α)) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α)))))))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsPreconnected.{u1} α _inst_2 s) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) s (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.univ.{u1} α) (Singleton.singleton.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instSingletonSet.{u1} (Set.{u1} α)) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α)))))))))))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))] {s : Set.{u1} α}, (IsPreconnected.{u1} α _inst_2 s) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) s (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Insert.insert.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instInsertSet.{u1} (Set.{u1} α)) (Set.univ.{u1} α) (Singleton.singleton.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instSingletonSet.{u1} (Set.{u1} α)) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α)))))))))))))
 Case conversion may be inaccurate. Consider using '#align is_preconnected.mem_intervals IsPreconnected.mem_intervalsₓ'. -/
 /-- A preconnected set in a conditionally complete linear order is either one of the intervals
 `[Inf s, Sup s]`, `[Inf s, Sup s)`, `(Inf s, Sup s]`, `(Inf s, Sup s)`, `[Inf s, +∞)`,
@@ -415,8 +415,8 @@ Case conversion may be inaccurate. Consider using '#align is_preconnected.mem_in
 `α` to be densely ordererd. -/
 theorem IsPreconnected.mem_intervals {s : Set α} (hs : IsPreconnected s) :
     s ∈
-      ({Icc (infₛ s) (supₛ s), Ico (infₛ s) (supₛ s), Ioc (infₛ s) (supₛ s), Ioo (infₛ s) (supₛ s),
-          Ici (infₛ s), Ioi (infₛ s), Iic (supₛ s), Iio (supₛ s), univ, ∅} :
+      ({Icc (sInf s) (sSup s), Ico (sInf s) (sSup s), Ioc (sInf s) (sSup s), Ioo (sInf s) (sSup s),
+          Ici (sInf s), Ioi (sInf s), Iic (sSup s), Iio (sSup s), univ, ∅} :
         Set (Set α)) :=
   by
   rcases s.eq_empty_or_nonempty with (rfl | hne)
@@ -424,20 +424,20 @@ theorem IsPreconnected.mem_intervals {s : Set α} (hs : IsPreconnected s) :
   have hs' : IsConnected s := ⟨hne, hs⟩
   by_cases hb : BddBelow s <;> by_cases ha : BddAbove s
   · rcases mem_Icc_Ico_Ioc_Ioo_of_subset_of_subset (hs'.Ioo_cInf_cSup_subset hb ha)
-        (subset_Icc_cinfₛ_csupₛ hb ha) with (hs | hs | hs | hs)
+        (subset_Icc_csInf_csSup hb ha) with (hs | hs | hs | hs)
     · exact Or.inl hs
     · exact Or.inr <| Or.inl hs
     · exact Or.inr <| Or.inr <| Or.inl hs
     · exact Or.inr <| Or.inr <| Or.inr <| Or.inl hs
   · refine' Or.inr <| Or.inr <| Or.inr <| Or.inr _
     cases'
-      mem_Ici_Ioi_of_subset_of_subset (hs.Ioi_cInf_subset hb ha) fun x hx => cinfₛ_le hb hx with
+      mem_Ici_Ioi_of_subset_of_subset (hs.Ioi_cInf_subset hb ha) fun x hx => csInf_le hb hx with
       hs hs
     · exact Or.inl hs
     · exact Or.inr (Or.inl hs)
   · iterate 6 apply Or.inr
     cases'
-      mem_Iic_Iio_of_subset_of_subset (hs.Iio_cSup_subset hb ha) fun x hx => le_csupₛ ha hx with
+      mem_Iic_Iio_of_subset_of_subset (hs.Iio_cSup_subset hb ha) fun x hx => le_csSup ha hx with
       hs hs
     · exact Or.inl hs
     · exact Or.inr (Or.inl hs)
@@ -509,12 +509,12 @@ theorem IsClosed.mem_of_ge_of_forall_exists_gt {a b : α} {s : Set α} (hs : IsC
   have Sbd : BddAbove S := ⟨b, fun z hz => hz.2.2⟩
   let c := Sup (s ∩ Icc a b)
   have c_mem : c ∈ S := hs.cSup_mem ⟨_, ha⟩ Sbd
-  have c_le : c ≤ b := csupₛ_le ⟨_, ha⟩ fun x hx => hx.2.2
+  have c_le : c ≤ b := csSup_le ⟨_, ha⟩ fun x hx => hx.2.2
   cases' eq_or_lt_of_le c_le with hc hc
   exact hc ▸ c_mem.1
   exfalso
   rcases hgt c ⟨c_mem.1, c_mem.2.1, hc⟩ with ⟨x, xs, cx, xb⟩
-  exact not_lt_of_le (le_csupₛ Sbd ⟨xs, le_trans (le_csupₛ Sbd ha) (le_of_lt cx), xb⟩) cx
+  exact not_lt_of_le (le_csSup Sbd ⟨xs, le_trans (le_csSup Sbd ha) (le_of_lt cx), xb⟩) cx
 #align is_closed.mem_of_ge_of_forall_exists_gt IsClosed.mem_of_ge_of_forall_exists_gt
 
 /- warning: is_closed.Icc_subset_of_forall_exists_gt -> IsClosed.Icc_subset_of_forall_exists_gt is a dubious translation:

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

@@ -120,9 +120,9 @@ theorem IsPreconnected.intermediate_value₂ {s : Set X} (hs : IsPreconnected s)
 
 /- warning: is_preconnected.intermediate_value₂_eventually₁ -> IsPreconnected.intermediate_value₂_eventually₁ is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) (f a) (g a)) -> (Filter.EventuallyLe.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l g f) -> (Exists.{succ u1} X (fun (x : X) => Exists.{0} (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) (fun (H : Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) => Eq.{succ u2} α (f x) (g x)))))))
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) (f a) (g a)) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l g f) -> (Exists.{succ u1} X (fun (x : X) => Exists.{0} (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) (fun (H : Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) => Eq.{succ u2} α (f x) (g x)))))))
 but is expected to have type
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (f a) (g a)) -> (Filter.EventuallyLe.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) l g f) -> (Exists.{succ u1} X (fun (x : X) => And (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x s) (Eq.{succ u2} α (f x) (g x)))))))
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {a : X} {l : Filter.{u1} X}, (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) a s) -> (forall [_inst_5 : Filter.NeBot.{u1} X l], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l (Filter.principal.{u1} X s)) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (f a) (g a)) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) l g f) -> (Exists.{succ u1} X (fun (x : X) => And (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x s) (Eq.{succ u2} α (f x) (g x)))))))
 Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value₂_eventually₁ IsPreconnected.intermediate_value₂_eventually₁ₓ'. -/
 theorem IsPreconnected.intermediate_value₂_eventually₁ {s : Set X} (hs : IsPreconnected s) {a : X}
     {l : Filter X} (ha : a ∈ s) [NeBot l] (hl : l ≤ 𝓟 s) {f g : X → α} (hf : ContinuousOn f s)
@@ -137,9 +137,9 @@ theorem IsPreconnected.intermediate_value₂_eventually₁ {s : Set X} (hs : IsP
 
