topology.order.basic ⟷ Mathlib.Topology.Order.Basic

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

@@ -3,7 +3,7 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
 -/
-import Data.Set.Intervals.Pi
+import Order.Interval.Set.Pi
 import Data.Set.Pointwise.Interval
 import Order.Filter.Interval
 import Topology.Support

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

@@ -1740,7 +1740,7 @@ theorem countable_of_isolated_left' [SecondCountableTopology α] :
     Set.Countable {x : α | ∃ y, y < x ∧ Ioo y x = ∅} :=
   by
   convert @countable_of_isolated_right' αᵒᵈ _ _ _ _
-  have : ∀ x y : α, Ioo x y = {z | z < y ∧ x < z} := by simp_rw [and_comm', Ioo];
+  have : ∀ x y : α, Ioo x y = {z | z < y ∧ x < z} := by simp_rw [and_comm, Ioo];
     simp only [eq_self_iff_true, forall₂_true_iff]
   simp_rw [this]
   rfl
@@ -3030,7 +3030,7 @@ theorem nhdsWithin_Ioi_self_neBot [NoMaxOrder α] (a : α) : NeBot (𝓝[>] a) :
 #print Filter.Eventually.exists_gt /-
 theorem Filter.Eventually.exists_gt [NoMaxOrder α] {a : α} {p : α → Prop} (h : ∀ᶠ x in 𝓝 a, p x) :
     ∃ b > a, p b := by
-  simpa only [exists_prop, gt_iff_lt, and_comm'] using
+  simpa only [exists_prop, gt_iff_lt, and_comm] using
     ((h.filter_mono (@nhdsWithin_le_nhds _ _ a (Ioi a))).And self_mem_nhdsWithin).exists
 #align filter.eventually.exists_gt Filter.Eventually.exists_gt
 -/

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

@@ -7,7 +7,7 @@ import Data.Set.Intervals.Pi
 import Data.Set.Pointwise.Interval
 import Order.Filter.Interval
 import Topology.Support
-import Topology.Algebra.Order.LeftRight
+import Topology.Order.LeftRight
 
 #align_import topology.order.basic from "leanprover-community/mathlib"@"3efd324a3a31eaa40c9d5bfc669c4fafee5f9423"
 
@@ -3279,7 +3279,7 @@ instance (x : α) [Nontrivial α] : NeBot (𝓝[≠] x) :=
   obtain ⟨z, hz⟩ : ∃ z, a < z ∧ z < x := exists_between hy.1
   exact ⟨z, us ⟨hab ⟨hz.1, hz.2.trans hy.2⟩, hz.2.Ne⟩⟩
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print Dense.exists_countable_dense_subset_no_bot_top /-
 /-- Let `s` be a dense set in a nontrivial dense linear order `α`. If `s` is a
 separable space (e.g., if `α` has a second countable topology), then there exists a countable

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

@@ -1214,7 +1214,7 @@ theorem induced_orderTopology' {α : Type u} {β : Type v} [Preorder α] [ta : T
     @OrderTopology _ (induced f ta) _ :=
   by
   letI := induced f ta
-  refine' ⟨eq_of_nhds_eq_nhds fun a => _⟩
+  refine' ⟨TopologicalSpace.ext_nhds fun a => _⟩
   rw [nhds_induced, nhds_generate_from, nhds_eq_order (f a)]
   apply le_antisymm
   · refine' le_iInf fun s => le_iInf fun hs => le_principal_iff.2 _
@@ -1265,7 +1265,7 @@ instance orderTopology_of_ordConnected {α : Type u} [ta : TopologicalSpace α]
     [OrderTopology α] {t : Set α} [ht : OrdConnected t] : OrderTopology t :=
   by
   letI := induced (coe : t → α) ta
-  refine' ⟨eq_of_nhds_eq_nhds fun a => _⟩
+  refine' ⟨TopologicalSpace.ext_nhds fun a => _⟩
   rw [nhds_induced, nhds_generate_from, nhds_eq_order (a : α)]
   apply le_antisymm
   · refine' le_iInf fun s => le_iInf fun hs => le_principal_iff.2 _
@@ -2271,7 +2271,7 @@ theorem nhds_eq_iInf_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 {b | |a - b| <
 theorem orderTopology_of_nhds_abs {α : Type _} [TopologicalSpace α] [LinearOrderedAddCommGroup α]
     (h_nhds : ∀ a : α, 𝓝 a = ⨅ r > 0, 𝓟 {b | |a - b| < r}) : OrderTopology α :=
   by
-  refine' ⟨eq_of_nhds_eq_nhds fun a => _⟩
+  refine' ⟨TopologicalSpace.ext_nhds fun a => _⟩
   rw [h_nhds]
   letI := Preorder.topology α; letI : OrderTopology α := ⟨rfl⟩
   exact (nhds_eq_iInf_abs_sub a).symm

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

@@ -964,7 +964,7 @@ theorem Dense.exists_le' {s : Set α} (hs : Dense s) (hbot : ∀ x, IsBot x →
     ∃ y ∈ s, y ≤ x := by
   by_cases hx : IsBot x
   · exact ⟨x, hbot x hx, le_rfl⟩
-  · simp only [IsBot, Classical.not_forall, not_le] at hx 
+  · simp only [IsBot, Classical.not_forall, not_le] at hx
     rcases hs.exists_mem_open isOpen_Iio hx with ⟨y, hys, hy : y < x⟩
     exact ⟨y, hys, hy.le⟩
 #align dense.exists_le' Dense.exists_le'
@@ -2341,8 +2341,8 @@ theorem nhds_basis_Ioo_pos [NoMinOrder α] [NoMaxOrder α] (a : α) :
       refine' ⟨min (a - l) (u - a), by apply lt_min <;> rwa [sub_pos], _⟩
       rintro x ⟨hx, hx'⟩
       apply h'
-      rw [sub_lt_comm, lt_min_iff, sub_lt_sub_iff_left] at hx 
-      rw [← sub_lt_iff_lt_add', lt_min_iff, sub_lt_sub_iff_right] at hx' 
+      rw [sub_lt_comm, lt_min_iff, sub_lt_sub_iff_left] at hx
+      rw [← sub_lt_iff_lt_add', lt_min_iff, sub_lt_sub_iff_right] at hx'
       exact ⟨hx.1, hx'.2⟩
     · rintro ⟨ε, ε_pos, h⟩
       exact ⟨(a - ε, a + ε), by simp [ε_pos], h⟩⟩
@@ -2484,7 +2484,7 @@ theorem isLUB_of_mem_nhds {s : Set α} {a : α} {f : Filter α} (hsa : a ∈ upp
 #print isLUB_of_mem_closure /-
 theorem isLUB_of_mem_closure {s : Set α} {a : α} (hsa : a ∈ upperBounds s) (hsf : a ∈ closure s) :
     IsLUB s a := by
-  rw [mem_closure_iff_clusterPt, ClusterPt, inf_comm] at hsf 
+  rw [mem_closure_iff_clusterPt, ClusterPt, inf_comm] at hsf
   haveI : (𝓟 s ⊓ 𝓝 a).ne_bot := hsf
   exact isLUB_of_mem_nhds hsa (mem_principal_self s)
 #align is_lub_of_mem_closure isLUB_of_mem_closure

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

@@ -144,27 +144,31 @@ theorem isClosed_le [TopologicalSpace β] {f g : β → α} (hf : Continuous f)
 #align is_closed_le isClosed_le
 -/
 
-#print ClosedIicTopology.isClosed_le' /-
-theorem ClosedIicTopology.isClosed_le' (a : α) : IsClosed {b | b ≤ a} :=
+/- warning: is_closed_le' clashes with is_closed_Iic -> isClosed_Iic
+Case conversion may be inaccurate. Consider using '#align is_closed_le' isClosed_Iicₓ'. -/
+#print isClosed_Iic /-
+theorem isClosed_Iic (a : α) : IsClosed {b | b ≤ a} :=
   isClosed_le continuous_id continuous_const
-#align is_closed_le' ClosedIicTopology.isClosed_le'
+#align is_closed_le' isClosed_Iic
 -/
 
 #print isClosed_Iic /-
 theorem isClosed_Iic {a : α} : IsClosed (Iic a) :=
-  ClosedIicTopology.isClosed_le' a
+  isClosed_Iic a
 #align is_closed_Iic isClosed_Iic
 -/
 
-#print ClosedIciTopology.isClosed_ge' /-
-theorem ClosedIciTopology.isClosed_ge' (a : α) : IsClosed {b | a ≤ b} :=
+/- warning: is_closed_ge' clashes with is_closed_Ici -> isClosed_Ici
+Case conversion may be inaccurate. Consider using '#align is_closed_ge' isClosed_Iciₓ'. -/
+#print isClosed_Ici /-
+theorem isClosed_Ici (a : α) : IsClosed {b | a ≤ b} :=
   isClosed_le continuous_const continuous_id
-#align is_closed_ge' ClosedIciTopology.isClosed_ge'
+#align is_closed_ge' isClosed_Ici
 -/
 
 #print isClosed_Ici /-
 theorem isClosed_Ici {a : α} : IsClosed (Ici a) :=
-  ClosedIciTopology.isClosed_ge' a
+  isClosed_Ici a
 #align is_closed_Ici isClosed_Ici
 -/
 
@@ -3649,17 +3653,13 @@ section LinearOrderedAddCommGroup
 
 variable [LinearOrder α] [Zero α] [TopologicalSpace α] [OrderTopology α]
 
-#print eventually_nhdsWithin_pos_mem_Ioo /-
 theorem eventually_nhdsWithin_pos_mem_Ioo {ε : α} (h : 0 < ε) : ∀ᶠ x in 𝓝[>] 0, x ∈ Ioo 0 ε :=
   Ioo_mem_nhdsWithin_Ioi (left_mem_Ico.2 h)
 #align eventually_nhds_within_pos_mem_Ioo eventually_nhdsWithin_pos_mem_Ioo
--/
 
-#print eventually_nhdsWithin_pos_mem_Ioc /-
 theorem eventually_nhdsWithin_pos_mem_Ioc {ε : α} (h : 0 < ε) : ∀ᶠ x in 𝓝[>] 0, x ∈ Ioc 0 ε :=
   Ioc_mem_nhdsWithin_Ioi (left_mem_Ico.2 h)
 #align eventually_nhds_within_pos_mem_Ioc eventually_nhdsWithin_pos_mem_Ioc
--/
 
 end LinearOrderedAddCommGroup
 

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

@@ -817,7 +817,7 @@ theorem Filter.Tendsto.eventually_lt {l : Filter γ} {f g : γ → α} {y z : α
   · filter_upwards [hf (Iio_mem_nhds hyz), hg (Ioi_mem_nhds hyz)]
     rw [h.Iio_eq]
     exact fun x hfx hgx => lt_of_le_of_lt hfx hgx
-  · obtain ⟨w, hyw, hwz⟩ := (not_covby_iff hyz).mp h
+  · obtain ⟨w, hyw, hwz⟩ := (not_covBy_iff hyz).mp h
     filter_upwards [hf (Iio_mem_nhds hyw), hg (Ioi_mem_nhds hwz)]
     exact fun x => lt_trans
 #align tendsto.eventually_lt Filter.Tendsto.eventually_lt

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

@@ -1716,11 +1716,11 @@ theorem countable_of_isolated_right' [SecondCountableTopology α] :
     rcases lt_or_gt_of_ne hxx' with (h' | h')
     · refine' disjoint_left.2 fun u ux ux' => xt.2.2.1 _
       refine' h'z x' x't ⟨ux'.1.trans_le (ux.2.trans (hy x xt.1).le), _⟩
-      by_contra' H
+      by_contra! H
       exact False.elim (lt_irrefl _ ((Hy _ _ xt.1 H).trans_lt h'))
     · refine' disjoint_left.2 fun u ux ux' => x't.2.2.1 _
       refine' h'z x xt ⟨ux.1.trans_le (ux'.2.trans (hy x' x't.1).le), _⟩
-      by_contra' H
+      by_contra! H
       exact False.elim (lt_irrefl _ ((Hy _ _ x't.1 H).trans_lt h'))
   refine' this.countable_of_is_open (fun x hx => _) fun x hx => ⟨x, hz x hx, le_rfl⟩
   suffices H : Ioc (z x) x = Ioo (z x) (y x)

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

@@ -274,7 +274,7 @@ theorem ContinuousWithinAt.closure_le [TopologicalSpace β] {f g : β → α} {s
 then the set `{x ∈ s | f x ≤ g x}` is a closed set. -/
 theorem IsClosed.isClosed_le [TopologicalSpace β] {f g : β → α} {s : Set β} (hs : IsClosed s)
     (hf : ContinuousOn f s) (hg : ContinuousOn g s) : IsClosed ({x ∈ s | f x ≤ g x}) :=
-  (hf.Prod hg).preimage_closed_of_closed hs OrderClosedTopology.isClosed_le'
+  (hf.Prod hg).preimage_isClosed_of_isClosed hs OrderClosedTopology.isClosed_le'
 #align is_closed.is_closed_le IsClosed.isClosed_le
 -/
 

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

@@ -960,7 +960,7 @@ theorem Dense.exists_le' {s : Set α} (hs : Dense s) (hbot : ∀ x, IsBot x →
     ∃ y ∈ s, y ≤ x := by
   by_cases hx : IsBot x
   · exact ⟨x, hbot x hx, le_rfl⟩
-  · simp only [IsBot, not_forall, not_le] at hx 
+  · simp only [IsBot, Classical.not_forall, not_le] at hx 
     rcases hs.exists_mem_open isOpen_Iio hx with ⟨y, hys, hy : y < x⟩
     exact ⟨y, hys, hy.le⟩
 #align dense.exists_le' Dense.exists_le'
@@ -1708,7 +1708,7 @@ theorem countable_of_isolated_right' [SecondCountableTopology α] :
   have : ∀ x ∈ t, ∃ z < x, Ioc z x ⊆ a := by
     intro x hx
     apply exists_Ioc_subset_of_mem_nhds (ha.mem_nhds hx.2.1)
-    simpa only [IsBot, not_forall, not_le] using hx.right.right.right
+    simpa only [IsBot, Classical.not_forall, not_le] using hx.right.right.right
   choose! z hz h'z using this
   have : pairwise_disjoint t fun x => Ioc (z x) x :=
     by

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

@@ -3,11 +3,11 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
 -/
-import Mathbin.Data.Set.Intervals.Pi
-import Mathbin.Data.Set.Pointwise.Interval
-import Mathbin.Order.Filter.Interval
-import Mathbin.Topology.Support
-import Mathbin.Topology.Algebra.Order.LeftRight
+import Data.Set.Intervals.Pi
+import Data.Set.Pointwise.Interval
+import Order.Filter.Interval
+import Topology.Support
+import Topology.Algebra.Order.LeftRight
 
 #align_import topology.order.basic from "leanprover-community/mathlib"@"3efd324a3a31eaa40c9d5bfc669c4fafee5f9423"
 
@@ -3275,7 +3275,7 @@ instance (x : α) [Nontrivial α] : NeBot (𝓝[≠] x) :=
   obtain ⟨z, hz⟩ : ∃ z, a < z ∧ z < x := exists_between hy.1
   exact ⟨z, us ⟨hab ⟨hz.1, hz.2.trans hy.2⟩, hz.2.Ne⟩⟩
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print Dense.exists_countable_dense_subset_no_bot_top /-
 /-- Let `s` be a dense set in a nontrivial dense linear order `α`. If `s` is a
 separable space (e.g., if `α` has a second countable topology), then there exists a countable

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

@@ -207,7 +207,7 @@ theorem le_of_tendsto_of_tendsto {f g : β → α} {b : Filter β} {a₁ a₂ :
 #align le_of_tendsto_of_tendsto le_of_tendsto_of_tendsto
 -/
 
-alias le_of_tendsto_of_tendsto ← tendsto_le_of_eventuallyLE
+alias tendsto_le_of_eventuallyLE := le_of_tendsto_of_tendsto
 #align tendsto_le_of_eventually_le tendsto_le_of_eventuallyLE
 
 #print le_of_tendsto_of_tendsto' /-
@@ -2583,7 +2583,7 @@ theorem IsLUB.mem_of_isClosed {a : α} {s : Set α} (ha : IsLUB s a) (hs : s.Non
 #align is_lub.mem_of_is_closed IsLUB.mem_of_isClosed
 -/
 
-alias IsLUB.mem_of_isClosed ← IsClosed.isLUB_mem
+alias IsClosed.isLUB_mem := IsLUB.mem_of_isClosed
 #align is_closed.is_lub_mem IsClosed.isLUB_mem
 
 #print IsGLB.mem_of_isClosed /-
@@ -2593,7 +2593,7 @@ theorem IsGLB.mem_of_isClosed {a : α} {s : Set α} (ha : IsGLB s a) (hs : s.Non
 #align is_glb.mem_of_is_closed IsGLB.mem_of_isClosed
 -/
 
-alias IsGLB.mem_of_isClosed ← IsClosed.isGLB_mem
+alias IsClosed.isGLB_mem := IsGLB.mem_of_isClosed
 #align is_closed.is_glb_mem IsClosed.isGLB_mem
 
 /-!

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

@@ -144,27 +144,27 @@ theorem isClosed_le [TopologicalSpace β] {f g : β → α} (hf : Continuous f)
 #align is_closed_le isClosed_le
 -/
 
-#print isClosed_le' /-
-theorem isClosed_le' (a : α) : IsClosed {b | b ≤ a} :=
+#print ClosedIicTopology.isClosed_le' /-
+theorem ClosedIicTopology.isClosed_le' (a : α) : IsClosed {b | b ≤ a} :=
   isClosed_le continuous_id continuous_const
-#align is_closed_le' isClosed_le'
+#align is_closed_le' ClosedIicTopology.isClosed_le'
 -/
 
 #print isClosed_Iic /-
 theorem isClosed_Iic {a : α} : IsClosed (Iic a) :=
-  isClosed_le' a
+  ClosedIicTopology.isClosed_le' a
 #align is_closed_Iic isClosed_Iic
 -/
 
-#print isClosed_ge' /-
-theorem isClosed_ge' (a : α) : IsClosed {b | a ≤ b} :=
+#print ClosedIciTopology.isClosed_ge' /-
+theorem ClosedIciTopology.isClosed_ge' (a : α) : IsClosed {b | a ≤ b} :=
   isClosed_le continuous_const continuous_id
-#align is_closed_ge' isClosed_ge'
+#align is_closed_ge' ClosedIciTopology.isClosed_ge'
 -/
 
 #print isClosed_Ici /-
 theorem isClosed_Ici {a : α} : IsClosed (Ici a) :=
-  isClosed_ge' a
+  ClosedIciTopology.isClosed_ge' a
 #align is_closed_Ici isClosed_Ici
 -/
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-
-! This file was ported from Lean 3 source module topology.order.basic
-! leanprover-community/mathlib commit 3efd324a3a31eaa40c9d5bfc669c4fafee5f9423
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Set.Intervals.Pi
 import Mathbin.Data.Set.Pointwise.Interval
@@ -14,6 +9,8 @@ import Mathbin.Order.Filter.Interval
 import Mathbin.Topology.Support
 import Mathbin.Topology.Algebra.Order.LeftRight
 
+#align_import topology.order.basic from "leanprover-community/mathlib"@"3efd324a3a31eaa40c9d5bfc669c4fafee5f9423"
+
 /-!
 # Theory of topology on ordered spaces
 
@@ -3278,7 +3275,7 @@ instance (x : α) [Nontrivial α] : NeBot (𝓝[≠] x) :=
   obtain ⟨z, hz⟩ : ∃ z, a < z ∧ z < x := exists_between hy.1
   exact ⟨z, us ⟨hab ⟨hz.1, hz.2.trans hy.2⟩, hz.2.Ne⟩⟩
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print Dense.exists_countable_dense_subset_no_bot_top /-
 /-- Let `s` be a dense set in a nontrivial dense linear order `α`. If `s` is a
 separable space (e.g., if `α` has a second countable topology), then there exists a countable

mathlib commit https://github.com/leanprover-community/mathlib/commit/6285167a053ad0990fc88e56c48ccd9fae6550eb

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module topology.order.basic
-! leanprover-community/mathlib commit c985ae9840e06836a71db38de372f20acb49b790
+! leanprover-community/mathlib commit 3efd324a3a31eaa40c9d5bfc669c4fafee5f9423
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -983,66 +983,6 @@ theorem Dense.exists_between [DenselyOrdered α] {s : Set α} (hs : Dense s) {x
 #align dense.exists_between Dense.exists_between
 -/
 