 /- warning: is_preconnected.intermediate_value₂_eventually₂ -> IsPreconnected.intermediate_value₂_eventually₂ is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (Filter.EventuallyLe.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l₁ f g) -> (Filter.EventuallyLe.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l₂ g f) -> (Exists.{succ u1} X (fun (x : X) => Exists.{0} (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) (fun (H : Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) => Eq.{succ u2} α (f x) (g x))))))
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.partialOrder.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l₁ f g) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (LinearOrder.toLattice.{u2} α _inst_2))))) l₂ g f) -> (Exists.{succ u1} X (fun (x : X) => Exists.{0} (Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) (fun (H : Membership.Mem.{u1, u1} X (Set.{u1} X) (Set.hasMem.{u1} X) x s) => Eq.{succ u2} α (f x) (g x))))))
 but is expected to have type
-  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (Filter.EventuallyLe.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) l₁ f g) -> (Filter.EventuallyLe.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) l₂ g f) -> (Exists.{succ u1} X (fun (x : X) => And (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x s) (Eq.{succ u2} α (f x) (g x))))))
+  forall {X : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : TopologicalSpace.{u2} α] [_inst_4 : OrderClosedTopology.{u2} α _inst_3 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {s : Set.{u1} X}, (IsPreconnected.{u1} X _inst_1 s) -> (forall {l₁ : Filter.{u1} X} {l₂ : Filter.{u1} X} [_inst_5 : Filter.NeBot.{u1} X l₁] [_inst_6 : Filter.NeBot.{u1} X l₂], (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₁ (Filter.principal.{u1} X s)) -> (LE.le.{u1} (Filter.{u1} X) (Preorder.toLE.{u1} (Filter.{u1} X) (PartialOrder.toPreorder.{u1} (Filter.{u1} X) (Filter.instPartialOrderFilter.{u1} X))) l₂ (Filter.principal.{u1} X s)) -> (forall {f : X -> α} {g : X -> α}, (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 f s) -> (ContinuousOn.{u1, u2} X α _inst_1 _inst_3 g s) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) l₁ f g) -> (Filter.EventuallyLE.{u1, u2} X α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) l₂ g f) -> (Exists.{succ u1} X (fun (x : X) => And (Membership.mem.{u1, u1} X (Set.{u1} X) (Set.instMembershipSet.{u1} X) x s) (Eq.{succ u2} α (f x) (g x))))))
 Case conversion may be inaccurate. Consider using '#align is_preconnected.intermediate_value₂_eventually₂ IsPreconnected.intermediate_value₂_eventually₂ₓ'. -/
 theorem IsPreconnected.intermediate_value₂_eventually₂ {s : Set X} (hs : IsPreconnected s)
     {l₁ l₂ : Filter X} [NeBot l₁] [NeBot l₂] (hl₁ : l₁ ≤ 𝓟 s) (hl₂ : l₂ ≤ 𝓟 s) {f g : X → α}

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

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

@@ -70,9 +70,9 @@ on a preconnected space and `f a ≤ g a` and `g b ≤ f b`, then for some `x` w
 theorem intermediate_value_univ₂ [PreconnectedSpace X] {a b : X} {f g : X → α} (hf : Continuous f)
     (hg : Continuous g) (ha : f a ≤ g a) (hb : g b ≤ f b) : ∃ x, f x = g x := by
   obtain ⟨x, _, hfg, hgf⟩ : (univ ∩ { x | f x ≤ g x ∧ g x ≤ f x }).Nonempty
-  exact
-    isPreconnected_closed_iff.1 PreconnectedSpace.isPreconnected_univ _ _ (isClosed_le hf hg)
-      (isClosed_le hg hf) (fun _ _ => le_total _ _) ⟨a, trivial, ha⟩ ⟨b, trivial, hb⟩
+  · exact
+      isPreconnected_closed_iff.1 PreconnectedSpace.isPreconnected_univ _ _ (isClosed_le hf hg)
+        (isClosed_le hg hf) (fun _ _ => le_total _ _) ⟨a, trivial, ha⟩ ⟨b, trivial, hb⟩
   exact ⟨x, le_antisymm hfg hgf⟩
 #align intermediate_value_univ₂ intermediate_value_univ₂
 
@@ -352,7 +352,7 @@ theorem IsClosed.mem_of_ge_of_forall_exists_gt {a b : α} {s : Set α} (hs : IsC
   have c_mem : c ∈ S := hs.csSup_mem ⟨_, ha⟩ Sbd
   have c_le : c ≤ b := csSup_le ⟨_, ha⟩ fun x hx => hx.2.2
   cases' eq_or_lt_of_le c_le with hc hc
-  exact hc ▸ c_mem.1
+  · exact hc ▸ c_mem.1
   exfalso
   rcases hgt c ⟨c_mem.1, c_mem.2.1, hc⟩ with ⟨x, xs, cx, xb⟩
   exact not_lt_of_le (le_csSup Sbd ⟨xs, le_trans (le_csSup Sbd ha) (le_of_lt cx), xb⟩) cx

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

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

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

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Alistair Tucker, Wen Yang
 -/
-import Mathlib.Data.Set.Intervals.Image
+import Mathlib.Order.Interval.Set.Image
 import Mathlib.Order.CompleteLatticeIntervals
 import Mathlib.Topology.Order.DenselyOrdered
 import Mathlib.Topology.Order.Monotone

@@ -517,6 +517,19 @@ theorem setOf_isPreconnected_eq_of_ordered :
     isPreconnected_univ, isPreconnected_empty]
 #align set_of_is_preconnected_eq_of_ordered setOf_isPreconnected_eq_of_ordered
 
+/-- This lemmas characterizes when a subset `s` of a densely ordered conditionally complete linear
+order is totally disconnected with respect to the order topology: between any two distinct points
+of `s` must lie a point not in `s`. -/
+lemma isTotallyDisconnected_iff_lt {s : Set α} :
+    IsTotallyDisconnected s ↔ ∀ x ∈ s, ∀ y ∈ s, x < y → ∃ z ∉ s, z ∈ Ioo x y := by
+  simp only [IsTotallyDisconnected, isPreconnected_iff_ordConnected, ← not_nontrivial_iff,
+    nontrivial_iff_exists_lt, not_exists, not_and]
+  refine ⟨fun h x hx y hy hxy ↦ ?_, fun h t hts ht x hx y hy hxy ↦ ?_⟩
+  · simp_rw [← not_ordConnected_inter_Icc_iff hx hy]
+    exact fun hs ↦ h _ (inter_subset_left _ _) hs _ ⟨hx, le_rfl, hxy.le⟩ _ ⟨hy, hxy.le, le_rfl⟩ hxy
+  · obtain ⟨z, h1z, h2z⟩ := h x (hts hx) y (hts hy) hxy
+    exact h1z <| hts <| ht.1 hx hy ⟨h2z.1.le, h2z.2.le⟩
+
 /-!
 ### Intermediate Value Theorem on an interval
 

This splits up the file Mathlib/Topology/Order/Basic.lean (currently > 2000 lines) into several smaller files.

@@ -5,7 +5,8 @@ Authors: Yury G. Kudryashov, Alistair Tucker, Wen Yang
 -/
 import Mathlib.Data.Set.Intervals.Image
 import Mathlib.Order.CompleteLatticeIntervals
-import Mathlib.Topology.Order.Basic
+import Mathlib.Topology.Order.DenselyOrdered
+import Mathlib.Topology.Order.Monotone
 
 #align_import topology.algebra.order.intermediate_value from "leanprover-community/mathlib"@"4c19a16e4b705bf135cf9a80ac18fcc99c438514"
 

A mix of various changes; generated with a script and manually tweaked.

@@ -203,7 +203,7 @@ theorem mem_range_of_exists_le_of_exists_ge [PreconnectedSpace X] {c : α} {f :
 
 In this section we prove the following results:
 
-* `IsPreconnected.ordConnected`: any preconnected set `s` in a linear order is `ord_connected`,
+* `IsPreconnected.ordConnected`: any preconnected set `s` in a linear order is `OrdConnected`,
   i.e. `a ∈ s` and `b ∈ s` imply `Icc a b ⊆ s`;
 
 * `IsPreconnected.mem_intervals`: any preconnected set `s` in a conditionally complete linear order
@@ -335,7 +335,7 @@ theorem setOf_isPreconnected_subset_of_ordered :
 /-!
 ### Intervals are connected
 
-In this section we prove that a closed interval (hence, any `ord_connected` set) in a dense
+In this section we prove that a closed interval (hence, any `OrdConnected` set) in a dense
 conditionally complete linear order is preconnected.
 -/
 

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

@@ -527,14 +527,14 @@ continuous on an interval.
 variable {δ : Type*} [LinearOrder δ] [TopologicalSpace δ] [OrderClosedTopology δ]
 
 /-- **Intermediate Value Theorem** for continuous functions on closed intervals, case
-`f a ≤ t ≤ f b`.-/
+`f a ≤ t ≤ f b`. -/
 theorem intermediate_value_Icc {a b : α} (hab : a ≤ b) {f : α → δ} (hf : ContinuousOn f (Icc a b)) :
     Icc (f a) (f b) ⊆ f '' Icc a b :=
   isPreconnected_Icc.intermediate_value (left_mem_Icc.2 hab) (right_mem_Icc.2 hab) hf
 #align intermediate_value_Icc intermediate_value_Icc
 
 /-- **Intermediate Value Theorem** for continuous functions on closed intervals, case
-`f a ≥ t ≥ f b`.-/
+`f a ≥ t ≥ f b`. -/
 theorem intermediate_value_Icc' {a b : α} (hab : a ≤ b) {f : α → δ}
     (hf : ContinuousOn f (Icc a b)) : Icc (f b) (f a) ⊆ f '' Icc a b :=
   isPreconnected_Icc.intermediate_value (right_mem_Icc.2 hab) (left_mem_Icc.2 hab) hf
@@ -679,7 +679,7 @@ theorem Continuous.strictMono_of_inj_boundedOrder' [BoundedOrder α] {f : α →
 
 /-- Suppose `α` is equipped with a conditionally complete linear dense order and `f : α → δ` is
 continuous and injective. Then `f` is strictly monotone (increasing) if
-it is strictly monotone (increasing) on some closed interval `[a, b]`.-/
+it is strictly monotone (increasing) on some closed interval `[a, b]`. -/
 theorem Continuous.strictMonoOn_of_inj_rigidity {f : α → δ}
     (hf_c : Continuous f) (hf_i : Injective f) {a b : α} (hab : a < b)
     (hf_mono : StrictMonoOn f (Icc a b)) : StrictMono f := by
@@ -708,7 +708,7 @@ theorem Continuous.strictMonoOn_of_inj_rigidity {f : α → δ}
   exact this (left_mem_Icc.mpr (le_of_lt hxy)) (right_mem_Icc.mpr (le_of_lt hxy)) hxy
 
 /-- Suppose `f : [a, b] → δ` is
-continuous and injective. Then `f` is strictly monotone (increasing) if `f(a) ≤ f(b)`.-/
+continuous and injective. Then `f` is strictly monotone (increasing) if `f(a) ≤ f(b)`. -/
 theorem ContinuousOn.strictMonoOn_of_injOn_Icc {a b : α} {f : α → δ}
     (hab : a ≤ b) (hfab : f a ≤ f b)
     (hf_c : ContinuousOn f (Icc a b)) (hf_i : InjOn f (Icc a b)) :
@@ -720,14 +720,14 @@ theorem ContinuousOn.strictMonoOn_of_injOn_Icc {a b : α} {f : α → δ}
   exact Continuous.strictMono_of_inj_boundedOrder (f := g) hf_c.restrict hgab hf_i.injective
 
 /-- Suppose `f : [a, b] → δ` is
-continuous and injective. Then `f` is strictly antitone (decreasing) if `f(b) ≤ f(a)`.-/
+continuous and injective. Then `f` is strictly antitone (decreasing) if `f(b) ≤ f(a)`. -/
 theorem ContinuousOn.strictAntiOn_of_injOn_Icc {a b : α} {f : α → δ}
     (hab : a ≤ b) (hfab : f b ≤ f a)
     (hf_c : ContinuousOn f (Icc a b)) (hf_i : InjOn f (Icc a b)) :
     StrictAntiOn f (Icc a b) := ContinuousOn.strictMonoOn_of_injOn_Icc (δ := δᵒᵈ) hab hfab hf_c hf_i
 
 /-- Suppose `f : [a, b] → δ` is continuous and injective. Then `f` is strictly monotone
-or antitone (increasing or decreasing).-/
+or antitone (increasing or decreasing). -/
 theorem ContinuousOn.strictMonoOn_of_injOn_Icc' {a b : α} {f : α → δ} (hab : a ≤ b)
     (hf_c : ContinuousOn f (Icc a b)) (hf_i : InjOn f (Icc a b)) :
     StrictMonoOn f (Icc a b) ∨ StrictAntiOn f (Icc a b) :=
@@ -736,7 +736,7 @@ theorem ContinuousOn.strictMonoOn_of_injOn_Icc' {a b : α} {f : α → δ} (hab
     (ContinuousOn.strictAntiOn_of_injOn_Icc hab · hf_c hf_i)
 
 /-- Suppose `α` is equipped with a conditionally complete linear dense order and `f : α → δ` is
-continuous and injective. Then `f` is strictly monotone or antitone (increasing or decreasing).-/
+continuous and injective. Then `f` is strictly monotone or antitone (increasing or decreasing). -/
 theorem Continuous.strictMono_of_inj {f : α → δ}
     (hf_c : Continuous f) (hf_i : Injective f) : StrictMono f ∨ StrictAnti f := by
   have H {c d : α} (hcd : c < d) : StrictMono f ∨ StrictAnti f :=
@@ -758,7 +758,7 @@ theorem Continuous.strictMono_of_inj {f : α → δ}
   · aesop
 
 /-- Every continuous injective `f : (a, b) → δ` is strictly monotone
-or antitone (increasing or decreasing).-/
+or antitone (increasing or decreasing). -/
 theorem ContinuousOn.strictMonoOn_of_injOn_Ioo {a b : α} {f : α → δ} (hab : a < b)
     (hf_c : ContinuousOn f (Ioo a b)) (hf_i : InjOn f (Ioo a b)) :
     StrictMonoOn f (Ioo a b) ∨ StrictAntiOn f (Ioo a b) := by

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.