-variable [Nonempty α] [TopologicalSpace β]
-
-#print IsCompact.bddBelow /-
-/-- A compact set is bounded below -/
-theorem IsCompact.bddBelow {s : Set α} (hs : IsCompact s) : BddBelow s :=
-  by
-  by_contra H
-  rcases hs.elim_finite_subcover_image (fun x (_ : x ∈ s) => @isOpen_Ioi _ _ _ _ x) _ with
-    ⟨t, st, ft, ht⟩
-  · refine' H (ft.bdd_below.imp fun C hC y hy => _)
-    rcases mem_Union₂.1 (ht hy) with ⟨x, hx, xy⟩
-    exact le_trans (hC hx) (le_of_lt xy)
-  · refine' fun x hx => mem_Union₂.2 (not_imp_comm.1 _ H)
-    exact fun h => ⟨x, fun y hy => le_of_not_lt (h.imp fun ys => ⟨_, hy, ys⟩)⟩
-#align is_compact.bdd_below IsCompact.bddBelow
--/
-
-#print IsCompact.bddAbove /-
-/-- A compact set is bounded above -/
-theorem IsCompact.bddAbove {s : Set α} (hs : IsCompact s) : BddAbove s :=
-  @IsCompact.bddBelow αᵒᵈ _ _ _ _ _ hs
-#align is_compact.bdd_above IsCompact.bddAbove
--/
-
-#print IsCompact.bddBelow_image /-
-/-- A continuous function is bounded below on a compact set. -/
-theorem IsCompact.bddBelow_image {f : β → α} {K : Set β} (hK : IsCompact K)
-    (hf : ContinuousOn f K) : BddBelow (f '' K) :=
-  (hK.image_of_continuousOn hf).BddBelow
-#align is_compact.bdd_below_image IsCompact.bddBelow_image
--/
-
-#print IsCompact.bddAbove_image /-
-/-- A continuous function is bounded above on a compact set. -/
-theorem IsCompact.bddAbove_image {f : β → α} {K : Set β} (hK : IsCompact K)
-    (hf : ContinuousOn f K) : BddAbove (f '' K) :=
-  @IsCompact.bddBelow_image αᵒᵈ _ _ _ _ _ _ _ _ hK hf
-#align is_compact.bdd_above_image IsCompact.bddAbove_image
--/
-
-#print Continuous.bddBelow_range_of_hasCompactMulSupport /-
-/-- A continuous function with compact support is bounded below. -/
-@[to_additive " A continuous function with compact support is bounded below. "]
-theorem Continuous.bddBelow_range_of_hasCompactMulSupport [One α] {f : β → α} (hf : Continuous f)
-    (h : HasCompactMulSupport f) : BddBelow (range f) :=
-  (h.isCompact_range hf).BddBelow
-#align continuous.bdd_below_range_of_has_compact_mul_support Continuous.bddBelow_range_of_hasCompactMulSupport
-#align continuous.bdd_below_range_of_has_compact_support Continuous.bddBelow_range_of_hasCompactSupport
--/
-
-#print Continuous.bddAbove_range_of_hasCompactMulSupport /-
-/-- A continuous function with compact support is bounded above. -/
-@[to_additive " A continuous function with compact support is bounded above. "]
-theorem Continuous.bddAbove_range_of_hasCompactMulSupport [One α] {f : β → α} (hf : Continuous f)
-    (h : HasCompactMulSupport f) : BddAbove (range f) :=
-  @Continuous.bddBelow_range_of_hasCompactMulSupport αᵒᵈ _ _ _ _ _ _ _ _ hf h
-#align continuous.bdd_above_range_of_has_compact_mul_support Continuous.bddAbove_range_of_hasCompactMulSupport
-#align continuous.bdd_above_range_of_has_compact_support Continuous.bddAbove_range_of_hasCompactSupport
--/
-
 end LinearOrder
 
 end OrderClosedTopology

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

@@ -124,8 +124,6 @@ section Preorder
 
 variable [TopologicalSpace α] [Preorder α] [t : OrderClosedTopology α]
 
-include t
-
 namespace Subtype
 
 instance {p : α → Prop} : OrderClosedTopology (Subtype p) :=
@@ -136,9 +134,11 @@ instance {p : α → Prop} : OrderClosedTopology (Subtype p) :=
 
 end Subtype
 
+#print isClosed_le_prod /-
 theorem isClosed_le_prod : IsClosed {p : α × α | p.1 ≤ p.2} :=
   t.isClosed_le'
 #align is_closed_le_prod isClosed_le_prod
+-/
 
 #print isClosed_le /-
 theorem isClosed_le [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
@@ -290,17 +290,19 @@ theorem le_on_closure [TopologicalSpace β] {f g : β → α} {s : Set β} (h :
 #align le_on_closure le_on_closure
 -/
 
+#print IsClosed.epigraph /-
 theorem IsClosed.epigraph [TopologicalSpace β] {f : β → α} {s : Set β} (hs : IsClosed s)
     (hf : ContinuousOn f s) : IsClosed {p : β × α | p.1 ∈ s ∧ f p.1 ≤ p.2} :=
   (hs.Preimage continuous_fst).isClosed_le (hf.comp continuousOn_fst Subset.rfl) continuousOn_snd
 #align is_closed.epigraph IsClosed.epigraph
+-/
 
+#print IsClosed.hypograph /-
 theorem IsClosed.hypograph [TopologicalSpace β] {f : β → α} {s : Set β} (hs : IsClosed s)
     (hf : ContinuousOn f s) : IsClosed {p : β × α | p.1 ∈ s ∧ p.2 ≤ f p.1} :=
   (hs.Preimage continuous_fst).isClosed_le continuousOn_snd (hf.comp continuousOn_fst Subset.rfl)
 #align is_closed.hypograph IsClosed.hypograph
-
-omit t
+-/
 
 #print nhdsWithin_Ici_neBot /-
 theorem nhdsWithin_Ici_neBot {a b : α} (H₂ : a ≤ b) : NeBot (𝓝[Ici a] b) :=
@@ -334,8 +336,6 @@ section PartialOrder
 
 variable [TopologicalSpace α] [PartialOrder α] [t : OrderClosedTopology α]
 
-include t
-
 #print OrderClosedTopology.to_t2Space /-
 -- see Note [lower instance priority]
 instance (priority := 90) OrderClosedTopology.to_t2Space : T2Space α :=
@@ -351,11 +351,13 @@ section LinearOrder
 
 variable [TopologicalSpace α] [LinearOrder α] [OrderClosedTopology α]
 
+#print isOpen_lt_prod /-
 theorem isOpen_lt_prod : IsOpen {p : α × α | p.1 < p.2} :=
   by
   simp_rw [← isClosed_compl_iff, compl_set_of, not_lt]
   exact isClosed_le continuous_snd continuous_fst
 #align is_open_lt_prod isOpen_lt_prod
+-/
 
 #print isOpen_lt /-
 theorem isOpen_lt [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
@@ -831,95 +833,132 @@ theorem ContinuousAt.eventually_lt {x₀ : β} (hf : ContinuousAt f x₀) (hg :
 #align continuous_at.eventually_lt ContinuousAt.eventually_lt
 -/
 
+#print Continuous.min /-
 @[continuity]
 theorem Continuous.min (hf : Continuous f) (hg : Continuous g) :
     Continuous fun b => min (f b) (g b) := by simp only [min_def];
   exact hf.if_le hg hf hg fun x => id
 #align continuous.min Continuous.min
+-/
 
+#print Continuous.max /-
 @[continuity]
 theorem Continuous.max (hf : Continuous f) (hg : Continuous g) :
     Continuous fun b => max (f b) (g b) :=
   @Continuous.min αᵒᵈ _ _ _ _ _ _ _ hf hg
 #align continuous.max Continuous.max
+-/
 
 end
 
+#print continuous_min /-
 theorem continuous_min : Continuous fun p : α × α => min p.1 p.2 :=
   continuous_fst.min continuous_snd
 #align continuous_min continuous_min
+-/
 
+#print continuous_max /-
 theorem continuous_max : Continuous fun p : α × α => max p.1 p.2 :=
   continuous_fst.max continuous_snd
 #align continuous_max continuous_max
+-/
 
+#print Filter.Tendsto.max /-
 theorem Filter.Tendsto.max {b : Filter β} {a₁ a₂ : α} (hf : Tendsto f b (𝓝 a₁))
     (hg : Tendsto g b (𝓝 a₂)) : Tendsto (fun b => max (f b) (g b)) b (𝓝 (max a₁ a₂)) :=
   (continuous_max.Tendsto (a₁, a₂)).comp (hf.prod_mk_nhds hg)
 #align filter.tendsto.max Filter.Tendsto.max
+-/
 
+#print Filter.Tendsto.min /-
 theorem Filter.Tendsto.min {b : Filter β} {a₁ a₂ : α} (hf : Tendsto f b (𝓝 a₁))
     (hg : Tendsto g b (𝓝 a₂)) : Tendsto (fun b => min (f b) (g b)) b (𝓝 (min a₁ a₂)) :=
   (continuous_min.Tendsto (a₁, a₂)).comp (hf.prod_mk_nhds hg)
 #align filter.tendsto.min Filter.Tendsto.min
+-/
 
+#print Filter.Tendsto.max_right /-
 theorem Filter.Tendsto.max_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
     Tendsto (fun i => max a (f i)) l (𝓝 a) := by
   convert ((continuous_max.comp (@Continuous.Prod.mk α α _ _ a)).Tendsto a).comp h; simp
 #align filter.tendsto.max_right Filter.Tendsto.max_right
+-/
 
+#print Filter.Tendsto.max_left /-
 theorem Filter.Tendsto.max_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
     Tendsto (fun i => max (f i) a) l (𝓝 a) := by simp_rw [max_comm _ a]; exact h.max_right
 #align filter.tendsto.max_left Filter.Tendsto.max_left
+-/
 
+#print Filter.tendsto_nhds_max_right /-
 theorem Filter.tendsto_nhds_max_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝[>] a)) :
     Tendsto (fun i => max a (f i)) l (𝓝[>] a) :=
   by
   obtain ⟨h₁ : tendsto f l (𝓝 a), h₂ : ∀ᶠ i in l, f i ∈ Ioi a⟩ := tendsto_nhds_within_iff.mp h
   exact tendsto_nhds_within_iff.mpr ⟨h₁.max_right, h₂.mono fun i hi => lt_max_of_lt_right hi⟩
 #align filter.tendsto_nhds_max_right Filter.tendsto_nhds_max_right
+-/
 
+#print Filter.tendsto_nhds_max_left /-
 theorem Filter.tendsto_nhds_max_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝[>] a)) :
     Tendsto (fun i => max (f i) a) l (𝓝[>] a) := by simp_rw [max_comm _ a];
   exact Filter.tendsto_nhds_max_right h
 #align filter.tendsto_nhds_max_left Filter.tendsto_nhds_max_left
+-/
 
+#print Filter.Tendsto.min_right /-
 theorem Filter.Tendsto.min_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
     Tendsto (fun i => min a (f i)) l (𝓝 a) :=
   @Filter.Tendsto.max_right αᵒᵈ β _ _ _ f l a h
 #align filter.tendsto.min_right Filter.Tendsto.min_right
+-/
 
+#print Filter.Tendsto.min_left /-
 theorem Filter.Tendsto.min_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
     Tendsto (fun i => min (f i) a) l (𝓝 a) :=
   @Filter.Tendsto.max_left αᵒᵈ β _ _ _ f l a h
 #align filter.tendsto.min_left Filter.Tendsto.min_left
+-/
 
+#print Filter.tendsto_nhds_min_right /-
 theorem Filter.tendsto_nhds_min_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝[<] a)) :
     Tendsto (fun i => min a (f i)) l (𝓝[<] a) :=
   @Filter.tendsto_nhds_max_right αᵒᵈ β _ _ _ f l a h
 #align filter.tendsto_nhds_min_right Filter.tendsto_nhds_min_right
+-/
 
+#print Filter.tendsto_nhds_min_left /-
 theorem Filter.tendsto_nhds_min_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝[<] a)) :
     Tendsto (fun i => min (f i) a) l (𝓝[<] a) :=
   @Filter.tendsto_nhds_max_left αᵒᵈ β _ _ _ f l a h
 #align filter.tendsto_nhds_min_left Filter.tendsto_nhds_min_left
+-/
 
+#print Dense.exists_lt /-
 theorem Dense.exists_lt [NoMinOrder α] {s : Set α} (hs : Dense s) (x : α) : ∃ y ∈ s, y < x :=
   hs.exists_mem_open isOpen_Iio (exists_lt x)
 #align dense.exists_lt Dense.exists_lt
+-/
 
+#print Dense.exists_gt /-
 theorem Dense.exists_gt [NoMaxOrder α] {s : Set α} (hs : Dense s) (x : α) : ∃ y ∈ s, x < y :=
   hs.OrderDual.exists_lt x
 #align dense.exists_gt Dense.exists_gt
+-/
 
+#print Dense.exists_le /-
 theorem Dense.exists_le [NoMinOrder α] {s : Set α} (hs : Dense s) (x : α) : ∃ y ∈ s, y ≤ x :=
   (hs.exists_lt x).imp fun y hy => ⟨hy.fst, hy.snd.le⟩
 #align dense.exists_le Dense.exists_le
+-/
 
+#print Dense.exists_ge /-
 theorem Dense.exists_ge [NoMaxOrder α] {s : Set α} (hs : Dense s) (x : α) : ∃ y ∈ s, x ≤ y :=
   hs.OrderDual.exists_le x
 #align dense.exists_ge Dense.exists_ge
+-/
 
+#print Dense.exists_le' /-
 theorem Dense.exists_le' {s : Set α} (hs : Dense s) (hbot : ∀ x, IsBot x → x ∈ s) (x : α) :
     ∃ y ∈ s, y ≤ x := by
   by_cases hx : IsBot x
@@ -928,16 +967,21 @@ theorem Dense.exists_le' {s : Set α} (hs : Dense s) (hbot : ∀ x, IsBot x →
     rcases hs.exists_mem_open isOpen_Iio hx with ⟨y, hys, hy : y < x⟩
     exact ⟨y, hys, hy.le⟩
 #align dense.exists_le' Dense.exists_le'
+-/
 
+#print Dense.exists_ge' /-
 theorem Dense.exists_ge' {s : Set α} (hs : Dense s) (htop : ∀ x, IsTop x → x ∈ s) (x : α) :
     ∃ y ∈ s, x ≤ y :=
   hs.OrderDual.exists_le' htop x
 #align dense.exists_ge' Dense.exists_ge'
+-/
 
+#print Dense.exists_between /-
 theorem Dense.exists_between [DenselyOrdered α] {s : Set α} (hs : Dense s) {x y : α} (h : x < y) :
     ∃ z ∈ s, z ∈ Ioo x y :=
   hs.exists_mem_open isOpen_Ioo (nonempty_Ioo.2 h)
 #align dense.exists_between Dense.exists_between
+-/
 
 variable [Nonempty α] [TopologicalSpace β]
 
@@ -1051,8 +1095,6 @@ section Preorder
 
 variable [TopologicalSpace α] [Preorder α] [t : OrderTopology α]
 
-include t
-
 instance : OrderTopology αᵒᵈ :=
   ⟨by
     convert @OrderTopology.topology_eq_generate_intervals α _ _ _ <;>
@@ -1102,6 +1144,7 @@ theorem ge_mem_nhds {a b : α} (h : a < b) : ∀ᶠ x in 𝓝 a, x ≤ b :=
 #align ge_mem_nhds ge_mem_nhds
 -/
 
+#print nhds_eq_order /-
 theorem nhds_eq_order (a : α) : 𝓝 a = (⨅ b ∈ Iio a, 𝓟 (Ioi b)) ⊓ ⨅ b ∈ Ioi a, 𝓟 (Iio b) := by
   rw [t.topology_eq_generate_intervals, nhds_generate_from] <;>
     exact
@@ -1115,6 +1158,7 @@ theorem nhds_eq_order (a : α) : 𝓝 a = (⨅ b ∈ Iio a, 𝓟 (Ioi b)) ⊓ 
             | _, h, Or.inl rfl => inf_le_of_left_le <| iInf_le_of_le b <| iInf_le _ h
             | _, h, Or.inr rfl => inf_le_of_right_le <| iInf_le_of_le b <| iInf_le _ h)
 #align nhds_eq_order nhds_eq_order
+-/
 
 #print tendsto_order /-
 theorem tendsto_order {f : β → α} {a : α} {x : Filter β} :
@@ -1174,6 +1218,7 @@ theorem tendsto_of_tendsto_of_tendsto_of_le_of_le {f g h : β → α} {b : Filte
 #align tendsto_of_tendsto_of_tendsto_of_le_of_le tendsto_of_tendsto_of_tendsto_of_le_of_le
 -/
 
+#print nhds_order_unbounded /-
 theorem nhds_order_unbounded {a : α} (hu : ∃ u, a < u) (hl : ∃ l, l < a) :
     𝓝 a = ⨅ (l) (h₂ : l < a) (u) (h₂ : a < u), 𝓟 (Ioo l u) :=
   by
@@ -1182,6 +1227,7 @@ theorem nhds_order_unbounded {a : α} (hu : ∃ u, a < u) (hl : ∃ l, l < a) :
   simp only [nhds_eq_order, inf_biInf, biInf_inf, *, inf_principal, Ioi_inter_Iio]
   rfl
 #align nhds_order_unbounded nhds_order_unbounded
+-/
 
 #print tendsto_order_unbounded /-
 theorem tendsto_order_unbounded {f : β → α} {a : α} {x : Filter β} (hu : ∃ u, a < u)
@@ -1220,6 +1266,7 @@ instance tendstoIccClassNhdsPi {ι : Type _} {α : ι → Type _} [∀ i, Preord
 #align tendsto_Icc_class_nhds_pi tendstoIccClassNhdsPi
 -/
 
+#print induced_orderTopology' /-
 theorem induced_orderTopology' {α : Type u} {β : Type v} [Preorder α] [ta : TopologicalSpace β]
     [Preorder β] [OrderTopology β] (f : α → β) (hf : ∀ {x y}, f x < f y ↔ x < y)
     (H₁ : ∀ {a x}, x < f a → ∃ b < a, x ≤ f b) (H₂ : ∀ {a x}, f a < x → ∃ b > a, f b ≤ x) :
@@ -1254,6 +1301,7 @@ theorem induced_orderTopology' {α : Type u} {β : Type v} [Preorder α] [ta : T
       refine' mem_infi_of_mem _ (mem_infi_of_mem ⟨ab, b, Or.inr rfl⟩ (mem_principal.2 _))
       exact fun c hc => lt_of_lt_of_le (hf.2 hc) xb
 #align induced_order_topology' induced_orderTopology'
+-/
 
 #print induced_orderTopology /-
 theorem induced_orderTopology {α : Type u} {β : Type v} [Preorder α] [ta : TopologicalSpace β]
@@ -1318,6 +1366,7 @@ instance orderTopology_of_ordConnected {α : Type u} [ta : TopologicalSpace α]
 #align order_topology_of_ord_connected orderTopology_of_ordConnected
 -/
 
+#print nhdsWithin_Ici_eq'' /-
 theorem nhdsWithin_Ici_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology α] (a : α) :
     𝓝[≥] a = (⨅ (u) (hu : a < u), 𝓟 (Iio u)) ⊓ 𝓟 (Ici a) :=
   by
@@ -1325,21 +1374,28 @@ theorem nhdsWithin_Ici_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology 
   refine' le_antisymm (inf_le_inf_right _ inf_le_right) (le_inf (le_inf _ inf_le_left) inf_le_right)
   exact inf_le_right.trans (le_iInf₂ fun l hl => principal_mono.2 <| Ici_subset_Ioi.2 hl)
 #align nhds_within_Ici_eq'' nhdsWithin_Ici_eq''
+-/
 
+#print nhdsWithin_Iic_eq'' /-
 theorem nhdsWithin_Iic_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology α] (a : α) :
     𝓝[≤] a = (⨅ l < a, 𝓟 (Ioi l)) ⊓ 𝓟 (Iic a) :=
   nhdsWithin_Ici_eq'' (toDual a)
 #align nhds_within_Iic_eq'' nhdsWithin_Iic_eq''
+-/
 
+#print nhdsWithin_Ici_eq' /-
 theorem nhdsWithin_Ici_eq' [TopologicalSpace α] [Preorder α] [OrderTopology α] {a : α}
     (ha : ∃ u, a < u) : 𝓝[≥] a = ⨅ (u) (hu : a < u), 𝓟 (Ico a u) := by
   simp only [nhdsWithin_Ici_eq'', biInf_inf ha, inf_principal, Iio_inter_Ici]
 #align nhds_within_Ici_eq' nhdsWithin_Ici_eq'
+-/
 
+#print nhdsWithin_Iic_eq' /-
 theorem nhdsWithin_Iic_eq' [TopologicalSpace α] [Preorder α] [OrderTopology α] {a : α}
     (ha : ∃ l, l < a) : 𝓝[≤] a = ⨅ l < a, 𝓟 (Ioc l a) := by
   simp only [nhdsWithin_Iic_eq'', biInf_inf ha, inf_principal, Ioi_inter_Iic]
 #align nhds_within_Iic_eq' nhdsWithin_Iic_eq'
+-/
 
 #print nhdsWithin_Ici_basis' /-
 theorem nhdsWithin_Ici_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopology α] {a : α}
@@ -1376,26 +1432,35 @@ theorem nhdsWithin_Iic_basis [TopologicalSpace α] [LinearOrder α] [OrderTopolo
 #align nhds_within_Iic_basis nhdsWithin_Iic_basis
 -/
 
+#print nhds_top_order /-
 theorem nhds_top_order [TopologicalSpace α] [Preorder α] [OrderTop α] [OrderTopology α] :
     𝓝 (⊤ : α) = ⨅ (l) (h₂ : l < ⊤), 𝓟 (Ioi l) := by simp [nhds_eq_order (⊤ : α)]
 #align nhds_top_order nhds_top_order
+-/
 
+#print nhds_bot_order /-
 theorem nhds_bot_order [TopologicalSpace α] [Preorder α] [OrderBot α] [OrderTopology α] :
     𝓝 (⊥ : α) = ⨅ (l) (h₂ : ⊥ < l), 𝓟 (Iio l) := by simp [nhds_eq_order (⊥ : α)]
 #align nhds_bot_order nhds_bot_order
+-/
 
+#print nhds_top_basis /-
 theorem nhds_top_basis [TopologicalSpace α] [LinearOrder α] [OrderTop α] [OrderTopology α]
     [Nontrivial α] : (𝓝 ⊤).HasBasis (fun a : α => a < ⊤) fun a : α => Ioi a :=
   by
   have : ∃ x : α, x < ⊤ := (exists_ne ⊤).imp fun x hx => hx.lt_top
   simpa only [Iic_top, nhdsWithin_univ, Ioc_top] using nhdsWithin_Iic_basis' this
 #align nhds_top_basis nhds_top_basis
+-/
 
+#print nhds_bot_basis /-
 theorem nhds_bot_basis [TopologicalSpace α] [LinearOrder α] [OrderBot α] [OrderTopology α]
     [Nontrivial α] : (𝓝 ⊥).HasBasis (fun a : α => ⊥ < a) fun a : α => Iio a :=
   @nhds_top_basis αᵒᵈ _ _ _ _ _
 #align nhds_bot_basis nhds_bot_basis
+-/
 
+#print nhds_top_basis_Ici /-
 theorem nhds_top_basis_Ici [TopologicalSpace α] [LinearOrder α] [OrderTop α] [OrderTopology α]
     [Nontrivial α] [DenselyOrdered α] : (𝓝 ⊤).HasBasis (fun a : α => a < ⊤) Ici :=
   nhds_top_basis.to_hasBasis
@@ -1404,12 +1469,16 @@ theorem nhds_top_basis_Ici [TopologicalSpace α] [LinearOrder α] [OrderTop α]
       ⟨b, hb, Ici_subset_Ioi.mpr hab⟩)
     fun a ha => ⟨a, ha, Ioi_subset_Ici_self⟩
 #align nhds_top_basis_Ici nhds_top_basis_Ici
+-/
 
+#print nhds_bot_basis_Iic /-
 theorem nhds_bot_basis_Iic [TopologicalSpace α] [LinearOrder α] [OrderBot α] [OrderTopology α]
     [Nontrivial α] [DenselyOrdered α] : (𝓝 ⊥).HasBasis (fun a : α => ⊥ < a) Iic :=
   @nhds_top_basis_Ici αᵒᵈ _ _ _ _ _ _
 #align nhds_bot_basis_Iic nhds_bot_basis_Iic
+-/
 
+#print tendsto_nhds_top_mono /-
 theorem tendsto_nhds_top_mono [TopologicalSpace β] [Preorder β] [OrderTop β] [OrderTopology β]
     {l : Filter α} {f g : α → β} (hf : Tendsto f l (𝓝 ⊤)) (hg : f ≤ᶠ[l] g) : Tendsto g l (𝓝 ⊤) :=
   by
@@ -1417,21 +1486,28 @@ theorem tendsto_nhds_top_mono [TopologicalSpace β] [Preorder β] [OrderTop β]
   intro x hx
   filter_upwards [hf x hx, hg] with _ using lt_of_lt_of_le
 #align tendsto_nhds_top_mono tendsto_nhds_top_mono
+-/
 
+#print tendsto_nhds_bot_mono /-
 theorem tendsto_nhds_bot_mono [TopologicalSpace β] [Preorder β] [OrderBot β] [OrderTopology β]
     {l : Filter α} {f g : α → β} (hf : Tendsto f l (𝓝 ⊥)) (hg : g ≤ᶠ[l] f) : Tendsto g l (𝓝 ⊥) :=
   @tendsto_nhds_top_mono α βᵒᵈ _ _ _ _ _ _ _ hf hg
 #align tendsto_nhds_bot_mono tendsto_nhds_bot_mono
+-/
 
+#print tendsto_nhds_top_mono' /-
 theorem tendsto_nhds_top_mono' [TopologicalSpace β] [Preorder β] [OrderTop β] [OrderTopology β]
     {l : Filter α} {f g : α → β} (hf : Tendsto f l (𝓝 ⊤)) (hg : f ≤ g) : Tendsto g l (𝓝 ⊤) :=
   tendsto_nhds_top_mono hf (eventually_of_forall hg)
 #align tendsto_nhds_top_mono' tendsto_nhds_top_mono'
+-/
 
+#print tendsto_nhds_bot_mono' /-
 theorem tendsto_nhds_bot_mono' [TopologicalSpace β] [Preorder β] [OrderBot β] [OrderTopology β]
     {l : Filter α} {f g : α → β} (hf : Tendsto f l (𝓝 ⊥)) (hg : g ≤ f) : Tendsto g l (𝓝 ⊥) :=
   tendsto_nhds_bot_mono hf (eventually_of_forall hg)
 #align tendsto_nhds_bot_mono' tendsto_nhds_bot_mono'
+-/
 
 section LinearOrder
 
@@ -1499,31 +1575,40 @@ instance (priority := 100) OrderTopology.to_orderClosedTopology : OrderClosedTop
 #align order_topology.to_order_closed_topology OrderTopology.to_orderClosedTopology
 -/
 
+#print exists_Ioc_subset_of_mem_nhds /-
 theorem exists_Ioc_subset_of_mem_nhds {a : α} {s : Set α} (hs : s ∈ 𝓝 a) (h : ∃ l, l < a) :
     ∃ l < a, Ioc l a ⊆ s :=
   (nhdsWithin_Iic_basis' h).mem_iff.mp (nhdsWithin_le_nhds hs)
 #align exists_Ioc_subset_of_mem_nhds exists_Ioc_subset_of_mem_nhds
+-/
 
+#print exists_Ioc_subset_of_mem_nhds' /-
 theorem exists_Ioc_subset_of_mem_nhds' {a : α} {s : Set α} (hs : s ∈ 𝓝 a) {l : α} (hl : l < a) :
     ∃ l' ∈ Ico l a, Ioc l' a ⊆ s :=
   let ⟨l', hl'a, hl's⟩ := exists_Ioc_subset_of_mem_nhds hs ⟨l, hl⟩
   ⟨max l l', ⟨le_max_left _ _, max_lt hl hl'a⟩,
     (Ioc_subset_Ioc_left <| le_max_right _ _).trans hl's⟩
 #align exists_Ioc_subset_of_mem_nhds' exists_Ioc_subset_of_mem_nhds'
+-/
 
+#print exists_Ico_subset_of_mem_nhds' /-
 theorem exists_Ico_subset_of_mem_nhds' {a : α} {s : Set α} (hs : s ∈ 𝓝 a) {u : α} (hu : a < u) :
     ∃ u' ∈ Ioc a u, Ico a u' ⊆ s := by
   simpa only [OrderDual.exists, exists_prop, dual_Ico, dual_Ioc] using
     exists_Ioc_subset_of_mem_nhds' (show of_dual ⁻¹' s ∈ 𝓝 (to_dual a) from hs) hu.dual
 #align exists_Ico_subset_of_mem_nhds' exists_Ico_subset_of_mem_nhds'
+-/
 
+#print exists_Ico_subset_of_mem_nhds /-
 theorem exists_Ico_subset_of_mem_nhds {a : α} {s : Set α} (hs : s ∈ 𝓝 a) (h : ∃ u, a < u) :
     ∃ (u : _) (_ : a < u), Ico a u ⊆ s :=
   let ⟨l', hl'⟩ := h
   let ⟨l, hl⟩ := exists_Ico_subset_of_mem_nhds' hs hl'
   ⟨l, hl.fst.1, hl.snd⟩
 #align exists_Ico_subset_of_mem_nhds exists_Ico_subset_of_mem_nhds
+-/
 
+#print exists_Icc_mem_subset_of_mem_nhdsWithin_Ici /-
 theorem exists_Icc_mem_subset_of_mem_nhdsWithin_Ici {a : α} {s : Set α} (hs : s ∈ 𝓝[≥] a) :
     ∃ (b : _) (_ : a ≤ b), Icc a b ∈ 𝓝[≥] a ∧ Icc a b ⊆ s :=
   by
@@ -1536,12 +1621,15 @@ theorem exists_Icc_mem_subset_of_mem_nhdsWithin_Ici {a : α} {s : Set α} (hs :
     · refine' ⟨c, hac.le, Icc_mem_nhdsWithin_Ici <| left_mem_Ico.mpr hac, _⟩
       exact (Icc_subset_Ico_right hcb).trans hbs
 #align exists_Icc_mem_subset_of_mem_nhds_within_Ici exists_Icc_mem_subset_of_mem_nhdsWithin_Ici
+-/
 
+#print exists_Icc_mem_subset_of_mem_nhdsWithin_Iic /-
 theorem exists_Icc_mem_subset_of_mem_nhdsWithin_Iic {a : α} {s : Set α} (hs : s ∈ 𝓝[≤] a) :
     ∃ b ≤ a, Icc b a ∈ 𝓝[≤] a ∧ Icc b a ⊆ s := by
   simpa only [dual_Icc, to_dual.surjective.exists] using
     @exists_Icc_mem_subset_of_mem_nhdsWithin_Ici αᵒᵈ _ _ _ (to_dual a) _ hs
 #align exists_Icc_mem_subset_of_mem_nhds_within_Iic exists_Icc_mem_subset_of_mem_nhdsWithin_Iic
+-/
 
 #print exists_Icc_mem_subset_of_mem_nhds /-
 theorem exists_Icc_mem_subset_of_mem_nhds {a : α} {s : Set α} (hs : s ∈ 𝓝 a) :
@@ -1574,6 +1662,7 @@ theorem IsOpen.exists_Ioo_subset [Nontrivial α] {s : Set α} (hs : IsOpen s) (h
 #align is_open.exists_Ioo_subset IsOpen.exists_Ioo_subset
 -/
 
+#print dense_of_exists_between /-
 theorem dense_of_exists_between [Nontrivial α] {s : Set α}
     (h : ∀ ⦃a b⦄, a < b → ∃ c ∈ s, a < c ∧ c < b) : Dense s :=
   by
@@ -1582,7 +1671,9 @@ theorem dense_of_exists_between [Nontrivial α] {s : Set α}
   obtain ⟨x, xs, hx⟩ : ∃ (x : α) (H : x ∈ s), a < x ∧ x < b := h hab
   exact ⟨x, ⟨H hx, xs⟩⟩
 #align dense_of_exists_between dense_of_exists_between
+-/
 
+#print dense_iff_exists_between /-
 /-- A set in a nontrivial densely linear ordered type is dense in the sense of topology if and only
 if for any `a < b` there exists `c ∈ s`, `a < c < b`. Each implication requires less typeclass
 assumptions. -/
@@ -1590,6 +1681,7 @@ theorem dense_iff_exists_between [DenselyOrdered α] [Nontrivial α] {s : Set α
     Dense s ↔ ∀ a b, a < b → ∃ c ∈ s, a < c ∧ c < b :=
   ⟨fun h a b hab => h.exists_between hab, dense_of_exists_between⟩
 #align dense_iff_exists_between dense_iff_exists_between
+-/
 
 #print mem_nhds_iff_exists_Ioo_subset' /-
 /-- A set is a neighborhood of `a` if and only if it contains an interval `(l, u)` containing `a`,
@@ -1714,6 +1806,7 @@ theorem countable_of_isolated_left' [SecondCountableTopology α] :
 #align countable_of_isolated_left countable_of_isolated_left'
 -/
 
+#print Set.PairwiseDisjoint.countable_of_Ioo /-
 /-- Consider a disjoint family of intervals `(x, y)` with `x < y` in a second-countable space.
 Then the family is countable.
 This is not a straightforward consequence of second-countability as some of these intervals might be
@@ -1733,6 +1826,7 @@ theorem Set.PairwiseDisjoint.countable_of_Ioo [SecondCountableTopology α] {y :
     · exact Or.inr ⟨y x, h' x hx, not_nonempty_iff_eq_empty.1 h'x⟩
   exact countable.mono this (t_count.union countable_of_isolated_right')
 #align set.pairwise_disjoint.countable_of_Ioo Set.PairwiseDisjoint.countable_of_Ioo
+-/
 
 section Pi
 
@@ -1754,9 +1848,11 @@ theorem pi_Iic_mem_nhds (ha : ∀ i, x i < a i) : Iic a ∈ 𝓝 x :=
 #align pi_Iic_mem_nhds pi_Iic_mem_nhds
 -/
 
+#print pi_Iic_mem_nhds' /-
 theorem pi_Iic_mem_nhds' (ha : ∀ i, x' i < a' i) : Iic a' ∈ 𝓝 x' :=
   pi_Iic_mem_nhds ha
 #align pi_Iic_mem_nhds' pi_Iic_mem_nhds'
+-/
 
 #print pi_Ici_mem_nhds /-
 theorem pi_Ici_mem_nhds (ha : ∀ i, a i < x i) : Ici a ∈ 𝓝 x :=
@@ -1764,9 +1860,11 @@ theorem pi_Ici_mem_nhds (ha : ∀ i, a i < x i) : Ici a ∈ 𝓝 x :=
 #align pi_Ici_mem_nhds pi_Ici_mem_nhds
 -/
 
+#print pi_Ici_mem_nhds' /-
 theorem pi_Ici_mem_nhds' (ha : ∀ i, a' i < x' i) : Ici a' ∈ 𝓝 x' :=
   pi_Ici_mem_nhds ha
 #align pi_Ici_mem_nhds' pi_Ici_mem_nhds'
+-/
 
 #print pi_Icc_mem_nhds /-
 theorem pi_Icc_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Icc a b ∈ 𝓝 x :=
@@ -1774,9 +1872,11 @@ theorem pi_Icc_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Icc a
 #align pi_Icc_mem_nhds pi_Icc_mem_nhds
 -/
 
+#print pi_Icc_mem_nhds' /-
 theorem pi_Icc_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : Icc a' b' ∈ 𝓝 x' :=
   pi_Icc_mem_nhds ha hb
 #align pi_Icc_mem_nhds' pi_Icc_mem_nhds'
+-/
 
 variable [Nonempty ι]
 
@@ -1788,9 +1888,11 @@ theorem pi_Iio_mem_nhds (ha : ∀ i, x i < a i) : Iio a ∈ 𝓝 x :=
 #align pi_Iio_mem_nhds pi_Iio_mem_nhds
 -/
 
+#print pi_Iio_mem_nhds' /-
 theorem pi_Iio_mem_nhds' (ha : ∀ i, x' i < a' i) : Iio a' ∈ 𝓝 x' :=
   pi_Iio_mem_nhds ha
 #align pi_Iio_mem_nhds' pi_Iio_mem_nhds'
+-/
 
 #print pi_Ioi_mem_nhds /-
 theorem pi_Ioi_mem_nhds (ha : ∀ i, a i < x i) : Ioi a ∈ 𝓝 x :=
@@ -1798,9 +1900,11 @@ theorem pi_Ioi_mem_nhds (ha : ∀ i, a i < x i) : Ioi a ∈ 𝓝 x :=
 #align pi_Ioi_mem_nhds pi_Ioi_mem_nhds
 -/
 
+#print pi_Ioi_mem_nhds' /-
 theorem pi_Ioi_mem_nhds' (ha : ∀ i, a' i < x' i) : Ioi a' ∈ 𝓝 x' :=
   pi_Ioi_mem_nhds ha
 #align pi_Ioi_mem_nhds' pi_Ioi_mem_nhds'
+-/
 
 #print pi_Ioc_mem_nhds /-
 theorem pi_Ioc_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Ioc a b ∈ 𝓝 x :=
@@ -1810,9 +1914,11 @@ theorem pi_Ioc_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Ioc a
 #align pi_Ioc_mem_nhds pi_Ioc_mem_nhds
 -/
 
+#print pi_Ioc_mem_nhds' /-
 theorem pi_Ioc_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : Ioc a' b' ∈ 𝓝 x' :=
   pi_Ioc_mem_nhds ha hb
 #align pi_Ioc_mem_nhds' pi_Ioc_mem_nhds'
+-/
 
 #print pi_Ico_mem_nhds /-
 theorem pi_Ico_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Ico a b ∈ 𝓝 x :=
@@ -1822,9 +1928,11 @@ theorem pi_Ico_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Ico a
 #align pi_Ico_mem_nhds pi_Ico_mem_nhds
 -/
 
+#print pi_Ico_mem_nhds' /-
 theorem pi_Ico_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : Ico a' b' ∈ 𝓝 x' :=
   pi_Ico_mem_nhds ha hb
 #align pi_Ico_mem_nhds' pi_Ico_mem_nhds'
+-/
 
 #print pi_Ioo_mem_nhds /-
 theorem pi_Ioo_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Ioo a b ∈ 𝓝 x :=
@@ -1834,32 +1942,42 @@ theorem pi_Ioo_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Ioo a
 #align pi_Ioo_mem_nhds pi_Ioo_mem_nhds
 -/
 
+#print pi_Ioo_mem_nhds' /-
 theorem pi_Ioo_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : Ioo a' b' ∈ 𝓝 x' :=
   pi_Ioo_mem_nhds ha hb
 #align pi_Ioo_mem_nhds' pi_Ioo_mem_nhds'
+-/
 
 end Pi
 
+#print disjoint_nhds_atTop /-
 theorem disjoint_nhds_atTop [NoMaxOrder α] (x : α) : Disjoint (𝓝 x) atTop :=
   by
   rcases exists_gt x with ⟨y, hy : x < y⟩
   refine' disjoint_of_disjoint_of_mem _ (Iio_mem_nhds hy) (mem_at_top y)
   exact disjoint_left.mpr fun z => not_le.2
 #align disjoint_nhds_at_top disjoint_nhds_atTop
+-/
 
+#print inf_nhds_atTop /-
 @[simp]
 theorem inf_nhds_atTop [NoMaxOrder α] (x : α) : 𝓝 x ⊓ atTop = ⊥ :=
   disjoint_iff.1 (disjoint_nhds_atTop x)
 #align inf_nhds_at_top inf_nhds_atTop
+-/
 
+#print disjoint_nhds_atBot /-
 theorem disjoint_nhds_atBot [NoMinOrder α] (x : α) : Disjoint (𝓝 x) atBot :=
   @disjoint_nhds_atTop αᵒᵈ _ _ _ _ x
 #align disjoint_nhds_at_bot disjoint_nhds_atBot
+-/
 
+#print inf_nhds_atBot /-
 @[simp]
 theorem inf_nhds_atBot [NoMinOrder α] (x : α) : 𝓝 x ⊓ atBot = ⊥ :=
   @inf_nhds_atTop αᵒᵈ _ _ _ _ x
 #align inf_nhds_at_bot inf_nhds_atBot
+-/
 
 #print not_tendsto_nhds_of_tendsto_atTop /-
 theorem not_tendsto_nhds_of_tendsto_atTop [NoMaxOrder α] {F : Filter β} [NeBot F] {f : β → α}
@@ -1897,6 +2015,7 @@ In an `order_topology`, such neighborhoods can be characterized as the sets cont
 intervals to the right or to the left of `a`. We give now these characterizations. -/
 
 
+#print TFAE_mem_nhdsWithin_Ioi /-
 -- NB: If you extend the list, append to the end please to avoid breaking the API
 /-- The following statements are equivalent:
 
@@ -1932,19 +2051,25 @@ theorem TFAE_mem_nhdsWithin_Ioi {a b : α} (hab : a < b) (s : Set α) :
     exact hx.1
   tfae_finish
 #align tfae_mem_nhds_within_Ioi TFAE_mem_nhdsWithin_Ioi
+-/
 
+#print mem_nhdsWithin_Ioi_iff_exists_mem_Ioc_Ioo_subset /-
 theorem mem_nhdsWithin_Ioi_iff_exists_mem_Ioc_Ioo_subset {a u' : α} {s : Set α} (hu' : a < u') :
     s ∈ 𝓝[>] a ↔ ∃ u ∈ Ioc a u', Ioo a u ⊆ s :=
   (TFAE_mem_nhdsWithin_Ioi hu' s).out 0 3
 #align mem_nhds_within_Ioi_iff_exists_mem_Ioc_Ioo_subset mem_nhdsWithin_Ioi_iff_exists_mem_Ioc_Ioo_subset
+-/
 
+#print mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' /-
 /-- A set is a neighborhood of `a` within `(a, +∞)` if and only if it contains an interval `(a, u)`
 with `a < u < u'`, provided `a` is not a top element. -/
 theorem mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' {a u' : α} {s : Set α} (hu' : a < u') :
     s ∈ 𝓝[>] a ↔ ∃ u ∈ Ioi a, Ioo a u ⊆ s :=
   (TFAE_mem_nhdsWithin_Ioi hu' s).out 0 4
 #align mem_nhds_within_Ioi_iff_exists_Ioo_subset' mem_nhdsWithin_Ioi_iff_exists_Ioo_subset'
+-/
 
+#print mem_nhdsWithin_Ioi_iff_exists_Ioo_subset /-
 /-- A set is a neighborhood of `a` within `(a, +∞)` if and only if it contains an interval `(a, u)`
 with `a < u`. -/
 theorem mem_nhdsWithin_Ioi_iff_exists_Ioo_subset [NoMaxOrder α] {a : α} {s : Set α} :
@@ -1952,7 +2077,9 @@ theorem mem_nhdsWithin_Ioi_iff_exists_Ioo_subset [NoMaxOrder α] {a : α} {s : S
   let ⟨u', hu'⟩ := exists_gt a
   mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' hu'
 #align mem_nhds_within_Ioi_iff_exists_Ioo_subset mem_nhdsWithin_Ioi_iff_exists_Ioo_subset
+-/
 
+#print mem_nhdsWithin_Ioi_iff_exists_Ioc_subset /-
 /-- A set is a neighborhood of `a` within `(a, +∞)` if and only if it contains an interval `(a, u]`
 with `a < u`. -/
 theorem mem_nhdsWithin_Ioi_iff_exists_Ioc_subset [NoMaxOrder α] [DenselyOrdered α] {a : α}
@@ -1966,7 +2093,9 @@ theorem mem_nhdsWithin_Ioi_iff_exists_Ioc_subset [NoMaxOrder α] [DenselyOrdered
   · rintro ⟨u, au, as⟩
     exact ⟨u, au, subset.trans Ioo_subset_Ioc_self as⟩
 #align mem_nhds_within_Ioi_iff_exists_Ioc_subset mem_nhdsWithin_Ioi_iff_exists_Ioc_subset
+-/
 
+#print TFAE_mem_nhdsWithin_Iio /-
 /-- The following statements are equivalent:
 
 0. `s` is a neighborhood of `b` within `(-∞, b)`
@@ -1987,19 +2116,25 @@ theorem TFAE_mem_nhdsWithin_Iio {a b : α} (h : a < b) (s : Set α) :
   simpa only [exists_prop, OrderDual.exists, dual_Ioi, dual_Ioc, dual_Ioo] using
     TFAE_mem_nhdsWithin_Ioi h.dual (of_dual ⁻¹' s)
 #align tfae_mem_nhds_within_Iio TFAE_mem_nhdsWithin_Iio
+-/
 