@@ -509,7 +509,7 @@ theorem setOf_isPreconnected_eq_of_ordered :
       -- unbounded intervals and `univ`
       (range Ici ∪ range Ioi ∪ range Iic ∪ range Iio ∪ {univ, ∅}) := by
   refine' Subset.antisymm setOf_isPreconnected_subset_of_ordered _
-  simp only [subset_def, forall_range_iff, uncurry, or_imp, forall_and, mem_union,
+  simp only [subset_def, forall_mem_range, uncurry, or_imp, forall_and, mem_union,
     mem_setOf_eq, insert_eq, mem_singleton_iff, forall_eq, forall_true_iff, and_true_iff,
     isPreconnected_Icc, isPreconnected_Ico, isPreconnected_Ioc, isPreconnected_Ioo,
     isPreconnected_Ioi, isPreconnected_Iio, isPreconnected_Ici, isPreconnected_Iic,

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -345,8 +345,7 @@ on a closed subset, contains `a`, and the set `s ∩ [a, b)` has no maximal poin
 theorem IsClosed.mem_of_ge_of_forall_exists_gt {a b : α} {s : Set α} (hs : IsClosed (s ∩ Icc a b))
     (ha : a ∈ s) (hab : a ≤ b) (hgt : ∀ x ∈ s ∩ Ico a b, (s ∩ Ioc x b).Nonempty) : b ∈ s := by
   let S := s ∩ Icc a b
-  replace ha : a ∈ S
-  exact ⟨ha, left_mem_Icc.2 hab⟩
+  replace ha : a ∈ S := ⟨ha, left_mem_Icc.2 hab⟩
   have Sbd : BddAbove S := ⟨b, fun z hz => hz.2.2⟩
   let c := sSup (s ∩ Icc a b)
   have c_mem : c ∈ S := hs.csSup_mem ⟨_, ha⟩ Sbd
@@ -396,8 +395,8 @@ theorem isPreconnected_Icc_aux (x y : α) (s t : Set α) (hxy : x ≤ y) (hs : I
     (Icc a b ∩ (s ∩ t)).Nonempty := by
   have xyab : Icc x y ⊆ Icc a b := Icc_subset_Icc hx.1.1 hy.1.2
   by_contra hst
-  suffices : Icc x y ⊆ s
-  exact hst ⟨y, xyab <| right_mem_Icc.2 hxy, this <| right_mem_Icc.2 hxy, hy.2⟩
+  suffices Icc x y ⊆ s from
+    hst ⟨y, xyab <| right_mem_Icc.2 hxy, this <| right_mem_Icc.2 hxy, hy.2⟩
   apply (IsClosed.inter hs isClosed_Icc).Icc_subset_of_forall_mem_nhdsWithin hx.2
   rintro z ⟨zs, hz⟩
   have zt : z ∈ tᶜ := fun zt => hst ⟨z, xyab <| Ico_subset_Icc_self hz, zs, zt⟩

Suppose f : [a, b] → δ or f : (a, b) → δ is continuous and injective. Then f is strictly monotone.

Co-authored-by: Johan Commelin <johan@commelin.net>

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net>

@@ -1,8 +1,9 @@
 /-
 Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Yury G. Kudryashov, Alistair Tucker
+Authors: Yury G. Kudryashov, Alistair Tucker, Wen Yang
 -/
+import Mathlib.Data.Set.Intervals.Image
 import Mathlib.Order.CompleteLatticeIntervals
 import Mathlib.Topology.Order.Basic
 
@@ -32,6 +33,9 @@ on intervals.
   is included `s`, then `[a, b] ⊆ s`.
 * `IsClosed.Icc_subset_of_forall_exists_gt`, `IsClosed.mem_of_ge_of_forall_exists_gt` : two
   other versions of the “continuous induction” principle.
+* `ContinuousOn.StrictMonoOn_of_InjOn_Ioo` :
+  Every continuous injective `f : (a, b) → δ` is strictly monotone
+  or antitone (increasing or decreasing).
 