+#print mem_nhdsWithin_Iio_iff_exists_mem_Ico_Ioo_subset /-
 theorem mem_nhdsWithin_Iio_iff_exists_mem_Ico_Ioo_subset {a l' : α} {s : Set α} (hl' : l' < a) :
     s ∈ 𝓝[<] a ↔ ∃ l ∈ Ico l' a, Ioo l a ⊆ s :=
   (TFAE_mem_nhdsWithin_Iio hl' s).out 0 3
 #align mem_nhds_within_Iio_iff_exists_mem_Ico_Ioo_subset mem_nhdsWithin_Iio_iff_exists_mem_Ico_Ioo_subset
+-/
 
+#print mem_nhdsWithin_Iio_iff_exists_Ioo_subset' /-
 /-- A set is a neighborhood of `a` within `(-∞, a)` if and only if it contains an interval `(l, a)`
 with `l < a`, provided `a` is not a bottom element. -/
 theorem mem_nhdsWithin_Iio_iff_exists_Ioo_subset' {a l' : α} {s : Set α} (hl' : l' < a) :
     s ∈ 𝓝[<] a ↔ ∃ l ∈ Iio a, Ioo l a ⊆ s :=
   (TFAE_mem_nhdsWithin_Iio hl' s).out 0 4
 #align mem_nhds_within_Iio_iff_exists_Ioo_subset' mem_nhdsWithin_Iio_iff_exists_Ioo_subset'
+-/
 
+#print mem_nhdsWithin_Iio_iff_exists_Ioo_subset /-
 /-- A set is a neighborhood of `a` within `(-∞, a)` if and only if it contains an interval `(l, a)`
 with `l < a`. -/
 theorem mem_nhdsWithin_Iio_iff_exists_Ioo_subset [NoMinOrder α] {a : α} {s : Set α} :
@@ -2007,7 +2142,9 @@ theorem mem_nhdsWithin_Iio_iff_exists_Ioo_subset [NoMinOrder α] {a : α} {s : S
   let ⟨l', hl'⟩ := exists_lt a
   mem_nhdsWithin_Iio_iff_exists_Ioo_subset' hl'
 #align mem_nhds_within_Iio_iff_exists_Ioo_subset mem_nhdsWithin_Iio_iff_exists_Ioo_subset
+-/
 
+#print mem_nhdsWithin_Iio_iff_exists_Ico_subset /-
 /-- A set is a neighborhood of `a` within `(-∞, a)` if and only if it contains an interval `[l, a)`
 with `l < a`. -/
 theorem mem_nhdsWithin_Iio_iff_exists_Ico_subset [NoMinOrder α] [DenselyOrdered α] {a : α}
@@ -2016,7 +2153,9 @@ theorem mem_nhdsWithin_Iio_iff_exists_Ico_subset [NoMinOrder α] [DenselyOrdered
   have : of_dual ⁻¹' s ∈ 𝓝[>] to_dual a ↔ _ := mem_nhdsWithin_Ioi_iff_exists_Ioc_subset
   simpa only [OrderDual.exists, exists_prop, dual_Ioc] using this
 #align mem_nhds_within_Iio_iff_exists_Ico_subset mem_nhdsWithin_Iio_iff_exists_Ico_subset
+-/
 
+#print TFAE_mem_nhdsWithin_Ici /-
 /-- The following statements are equivalent:
 
 0. `s` is a neighborhood of `a` within `[a, +∞)`
@@ -2047,19 +2186,25 @@ theorem TFAE_mem_nhdsWithin_Ici {a b : α} (hab : a < b) (s : Set α) :
         (Ico_subset_Ico_right <| min_le_left _ _).trans hus⟩
   tfae_finish
 #align tfae_mem_nhds_within_Ici TFAE_mem_nhdsWithin_Ici
+-/
 
+#print mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subset /-
 theorem mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subset {a u' : α} {s : Set α} (hu' : a < u') :
     s ∈ 𝓝[≥] a ↔ ∃ u ∈ Ioc a u', Ico a u ⊆ s :=
   (TFAE_mem_nhdsWithin_Ici hu' s).out 0 3 (by norm_num) (by norm_num)
 #align mem_nhds_within_Ici_iff_exists_mem_Ioc_Ico_subset mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subset
+-/
 
+#print mem_nhdsWithin_Ici_iff_exists_Ico_subset' /-
 /-- A set is a neighborhood of `a` within `[a, +∞)` if and only if it contains an interval `[a, u)`
 with `a < u < u'`, provided `a` is not a top element. -/
 theorem mem_nhdsWithin_Ici_iff_exists_Ico_subset' {a u' : α} {s : Set α} (hu' : a < u') :
     s ∈ 𝓝[≥] a ↔ ∃ u ∈ Ioi a, Ico a u ⊆ s :=
   (TFAE_mem_nhdsWithin_Ici hu' s).out 0 4 (by norm_num) (by norm_num)
 #align mem_nhds_within_Ici_iff_exists_Ico_subset' mem_nhdsWithin_Ici_iff_exists_Ico_subset'
+-/
 
+#print mem_nhdsWithin_Ici_iff_exists_Ico_subset /-
 /-- A set is a neighborhood of `a` within `[a, +∞)` if and only if it contains an interval `[a, u)`
 with `a < u`. -/
 theorem mem_nhdsWithin_Ici_iff_exists_Ico_subset [NoMaxOrder α] {a : α} {s : Set α} :
@@ -2067,6 +2212,7 @@ theorem mem_nhdsWithin_Ici_iff_exists_Ico_subset [NoMaxOrder α] {a : α} {s : S
   let ⟨u', hu'⟩ := exists_gt a
   mem_nhdsWithin_Ici_iff_exists_Ico_subset' hu'
 #align mem_nhds_within_Ici_iff_exists_Ico_subset mem_nhdsWithin_Ici_iff_exists_Ico_subset
+-/
 
 #print nhdsWithin_Ici_basis_Ico /-
 theorem nhdsWithin_Ici_basis_Ico [NoMaxOrder α] (a : α) :
@@ -2091,6 +2237,7 @@ theorem mem_nhdsWithin_Ici_iff_exists_Icc_subset [NoMaxOrder α] [DenselyOrdered
 #align mem_nhds_within_Ici_iff_exists_Icc_subset mem_nhdsWithin_Ici_iff_exists_Icc_subset
 -/
 
+#print TFAE_mem_nhdsWithin_Iic /-
 /-- The following statements are equivalent:
 
 0. `s` is a neighborhood of `b` within `(-∞, b]`
@@ -2111,19 +2258,25 @@ theorem TFAE_mem_nhdsWithin_Iic {a b : α} (h : a < b) (s : Set α) :
   simpa only [exists_prop, OrderDual.exists, dual_Ici, dual_Ioc, dual_Icc, dual_Ico] using
     TFAE_mem_nhdsWithin_Ici h.dual (of_dual ⁻¹' s)
 #align tfae_mem_nhds_within_Iic TFAE_mem_nhdsWithin_Iic
+-/
 
+#print mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subset /-
 theorem mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subset {a l' : α} {s : Set α} (hl' : l' < a) :
     s ∈ 𝓝[≤] a ↔ ∃ l ∈ Ico l' a, Ioc l a ⊆ s :=
   (TFAE_mem_nhdsWithin_Iic hl' s).out 0 3 (by norm_num) (by norm_num)
 #align mem_nhds_within_Iic_iff_exists_mem_Ico_Ioc_subset mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subset
+-/
 
+#print mem_nhdsWithin_Iic_iff_exists_Ioc_subset' /-
 /-- A set is a neighborhood of `a` within `(-∞, a]` if and only if it contains an interval `(l, a]`
 with `l < a`, provided `a` is not a bottom element. -/
 theorem mem_nhdsWithin_Iic_iff_exists_Ioc_subset' {a l' : α} {s : Set α} (hl' : l' < a) :
     s ∈ 𝓝[≤] a ↔ ∃ l ∈ Iio a, Ioc l a ⊆ s :=
   (TFAE_mem_nhdsWithin_Iic hl' s).out 0 4 (by norm_num) (by norm_num)
 #align mem_nhds_within_Iic_iff_exists_Ioc_subset' mem_nhdsWithin_Iic_iff_exists_Ioc_subset'
+-/
 
+#print mem_nhdsWithin_Iic_iff_exists_Ioc_subset /-
 /-- A set is a neighborhood of `a` within `(-∞, a]` if and only if it contains an interval `(l, a]`
 with `l < a`. -/
 theorem mem_nhdsWithin_Iic_iff_exists_Ioc_subset [NoMinOrder α] {a : α} {s : Set α} :
@@ -2131,6 +2284,7 @@ theorem mem_nhdsWithin_Iic_iff_exists_Ioc_subset [NoMinOrder α] {a : α} {s : S
   let ⟨l', hl'⟩ := exists_lt a
   mem_nhdsWithin_Iic_iff_exists_Ioc_subset' hl'
 #align mem_nhds_within_Iic_iff_exists_Ioc_subset mem_nhdsWithin_Iic_iff_exists_Ioc_subset
+-/
 
 #print mem_nhdsWithin_Iic_iff_exists_Icc_subset /-
 /-- A set is a neighborhood of `a` within `(-∞, a]` if and only if it contains an interval `[l, a]`
@@ -2154,6 +2308,7 @@ variable [TopologicalSpace α] [LinearOrderedAddCommGroup α] [OrderTopology α]
 
 variable {l : Filter β} {f g : β → α}
 
+#print nhds_eq_iInf_abs_sub /-
 theorem nhds_eq_iInf_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 {b | |a - b| < r} :=
   by
   simp only [le_antisymm_iff, nhds_eq_order, le_inf_iff, le_iInf_iff, le_principal_iff, mem_Ioi,
@@ -2169,7 +2324,9 @@ theorem nhds_eq_iInf_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 {b | |a - b| <
   · intro b hb
     exact mem_infi_of_mem (b - a) (mem_infi_of_mem (sub_pos.2 hb) (by simp [Iio]))
 #align nhds_eq_infi_abs_sub nhds_eq_iInf_abs_sub
+-/
 
+#print orderTopology_of_nhds_abs /-
 theorem orderTopology_of_nhds_abs {α : Type _} [TopologicalSpace α] [LinearOrderedAddCommGroup α]
     (h_nhds : ∀ a : α, 𝓝 a = ⨅ r > 0, 𝓟 {b | |a - b| < r}) : OrderTopology α :=
   by
@@ -2178,17 +2335,23 @@ theorem orderTopology_of_nhds_abs {α : Type _} [TopologicalSpace α] [LinearOrd
   letI := Preorder.topology α; letI : OrderTopology α := ⟨rfl⟩
   exact (nhds_eq_iInf_abs_sub a).symm
 #align order_topology_of_nhds_abs orderTopology_of_nhds_abs
+-/
 
+#print LinearOrderedAddCommGroup.tendsto_nhds /-
 theorem LinearOrderedAddCommGroup.tendsto_nhds {x : Filter β} {a : α} :
     Tendsto f x (𝓝 a) ↔ ∀ ε > (0 : α), ∀ᶠ b in x, |f b - a| < ε := by
   simp [nhds_eq_iInf_abs_sub, abs_sub_comm a]
 #align linear_ordered_add_comm_group.tendsto_nhds LinearOrderedAddCommGroup.tendsto_nhds
+-/
 
+#print eventually_abs_sub_lt /-
 theorem eventually_abs_sub_lt (a : α) {ε : α} (hε : 0 < ε) : ∀ᶠ x in 𝓝 a, |x - a| < ε :=
   (nhds_eq_iInf_abs_sub a).symm ▸
     mem_iInf_of_mem ε (mem_iInf_of_mem hε <| by simp only [abs_sub_comm, mem_principal_self])
 #align eventually_abs_sub_lt eventually_abs_sub_lt
+-/
 
+#print Filter.Tendsto.add_atTop /-
 /-- In a linearly ordered additive commutative group with the order topology, if `f` tends to `C`
 and `g` tends to `at_top` then `f + g` tends to `at_top`. -/
 theorem Filter.Tendsto.add_atTop {C : α} (hf : Tendsto f l (𝓝 C)) (hg : Tendsto g l atTop) :
@@ -2199,28 +2362,36 @@ theorem Filter.Tendsto.add_atTop {C : α} (hf : Tendsto f l (𝓝 C)) (hg : Tend
   refine' tendsto_at_top_add_left_of_le' _ C' _ hg
   exact (hf.eventually (lt_mem_nhds hC')).mono fun x => le_of_lt
 #align filter.tendsto.add_at_top Filter.Tendsto.add_atTop
+-/
 
+#print Filter.Tendsto.add_atBot /-
 /-- In a linearly ordered additive commutative group with the order topology, if `f` tends to `C`
 and `g` tends to `at_bot` then `f + g` tends to `at_bot`. -/
 theorem Filter.Tendsto.add_atBot {C : α} (hf : Tendsto f l (𝓝 C)) (hg : Tendsto g l atBot) :
     Tendsto (fun x => f x + g x) l atBot :=
   @Filter.Tendsto.add_atTop αᵒᵈ _ _ _ _ _ _ _ _ hf hg
 #align filter.tendsto.add_at_bot Filter.Tendsto.add_atBot
+-/
 
+#print Filter.Tendsto.atTop_add /-
 /-- In a linearly ordered additive commutative group with the order topology, if `f` tends to
 `at_top` and `g` tends to `C` then `f + g` tends to `at_top`. -/
 theorem Filter.Tendsto.atTop_add {C : α} (hf : Tendsto f l atTop) (hg : Tendsto g l (𝓝 C)) :
     Tendsto (fun x => f x + g x) l atTop := by conv in _ + _ => rw [add_comm];
   exact hg.add_at_top hf
 #align filter.tendsto.at_top_add Filter.Tendsto.atTop_add
+-/
 
+#print Filter.Tendsto.atBot_add /-
 /-- In a linearly ordered additive commutative group with the order topology, if `f` tends to
 `at_bot` and `g` tends to `C` then `f + g` tends to `at_bot`. -/
 theorem Filter.Tendsto.atBot_add {C : α} (hf : Tendsto f l atBot) (hg : Tendsto g l (𝓝 C)) :
     Tendsto (fun x => f x + g x) l atBot := by conv in _ + _ => rw [add_comm];
   exact hg.add_at_bot hf
 #align filter.tendsto.at_bot_add Filter.Tendsto.atBot_add
+-/
 
+#print nhds_basis_Ioo_pos /-
 theorem nhds_basis_Ioo_pos [NoMinOrder α] [NoMaxOrder α] (a : α) :
     (𝓝 a).HasBasis (fun ε : α => (0 : α) < ε) fun ε => Ioo (a - ε) (a + ε) :=
   ⟨by
@@ -2235,7 +2406,9 @@ theorem nhds_basis_Ioo_pos [NoMinOrder α] [NoMaxOrder α] (a : α) :
     · rintro ⟨ε, ε_pos, h⟩
       exact ⟨(a - ε, a + ε), by simp [ε_pos], h⟩⟩
 #align nhds_basis_Ioo_pos nhds_basis_Ioo_pos
+-/
 
+#print nhds_basis_abs_sub_lt /-
 theorem nhds_basis_abs_sub_lt [NoMinOrder α] [NoMaxOrder α] (a : α) :
     (𝓝 a).HasBasis (fun ε : α => (0 : α) < ε) fun ε => {b | |b - a| < ε} :=
   by
@@ -2244,16 +2417,20 @@ theorem nhds_basis_abs_sub_lt [NoMinOrder α] [NoMaxOrder α] (a : α) :
     change |x - a| < ε ↔ a - ε < x ∧ x < a + ε
     simp [abs_lt, sub_lt_iff_lt_add, add_comm ε a, add_comm x ε]
 #align nhds_basis_abs_sub_lt nhds_basis_abs_sub_lt
+-/
 
 variable (α)
 
+#print nhds_basis_zero_abs_sub_lt /-
 theorem nhds_basis_zero_abs_sub_lt [NoMinOrder α] [NoMaxOrder α] :
     (𝓝 (0 : α)).HasBasis (fun ε : α => (0 : α) < ε) fun ε => {b | |b| < ε} := by
   simpa using nhds_basis_abs_sub_lt (0 : α)
 #align nhds_basis_zero_abs_sub_lt nhds_basis_zero_abs_sub_lt
+-/
 
 variable {α}
 
+#print nhds_basis_Ioo_pos_of_pos /-
 /-- If `a` is positive we can form a basis from only nonnegative `Ioo` intervals -/
 theorem nhds_basis_Ioo_pos_of_pos [NoMinOrder α] [NoMaxOrder α] {a : α} (ha : 0 < a) :
     (𝓝 a).HasBasis (fun ε : α => (0 : α) < ε ∧ ε ≤ a) fun ε => Ioo (a - ε) (a + ε) :=
@@ -2270,17 +2447,22 @@ theorem nhds_basis_Ioo_pos_of_pos [NoMinOrder α] [NoMaxOrder α] {a : α} (ha :
         let ⟨i, hi, hit⟩ := h
         ⟨i, hi.1, hit⟩⟩⟩
 #align nhds_basis_Ioo_pos_of_pos nhds_basis_Ioo_pos_of_pos
+-/
 
 end LinearOrderedAddCommGroup
 
+#print preimage_neg /-
 theorem preimage_neg [AddGroup α] : preimage (Neg.neg : α → α) = image (Neg.neg : α → α) :=
   (image_eq_preimage_of_inverse neg_neg neg_neg).symm
 #align preimage_neg preimage_neg
+-/
 
+#print Filter.map_neg_eq_comap_neg /-
 theorem Filter.map_neg_eq_comap_neg [AddGroup α] :
     map (Neg.neg : α → α) = comap (Neg.neg : α → α) :=
   funext fun f => map_eq_comap_of_inverse (funext neg_neg) (funext neg_neg)
 #align filter.map_neg_eq_comap_neg Filter.map_neg_eq_comap_neg
+-/
 
 section OrderTopology
 
@@ -2346,6 +2528,7 @@ theorem IsGLB.nhdsWithin_neBot : ∀ {a : α} {s : Set α}, IsGLB s a → s.None
 #align is_glb.nhds_within_ne_bot IsGLB.nhdsWithin_neBot
 -/
 
+#print isLUB_of_mem_nhds /-
 theorem isLUB_of_mem_nhds {s : Set α} {a : α} {f : Filter α} (hsa : a ∈ upperBounds s) (hsf : s ∈ f)
     [NeBot (f ⊓ 𝓝 a)] : IsLUB s a :=
   ⟨hsa, fun b hb =>
@@ -2355,6 +2538,7 @@ theorem isLUB_of_mem_nhds {s : Set α} {a : α} {f : Filter α} (hsa : a ∈ upp
       have : b < b := lt_of_lt_of_le hxb <| hb hxs
       lt_irrefl b this⟩
 #align is_lub_of_mem_nhds isLUB_of_mem_nhds
+-/
 
 #print isLUB_of_mem_closure /-
 theorem isLUB_of_mem_closure {s : Set α} {a : α} (hsa : a ∈ upperBounds s) (hsf : a ∈ closure s) :
@@ -2365,10 +2549,12 @@ theorem isLUB_of_mem_closure {s : Set α} {a : α} (hsa : a ∈ upperBounds s) (
 #align is_lub_of_mem_closure isLUB_of_mem_closure
 -/
 
+#print isGLB_of_mem_nhds /-
 theorem isGLB_of_mem_nhds :
     ∀ {s : Set α} {a : α} {f : Filter α}, a ∈ lowerBounds s → s ∈ f → NeBot (f ⊓ 𝓝 a) → IsGLB s a :=
   @isLUB_of_mem_nhds αᵒᵈ _ _ _
 #align is_glb_of_mem_nhds isGLB_of_mem_nhds
+-/
 
 #print isGLB_of_mem_closure /-
 theorem isGLB_of_mem_closure {s : Set α} {a : α} (hsa : a ∈ lowerBounds s) (hsf : a ∈ closure s) :
@@ -2561,6 +2747,7 @@ theorem exists_seq_strictMono_tendsto_nhdsWithin [DenselyOrdered α] [NoMinOrder
 #align exists_seq_strict_mono_tendsto_nhds_within exists_seq_strictMono_tendsto_nhdsWithin
 -/
 
+#print exists_seq_tendsto_sSup /-
 theorem exists_seq_tendsto_sSup {α : Type _} [ConditionallyCompleteLinearOrder α]
     [TopologicalSpace α] [OrderTopology α] [FirstCountableTopology α] {S : Set α} (hS : S.Nonempty)
     (hS' : BddAbove S) : ∃ u : ℕ → α, Monotone u ∧ Tendsto u atTop (𝓝 (sSup S)) ∧ ∀ n, u n ∈ S :=
@@ -2568,6 +2755,7 @@ theorem exists_seq_tendsto_sSup {α : Type _} [ConditionallyCompleteLinearOrder
   rcases(isLUB_csSup hS hS').exists_seq_monotone_tendsto hS with ⟨u, hu⟩
   exact ⟨u, hu.1, hu.2.2⟩
 #align exists_seq_tendsto_Sup exists_seq_tendsto_sSup
+-/
 
 #print IsGLB.exists_seq_strictAnti_tendsto_of_not_mem /-
 theorem IsGLB.exists_seq_strictAnti_tendsto_of_not_mem {t : Set α} {x : α}
@@ -2625,11 +2813,13 @@ theorem exists_seq_strictAnti_strictMono_tendsto [DenselyOrdered α] [FirstCount
 #align exists_seq_strict_anti_strict_mono_tendsto exists_seq_strictAnti_strictMono_tendsto
 -/
 
+#print exists_seq_tendsto_sInf /-
 theorem exists_seq_tendsto_sInf {α : Type _} [ConditionallyCompleteLinearOrder α]
     [TopologicalSpace α] [OrderTopology α] [FirstCountableTopology α] {S : Set α} (hS : S.Nonempty)
     (hS' : BddBelow S) : ∃ u : ℕ → α, Antitone u ∧ Tendsto u atTop (𝓝 (sInf S)) ∧ ∀ n, u n ∈ S :=
   @exists_seq_tendsto_sSup αᵒᵈ _ _ _ _ S hS hS'
 #align exists_seq_tendsto_Inf exists_seq_tendsto_sInf
+-/
 
 end OrderTopology
 
@@ -2896,11 +3086,13 @@ theorem nhdsWithin_Ioi_self_neBot [NoMaxOrder α] (a : α) : NeBot (𝓝[>] a) :
 #align nhds_within_Ioi_self_ne_bot nhdsWithin_Ioi_self_neBot
 -/
 
+#print Filter.Eventually.exists_gt /-
 theorem Filter.Eventually.exists_gt [NoMaxOrder α] {a : α} {p : α → Prop} (h : ∀ᶠ x in 𝓝 a, p x) :
     ∃ b > a, p b := by
   simpa only [exists_prop, gt_iff_lt, and_comm'] using
     ((h.filter_mono (@nhdsWithin_le_nhds _ _ a (Ioi a))).And self_mem_nhdsWithin).exists
 #align filter.eventually.exists_gt Filter.Eventually.exists_gt
+-/
 
 #print nhdsWithin_Iio_neBot' /-
 theorem nhdsWithin_Iio_neBot' {b c : α} (H₁ : (Iio c).Nonempty) (H₂ : b ≤ c) : NeBot (𝓝[Iio c] b) :=
@@ -2927,10 +3119,12 @@ theorem nhdsWithin_Iio_self_neBot [NoMinOrder α] (a : α) : NeBot (𝓝[<] a) :
 #align nhds_within_Iio_self_ne_bot nhdsWithin_Iio_self_neBot
 -/
 
+#print Filter.Eventually.exists_lt /-
 theorem Filter.Eventually.exists_lt [NoMinOrder α] {a : α} {p : α → Prop} (h : ∀ᶠ x in 𝓝 a, p x) :
     ∃ b < a, p b :=
   @Filter.Eventually.exists_gt αᵒᵈ _ _ _ _ _ _ _ h
 #align filter.eventually.exists_lt Filter.Eventually.exists_lt
+-/
 
 #print right_nhdsWithin_Ico_neBot /-
 theorem right_nhdsWithin_Ico_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ico a b] b) :=
@@ -2956,6 +3150,7 @@ theorem right_nhdsWithin_Ioo_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ioo a b]
 #align right_nhds_within_Ioo_ne_bot right_nhdsWithin_Ioo_neBot
 -/
 
+#print comap_coe_nhdsWithin_Iio_of_Ioo_subset /-
 theorem comap_coe_nhdsWithin_Iio_of_Ioo_subset (hb : s ⊆ Iio b)
     (hs : s.Nonempty → ∃ a < b, Ioo a b ⊆ s) : comap (coe : s → α) (𝓝[<] b) = atTop :=
   by
@@ -2974,13 +3169,17 @@ theorem comap_coe_nhdsWithin_Iio_of_Ioo_subset (hb : s ⊆ Iio b)
     obtain ⟨x : s, hx : ∀ z, x ≤ z → z ∈ u⟩ := mem_at_top_sets.1 hu
     exact ⟨Ioo x b, Ioo_mem_nhdsWithin_Iio (right_mem_Ioc.2 <| hb x.2), fun z hz => hx _ hz.1.le⟩
 #align comap_coe_nhds_within_Iio_of_Ioo_subset comap_coe_nhdsWithin_Iio_of_Ioo_subset
+-/
 
+#print comap_coe_nhdsWithin_Ioi_of_Ioo_subset /-
 theorem comap_coe_nhdsWithin_Ioi_of_Ioo_subset (ha : s ⊆ Ioi a)
     (hs : s.Nonempty → ∃ b > a, Ioo a b ⊆ s) : comap (coe : s → α) (𝓝[>] a) = atBot :=
   comap_coe_nhdsWithin_Iio_of_Ioo_subset (show ofDual ⁻¹' s ⊆ Iio (toDual a) from ha) fun h => by
     simpa only [OrderDual.exists, dual_Ioo] using hs h
 #align comap_coe_nhds_within_Ioi_of_Ioo_subset comap_coe_nhdsWithin_Ioi_of_Ioo_subset
+-/
 
+#print map_coe_atTop_of_Ioo_subset /-
 theorem map_coe_atTop_of_Ioo_subset (hb : s ⊆ Iio b) (hs : ∀ a' < b, ∃ a < b, Ioo a b ⊆ s) :
     map (coe : s → α) atTop = 𝓝[<] b :=
   by
@@ -2991,7 +3190,9 @@ theorem map_coe_atTop_of_Ioo_subset (hb : s ⊆ Iio b) (hs : ∀ a' < b, ∃ a <
     rw [Subtype.range_coe]
     exact (mem_nhdsWithin_Iio_iff_exists_Ioo_subset' ha).2 (hs a ha)
 #align map_coe_at_top_of_Ioo_subset map_coe_atTop_of_Ioo_subset
+-/
 
+#print map_coe_atBot_of_Ioo_subset /-
 theorem map_coe_atBot_of_Ioo_subset (ha : s ⊆ Ioi a) (hs : ∀ b' > a, ∃ b > a, Ioo a b ⊆ s) :
     map (coe : s → α) atBot = 𝓝[>] a :=
   by
@@ -3000,6 +3201,7 @@ theorem map_coe_atBot_of_Ioo_subset (ha : s ⊆ Ioi a) (hs : ∀ b' > a, ∃ b >
     (map_coe_atTop_of_Ioo_subset (show of_dual ⁻¹' s ⊆ Iio (to_dual a) from ha) fun b' hb' => _ : _)
   simpa only [OrderDual.exists, dual_Ioo] using hs b' hb'
 #align map_coe_at_bot_of_Ioo_subset map_coe_atBot_of_Ioo_subset
+-/
 
 #print comap_coe_Ioo_nhdsWithin_Iio /-
 /-- The `at_top` filter for an open interval `Ioo a b` comes from the left-neighbourhoods filter at
@@ -3137,6 +3339,7 @@ instance (x : α) [Nontrivial α] : NeBot (𝓝[≠] x) :=
   exact ⟨z, us ⟨hab ⟨hz.1, hz.2.trans hy.2⟩, hz.2.Ne⟩⟩
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+#print Dense.exists_countable_dense_subset_no_bot_top /-
 /-- Let `s` be a dense set in a nontrivial dense linear order `α`. If `s` is a
 separable space (e.g., if `α` has a second countable topology), then there exists a countable
 dense subset `t ⊆ s` such that `t` does not contain bottom/top elements of `α`. -/
@@ -3152,6 +3355,7 @@ theorem Dense.exists_countable_dense_subset_no_bot_top [Nontrivial α] {s : Set
   · intro x hx; simp [hx]
   · intro x hx; simp [hx]
 #align dense.exists_countable_dense_subset_no_bot_top Dense.exists_countable_dense_subset_no_bot_top
+-/
 
 variable (α)
 
@@ -3173,26 +3377,35 @@ section CompleteLinearOrder
 variable [CompleteLinearOrder α] [TopologicalSpace α] [OrderTopology α] [CompleteLinearOrder β]
   [TopologicalSpace β] [OrderClosedTopology β] [Nonempty γ]
 
+#print sSup_mem_closure /-
 theorem sSup_mem_closure {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
     {s : Set α} (hs : s.Nonempty) : sSup s ∈ closure s :=
   (isLUB_sSup s).mem_closure hs
 #align Sup_mem_closure sSup_mem_closure
+-/
 
+#print sInf_mem_closure /-
 theorem sInf_mem_closure {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
     {s : Set α} (hs : s.Nonempty) : sInf s ∈ closure s :=
   (isGLB_sInf s).mem_closure hs
 #align Inf_mem_closure sInf_mem_closure
+-/
 
+#print IsClosed.sSup_mem /-
 theorem IsClosed.sSup_mem {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α]
     [OrderTopology α] {s : Set α} (hs : s.Nonempty) (hc : IsClosed s) : sSup s ∈ s :=
   (isLUB_sSup s).mem_of_isClosed hs hc
 #align is_closed.Sup_mem IsClosed.sSup_mem
+-/
 
+#print IsClosed.sInf_mem /-
 theorem IsClosed.sInf_mem {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α]
     [OrderTopology α] {s : Set α} (hs : s.Nonempty) (hc : IsClosed s) : sInf s ∈ s :=
   (isGLB_sInf s).mem_of_isClosed hs hc
 #align is_closed.Inf_mem IsClosed.sInf_mem
+-/
 
+#print Monotone.map_sSup_of_continuousAt' /-
 /-- A monotone function continuous at the supremum of a nonempty set sends this supremum to
 the supremum of the image of this set. -/
 theorem Monotone.map_sSup_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
@@ -3203,7 +3416,9 @@ theorem Monotone.map_sSup_of_continuousAt' {f : α → β} {s : Set α} (Cf : Co
           (fun x hx y hy xy => Mf xy) hs <|
         Cf.mono_left inf_le_left).sSup_eq.symm
 #align monotone.map_Sup_of_continuous_at' Monotone.map_sSup_of_continuousAt'
+-/
 
+#print Monotone.map_sSup_of_continuousAt /-
 /-- A monotone function `f` sending `bot` to `bot` and continuous at the supremum of a set sends
 this supremum to the supremum of the image of this set. -/
 theorem Monotone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
@@ -3213,14 +3428,18 @@ theorem Monotone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : Con
   · simp [h, fbot]
   · exact Mf.map_Sup_of_continuous_at' Cf h
 #align monotone.map_Sup_of_continuous_at Monotone.map_sSup_of_continuousAt
+-/
 
+#print Monotone.map_iSup_of_continuousAt' /-
 /-- A monotone function continuous at the indexed supremum over a nonempty `Sort` sends this indexed
 supremum to the indexed supremum of the composition. -/
 theorem Monotone.map_iSup_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
     (Cf : ContinuousAt f (iSup g)) (Mf : Monotone f) : f (⨆ i, g i) = ⨆ i, f (g i) := by
   rw [iSup, Mf.map_Sup_of_continuous_at' Cf (range_nonempty g), ← range_comp, iSup]
 #align monotone.map_supr_of_continuous_at' Monotone.map_iSup_of_continuousAt'
+-/
 
+#print Monotone.map_iSup_of_continuousAt /-
 /-- If a monotone function sending `bot` to `bot` is continuous at the indexed supremum over
 a `Sort`, then it sends this indexed supremum to the indexed supremum of the composition. -/
 theorem Monotone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
@@ -3228,35 +3447,45 @@ theorem Monotone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι
     f (⨆ i, g i) = ⨆ i, f (g i) := by
   rw [iSup, Mf.map_Sup_of_continuous_at Cf fbot, ← range_comp, iSup]
 #align monotone.map_supr_of_continuous_at Monotone.map_iSup_of_continuousAt
+-/
 
+#print Monotone.map_sInf_of_continuousAt' /-
 /-- A monotone function continuous at the infimum of a nonempty set sends this infimum to
 the infimum of the image of this set. -/
 theorem Monotone.map_sInf_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
     (Mf : Monotone f) (hs : s.Nonempty) : f (sInf s) = sInf (f '' s) :=
   @Monotone.map_sSup_of_continuousAt' αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual hs
 #align monotone.map_Inf_of_continuous_at' Monotone.map_sInf_of_continuousAt'
+-/
 
+#print Monotone.map_sInf_of_continuousAt /-
 /-- A monotone function `f` sending `top` to `top` and continuous at the infimum of a set sends
 this infimum to the infimum of the image of this set. -/
 theorem Monotone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
     (Mf : Monotone f) (ftop : f ⊤ = ⊤) : f (sInf s) = sInf (f '' s) :=
   @Monotone.map_sSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual ftop
 #align monotone.map_Inf_of_continuous_at Monotone.map_sInf_of_continuousAt
+-/
 
+#print Monotone.map_iInf_of_continuousAt' /-
 /-- A monotone function continuous at the indexed infimum over a nonempty `Sort` sends this indexed
 infimum to the indexed infimum of the composition. -/
 theorem Monotone.map_iInf_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
     (Cf : ContinuousAt f (iInf g)) (Mf : Monotone f) : f (⨅ i, g i) = ⨅ i, f (g i) :=
   @Monotone.map_iSup_of_continuousAt' αᵒᵈ βᵒᵈ _ _ _ _ _ _ ι _ f g Cf Mf.dual
 #align monotone.map_infi_of_continuous_at' Monotone.map_iInf_of_continuousAt'
+-/
 
+#print Monotone.map_iInf_of_continuousAt /-
 /-- If a monotone function sending `top` to `top` is continuous at the indexed infimum over
 a `Sort`, then it sends this indexed infimum to the indexed infimum of the composition. -/
 theorem Monotone.map_iInf_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
     (Cf : ContinuousAt f (iInf g)) (Mf : Monotone f) (ftop : f ⊤ = ⊤) : f (iInf g) = iInf (f ∘ g) :=
   @Monotone.map_iSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ ι f g Cf Mf.dual ftop
 #align monotone.map_infi_of_continuous_at Monotone.map_iInf_of_continuousAt
+-/
 
+#print Antitone.map_sSup_of_continuousAt' /-
 /-- An antitone function continuous at the supremum of a nonempty set sends this supremum to
 the infimum of the image of this set. -/
 theorem Antitone.map_sSup_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
@@ -3264,7 +3493,9 @@ theorem Antitone.map_sSup_of_continuousAt' {f : α → β} {s : Set α} (Cf : Co
   Monotone.map_sSup_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (sSup s) from Cf) Af
     hs
 #align antitone.map_Sup_of_continuous_at' Antitone.map_sSup_of_continuousAt'
+-/
 
+#print Antitone.map_sSup_of_continuousAt /-
 /-- An antitone function `f` sending `bot` to `top` and continuous at the supremum of a set sends
 this supremum to the infimum of the image of this set. -/
 theorem Antitone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
@@ -3272,14 +3503,18 @@ theorem Antitone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : Con
   Monotone.map_sSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (sSup s) from Cf) Af
     fbot
 #align antitone.map_Sup_of_continuous_at Antitone.map_sSup_of_continuousAt
+-/
 
+#print Antitone.map_iSup_of_continuousAt' /-
 /-- An antitone function continuous at the indexed supremum over a nonempty `Sort` sends this
 indexed supremum to the indexed infimum of the composition. -/
 theorem Antitone.map_iSup_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
     (Cf : ContinuousAt f (iSup g)) (Af : Antitone f) : f (⨆ i, g i) = ⨅ i, f (g i) :=
   Monotone.map_iSup_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (iSup g) from Cf) Af
 #align antitone.map_supr_of_continuous_at' Antitone.map_iSup_of_continuousAt'
+-/
 
+#print Antitone.map_iSup_of_continuousAt /-
 /-- An antitone function sending `bot` to `top` is continuous at the indexed supremum over
 a `Sort`, then it sends this indexed supremum to the indexed supremum of the composition. -/
 theorem Antitone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
@@ -3288,7 +3523,9 @@ theorem Antitone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι
   Monotone.map_iSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (iSup g) from Cf) Af
     fbot
 #align antitone.map_supr_of_continuous_at Antitone.map_iSup_of_continuousAt
+-/
 
+#print Antitone.map_sInf_of_continuousAt' /-
 /-- An antitone function continuous at the infimum of a nonempty set sends this infimum to
 the supremum of the image of this set. -/
 theorem Antitone.map_sInf_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
@@ -3296,7 +3533,9 @@ theorem Antitone.map_sInf_of_continuousAt' {f : α → β} {s : Set α} (Cf : Co
   Monotone.map_sInf_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (sInf s) from Cf) Af
     hs
 #align antitone.map_Inf_of_continuous_at' Antitone.map_sInf_of_continuousAt'
+-/
 
+#print Antitone.map_sInf_of_continuousAt /-
 /-- An antitone function `f` sending `top` to `bot` and continuous at the infimum of a set sends
 this infimum to the supremum of the image of this set. -/
 theorem Antitone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
@@ -3304,14 +3543,18 @@ theorem Antitone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : Con
   Monotone.map_sInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (sInf s) from Cf) Af
     ftop
 #align antitone.map_Inf_of_continuous_at Antitone.map_sInf_of_continuousAt
+-/
 
+#print Antitone.map_iInf_of_continuousAt' /-
 /-- An antitone function continuous at the indexed infimum over a nonempty `Sort` sends this indexed
 infimum to the indexed supremum of the composition. -/
 theorem Antitone.map_iInf_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
     (Cf : ContinuousAt f (iInf g)) (Af : Antitone f) : f (⨅ i, g i) = ⨆ i, f (g i) :=
   Monotone.map_iInf_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (iInf g) from Cf) Af
 #align antitone.map_infi_of_continuous_at' Antitone.map_iInf_of_continuousAt'
+-/
 
+#print Antitone.map_iInf_of_continuousAt /-
 /-- If an antitone function sending `top` to `bot` is continuous at the indexed infimum over
 a `Sort`, then it sends this indexed infimum to the indexed supremum of the composition. -/
 theorem Antitone.map_iInf_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
@@ -3319,6 +3562,7 @@ theorem Antitone.map_iInf_of_continuousAt {ι : Sort _} {f : α → β} {g : ι
   Monotone.map_iInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (iInf g) from Cf) Af
     ftop
 #align antitone.map_infi_of_continuous_at Antitone.map_iInf_of_continuousAt
+-/
 
 end CompleteLinearOrder
 
@@ -3327,24 +3571,33 @@ section ConditionallyCompleteLinearOrder
 variable [ConditionallyCompleteLinearOrder α] [TopologicalSpace α] [OrderTopology α]
   [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderClosedTopology β] [Nonempty γ]
 
+#print csSup_mem_closure /-
 theorem csSup_mem_closure {s : Set α} (hs : s.Nonempty) (B : BddAbove s) : sSup s ∈ closure s :=
   (isLUB_csSup hs B).mem_closure hs
 #align cSup_mem_closure csSup_mem_closure
+-/
 
+#print csInf_mem_closure /-
 theorem csInf_mem_closure {s : Set α} (hs : s.Nonempty) (B : BddBelow s) : sInf s ∈ closure s :=
   (isGLB_csInf hs B).mem_closure hs
 #align cInf_mem_closure csInf_mem_closure
+-/
 
+#print IsClosed.csSup_mem /-
 theorem IsClosed.csSup_mem {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddAbove s) :
     sSup s ∈ s :=
   (isLUB_csSup hs B).mem_of_isClosed hs hc
 #align is_closed.cSup_mem IsClosed.csSup_mem
+-/
 
+#print IsClosed.csInf_mem /-
 theorem IsClosed.csInf_mem {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddBelow s) :
     sInf s ∈ s :=
   (isGLB_csInf hs B).mem_of_isClosed hs hc
 #align is_closed.cInf_mem IsClosed.csInf_mem
+-/
 
+#print Monotone.map_csSup_of_continuousAt /-
 /-- If a monotone function is continuous at the supremum of a nonempty bounded above set `s`,
 then it sends this supremum to the supremum of the image of `s`. -/
 theorem Monotone.map_csSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
@@ -3354,28 +3607,36 @@ theorem Monotone.map_csSup_of_continuousAt {f : α → β} {s : Set α} (Cf : Co
   refine' (isLUB_csSup Ne H).isLUB_of_tendsto (fun x hx y hy xy => Mf xy) Ne _
   exact Cf.mono_left inf_le_left
 #align monotone.map_cSup_of_continuous_at Monotone.map_csSup_of_continuousAt
+-/
 
+#print Monotone.map_ciSup_of_continuousAt /-
 /-- If a monotone function is continuous at the indexed supremum of a bounded function on
 a nonempty `Sort`, then it sends this supremum to the supremum of the composition. -/
 theorem Monotone.map_ciSup_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
     (Mf : Monotone f) (H : BddAbove (range g)) : f (⨆ i, g i) = ⨆ i, f (g i) := by
   rw [iSup, Mf.map_cSup_of_continuous_at Cf (range_nonempty _) H, ← range_comp, iSup]
 #align monotone.map_csupr_of_continuous_at Monotone.map_ciSup_of_continuousAt
+-/
 
+#print Monotone.map_csInf_of_continuousAt /-
 /-- If a monotone function is continuous at the infimum of a nonempty bounded below set `s`,
 then it sends this infimum to the infimum of the image of `s`. -/
 theorem Monotone.map_csInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
     (Mf : Monotone f) (ne : s.Nonempty) (H : BddBelow s) : f (sInf s) = sInf (f '' s) :=
   @Monotone.map_csSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual Ne H
 #align monotone.map_cInf_of_continuous_at Monotone.map_csInf_of_continuousAt
+-/
 
+#print Monotone.map_ciInf_of_continuousAt /-
 /-- A continuous monotone function sends indexed infimum to indexed infimum in conditionally
 complete linear order, under a boundedness assumption. -/
 theorem Monotone.map_ciInf_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
     (Mf : Monotone f) (H : BddBelow (range g)) : f (⨅ i, g i) = ⨅ i, f (g i) :=
   @Monotone.map_ciSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ _ Cf Mf.dual H
 #align monotone.map_cinfi_of_continuous_at Monotone.map_ciInf_of_continuousAt
+-/
 
+#print Antitone.map_csSup_of_continuousAt /-
 /-- If an antitone function is continuous at the supremum of a nonempty bounded above set `s`,
 then it sends this supremum to the infimum of the image of `s`. -/
 theorem Antitone.map_csSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
@@ -3383,7 +3644,9 @@ theorem Antitone.map_csSup_of_continuousAt {f : α → β} {s : Set α} (Cf : Co
   Monotone.map_csSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (sSup s) from Cf) Af
     Ne H
 #align antitone.map_cSup_of_continuous_at Antitone.map_csSup_of_continuousAt
+-/
 