 ## Tags
 
@@ -644,3 +648,123 @@ theorem ContinuousOn.surjOn_of_tendsto' {f : α → δ} {s : Set α} [OrdConnect
     (htop : Tendsto (fun x : s => f x) atTop atBot) : SurjOn f s univ :=
   @ContinuousOn.surjOn_of_tendsto α _ _ _ _ δᵒᵈ _ _ _ _ _ _ hs hf hbot htop
 #align continuous_on.surj_on_of_tendsto' ContinuousOn.surjOn_of_tendsto'
+
+theorem Continuous.strictMono_of_inj_boundedOrder [BoundedOrder α] {f : α → δ}
+    (hf_c : Continuous f) (hf : f ⊥ ≤ f ⊤) (hf_i : Injective f) : StrictMono f := by
+  intro a b hab
+  by_contra! h
+  have H : f b < f a := lt_of_le_of_ne h <| hf_i.ne hab.ne'
+  by_cases ha : f a ≤ f ⊥
+  · obtain ⟨u, hu⟩ := intermediate_value_Ioc le_top hf_c.continuousOn ⟨H.trans_le ha, hf⟩
+    have : u = ⊥ := hf_i hu.2
+    aesop
+  · by_cases hb : f ⊥ < f b
+    · obtain ⟨u, hu⟩ := intermediate_value_Ioo bot_le hf_c.continuousOn ⟨hb, H⟩
+      rw [hf_i hu.2] at hu
+      exact (hab.trans hu.1.2).false
+    · push_neg at ha hb
+      replace hb : f b < f ⊥ := lt_of_le_of_ne hb <| hf_i.ne (lt_of_lt_of_le' hab bot_le).ne'
+      obtain ⟨u, hu⟩ := intermediate_value_Ioo' hab.le hf_c.continuousOn ⟨hb, ha⟩
+      have : u = ⊥ := hf_i hu.2
+      aesop
+
+theorem Continuous.strictAnti_of_inj_boundedOrder [BoundedOrder α] {f : α → δ}
+    (hf_c : Continuous f) (hf : f ⊤ ≤ f ⊥) (hf_i : Injective f) : StrictAnti f :=
+  hf_c.strictMono_of_inj_boundedOrder (δ := δᵒᵈ) hf hf_i
+
+theorem Continuous.strictMono_of_inj_boundedOrder' [BoundedOrder α] {f : α → δ}
+    (hf_c : Continuous f) (hf_i : Injective f) : StrictMono f ∨ StrictAnti f :=
+  (le_total (f ⊥) (f ⊤)).imp
+    (hf_c.strictMono_of_inj_boundedOrder · hf_i)
+    (hf_c.strictAnti_of_inj_boundedOrder · hf_i)
+
+/-- Suppose `α` is equipped with a conditionally complete linear dense order and `f : α → δ` is
+continuous and injective. Then `f` is strictly monotone (increasing) if
+it is strictly monotone (increasing) on some closed interval `[a, b]`.-/
+theorem Continuous.strictMonoOn_of_inj_rigidity {f : α → δ}
+    (hf_c : Continuous f) (hf_i : Injective f) {a b : α} (hab : a < b)
+    (hf_mono : StrictMonoOn f (Icc a b)) : StrictMono f := by
+  intro x y hxy
+  let s := min a x
+  let t := max b y
+  have hsa : s ≤ a := min_le_left a x
+  have hbt : b ≤ t := le_max_left b y
+  have hst : s ≤ t := hsa.trans $ hbt.trans' hab.le
+  have hf_mono_st : StrictMonoOn f (Icc s t) ∨ StrictAntiOn f (Icc s t) := by
+    letI := Icc.completeLinearOrder hst
+    have := Continuous.strictMono_of_inj_boundedOrder' (f := Set.restrict (Icc s t) f)
+      hf_c.continuousOn.restrict (hf_i.injOn _).injective
+    exact this.imp strictMono_restrict.mp strictAntiOn_iff_strictAnti.mpr
+  have (h : StrictAntiOn f (Icc s t)) : False := by
+    have : Icc a b ⊆ Icc s t := Icc_subset_Icc hsa hbt
+    replace : StrictAntiOn f (Icc a b) := StrictAntiOn.mono h this
+    replace : IsAntichain (· ≤ ·) (Icc a b) :=
+      IsAntichain.of_strictMonoOn_antitoneOn hf_mono this.antitoneOn
+    exact this.not_lt (left_mem_Icc.mpr (le_of_lt hab)) (right_mem_Icc.mpr (le_of_lt hab)) hab
+  replace hf_mono_st : StrictMonoOn f (Icc s t) := hf_mono_st.resolve_right this
+  have hsx : s ≤ x := min_le_right a x
+  have hyt : y ≤ t := le_max_right b y
+  replace : Icc x y ⊆ Icc s t := Icc_subset_Icc hsx hyt
+  replace : StrictMonoOn f (Icc x y) := StrictMonoOn.mono hf_mono_st this
+  exact this (left_mem_Icc.mpr (le_of_lt hxy)) (right_mem_Icc.mpr (le_of_lt hxy)) hxy
+
+/-- Suppose `f : [a, b] → δ` is
+continuous and injective. Then `f` is strictly monotone (increasing) if `f(a) ≤ f(b)`.-/
+theorem ContinuousOn.strictMonoOn_of_injOn_Icc {a b : α} {f : α → δ}
+    (hab : a ≤ b) (hfab : f a ≤ f b)
+    (hf_c : ContinuousOn f (Icc a b)) (hf_i : InjOn f (Icc a b)) :
+    StrictMonoOn f (Icc a b) := by
+  letI := Icc.completeLinearOrder hab
+  refine StrictMono.of_restrict ?_
+  set g : Icc a b → δ := Set.restrict (Icc a b) f
+  have hgab : g ⊥ ≤ g ⊤ := by aesop
+  exact Continuous.strictMono_of_inj_boundedOrder (f := g) hf_c.restrict hgab hf_i.injective
+
+/-- Suppose `f : [a, b] → δ` is
+continuous and injective. Then `f` is strictly antitone (decreasing) if `f(b) ≤ f(a)`.-/
+theorem ContinuousOn.strictAntiOn_of_injOn_Icc {a b : α} {f : α → δ}
+    (hab : a ≤ b) (hfab : f b ≤ f a)
+    (hf_c : ContinuousOn f (Icc a b)) (hf_i : InjOn f (Icc a b)) :
+    StrictAntiOn f (Icc a b) := ContinuousOn.strictMonoOn_of_injOn_Icc (δ := δᵒᵈ) hab hfab hf_c hf_i
+
+/-- Suppose `f : [a, b] → δ` is continuous and injective. Then `f` is strictly monotone
+or antitone (increasing or decreasing).-/
+theorem ContinuousOn.strictMonoOn_of_injOn_Icc' {a b : α} {f : α → δ} (hab : a ≤ b)
+    (hf_c : ContinuousOn f (Icc a b)) (hf_i : InjOn f (Icc a b)) :
+    StrictMonoOn f (Icc a b) ∨ StrictAntiOn f (Icc a b) :=
+  (le_total (f a) (f b)).imp
+    (ContinuousOn.strictMonoOn_of_injOn_Icc hab · hf_c hf_i)
+    (ContinuousOn.strictAntiOn_of_injOn_Icc hab · hf_c hf_i)
+
+/-- Suppose `α` is equipped with a conditionally complete linear dense order and `f : α → δ` is
+continuous and injective. Then `f` is strictly monotone or antitone (increasing or decreasing).-/
+theorem Continuous.strictMono_of_inj {f : α → δ}
+    (hf_c : Continuous f) (hf_i : Injective f) : StrictMono f ∨ StrictAnti f := by
+  have H {c d : α} (hcd : c < d) : StrictMono f ∨ StrictAnti f :=
+    (hf_c.continuousOn.strictMonoOn_of_injOn_Icc' hcd.le (hf_i.injOn _)).imp
+      (hf_c.strictMonoOn_of_inj_rigidity hf_i hcd)
+      (hf_c.strictMonoOn_of_inj_rigidity (δ := δᵒᵈ) hf_i hcd)
+  by_cases hn : Nonempty α
+  · let a : α := Classical.choice ‹_›
+    by_cases h : ∃ b : α, a ≠ b
+    · choose b hb using h
+      by_cases hab : a < b
+      · exact H hab
+      · push_neg at hab
+        have : b < a := by exact Ne.lt_of_le (id (Ne.symm hb)) hab
+        exact H this
+    · push_neg at h
+      haveI : Subsingleton α := ⟨fun c d => Trans.trans (h c).symm (h d)⟩
+      exact Or.inl <| Subsingleton.strictMono f
+  · aesop
+
+/-- Every continuous injective `f : (a, b) → δ` is strictly monotone
+or antitone (increasing or decreasing).-/
+theorem ContinuousOn.strictMonoOn_of_injOn_Ioo {a b : α} {f : α → δ} (hab : a < b)
+    (hf_c : ContinuousOn f (Ioo a b)) (hf_i : InjOn f (Ioo a b)) :
+    StrictMonoOn f (Ioo a b) ∨ StrictAntiOn f (Ioo a b) := by
+  haveI : Inhabited (Ioo a b) := Classical.inhabited_of_nonempty (nonempty_Ioo_subtype hab)
+  let g : Ioo a b → δ := Set.restrict (Ioo a b) f
+  have : StrictMono g ∨ StrictAnti g :=
+    Continuous.strictMono_of_inj hf_c.restrict hf_i.injective
+  exact this.imp strictMono_restrict.mp strictAntiOn_iff_strictAnti.mpr