+#print Antitone.map_ciSup_of_continuousAt /-
 /-- If an antitone function is continuous at the indexed supremum of a bounded function on
 a nonempty `Sort`, then it sends this supremum to the infimum of the composition. -/
 theorem Antitone.map_ciSup_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
@@ -3391,7 +3654,9 @@ theorem Antitone.map_ciSup_of_continuousAt {f : α → β} {g : γ → α} (Cf :
   Monotone.map_ciSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (⨆ i, g i) from Cf)
     Af H
 #align antitone.map_csupr_of_continuous_at Antitone.map_ciSup_of_continuousAt
+-/
 
+#print Antitone.map_csInf_of_continuousAt /-
 /-- If an antitone function is continuous at the infimum of a nonempty bounded below set `s`,
 then it sends this infimum to the supremum of the image of `s`. -/
 theorem Antitone.map_csInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
@@ -3399,7 +3664,9 @@ theorem Antitone.map_csInf_of_continuousAt {f : α → β} {s : Set α} (Cf : Co
   Monotone.map_csInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (sInf s) from Cf) Af
     Ne H
 #align antitone.map_cInf_of_continuous_at Antitone.map_csInf_of_continuousAt
+-/
 
+#print Antitone.map_ciInf_of_continuousAt /-
 /-- A continuous antitone function sends indexed infimum to indexed supremum in conditionally
 complete linear order, under a boundedness assumption. -/
 theorem Antitone.map_ciInf_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
@@ -3407,7 +3674,9 @@ theorem Antitone.map_ciInf_of_continuousAt {f : α → β} {g : γ → α} (Cf :
   Monotone.map_ciInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (⨅ i, g i) from Cf)
     Af H
 #align antitone.map_cinfi_of_continuous_at Antitone.map_ciInf_of_continuousAt
+-/
 
+#print Monotone.tendsto_nhdsWithin_Iio /-
 /-- A monotone map has a limit to the left of any point `x`, equal to `Sup (f '' (Iio x))`. -/
 theorem Monotone.tendsto_nhdsWithin_Iio {α β : Type _} [LinearOrder α] [TopologicalSpace α]
     [OrderTopology α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderTopology β]
@@ -3424,13 +3693,16 @@ theorem Monotone.tendsto_nhdsWithin_Iio {α β : Type _} [LinearOrder α] [Topol
     apply lt_of_le_of_lt _ hm
     exact le_csSup (Mf.map_bdd_above bddAbove_Iio) (mem_image_of_mem _ hy)
 #align monotone.tendsto_nhds_within_Iio Monotone.tendsto_nhdsWithin_Iio
+-/
 
+#print Monotone.tendsto_nhdsWithin_Ioi /-
 /-- A monotone map has a limit to the right of any point `x`, equal to `Inf (f '' (Ioi x))`. -/
 theorem Monotone.tendsto_nhdsWithin_Ioi {α β : Type _} [LinearOrder α] [TopologicalSpace α]
     [OrderTopology α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderTopology β]
     {f : α → β} (Mf : Monotone f) (x : α) : Tendsto f (𝓝[>] x) (𝓝 (sInf (f '' Ioi x))) :=
   @Monotone.tendsto_nhdsWithin_Iio αᵒᵈ βᵒᵈ _ _ _ _ _ _ f Mf.dual x
 #align monotone.tendsto_nhds_within_Ioi Monotone.tendsto_nhdsWithin_Ioi
+-/
 
 end ConditionallyCompleteLinearOrder
 

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

@@ -1483,8 +1483,7 @@ theorem order_separated {a₁ a₂ : α} (h : a₁ < a₂) :
       calc
         b₁ ≤ a₁ := h₂ _ hb₁
         _ < a₂ := h
-        _ ≤ b₂ := h₁ _ hb₂
-        ⟩
+        _ ≤ b₂ := h₁ _ hb₂⟩
 #align order_separated order_separated
 -/
 
@@ -2769,7 +2768,6 @@ theorem closure_interior_Icc {a b : α} (h : a ≠ b) : closure (interior (Icc a
       Icc a b = closure (Ioo a b) := (closure_Ioo h).symm
       _ ⊆ closure (interior (Icc a b)) :=
         closure_mono (interior_maximal Ioo_subset_Icc_self isOpen_Ioo)
-      
 #align closure_interior_Icc closure_interior_Icc
 -/
 
@@ -2784,7 +2782,6 @@ theorem Ioc_subset_closure_interior (a b : α) : Ioc a b ⊆ closure (interior (
       _ = closure (Ioo a b) := (closure_Ioo h).symm
       _ ⊆ closure (interior (Ioc a b)) :=
         closure_mono (interior_maximal Ioo_subset_Ioc_self isOpen_Ioo)
-      
 #align Ioc_subset_closure_interior Ioc_subset_closure_interior
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -3139,7 +3139,7 @@ instance (x : α) [Nontrivial α] : NeBot (𝓝[≠] x) :=
   obtain ⟨z, hz⟩ : ∃ z, a < z ∧ z < x := exists_between hy.1
   exact ⟨z, us ⟨hab ⟨hz.1, hz.2.trans hy.2⟩, hz.2.Ne⟩⟩
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 /-- Let `s` be a dense set in a nontrivial dense linear order `α`. If `s` is a
 separable space (e.g., if `α` has a second countable topology), then there exists a countable
 dense subset `t ⊆ s` such that `t` does not contain bottom/top elements of `α`. -/

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

@@ -101,7 +101,7 @@ set of points `(x, y)` with `x ≤ y` is closed in the product space. We introdu
 This property is satisfied for the order topology on a linear order, but it can be satisfied more
 generally, and suffices to derive many interesting properties relating order and topology. -/
 class OrderClosedTopology (α : Type _) [TopologicalSpace α] [Preorder α] : Prop where
-  isClosed_le' : IsClosed { p : α × α | p.1 ≤ p.2 }
+  isClosed_le' : IsClosed {p : α × α | p.1 ≤ p.2}
 #align order_closed_topology OrderClosedTopology
 -/
 
@@ -136,19 +136,19 @@ instance {p : α → Prop} : OrderClosedTopology (Subtype p) :=
 
 end Subtype
 
-theorem isClosed_le_prod : IsClosed { p : α × α | p.1 ≤ p.2 } :=
+theorem isClosed_le_prod : IsClosed {p : α × α | p.1 ≤ p.2} :=
   t.isClosed_le'
 #align is_closed_le_prod isClosed_le_prod
 
 #print isClosed_le /-
 theorem isClosed_le [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
-    IsClosed { b | f b ≤ g b } :=
+    IsClosed {b | f b ≤ g b} :=
   continuous_iff_isClosed.mp (hf.prod_mk hg) _ isClosed_le_prod
 #align is_closed_le isClosed_le
 -/
 
 #print isClosed_le' /-
-theorem isClosed_le' (a : α) : IsClosed { b | b ≤ a } :=
+theorem isClosed_le' (a : α) : IsClosed {b | b ≤ a} :=
   isClosed_le continuous_id continuous_const
 #align is_closed_le' isClosed_le'
 -/
@@ -160,7 +160,7 @@ theorem isClosed_Iic {a : α} : IsClosed (Iic a) :=
 -/
 
 #print isClosed_ge' /-
-theorem isClosed_ge' (a : α) : IsClosed { b | a ≤ b } :=
+theorem isClosed_ge' (a : α) : IsClosed {b | a ≤ b} :=
   isClosed_le continuous_const continuous_id
 #align is_closed_ge' isClosed_ge'
 -/
@@ -206,7 +206,7 @@ theorem le_of_tendsto_of_tendsto {f g : β → α} {b : Filter β} {a₁ a₂ :
     (hf : Tendsto f b (𝓝 a₁)) (hg : Tendsto g b (𝓝 a₂)) (h : f ≤ᶠ[b] g) : a₁ ≤ a₂ :=
   have : Tendsto (fun b => (f b, g b)) b (𝓝 (a₁, a₂)) := by
     rw [nhds_prod_eq] <;> exact hf.prod_mk hg
-  show (a₁, a₂) ∈ { p : α × α | p.1 ≤ p.2 } from t.isClosed_le'.mem_of_tendsto this h
+  show (a₁, a₂) ∈ {p : α × α | p.1 ≤ p.2} from t.isClosed_le'.mem_of_tendsto this h
 #align le_of_tendsto_of_tendsto le_of_tendsto_of_tendsto
 -/
 
@@ -251,14 +251,14 @@ theorem ge_of_tendsto' {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim
 #print closure_le_eq /-
 @[simp]
 theorem closure_le_eq [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
-    closure { b | f b ≤ g b } = { b | f b ≤ g b } :=
+    closure {b | f b ≤ g b} = {b | f b ≤ g b} :=
   (isClosed_le hf hg).closure_eq
 #align closure_le_eq closure_le_eq
 -/
 
 #print closure_lt_subset_le /-
 theorem closure_lt_subset_le [TopologicalSpace β] {f g : β → α} (hf : Continuous f)
-    (hg : Continuous g) : closure { b | f b < g b } ⊆ { b | f b ≤ g b } :=
+    (hg : Continuous g) : closure {b | f b < g b} ⊆ {b | f b ≤ g b} :=
   (closure_minimal fun x => le_of_lt) <| isClosed_le hf hg
 #align closure_lt_subset_le closure_lt_subset_le
 -/
@@ -267,7 +267,7 @@ theorem closure_lt_subset_le [TopologicalSpace β] {f g : β → α} (hf : Conti
 theorem ContinuousWithinAt.closure_le [TopologicalSpace β] {f g : β → α} {s : Set β} {x : β}
     (hx : x ∈ closure s) (hf : ContinuousWithinAt f s x) (hg : ContinuousWithinAt g s x)
     (h : ∀ y ∈ s, f y ≤ g y) : f x ≤ g x :=
-  show (f x, g x) ∈ { p : α × α | p.1 ≤ p.2 } from
+  show (f x, g x) ∈ {p : α × α | p.1 ≤ p.2} from
     OrderClosedTopology.isClosed_le'.closure_subset ((hf.Prod hg).mem_closure hx h)
 #align continuous_within_at.closure_le ContinuousWithinAt.closure_le
 -/
@@ -276,7 +276,7 @@ theorem ContinuousWithinAt.closure_le [TopologicalSpace β] {f g : β → α} {s
 /-- If `s` is a closed set and two functions `f` and `g` are continuous on `s`,
 then the set `{x ∈ s | f x ≤ g x}` is a closed set. -/
 theorem IsClosed.isClosed_le [TopologicalSpace β] {f g : β → α} {s : Set β} (hs : IsClosed s)
-    (hf : ContinuousOn f s) (hg : ContinuousOn g s) : IsClosed ({ x ∈ s | f x ≤ g x }) :=
+    (hf : ContinuousOn f s) (hg : ContinuousOn g s) : IsClosed ({x ∈ s | f x ≤ g x}) :=
   (hf.Prod hg).preimage_closed_of_closed hs OrderClosedTopology.isClosed_le'
 #align is_closed.is_closed_le IsClosed.isClosed_le
 -/
@@ -285,18 +285,18 @@ theorem IsClosed.isClosed_le [TopologicalSpace β] {f g : β → α} {s : Set β
 theorem le_on_closure [TopologicalSpace β] {f g : β → α} {s : Set β} (h : ∀ x ∈ s, f x ≤ g x)
     (hf : ContinuousOn f (closure s)) (hg : ContinuousOn g (closure s)) ⦃x⦄ (hx : x ∈ closure s) :
     f x ≤ g x :=
-  have : s ⊆ { y ∈ closure s | f y ≤ g y } := fun y hy => ⟨subset_closure hy, h y hy⟩
+  have : s ⊆ {y ∈ closure s | f y ≤ g y} := fun y hy => ⟨subset_closure hy, h y hy⟩
   (closure_minimal this (isClosed_closure.isClosed_le hf hg) hx).2
 #align le_on_closure le_on_closure
 -/
 
 theorem IsClosed.epigraph [TopologicalSpace β] {f : β → α} {s : Set β} (hs : IsClosed s)
-    (hf : ContinuousOn f s) : IsClosed { p : β × α | p.1 ∈ s ∧ f p.1 ≤ p.2 } :=
+    (hf : ContinuousOn f s) : IsClosed {p : β × α | p.1 ∈ s ∧ f p.1 ≤ p.2} :=
   (hs.Preimage continuous_fst).isClosed_le (hf.comp continuousOn_fst Subset.rfl) continuousOn_snd
 #align is_closed.epigraph IsClosed.epigraph
 
 theorem IsClosed.hypograph [TopologicalSpace β] {f : β → α} {s : Set β} (hs : IsClosed s)
-    (hf : ContinuousOn f s) : IsClosed { p : β × α | p.1 ∈ s ∧ p.2 ≤ f p.1 } :=
+    (hf : ContinuousOn f s) : IsClosed {p : β × α | p.1 ∈ s ∧ p.2 ≤ f p.1} :=
   (hs.Preimage continuous_fst).isClosed_le continuousOn_snd (hf.comp continuousOn_fst Subset.rfl)
 #align is_closed.hypograph IsClosed.hypograph
 
@@ -351,7 +351,7 @@ section LinearOrder
 
 variable [TopologicalSpace α] [LinearOrder α] [OrderClosedTopology α]
 
-theorem isOpen_lt_prod : IsOpen { p : α × α | p.1 < p.2 } :=
+theorem isOpen_lt_prod : IsOpen {p : α × α | p.1 < p.2} :=
   by
   simp_rw [← isClosed_compl_iff, compl_set_of, not_lt]
   exact isClosed_le continuous_snd continuous_fst
@@ -359,7 +359,7 @@ theorem isOpen_lt_prod : IsOpen { p : α × α | p.1 < p.2 } :=
 
 #print isOpen_lt /-
 theorem isOpen_lt [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
-    IsOpen { b | f b < g b } := by
+    IsOpen {b | f b < g b} := by
   simp [lt_iff_not_ge, -not_le] <;> exact (isClosed_le hg hf).isOpen_compl
 #align is_open_lt isOpen_lt
 -/
@@ -755,14 +755,14 @@ variable [TopologicalSpace β]
 
 #print lt_subset_interior_le /-
 theorem lt_subset_interior_le (hf : Continuous f) (hg : Continuous g) :
-    { b | f b < g b } ⊆ interior { b | f b ≤ g b } :=
+    {b | f b < g b} ⊆ interior {b | f b ≤ g b} :=
   (interior_maximal fun p => le_of_lt) <| isOpen_lt hf hg
 #align lt_subset_interior_le lt_subset_interior_le
 -/
 
 #print frontier_le_subset_eq /-
 theorem frontier_le_subset_eq (hf : Continuous f) (hg : Continuous g) :
-    frontier { b | f b ≤ g b } ⊆ { b | f b = g b } :=
+    frontier {b | f b ≤ g b} ⊆ {b | f b = g b} :=
   by
   rw [frontier_eq_closure_inter_closure, closure_le_eq hf hg]
   rintro b ⟨hb₁, hb₂⟩
@@ -785,15 +785,15 @@ theorem frontier_Ici_subset (a : α) : frontier (Ici a) ⊆ {a} :=
 
 #print frontier_lt_subset_eq /-
 theorem frontier_lt_subset_eq (hf : Continuous f) (hg : Continuous g) :
-    frontier { b | f b < g b } ⊆ { b | f b = g b } := by
+    frontier {b | f b < g b} ⊆ {b | f b = g b} := by
   rw [← frontier_compl] <;> convert frontier_le_subset_eq hg hf <;> simp [ext_iff, eq_comm]
 #align frontier_lt_subset_eq frontier_lt_subset_eq
 -/
 
 #print continuous_if_le /-
 theorem continuous_if_le [TopologicalSpace γ] [∀ x, Decidable (f x ≤ g x)] {f' g' : β → γ}
-    (hf : Continuous f) (hg : Continuous g) (hf' : ContinuousOn f' { x | f x ≤ g x })
-    (hg' : ContinuousOn g' { x | g x ≤ f x }) (hfg : ∀ x, f x = g x → f' x = g' x) :
+    (hf : Continuous f) (hg : Continuous g) (hf' : ContinuousOn f' {x | f x ≤ g x})
+    (hg' : ContinuousOn g' {x | g x ≤ f x}) (hfg : ∀ x, f x = g x → f' x = g' x) :
     Continuous fun x => if f x ≤ g x then f' x else g' x :=
   by
   refine' continuous_if (fun a ha => hfg _ (frontier_le_subset_eq hf hg ha)) _ (hg'.mono _)
@@ -865,7 +865,7 @@ theorem Filter.Tendsto.min {b : Filter β} {a₁ a₂ : α} (hf : Tendsto f b (
 
 theorem Filter.Tendsto.max_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
     Tendsto (fun i => max a (f i)) l (𝓝 a) := by
-  convert((continuous_max.comp (@Continuous.Prod.mk α α _ _ a)).Tendsto a).comp h; simp
+  convert ((continuous_max.comp (@Continuous.Prod.mk α α _ _ a)).Tendsto a).comp h; simp
 #align filter.tendsto.max_right Filter.Tendsto.max_right
 
 theorem Filter.Tendsto.max_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
@@ -1031,7 +1031,7 @@ it on a preorder, but it is mostly interesting in linear orders, where it is als
 We define it as a mixin. If you want to introduce the order topology on a preorder, use
 `preorder.topology`. -/
 class OrderTopology (α : Type _) [t : TopologicalSpace α] [Preorder α] : Prop where
-  topology_eq_generate_intervals : t = generateFrom { s | ∃ a, s = Ioi a ∨ s = Iio a }
+  topology_eq_generate_intervals : t = generateFrom {s | ∃ a, s = Ioi a ∨ s = Iio a}
 #align order_topology OrderTopology
 -/
 
@@ -1041,7 +1041,7 @@ class OrderTopology (α : Type _) [t : TopologicalSpace α] [Preorder α] : Prop
 instance as many ordered sets are already endowed with the same topology, most often in a non-defeq
 way though. Register as a local instance when necessary. -/
 def Preorder.topology (α : Type _) [Preorder α] : TopologicalSpace α :=
-  generateFrom { s : Set α | ∃ a : α, s = { b : α | a < b } ∨ s = { b : α | b < a } }
+  generateFrom {s : Set α | ∃ a : α, s = {b : α | a < b} ∨ s = {b : α | b < a}}
 #align preorder.topology Preorder.topology
 -/
 
@@ -1055,25 +1055,25 @@ include t
 
 instance : OrderTopology αᵒᵈ :=
   ⟨by
-    convert@OrderTopology.topology_eq_generate_intervals α _ _ _ <;>
+    convert @OrderTopology.topology_eq_generate_intervals α _ _ _ <;>
         conv in _ ∨ _ => rw [or_comm] <;>
       rfl⟩
 
 #print isOpen_iff_generate_intervals /-
 theorem isOpen_iff_generate_intervals {s : Set α} :
-    IsOpen s ↔ GenerateOpen { s | ∃ a, s = Ioi a ∨ s = Iio a } s := by
+    IsOpen s ↔ GenerateOpen {s | ∃ a, s = Ioi a ∨ s = Iio a} s := by
   rw [t.topology_eq_generate_intervals] <;> rfl
 #align is_open_iff_generate_intervals isOpen_iff_generate_intervals
 -/
 
 #print isOpen_lt' /-
-theorem isOpen_lt' (a : α) : IsOpen { b : α | a < b } := by
+theorem isOpen_lt' (a : α) : IsOpen {b : α | a < b} := by
   rw [@isOpen_iff_generate_intervals α _ _ t] <;> exact generate_open.basic _ ⟨a, Or.inl rfl⟩
 #align is_open_lt' isOpen_lt'
 -/
 
 #print isOpen_gt' /-
-theorem isOpen_gt' (a : α) : IsOpen { b : α | b < a } := by
+theorem isOpen_gt' (a : α) : IsOpen {b : α | b < a} := by
   rw [@isOpen_iff_generate_intervals α _ _ t] <;> exact generate_open.basic _ ⟨a, Or.inr rfl⟩
 #align is_open_gt' isOpen_gt'
 -/
@@ -1107,8 +1107,8 @@ theorem nhds_eq_order (a : α) : 𝓝 a = (⨅ b ∈ Iio a, 𝓟 (Ioi b)) ⊓ 
     exact
       le_antisymm
         (le_inf
-          (le_iInf₂ fun b hb => iInf_le_of_le { c : α | b < c } <| iInf_le _ ⟨hb, b, Or.inl rfl⟩)
-          (le_iInf₂ fun b hb => iInf_le_of_le { c : α | c < b } <| iInf_le _ ⟨hb, b, Or.inr rfl⟩))
+          (le_iInf₂ fun b hb => iInf_le_of_le {c : α | b < c} <| iInf_le _ ⟨hb, b, Or.inl rfl⟩)
+          (le_iInf₂ fun b hb => iInf_le_of_le {c : α | c < b} <| iInf_le _ ⟨hb, b, Or.inr rfl⟩))
         (le_iInf fun s =>
           le_iInf fun ⟨ha, b, hs⟩ =>
             match s, ha, hs with
@@ -1234,14 +1234,14 @@ theorem induced_orderTopology' {α : Type u} {β : Type v} [Preorder α] [ta : T
     ·
       exact
         mem_comap.2
-          ⟨{ x | f b < x },
+          ⟨{x | f b < x},
             mem_inf_of_left <|
               mem_infi_of_mem _ <| mem_infi_of_mem (hf.2 ab) <| mem_principal_self _,
             fun x => hf.1⟩
     ·
       exact
         mem_comap.2
-          ⟨{ x | x < f b },
+          ⟨{x | x < f b},
             mem_inf_of_right <|
               mem_infi_of_mem _ <| mem_infi_of_mem (hf.2 ab) <| mem_principal_self _,
             fun x => hf.1⟩
@@ -1357,7 +1357,7 @@ theorem nhdsWithin_Ici_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopol
 theorem nhdsWithin_Iic_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopology α] {a : α}
     (ha : ∃ l, l < a) : (𝓝[≤] a).HasBasis (fun l => l < a) fun l => Ioc l a :=
   by
-  convert@nhdsWithin_Ici_basis' αᵒᵈ _ _ _ (to_dual a) ha
+  convert @nhdsWithin_Ici_basis' αᵒᵈ _ _ _ (to_dual a) ha
   exact funext fun x => (@dual_Ico _ _ _ _).symm
 #align nhds_within_Iic_basis' nhdsWithin_Iic_basis'
 -/
@@ -1415,7 +1415,7 @@ theorem tendsto_nhds_top_mono [TopologicalSpace β] [Preorder β] [OrderTop β]
   by
   simp only [nhds_top_order, tendsto_infi, tendsto_principal] at hf ⊢
   intro x hx
-  filter_upwards [hf x hx, hg]with _ using lt_of_lt_of_le
+  filter_upwards [hf x hx, hg] with _ using lt_of_lt_of_le
 #align tendsto_nhds_top_mono tendsto_nhds_top_mono
 
 theorem tendsto_nhds_bot_mono [TopologicalSpace β] [Preorder β] [OrderBot β] [OrderTopology β]
@@ -1476,10 +1476,10 @@ theorem order_separated {a₁ a₂ : α} (h : a₁ < a₂) :
     ∃ u v : Set α, IsOpen u ∧ IsOpen v ∧ a₁ ∈ u ∧ a₂ ∈ v ∧ ∀ b₁ ∈ u, ∀ b₂ ∈ v, b₁ < b₂ :=
   match dense_or_discrete a₁ a₂ with
   | Or.inl ⟨a, ha₁, ha₂⟩ =>
-    ⟨{ a' | a' < a }, { a' | a < a' }, isOpen_gt' a, isOpen_lt' a, ha₁, ha₂, fun b₁ h₁ b₂ h₂ =>
+    ⟨{a' | a' < a}, {a' | a < a'}, isOpen_gt' a, isOpen_lt' a, ha₁, ha₂, fun b₁ h₁ b₂ h₂ =>
       lt_trans h₁ h₂⟩
   | Or.inr ⟨h₁, h₂⟩ =>
-    ⟨{ a | a < a₂ }, { a | a₁ < a }, isOpen_gt' a₂, isOpen_lt' a₁, h, h, fun b₁ hb₁ b₂ hb₂ =>
+    ⟨{a | a < a₂}, {a | a₁ < a}, isOpen_gt' a₂, isOpen_lt' a₁, h, h, fun b₁ hb₁ b₂ hb₂ =>
       calc
         b₁ ≤ a₁ := h₂ _ hb₁
         _ < a₂ := h
@@ -1633,7 +1633,7 @@ theorem nhds_basis_Ioo [NoMaxOrder α] [NoMinOrder α] (a : α) :
 
 #print Filter.Eventually.exists_Ioo_subset /-
 theorem Filter.Eventually.exists_Ioo_subset [NoMaxOrder α] [NoMinOrder α] {a : α} {p : α → Prop}
-    (hp : ∀ᶠ x in 𝓝 a, p x) : ∃ l u, a ∈ Ioo l u ∧ Ioo l u ⊆ { x | p x } :=
+    (hp : ∀ᶠ x in 𝓝 a, p x) : ∃ l u, a ∈ Ioo l u ∧ Ioo l u ⊆ {x | p x} :=
   mem_nhds_iff_exists_Ioo_subset.1 hp
 #align filter.eventually.exists_Ioo_subset Filter.Eventually.exists_Ioo_subset
 -/
@@ -1642,10 +1642,10 @@ theorem Filter.Eventually.exists_Ioo_subset [NoMaxOrder α] [NoMinOrder α] {a :
 /-- The set of points which are isolated on the right is countable when the space is
 second-countable. -/
 theorem countable_of_isolated_right' [SecondCountableTopology α] :
-    Set.Countable { x : α | ∃ y, x < y ∧ Ioo x y = ∅ } :=
+    Set.Countable {x : α | ∃ y, x < y ∧ Ioo x y = ∅} :=
   by
   nontriviality α
-  let s := { x : α | ∃ y, x < y ∧ Ioo x y = ∅ }
+  let s := {x : α | ∃ y, x < y ∧ Ioo x y = ∅}
   have : ∀ x ∈ s, ∃ y, x < y ∧ Ioo x y = ∅ := fun x => id
   choose! y hy h'y using this
   have Hy : ∀ x z, x ∈ s → z < y x → z ≤ x :=
@@ -1654,8 +1654,8 @@ theorem countable_of_isolated_right' [SecondCountableTopology α] :
     have A : Ioo x (y x) = ∅ := h'y _ xs
     contrapose! A
     exact nonempty.ne_empty ⟨z, A, hz⟩
-  suffices H : ∀ a : Set α, IsOpen a → Set.Countable { x | x ∈ s ∧ x ∈ a ∧ y x ∉ a }
-  · have : s ⊆ ⋃ a ∈ countable_basis α, { x | x ∈ s ∧ x ∈ a ∧ y x ∉ a } :=
+  suffices H : ∀ a : Set α, IsOpen a → Set.Countable {x | x ∈ s ∧ x ∈ a ∧ y x ∉ a}
+  · have : s ⊆ ⋃ a ∈ countable_basis α, {x | x ∈ s ∧ x ∈ a ∧ y x ∉ a} :=
       by
       intro x hx
       rcases(is_basis_countable_basis α).exists_mem_of_ne (hy x hx).Ne with ⟨a, ab, xa, ya⟩
@@ -1665,10 +1665,9 @@ theorem countable_of_isolated_right' [SecondCountableTopology α] :
     refine' countable.bUnion (countable_countable_basis α) fun a ha => H _ _
     exact is_open_of_mem_countable_basis ha
   intro a ha
-  suffices H : Set.Countable { x | x ∈ s ∧ x ∈ a ∧ y x ∉ a ∧ ¬IsBot x }
+  suffices H : Set.Countable {x | x ∈ s ∧ x ∈ a ∧ y x ∉ a ∧ ¬IsBot x}
   · have :
-      { x | x ∈ s ∧ x ∈ a ∧ y x ∉ a } ⊆
-        { x | x ∈ s ∧ x ∈ a ∧ y x ∉ a ∧ ¬IsBot x } ∪ { x | IsBot x } :=
+      {x | x ∈ s ∧ x ∈ a ∧ y x ∉ a} ⊆ {x | x ∈ s ∧ x ∈ a ∧ y x ∉ a ∧ ¬IsBot x} ∪ {x | IsBot x} :=
       by
       intro x hx
       by_cases h'x : IsBot x
@@ -1677,7 +1676,7 @@ theorem countable_of_isolated_right' [SecondCountableTopology α] :
         simpa only [h'x, hx.2.1, hx.2.2, mem_set_of_eq, mem_union, not_false_iff, and_true_iff,
           or_false_iff] using hx.left
     exact countable.mono this (H.union (subsingleton_is_bot α).Countable)
-  let t := { x | x ∈ s ∧ x ∈ a ∧ y x ∉ a ∧ ¬IsBot x }
+  let t := {x | x ∈ s ∧ x ∈ a ∧ y x ∉ a ∧ ¬IsBot x}
   have : ∀ x ∈ t, ∃ z < x, Ioc z x ⊆ a := by
     intro x hx
     apply exists_Ioc_subset_of_mem_nhds (ha.mem_nhds hx.2.1)
@@ -1706,10 +1705,10 @@ theorem countable_of_isolated_right' [SecondCountableTopology α] :
 /-- The set of points which are isolated on the left is countable when the space is
 second-countable. -/
 theorem countable_of_isolated_left' [SecondCountableTopology α] :
-    Set.Countable { x : α | ∃ y, y < x ∧ Ioo y x = ∅ } :=
+    Set.Countable {x : α | ∃ y, y < x ∧ Ioo y x = ∅} :=
   by
-  convert@countable_of_isolated_right' αᵒᵈ _ _ _ _
-  have : ∀ x y : α, Ioo x y = { z | z < y ∧ x < z } := by simp_rw [and_comm', Ioo];
+  convert @countable_of_isolated_right' αᵒᵈ _ _ _ _
+  have : ∀ x y : α, Ioo x y = {z | z < y ∧ x < z} := by simp_rw [and_comm', Ioo];
     simp only [eq_self_iff_true, forall₂_true_iff]
   simp_rw [this]
   rfl
@@ -1723,11 +1722,11 @@ empty (but in fact this can happen only for countably many of them). -/
 theorem Set.PairwiseDisjoint.countable_of_Ioo [SecondCountableTopology α] {y : α → α} {s : Set α}
     (h : PairwiseDisjoint s fun x => Ioo x (y x)) (h' : ∀ x ∈ s, x < y x) : s.Countable :=
   by
-  let t := { x | x ∈ s ∧ (Ioo x (y x)).Nonempty }
+  let t := {x | x ∈ s ∧ (Ioo x (y x)).Nonempty}
   have t_count : t.countable :=
     haveI : t ⊆ s := fun x hx => hx.1
     (h.subset this).countable_of_isOpen (fun x hx => isOpen_Ioo) fun x hx => hx.2
-  have : s ⊆ t ∪ { x : α | ∃ x', x < x' ∧ Ioo x x' = ∅ } :=
+  have : s ⊆ t ∪ {x : α | ∃ x', x < x' ∧ Ioo x x' = ∅} :=
     by
     intro x hx
     by_cases h'x : (Ioo x (y x)).Nonempty
@@ -2140,7 +2139,7 @@ with `l < a`. -/
 theorem mem_nhdsWithin_Iic_iff_exists_Icc_subset [NoMinOrder α] [DenselyOrdered α] {a : α}
     {s : Set α} : s ∈ 𝓝[≤] a ↔ ∃ l, l < a ∧ Icc l a ⊆ s :=
   by
-  convert@mem_nhdsWithin_Ici_iff_exists_Icc_subset αᵒᵈ _ _ _ _ _ _ _
+  convert @mem_nhdsWithin_Ici_iff_exists_Icc_subset αᵒᵈ _ _ _ _ _ _ _
   simp_rw [show ∀ u : αᵒᵈ, @Icc αᵒᵈ _ a u = @Icc α _ u a from fun u => dual_Icc]
   rfl
 #align mem_nhds_within_Iic_iff_exists_Icc_subset mem_nhdsWithin_Iic_iff_exists_Icc_subset
@@ -2156,7 +2155,7 @@ variable [TopologicalSpace α] [LinearOrderedAddCommGroup α] [OrderTopology α]
 
 variable {l : Filter β} {f g : β → α}
 
-theorem nhds_eq_iInf_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r } :=
+theorem nhds_eq_iInf_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 {b | |a - b| < r} :=
   by
   simp only [le_antisymm_iff, nhds_eq_order, le_inf_iff, le_iInf_iff, le_principal_iff, mem_Ioi,
     mem_Iio, abs_sub_lt_iff, @sub_lt_iff_lt_add _ _ _ _ _ _ a, @sub_lt_comm _ _ _ _ a, set_of_and]
@@ -2173,7 +2172,7 @@ theorem nhds_eq_iInf_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| <
 #align nhds_eq_infi_abs_sub nhds_eq_iInf_abs_sub
 
 theorem orderTopology_of_nhds_abs {α : Type _} [TopologicalSpace α] [LinearOrderedAddCommGroup α]
-    (h_nhds : ∀ a : α, 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r }) : OrderTopology α :=
+    (h_nhds : ∀ a : α, 𝓝 a = ⨅ r > 0, 𝓟 {b | |a - b| < r}) : OrderTopology α :=
   by
   refine' ⟨eq_of_nhds_eq_nhds fun a => _⟩
   rw [h_nhds]
@@ -2239,7 +2238,7 @@ theorem nhds_basis_Ioo_pos [NoMinOrder α] [NoMaxOrder α] (a : α) :
 #align nhds_basis_Ioo_pos nhds_basis_Ioo_pos
 
 theorem nhds_basis_abs_sub_lt [NoMinOrder α] [NoMaxOrder α] (a : α) :
-    (𝓝 a).HasBasis (fun ε : α => (0 : α) < ε) fun ε => { b | |b - a| < ε } :=
+    (𝓝 a).HasBasis (fun ε : α => (0 : α) < ε) fun ε => {b | |b - a| < ε} :=
   by
   convert nhds_basis_Ioo_pos a
   · ext ε
@@ -2250,7 +2249,7 @@ theorem nhds_basis_abs_sub_lt [NoMinOrder α] [NoMaxOrder α] (a : α) :
 variable (α)
 
 theorem nhds_basis_zero_abs_sub_lt [NoMinOrder α] [NoMaxOrder α] :
-    (𝓝 (0 : α)).HasBasis (fun ε : α => (0 : α) < ε) fun ε => { b | |b| < ε } := by
+    (𝓝 (0 : α)).HasBasis (fun ε : α => (0 : α) < ε) fun ε => {b | |b| < ε} := by
   simpa using nhds_basis_abs_sub_lt (0 : α)
 #align nhds_basis_zero_abs_sub_lt nhds_basis_zero_abs_sub_lt
 
@@ -2352,7 +2351,7 @@ theorem isLUB_of_mem_nhds {s : Set α} {a : α} {f : Filter α} (hsa : a ∈ upp
     [NeBot (f ⊓ 𝓝 a)] : IsLUB s a :=
   ⟨hsa, fun b hb =>
     not_lt.1 fun hba =>
-      have : s ∩ { a | b < a } ∈ f ⊓ 𝓝 a := inter_mem_inf hsf (IsOpen.mem_nhds (isOpen_lt' _) hba)
+      have : s ∩ {a | b < a} ∈ f ⊓ 𝓝 a := inter_mem_inf hsf (IsOpen.mem_nhds (isOpen_lt' _) hba)
       let ⟨x, ⟨hxs, hxb⟩⟩ := Filter.nonempty_of_mem this
       have : b < b := lt_of_lt_of_le hxb <| hb hxs
       lt_irrefl b this⟩
@@ -3149,7 +3148,7 @@ theorem Dense.exists_countable_dense_subset_no_bot_top [Nontrivial α] {s : Set
     ∃ (t : _) (_ : t ⊆ s), t.Countable ∧ Dense t ∧ (∀ x, IsBot x → x ∉ t) ∧ ∀ x, IsTop x → x ∉ t :=
   by
   rcases hs.exists_countable_dense_subset with ⟨t, hts, htc, htd⟩
-  refine' ⟨t \ ({ x | IsBot x } ∪ { x | IsTop x }), _, _, _, _, _⟩
+  refine' ⟨t \ ({x | IsBot x} ∪ {x | IsTop x}), _, _, _, _, _⟩
   · exact (diff_subset _ _).trans hts
   · exact htc.mono (diff_subset _ _)
   · exact htd.diff_finite ((subsingleton_is_bot α).Finite.union (subsingleton_is_top α).Finite)
@@ -3424,7 +3423,7 @@ theorem Monotone.tendsto_nhdsWithin_Iio {α β : Type _} [LinearOrder α] [Topol
         exists_lt_of_lt_csSup (nonempty_image_iff.2 h) hl
     exact
       (mem_nhdsWithin_Iio_iff_exists_Ioo_subset' zx).2 ⟨z, zx, fun y hy => lz.trans_le (Mf hy.1.le)⟩
-  · filter_upwards [self_mem_nhdsWithin]with _ hy
+  · filter_upwards [self_mem_nhdsWithin] with _ hy
     apply lt_of_le_of_lt _ hm
     exact le_csSup (Mf.map_bdd_above bddAbove_Iio) (mem_image_of_mem _ hy)
 #align monotone.tendsto_nhds_within_Iio Monotone.tendsto_nhdsWithin_Iio

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

@@ -924,7 +924,7 @@ theorem Dense.exists_le' {s : Set α} (hs : Dense s) (hbot : ∀ x, IsBot x →
     ∃ y ∈ s, y ≤ x := by
   by_cases hx : IsBot x
   · exact ⟨x, hbot x hx, le_rfl⟩
-  · simp only [IsBot, not_forall, not_le] at hx
+  · simp only [IsBot, not_forall, not_le] at hx 
     rcases hs.exists_mem_open isOpen_Iio hx with ⟨y, hys, hy : y < x⟩
     exact ⟨y, hys, hy.le⟩
 #align dense.exists_le' Dense.exists_le'
@@ -1131,7 +1131,7 @@ instance tendstoIccClassNhds (a : α) : TendstoIxxClass Icc (𝓝 a) (𝓝 a) :=
     ((has_basis_infi_principal_finite _).inf (has_basis_infi_principal_finite _)).TendstoIxxClass
       fun s hs => _
   refine' ((ord_connected_bInter _).inter (ord_connected_bInter _)).out <;> intro _ _
-  exacts[ord_connected_Ioi, ord_connected_Iio]
+  exacts [ord_connected_Ioi, ord_connected_Iio]
 #align tendsto_Icc_class_nhds tendstoIccClassNhds
 -/
 
@@ -1413,7 +1413,7 @@ theorem nhds_bot_basis_Iic [TopologicalSpace α] [LinearOrder α] [OrderBot α]
 theorem tendsto_nhds_top_mono [TopologicalSpace β] [Preorder β] [OrderTop β] [OrderTopology β]
     {l : Filter α} {f g : α → β} (hf : Tendsto f l (𝓝 ⊤)) (hg : f ≤ᶠ[l] g) : Tendsto g l (𝓝 ⊤) :=
   by
-  simp only [nhds_top_order, tendsto_infi, tendsto_principal] at hf⊢
+  simp only [nhds_top_order, tendsto_infi, tendsto_principal] at hf ⊢
   intro x hx
   filter_upwards [hf x hx, hg]with _ using lt_of_lt_of_le
 #align tendsto_nhds_top_mono tendsto_nhds_top_mono
@@ -1519,14 +1519,14 @@ theorem exists_Ico_subset_of_mem_nhds' {a : α} {s : Set α} (hs : s ∈ 𝓝 a)
 #align exists_Ico_subset_of_mem_nhds' exists_Ico_subset_of_mem_nhds'
 
 theorem exists_Ico_subset_of_mem_nhds {a : α} {s : Set α} (hs : s ∈ 𝓝 a) (h : ∃ u, a < u) :
-    ∃ (u : _)(_ : a < u), Ico a u ⊆ s :=
+    ∃ (u : _) (_ : a < u), Ico a u ⊆ s :=
   let ⟨l', hl'⟩ := h
   let ⟨l, hl⟩ := exists_Ico_subset_of_mem_nhds' hs hl'
   ⟨l, hl.fst.1, hl.snd⟩
 #align exists_Ico_subset_of_mem_nhds exists_Ico_subset_of_mem_nhds
 
 theorem exists_Icc_mem_subset_of_mem_nhdsWithin_Ici {a : α} {s : Set α} (hs : s ∈ 𝓝[≥] a) :
-    ∃ (b : _)(_ : a ≤ b), Icc a b ∈ 𝓝[≥] a ∧ Icc a b ⊆ s :=
+    ∃ (b : _) (_ : a ≤ b), Icc a b ∈ 𝓝[≥] a ∧ Icc a b ⊆ s :=
   by
   rcases(em (IsMax a)).imp_right not_is_max_iff.mp with (ha | ha)
   · use a; simpa [ha.Ici_eq] using hs
@@ -1565,11 +1565,11 @@ theorem IsOpen.exists_Ioo_subset [Nontrivial α] {s : Set α} (hs : IsOpen s) (h
   obtain ⟨x, hx⟩ : ∃ x, x ∈ s := h
   obtain ⟨y, hy⟩ : ∃ y, y ≠ x := exists_ne x
   rcases lt_trichotomy x y with (H | rfl | H)
-  · obtain ⟨u, xu, hu⟩ : ∃ (u : α)(hu : x < u), Ico x u ⊆ s :=
+  · obtain ⟨u, xu, hu⟩ : ∃ (u : α) (hu : x < u), Ico x u ⊆ s :=
       exists_Ico_subset_of_mem_nhds (hs.mem_nhds hx) ⟨y, H⟩
     exact ⟨x, u, xu, Ioo_subset_Ico_self.trans hu⟩
   · exact (hy rfl).elim
-  · obtain ⟨l, lx, hl⟩ : ∃ (l : α)(hl : l < x), Ioc l x ⊆ s :=
+  · obtain ⟨l, lx, hl⟩ : ∃ (l : α) (hl : l < x), Ioc l x ⊆ s :=
       exists_Ioc_subset_of_mem_nhds (hs.mem_nhds hx) ⟨y, H⟩
     exact ⟨l, x, lx, Ioo_subset_Ioc_self.trans hl⟩
 #align is_open.exists_Ioo_subset IsOpen.exists_Ioo_subset
@@ -1580,7 +1580,7 @@ theorem dense_of_exists_between [Nontrivial α] {s : Set α}
   by
   apply dense_iff_inter_open.2 fun U U_open U_nonempty => _
   obtain ⟨a, b, hab, H⟩ : ∃ a b : α, a < b ∧ Ioo a b ⊆ U := U_open.exists_Ioo_subset U_nonempty
-  obtain ⟨x, xs, hx⟩ : ∃ (x : α)(H : x ∈ s), a < x ∧ x < b := h hab
+  obtain ⟨x, xs, hx⟩ : ∃ (x : α) (H : x ∈ s), a < x ∧ x < b := h hab
   exact ⟨x, ⟨H hx, xs⟩⟩
 #align dense_of_exists_between dense_of_exists_between
 