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

@@ -411,7 +411,7 @@ theorem isPreconnected_Icc : IsPreconnected (Icc a b) :=
     (by
       rintro s t hs ht hab ⟨x, hx⟩ ⟨y, hy⟩
       -- This used to use `wlog`, but it was causing timeouts.
-      cases' le_total x y with h h
+      rcases le_total x y with h | h
       · exact isPreconnected_Icc_aux x y s t h hs ht hab hx hy
       · rw [inter_comm s t]
         rw [union_comm s t] at hab
@@ -606,7 +606,7 @@ theorem ContinuousOn.surjOn_Icc {s : Set α} [hs : OrdConnected s] {f : α → 
 `b` are two points of this set, then `f` sends `s` to a superset of `[f x, f y]`. -/
 theorem ContinuousOn.surjOn_uIcc {s : Set α} [hs : OrdConnected s] {f : α → δ}
     (hf : ContinuousOn f s) {a b : α} (ha : a ∈ s) (hb : b ∈ s) : SurjOn f s (uIcc (f a) (f b)) :=
-  by cases' le_total (f a) (f b) with hab hab <;> simp [hf.surjOn_Icc, *]
+  by rcases le_total (f a) (f b) with hab | hab <;> simp [hf.surjOn_Icc, *]
 #align continuous_on.surj_on_uIcc ContinuousOn.surjOn_uIcc
 
 /-- A continuous function which tendsto `Filter.atTop` along `Filter.atTop` and to `atBot` along

Using Lean4's named arguments, we manage to remove a few hard-to-read explicit function calls [@foo](https://github.com/foo) _ _ _ _ _ ... which used to be necessary in Lean3.

Occasionally, this results in slightly longer code. The benefit of named arguments is readability, as well as to reduce the brittleness of the code when the argument order is changed.

Co-authored-by: Michael Rothgang <rothgami@math.hu-berlin.de>

@@ -621,7 +621,7 @@ theorem Continuous.surjective {f : α → δ} (hf : Continuous f) (h_top : Tends
 along `atBot` is surjective. -/
 theorem Continuous.surjective' {f : α → δ} (hf : Continuous f) (h_top : Tendsto f atBot atTop)
     (h_bot : Tendsto f atTop atBot) : Function.Surjective f :=
-  @Continuous.surjective αᵒᵈ _ _ _ _ _ _ _ _ _ hf h_top h_bot
+  Continuous.surjective (α := αᵒᵈ) hf h_top h_bot
 #align continuous.surjective' Continuous.surjective'
 
 /-- If a function `f : α → β` is continuous on a nonempty interval `s`, its restriction to `s`

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

This has nice performance benefits.

@@ -521,7 +521,7 @@ continuous on an interval.
 -/
 
 
-variable {δ : Type _} [LinearOrder δ] [TopologicalSpace δ] [OrderClosedTopology δ]
+variable {δ : Type*} [LinearOrder δ] [TopologicalSpace δ] [OrderClosedTopology δ]
 
 /-- **Intermediate Value Theorem** for continuous functions on closed intervals, case
 `f a ≤ t ≤ f b`.-/

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Alistair Tucker
-
-! This file was ported from Lean 3 source module topology.algebra.order.intermediate_value
-! leanprover-community/mathlib commit 4c19a16e4b705bf135cf9a80ac18fcc99c438514
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Order.CompleteLatticeIntervals
 import Mathlib.Topology.Order.Basic
 
+#align_import topology.algebra.order.intermediate_value from "leanprover-community/mathlib"@"4c19a16e4b705bf135cf9a80ac18fcc99c438514"
+
 /-!
 # Intermediate Value Theorem
 

These are all doc fixes

@@ -276,7 +276,7 @@ theorem IsPreconnected.Iio_csSup_subset {s : Set α} (hs : IsPreconnected s) (hb
 /-- A preconnected set in a conditionally complete linear order is either one of the intervals
 `[Inf s, Sup s]`, `[Inf s, Sup s)`, `(Inf s, Sup s]`, `(Inf s, Sup s)`, `[Inf s, +∞)`,
 `(Inf s, +∞)`, `(-∞, Sup s]`, `(-∞, Sup s)`, `(-∞, +∞)`, or `∅`. The converse statement requires
-`α` to be densely ordererd. -/
+`α` to be densely ordered. -/
 theorem IsPreconnected.mem_intervals {s : Set α} (hs : IsPreconnected s) :
     s ∈
       ({Icc (sInf s) (sSup s), Ico (sInf s) (sSup s), Ioc (sInf s) (sSup s), Ioo (sInf s) (sSup s),
@@ -612,7 +612,7 @@ theorem ContinuousOn.surjOn_uIcc {s : Set α} [hs : OrdConnected s] {f : α →
   by cases' le_total (f a) (f b) with hab hab <;> simp [hf.surjOn_Icc, *]
 #align continuous_on.surj_on_uIcc ContinuousOn.surjOn_uIcc
 
-/-- A continuous function which tendsto `Fitler.atTop` along `Filter.atTop` and to `atBot` along
+/-- A continuous function which tendsto `Filter.atTop` along `Filter.atTop` and to `atBot` along
 `at_bot` is surjective. -/
 theorem Continuous.surjective {f : α → δ} (hf : Continuous f) (h_top : Tendsto f atTop atTop)
     (h_bot : Tendsto f atBot atBot) : Function.Surjective f := fun p =>

As discussed on Zulip

Renames

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

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

@@ -247,31 +247,31 @@ variable {α : Type u} {β : Type v} {γ : Type w} [ConditionallyCompleteLinearO
 
 /-- A bounded connected subset of a conditionally complete linear order includes the open interval
 `(Inf s, Sup s)`. -/
-theorem IsConnected.Ioo_cinfₛ_csupₛ_subset {s : Set α} (hs : IsConnected s) (hb : BddBelow s)
-    (ha : BddAbove s) : Ioo (infₛ s) (supₛ s) ⊆ s := fun _x hx =>
-  let ⟨_y, ys, hy⟩ := (isGLB_lt_iff (isGLB_cinfₛ hs.nonempty hb)).1 hx.1
-  let ⟨_z, zs, hz⟩ := (lt_isLUB_iff (isLUB_csupₛ hs.nonempty ha)).1 hx.2
+theorem IsConnected.Ioo_csInf_csSup_subset {s : Set α} (hs : IsConnected s) (hb : BddBelow s)
+    (ha : BddAbove s) : Ioo (sInf s) (sSup s) ⊆ s := fun _x hx =>
+  let ⟨_y, ys, hy⟩ := (isGLB_lt_iff (isGLB_csInf hs.nonempty hb)).1 hx.1
+  let ⟨_z, zs, hz⟩ := (lt_isLUB_iff (isLUB_csSup hs.nonempty ha)).1 hx.2
   hs.Icc_subset ys zs ⟨hy.le, hz.le⟩
-#align is_connected.Ioo_cInf_cSup_subset IsConnected.Ioo_cinfₛ_csupₛ_subset
+#align is_connected.Ioo_cInf_cSup_subset IsConnected.Ioo_csInf_csSup_subset
 
-theorem eq_Icc_cinfₛ_csupₛ_of_connected_bdd_closed {s : Set α} (hc : IsConnected s)
-    (hb : BddBelow s) (ha : BddAbove s) (hcl : IsClosed s) : s = Icc (infₛ s) (supₛ s) :=
-  (subset_Icc_cinfₛ_csupₛ hb ha).antisymm <|
-    hc.Icc_subset (hcl.cinfₛ_mem hc.nonempty hb) (hcl.csupₛ_mem hc.nonempty ha)
-#align eq_Icc_cInf_cSup_of_connected_bdd_closed eq_Icc_cinfₛ_csupₛ_of_connected_bdd_closed
+theorem eq_Icc_csInf_csSup_of_connected_bdd_closed {s : Set α} (hc : IsConnected s)
+    (hb : BddBelow s) (ha : BddAbove s) (hcl : IsClosed s) : s = Icc (sInf s) (sSup s) :=
+  (subset_Icc_csInf_csSup hb ha).antisymm <|
+    hc.Icc_subset (hcl.csInf_mem hc.nonempty hb) (hcl.csSup_mem hc.nonempty ha)
+#align eq_Icc_cInf_cSup_of_connected_bdd_closed eq_Icc_csInf_csSup_of_connected_bdd_closed
 
-theorem IsPreconnected.Ioi_cinfₛ_subset {s : Set α} (hs : IsPreconnected s) (hb : BddBelow s)
-    (ha : ¬BddAbove s) : Ioi (infₛ s) ⊆ s := fun x hx =>
+theorem IsPreconnected.Ioi_csInf_subset {s : Set α} (hs : IsPreconnected s) (hb : BddBelow s)
+    (ha : ¬BddAbove s) : Ioi (sInf s) ⊆ s := fun x hx =>
   have sne : s.Nonempty := nonempty_of_not_bddAbove ha
-  let ⟨_y, ys, hy⟩ : ∃ y ∈ s, y < x := (isGLB_lt_iff (isGLB_cinfₛ sne hb)).1 hx
+  let ⟨_y, ys, hy⟩ : ∃ y ∈ s, y < x := (isGLB_lt_iff (isGLB_csInf sne hb)).1 hx
   let ⟨_z, zs, hz⟩ : ∃ z ∈ s, x < z := not_bddAbove_iff.1 ha x
   hs.Icc_subset ys zs ⟨hy.le, hz.le⟩
-#align is_preconnected.Ioi_cInf_subset IsPreconnected.Ioi_cinfₛ_subset
+#align is_preconnected.Ioi_cInf_subset IsPreconnected.Ioi_csInf_subset
 
-theorem IsPreconnected.Iio_csupₛ_subset {s : Set α} (hs : IsPreconnected s) (hb : ¬BddBelow s)
-    (ha : BddAbove s) : Iio (supₛ s) ⊆ s :=
-  @IsPreconnected.Ioi_cinfₛ_subset αᵒᵈ _ _ _ s hs ha hb
-#align is_preconnected.Iio_cSup_subset IsPreconnected.Iio_csupₛ_subset
+theorem IsPreconnected.Iio_csSup_subset {s : Set α} (hs : IsPreconnected s) (hb : ¬BddBelow s)
+    (ha : BddAbove s) : Iio (sSup s) ⊆ s :=
+  @IsPreconnected.Ioi_csInf_subset αᵒᵈ _ _ _ s hs ha hb
+#align is_preconnected.Iio_cSup_subset IsPreconnected.Iio_csSup_subset
 
 /-- A preconnected set in a conditionally complete linear order is either one of the intervals
 `[Inf s, Sup s]`, `[Inf s, Sup s)`, `(Inf s, Sup s]`, `(Inf s, Sup s)`, `[Inf s, +∞)`,
@@ -279,27 +279,27 @@ theorem IsPreconnected.Iio_csupₛ_subset {s : Set α} (hs : IsPreconnected s) (
 `α` to be densely ordererd. -/
 theorem IsPreconnected.mem_intervals {s : Set α} (hs : IsPreconnected s) :
     s ∈
-      ({Icc (infₛ s) (supₛ s), Ico (infₛ s) (supₛ s), Ioc (infₛ s) (supₛ s), Ioo (infₛ s) (supₛ s),
-          Ici (infₛ s), Ioi (infₛ s), Iic (supₛ s), Iio (supₛ s), univ, ∅} :
+      ({Icc (sInf s) (sSup s), Ico (sInf s) (sSup s), Ioc (sInf s) (sSup s), Ioo (sInf s) (sSup s),
+          Ici (sInf s), Ioi (sInf s), Iic (sSup s), Iio (sSup s), univ, ∅} :
         Set (Set α)) := by
   rcases s.eq_empty_or_nonempty with (rfl | hne)
   · apply_rules [Or.inr, mem_singleton]
   have hs' : IsConnected s := ⟨hne, hs⟩
   by_cases hb : BddBelow s <;> by_cases ha : BddAbove s
-  · rcases mem_Icc_Ico_Ioc_Ioo_of_subset_of_subset (hs'.Ioo_cinfₛ_csupₛ_subset hb ha)
-        (subset_Icc_cinfₛ_csupₛ hb ha) with (hs | hs | hs | hs)
+  · rcases mem_Icc_Ico_Ioc_Ioo_of_subset_of_subset (hs'.Ioo_csInf_csSup_subset hb ha)
+        (subset_Icc_csInf_csSup hb ha) with (hs | hs | hs | hs)
     · exact Or.inl hs
     · exact Or.inr <| Or.inl hs
     · exact Or.inr <| Or.inr <| Or.inl hs
     · exact Or.inr <| Or.inr <| Or.inr <| Or.inl hs
   · refine' Or.inr <| Or.inr <| Or.inr <| Or.inr _
     cases'
-      mem_Ici_Ioi_of_subset_of_subset (hs.Ioi_cinfₛ_subset hb ha) fun x hx => cinfₛ_le hb hx with
+      mem_Ici_Ioi_of_subset_of_subset (hs.Ioi_csInf_subset hb ha) fun x hx => csInf_le hb hx with
       hs hs
     · exact Or.inl hs
     · exact Or.inr (Or.inl hs)
   · iterate 6 apply Or.inr
-    cases' mem_Iic_Iio_of_subset_of_subset (hs.Iio_csupₛ_subset hb ha) fun x hx => le_csupₛ ha hx
+    cases' mem_Iic_Iio_of_subset_of_subset (hs.Iio_csSup_subset hb ha) fun x hx => le_csSup ha hx
       with hs hs
     · exact Or.inl hs
     · exact Or.inr (Or.inl hs)
@@ -319,14 +319,14 @@ theorem setOf_isPreconnected_subset_of_ordered :
       (range Ici ∪ range Ioi ∪ range Iic ∪ range Iio ∪ {univ, ∅}) := by
   intro s hs
   rcases hs.mem_intervals with (hs | hs | hs | hs | hs | hs | hs | hs | hs | hs)
-  · exact Or.inl <| Or.inl <| Or.inl <| Or.inl ⟨(infₛ s, supₛ s), hs.symm⟩
-  · exact Or.inl <| Or.inl <| Or.inl <| Or.inr ⟨(infₛ s, supₛ s), hs.symm⟩
-  · exact Or.inl <| Or.inl <| Or.inr ⟨(infₛ s, supₛ s), hs.symm⟩
-  · exact Or.inl <| Or.inr ⟨(infₛ s, supₛ s), hs.symm⟩
-  · exact Or.inr <| Or.inl <| Or.inl <| Or.inl <| Or.inl ⟨infₛ s, hs.symm⟩
-  · exact Or.inr <| Or.inl <| Or.inl <| Or.inl <| Or.inr ⟨infₛ s, hs.symm⟩
-  · exact Or.inr <| Or.inl <| Or.inl <| Or.inr ⟨supₛ s, hs.symm⟩
-  · exact Or.inr <| Or.inl <| Or.inr ⟨supₛ s, hs.symm⟩
+  · exact Or.inl <| Or.inl <| Or.inl <| Or.inl ⟨(sInf s, sSup s), hs.symm⟩
+  · exact Or.inl <| Or.inl <| Or.inl <| Or.inr ⟨(sInf s, sSup s), hs.symm⟩
+  · exact Or.inl <| Or.inl <| Or.inr ⟨(sInf s, sSup s), hs.symm⟩
+  · exact Or.inl <| Or.inr ⟨(sInf s, sSup s), hs.symm⟩
+  · exact Or.inr <| Or.inl <| Or.inl <| Or.inl <| Or.inl ⟨sInf s, hs.symm⟩
+  · exact Or.inr <| Or.inl <| Or.inl <| Or.inl <| Or.inr ⟨sInf s, hs.symm⟩
+  · exact Or.inr <| Or.inl <| Or.inl <| Or.inr ⟨sSup s, hs.symm⟩
+  · exact Or.inr <| Or.inl <| Or.inr ⟨sSup s, hs.symm⟩
   · exact Or.inr <| Or.inr <| Or.inl hs
   · exact Or.inr <| Or.inr <| Or.inr hs
 #align set_of_is_preconnected_subset_of_ordered setOf_isPreconnected_subset_of_ordered
@@ -347,14 +347,14 @@ theorem IsClosed.mem_of_ge_of_forall_exists_gt {a b : α} {s : Set α} (hs : IsC
   replace ha : a ∈ S
   exact ⟨ha, left_mem_Icc.2 hab⟩
   have Sbd : BddAbove S := ⟨b, fun z hz => hz.2.2⟩
-  let c := supₛ (s ∩ Icc a b)
-  have c_mem : c ∈ S := hs.csupₛ_mem ⟨_, ha⟩ Sbd
-  have c_le : c ≤ b := csupₛ_le ⟨_, ha⟩ fun x hx => hx.2.2
+  let c := sSup (s ∩ Icc a b)
+  have c_mem : c ∈ S := hs.csSup_mem ⟨_, ha⟩ Sbd
+  have c_le : c ≤ b := csSup_le ⟨_, ha⟩ fun x hx => hx.2.2
   cases' eq_or_lt_of_le c_le with hc hc
   exact hc ▸ c_mem.1
   exfalso
   rcases hgt c ⟨c_mem.1, c_mem.2.1, hc⟩ with ⟨x, xs, cx, xb⟩
-  exact not_lt_of_le (le_csupₛ Sbd ⟨xs, le_trans (le_csupₛ Sbd ha) (le_of_lt cx), xb⟩) cx
+  exact not_lt_of_le (le_csSup Sbd ⟨xs, le_trans (le_csSup Sbd ha) (le_of_lt cx), xb⟩) cx
 #align is_closed.mem_of_ge_of_forall_exists_gt IsClosed.mem_of_ge_of_forall_exists_gt
 
 /-- A "continuous induction principle" for a closed interval: if a set `s` meets `[a, b]`
@@ -500,7 +500,7 @@ instance (priority := 100) ordered_connected_space : PreconnectedSpace α :=
 
 /-- In a dense conditionally complete linear order, the set of preconnected sets is exactly
 the set of the intervals `Icc`, `Ico`, `Ioc`, `Ioo`, `Ici`, `Ioi`, `Iic`, `Iio`, `(-∞, +∞)`,
-or `∅`. Though one can represent `∅` as `(infₛ s, infₛ s)`, we include it into the list of
+or `∅`. Though one can represent `∅` as `(sInf s, sInf s)`, we include it into the list of
 possible cases to improve readability. -/
 theorem setOf_isPreconnected_eq_of_ordered :
     { s : Set α | IsPreconnected s } =

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

@@ -363,10 +363,8 @@ is not empty, then `[a, b] ⊆ s`. -/
 theorem IsClosed.Icc_subset_of_forall_exists_gt {a b : α} {s : Set α} (hs : IsClosed (s ∩ Icc a b))
     (ha : a ∈ s) (hgt : ∀ x ∈ s ∩ Ico a b, ∀ y ∈ Ioi x, (s ∩ Ioc x y).Nonempty) : Icc a b ⊆ s := by
   intro y hy
-  have : IsClosed (s ∩ Icc a y) :=
-    by
-    suffices s ∩ Icc a y = s ∩ Icc a b ∩ Icc a y
-      by
+  have : IsClosed (s ∩ Icc a y) := by
+    suffices s ∩ Icc a y = s ∩ Icc a b ∩ Icc a y by
       rw [this]
       exact IsClosed.inter hs isClosed_Icc
     rw [inter_assoc]
@@ -402,8 +400,7 @@ theorem isPreconnected_Icc_aux (x y : α) (s t : Set α) (hxy : x ≤ y) (hs : I
   apply (IsClosed.inter hs isClosed_Icc).Icc_subset_of_forall_mem_nhdsWithin hx.2
   rintro z ⟨zs, hz⟩
   have zt : z ∈ tᶜ := fun zt => hst ⟨z, xyab <| Ico_subset_Icc_self hz, zs, zt⟩
-  have : tᶜ ∩ Ioc z y ∈ 𝓝[>] z :=
-    by
+  have : tᶜ ∩ Ioc z y ∈ 𝓝[>] z := by
     rw [← nhdsWithin_Ioc_eq_nhdsWithin_Ioi hz.2]
     exact mem_nhdsWithin.2 ⟨tᶜ, ht.isOpen_compl, zt, Subset.rfl⟩
   apply mem_of_superset this

Co-authored-by: Johan Commelin <johan@commelin.net>