@@ -2231,8 +2231,8 @@ theorem nhds_basis_Ioo_pos [NoMinOrder α] [NoMaxOrder α] (a : α) :
       refine' ⟨min (a - l) (u - a), by apply lt_min <;> rwa [sub_pos], _⟩
       rintro x ⟨hx, hx'⟩
       apply h'
-      rw [sub_lt_comm, lt_min_iff, sub_lt_sub_iff_left] at hx
-      rw [← sub_lt_iff_lt_add', lt_min_iff, sub_lt_sub_iff_right] at hx'
+      rw [sub_lt_comm, lt_min_iff, sub_lt_sub_iff_left] at hx 
+      rw [← sub_lt_iff_lt_add', lt_min_iff, sub_lt_sub_iff_right] at hx' 
       exact ⟨hx.1, hx'.2⟩
     · rintro ⟨ε, ε_pos, h⟩
       exact ⟨(a - ε, a + ε), by simp [ε_pos], h⟩⟩
@@ -2361,7 +2361,7 @@ theorem isLUB_of_mem_nhds {s : Set α} {a : α} {f : Filter α} (hsa : a ∈ upp
 #print isLUB_of_mem_closure /-
 theorem isLUB_of_mem_closure {s : Set α} {a : α} (hsa : a ∈ upperBounds s) (hsf : a ∈ closure s) :
     IsLUB s a := by
-  rw [mem_closure_iff_clusterPt, ClusterPt, inf_comm] at hsf
+  rw [mem_closure_iff_clusterPt, ClusterPt, inf_comm] at hsf 
   haveI : (𝓟 s ⊓ 𝓝 a).ne_bot := hsf
   exact isLUB_of_mem_nhds hsa (mem_principal_self s)
 #align is_lub_of_mem_closure isLUB_of_mem_closure
@@ -2493,7 +2493,7 @@ theorem IsLUB.exists_seq_strictMono_tendsto_of_not_mem {t : Set α} {x : α}
   have : ∀ n k, k < x → ∃ y, Icc y x ⊆ s n ∧ k < y ∧ y < x ∧ y ∈ t :=
     by
     intro n k hk
-    obtain ⟨L, hL, h⟩ : ∃ (L : α)(hL : L ∈ Ico k x), Ioc L x ⊆ s n :=
+    obtain ⟨L, hL, h⟩ : ∃ (L : α) (hL : L ∈ Ico k x), Ioc L x ⊆ s n :=
       exists_Ioc_subset_of_mem_nhds' (hs.mem_of_mem trivial) hk
     obtain ⟨y, hy⟩ : ∃ y : α, L < y ∧ y < x ∧ y ∈ t :=
       by
@@ -3146,7 +3146,7 @@ separable space (e.g., if `α` has a second countable topology), then there exis
 dense subset `t ⊆ s` such that `t` does not contain bottom/top elements of `α`. -/
 theorem Dense.exists_countable_dense_subset_no_bot_top [Nontrivial α] {s : Set α} [SeparableSpace s]
     (hs : Dense s) :
-    ∃ (t : _)(_ : t ⊆ s), t.Countable ∧ Dense t ∧ (∀ x, IsBot x → x ∉ t) ∧ ∀ x, IsTop x → x ∉ t :=
+    ∃ (t : _) (_ : t ⊆ s), t.Countable ∧ Dense t ∧ (∀ x, IsBot x → x ∉ t) ∧ ∀ x, IsTop x → x ∉ t :=
   by
   rcases hs.exists_countable_dense_subset with ⟨t, hts, htc, htd⟩
   refine' ⟨t \ ({ x | IsBot x } ∪ { x | IsTop x }), _, _, _, _, _⟩

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

@@ -89,7 +89,7 @@ open Function
 
 open OrderDual (toDual ofDual)
 
-open Topology Classical Filter
+open scoped Topology Classical Filter
 
 universe u v w
 
@@ -140,14 +140,18 @@ theorem isClosed_le_prod : IsClosed { p : α × α | p.1 ≤ p.2 } :=
   t.isClosed_le'
 #align is_closed_le_prod isClosed_le_prod
 
+#print isClosed_le /-
 theorem isClosed_le [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
     IsClosed { b | f b ≤ g b } :=
   continuous_iff_isClosed.mp (hf.prod_mk hg) _ isClosed_le_prod
 #align is_closed_le isClosed_le
+-/
 
+#print isClosed_le' /-
 theorem isClosed_le' (a : α) : IsClosed { b | b ≤ a } :=
   isClosed_le continuous_id continuous_const
 #align is_closed_le' isClosed_le'
+-/
 
 #print isClosed_Iic /-
 theorem isClosed_Iic {a : α} : IsClosed (Iic a) :=
@@ -155,9 +159,11 @@ theorem isClosed_Iic {a : α} : IsClosed (Iic a) :=
 #align is_closed_Iic isClosed_Iic
 -/
 
+#print isClosed_ge' /-
 theorem isClosed_ge' (a : α) : IsClosed { b | a ≤ b } :=
   isClosed_le continuous_const continuous_id
 #align is_closed_ge' isClosed_ge'
+-/
 
 #print isClosed_Ici /-
 theorem isClosed_Ici {a : α} : IsClosed (Ici a) :=
@@ -195,72 +201,94 @@ theorem closure_Ici (a : α) : closure (Ici a) = Ici a :=
 #align closure_Ici closure_Ici
 -/
 
+#print le_of_tendsto_of_tendsto /-
 theorem le_of_tendsto_of_tendsto {f g : β → α} {b : Filter β} {a₁ a₂ : α} [NeBot b]
     (hf : Tendsto f b (𝓝 a₁)) (hg : Tendsto g b (𝓝 a₂)) (h : f ≤ᶠ[b] g) : a₁ ≤ a₂ :=
   have : Tendsto (fun b => (f b, g b)) b (𝓝 (a₁, a₂)) := by
     rw [nhds_prod_eq] <;> exact hf.prod_mk hg
   show (a₁, a₂) ∈ { p : α × α | p.1 ≤ p.2 } from t.isClosed_le'.mem_of_tendsto this h
 #align le_of_tendsto_of_tendsto le_of_tendsto_of_tendsto
+-/
 
 alias le_of_tendsto_of_tendsto ← tendsto_le_of_eventuallyLE
 #align tendsto_le_of_eventually_le tendsto_le_of_eventuallyLE
 
+#print le_of_tendsto_of_tendsto' /-
 theorem le_of_tendsto_of_tendsto' {f g : β → α} {b : Filter β} {a₁ a₂ : α} [NeBot b]
     (hf : Tendsto f b (𝓝 a₁)) (hg : Tendsto g b (𝓝 a₂)) (h : ∀ x, f x ≤ g x) : a₁ ≤ a₂ :=
   le_of_tendsto_of_tendsto hf hg (eventually_of_forall h)
 #align le_of_tendsto_of_tendsto' le_of_tendsto_of_tendsto'
+-/
 
+#print le_of_tendsto /-
 theorem le_of_tendsto {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
     (h : ∀ᶠ c in x, f c ≤ b) : a ≤ b :=
   le_of_tendsto_of_tendsto limUnder tendsto_const_nhds h
 #align le_of_tendsto le_of_tendsto
+-/
 
+#print le_of_tendsto' /-
 theorem le_of_tendsto' {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
     (h : ∀ c, f c ≤ b) : a ≤ b :=
   le_of_tendsto limUnder (eventually_of_forall h)
 #align le_of_tendsto' le_of_tendsto'
+-/
 
+#print ge_of_tendsto /-
 theorem ge_of_tendsto {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
     (h : ∀ᶠ c in x, b ≤ f c) : b ≤ a :=
   le_of_tendsto_of_tendsto tendsto_const_nhds limUnder h
 #align ge_of_tendsto ge_of_tendsto
+-/
 
+#print ge_of_tendsto' /-
 theorem ge_of_tendsto' {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
     (h : ∀ c, b ≤ f c) : b ≤ a :=
   ge_of_tendsto limUnder (eventually_of_forall h)
 #align ge_of_tendsto' ge_of_tendsto'
+-/
 
+#print closure_le_eq /-
 @[simp]
 theorem closure_le_eq [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
     closure { b | f b ≤ g b } = { b | f b ≤ g b } :=
   (isClosed_le hf hg).closure_eq
 #align closure_le_eq closure_le_eq
+-/
 
+#print closure_lt_subset_le /-
 theorem closure_lt_subset_le [TopologicalSpace β] {f g : β → α} (hf : Continuous f)
     (hg : Continuous g) : closure { b | f b < g b } ⊆ { b | f b ≤ g b } :=
   (closure_minimal fun x => le_of_lt) <| isClosed_le hf hg
 #align closure_lt_subset_le closure_lt_subset_le
+-/
 
+#print ContinuousWithinAt.closure_le /-
 theorem ContinuousWithinAt.closure_le [TopologicalSpace β] {f g : β → α} {s : Set β} {x : β}
     (hx : x ∈ closure s) (hf : ContinuousWithinAt f s x) (hg : ContinuousWithinAt g s x)
     (h : ∀ y ∈ s, f y ≤ g y) : f x ≤ g x :=
   show (f x, g x) ∈ { p : α × α | p.1 ≤ p.2 } from
     OrderClosedTopology.isClosed_le'.closure_subset ((hf.Prod hg).mem_closure hx h)
 #align continuous_within_at.closure_le ContinuousWithinAt.closure_le
+-/
 
+#print IsClosed.isClosed_le /-
 /-- If `s` is a closed set and two functions `f` and `g` are continuous on `s`,
 then the set `{x ∈ s | f x ≤ g x}` is a closed set. -/
 theorem IsClosed.isClosed_le [TopologicalSpace β] {f g : β → α} {s : Set β} (hs : IsClosed s)
     (hf : ContinuousOn f s) (hg : ContinuousOn g s) : IsClosed ({ x ∈ s | f x ≤ g x }) :=
   (hf.Prod hg).preimage_closed_of_closed hs OrderClosedTopology.isClosed_le'
 #align is_closed.is_closed_le IsClosed.isClosed_le
+-/
 
+#print le_on_closure /-
 theorem le_on_closure [TopologicalSpace β] {f g : β → α} {s : Set β} (h : ∀ x ∈ s, f x ≤ g x)
     (hf : ContinuousOn f (closure s)) (hg : ContinuousOn g (closure s)) ⦃x⦄ (hx : x ∈ closure s) :
     f x ≤ g x :=
   have : s ⊆ { y ∈ closure s | f y ≤ g y } := fun y hy => ⟨subset_closure hy, h y hy⟩
   (closure_minimal this (isClosed_closure.isClosed_le hf hg) hx).2
 #align le_on_closure le_on_closure
+-/
 
 theorem IsClosed.epigraph [TopologicalSpace β] {f : β → α} {s : Set β} (hs : IsClosed s)
     (hf : ContinuousOn f s) : IsClosed { p : β × α | p.1 ∈ s ∧ f p.1 ≤ p.2 } :=
@@ -274,9 +302,11 @@ theorem IsClosed.hypograph [TopologicalSpace β] {f : β → α} {s : Set β} (h
 
 omit t
 
+#print nhdsWithin_Ici_neBot /-
 theorem nhdsWithin_Ici_neBot {a b : α} (H₂ : a ≤ b) : NeBot (𝓝[Ici a] b) :=
   nhdsWithin_neBot_of_mem H₂
 #align nhds_within_Ici_ne_bot nhdsWithin_Ici_neBot
+-/
 
 #print nhdsWithin_Ici_self_neBot /-
 @[instance]
@@ -285,9 +315,11 @@ theorem nhdsWithin_Ici_self_neBot (a : α) : NeBot (𝓝[≥] a) :=
 #align nhds_within_Ici_self_ne_bot nhdsWithin_Ici_self_neBot
 -/
 
+#print nhdsWithin_Iic_neBot /-
 theorem nhdsWithin_Iic_neBot {a b : α} (H : a ≤ b) : NeBot (𝓝[Iic b] a) :=
   nhdsWithin_neBot_of_mem H
 #align nhds_within_Iic_ne_bot nhdsWithin_Iic_neBot
+-/
 
 #print nhdsWithin_Iic_self_neBot /-
 @[instance]
@@ -325,10 +357,12 @@ theorem isOpen_lt_prod : IsOpen { p : α × α | p.1 < p.2 } :=
   exact isClosed_le continuous_snd continuous_fst
 #align is_open_lt_prod isOpen_lt_prod
 
+#print isOpen_lt /-
 theorem isOpen_lt [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
     IsOpen { b | f b < g b } := by
   simp [lt_iff_not_ge, -not_le] <;> exact (isClosed_le hg hf).isOpen_compl
 #align is_open_lt isOpen_lt
+-/
 
 variable {a b : α}
 
@@ -377,57 +411,81 @@ theorem Ioo_subset_closure_interior : Ioo a b ⊆ closure (interior (Ioo a b)) :
 #align Ioo_subset_closure_interior Ioo_subset_closure_interior
 -/
 
+#print Iio_mem_nhds /-
 theorem Iio_mem_nhds {a b : α} (h : a < b) : Iio b ∈ 𝓝 a :=
   IsOpen.mem_nhds isOpen_Iio h
 #align Iio_mem_nhds Iio_mem_nhds
+-/
 
+#print Ioi_mem_nhds /-
 theorem Ioi_mem_nhds {a b : α} (h : a < b) : Ioi a ∈ 𝓝 b :=
   IsOpen.mem_nhds isOpen_Ioi h
 #align Ioi_mem_nhds Ioi_mem_nhds
+-/
 
+#print Iic_mem_nhds /-
 theorem Iic_mem_nhds {a b : α} (h : a < b) : Iic b ∈ 𝓝 a :=
   mem_of_superset (Iio_mem_nhds h) Iio_subset_Iic_self
 #align Iic_mem_nhds Iic_mem_nhds
+-/
 
+#print Ici_mem_nhds /-
 theorem Ici_mem_nhds {a b : α} (h : a < b) : Ici a ∈ 𝓝 b :=
   mem_of_superset (Ioi_mem_nhds h) Ioi_subset_Ici_self
 #align Ici_mem_nhds Ici_mem_nhds
+-/
 
+#print Ioo_mem_nhds /-
 theorem Ioo_mem_nhds {a b x : α} (ha : a < x) (hb : x < b) : Ioo a b ∈ 𝓝 x :=
   IsOpen.mem_nhds isOpen_Ioo ⟨ha, hb⟩
 #align Ioo_mem_nhds Ioo_mem_nhds
+-/
 
+#print Ioc_mem_nhds /-
 theorem Ioc_mem_nhds {a b x : α} (ha : a < x) (hb : x < b) : Ioc a b ∈ 𝓝 x :=
   mem_of_superset (Ioo_mem_nhds ha hb) Ioo_subset_Ioc_self
 #align Ioc_mem_nhds Ioc_mem_nhds
+-/
 
+#print Ico_mem_nhds /-
 theorem Ico_mem_nhds {a b x : α} (ha : a < x) (hb : x < b) : Ico a b ∈ 𝓝 x :=
   mem_of_superset (Ioo_mem_nhds ha hb) Ioo_subset_Ico_self
 #align Ico_mem_nhds Ico_mem_nhds
+-/
 
+#print Icc_mem_nhds /-
 theorem Icc_mem_nhds {a b x : α} (ha : a < x) (hb : x < b) : Icc a b ∈ 𝓝 x :=
   mem_of_superset (Ioo_mem_nhds ha hb) Ioo_subset_Icc_self
 #align Icc_mem_nhds Icc_mem_nhds
+-/
 
+#print eventually_lt_of_tendsto_lt /-
 theorem eventually_lt_of_tendsto_lt {l : Filter γ} {f : γ → α} {u v : α} (hv : v < u)
     (h : Filter.Tendsto f l (𝓝 v)) : ∀ᶠ a in l, f a < u :=
   tendsto_nhds.1 h (· < u) isOpen_Iio hv
 #align eventually_lt_of_tendsto_lt eventually_lt_of_tendsto_lt
+-/
 
+#print eventually_gt_of_tendsto_gt /-
 theorem eventually_gt_of_tendsto_gt {l : Filter γ} {f : γ → α} {u v : α} (hv : u < v)
     (h : Filter.Tendsto f l (𝓝 v)) : ∀ᶠ a in l, u < f a :=
   tendsto_nhds.1 h (· > u) isOpen_Ioi hv
 #align eventually_gt_of_tendsto_gt eventually_gt_of_tendsto_gt
+-/
 
+#print eventually_le_of_tendsto_lt /-
 theorem eventually_le_of_tendsto_lt {l : Filter γ} {f : γ → α} {u v : α} (hv : v < u)
     (h : Tendsto f l (𝓝 v)) : ∀ᶠ a in l, f a ≤ u :=
   (eventually_lt_of_tendsto_lt hv h).mono fun v => le_of_lt
 #align eventually_le_of_tendsto_lt eventually_le_of_tendsto_lt
+-/
 
+#print eventually_ge_of_tendsto_gt /-
 theorem eventually_ge_of_tendsto_gt {l : Filter γ} {f : γ → α} {u v : α} (hv : u < v)
     (h : Tendsto f l (𝓝 v)) : ∀ᶠ a in l, u ≤ f a :=
   (eventually_gt_of_tendsto_gt hv h).mono fun v => le_of_lt
 #align eventually_ge_of_tendsto_gt eventually_ge_of_tendsto_gt
+-/
 
 variable [TopologicalSpace γ]
 
@@ -471,29 +529,37 @@ theorem Icc_mem_nhdsWithin_Ioi {a b c : α} (H : b ∈ Ico a c) : Icc a c ∈ 
 #align Icc_mem_nhds_within_Ioi Icc_mem_nhdsWithin_Ioi
 -/
 
+#print nhdsWithin_Ioc_eq_nhdsWithin_Ioi /-
 @[simp]
 theorem nhdsWithin_Ioc_eq_nhdsWithin_Ioi {a b : α} (h : a < b) : 𝓝[Ioc a b] a = 𝓝[>] a :=
   le_antisymm (nhdsWithin_mono _ Ioc_subset_Ioi_self) <|
     nhdsWithin_le_of_mem <| Ioc_mem_nhdsWithin_Ioi <| left_mem_Ico.2 h
 #align nhds_within_Ioc_eq_nhds_within_Ioi nhdsWithin_Ioc_eq_nhdsWithin_Ioi
+-/
 
+#print nhdsWithin_Ioo_eq_nhdsWithin_Ioi /-
 @[simp]
 theorem nhdsWithin_Ioo_eq_nhdsWithin_Ioi {a b : α} (h : a < b) : 𝓝[Ioo a b] a = 𝓝[>] a :=
   le_antisymm (nhdsWithin_mono _ Ioo_subset_Ioi_self) <|
     nhdsWithin_le_of_mem <| Ioo_mem_nhdsWithin_Ioi <| left_mem_Ico.2 h
 #align nhds_within_Ioo_eq_nhds_within_Ioi nhdsWithin_Ioo_eq_nhdsWithin_Ioi
+-/
 
+#print continuousWithinAt_Ioc_iff_Ioi /-
 @[simp]
 theorem continuousWithinAt_Ioc_iff_Ioi [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Ioc a b) a ↔ ContinuousWithinAt f (Ioi a) a := by
   simp only [ContinuousWithinAt, nhdsWithin_Ioc_eq_nhdsWithin_Ioi h]
 #align continuous_within_at_Ioc_iff_Ioi continuousWithinAt_Ioc_iff_Ioi
+-/
 
+#print continuousWithinAt_Ioo_iff_Ioi /-
 @[simp]
 theorem continuousWithinAt_Ioo_iff_Ioi [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Ioo a b) a ↔ ContinuousWithinAt f (Ioi a) a := by
   simp only [ContinuousWithinAt, nhdsWithin_Ioo_eq_nhdsWithin_Ioi h]
 #align continuous_within_at_Ioo_iff_Ioi continuousWithinAt_Ioo_iff_Ioi
+-/
 
 /-!
 #### Left neighborhoods, point excluded
@@ -525,27 +591,35 @@ theorem Icc_mem_nhdsWithin_Iio {a b c : α} (H : b ∈ Ioc a c) : Icc a c ∈ 
 #align Icc_mem_nhds_within_Iio Icc_mem_nhdsWithin_Iio
 -/
 
+#print nhdsWithin_Ico_eq_nhdsWithin_Iio /-
 @[simp]
 theorem nhdsWithin_Ico_eq_nhdsWithin_Iio {a b : α} (h : a < b) : 𝓝[Ico a b] b = 𝓝[<] b := by
   simpa only [dual_Ioc] using nhdsWithin_Ioc_eq_nhdsWithin_Ioi h.dual
 #align nhds_within_Ico_eq_nhds_within_Iio nhdsWithin_Ico_eq_nhdsWithin_Iio
+-/
 
+#print nhdsWithin_Ioo_eq_nhdsWithin_Iio /-
 @[simp]
 theorem nhdsWithin_Ioo_eq_nhdsWithin_Iio {a b : α} (h : a < b) : 𝓝[Ioo a b] b = 𝓝[<] b := by
   simpa only [dual_Ioo] using nhdsWithin_Ioo_eq_nhdsWithin_Ioi h.dual
 #align nhds_within_Ioo_eq_nhds_within_Iio nhdsWithin_Ioo_eq_nhdsWithin_Iio
+-/
 
+#print continuousWithinAt_Ico_iff_Iio /-
 @[simp]
 theorem continuousWithinAt_Ico_iff_Iio {a b : α} {f : α → γ} (h : a < b) :
     ContinuousWithinAt f (Ico a b) b ↔ ContinuousWithinAt f (Iio b) b := by
   simp only [ContinuousWithinAt, nhdsWithin_Ico_eq_nhdsWithin_Iio h]
 #align continuous_within_at_Ico_iff_Iio continuousWithinAt_Ico_iff_Iio
+-/
 
+#print continuousWithinAt_Ioo_iff_Iio /-
 @[simp]
 theorem continuousWithinAt_Ioo_iff_Iio {a b : α} {f : α → γ} (h : a < b) :
     ContinuousWithinAt f (Ioo a b) b ↔ ContinuousWithinAt f (Iio b) b := by
   simp only [ContinuousWithinAt, nhdsWithin_Ioo_eq_nhdsWithin_Iio h]
 #align continuous_within_at_Ioo_iff_Iio continuousWithinAt_Ioo_iff_Iio
+-/
 
 /-!
 #### Right neighborhoods, point included
@@ -577,29 +651,37 @@ theorem Icc_mem_nhdsWithin_Ici {a b c : α} (H : b ∈ Ico a c) : Icc a c ∈ 
 #align Icc_mem_nhds_within_Ici Icc_mem_nhdsWithin_Ici
 -/
 
+#print nhdsWithin_Icc_eq_nhdsWithin_Ici /-
 @[simp]
 theorem nhdsWithin_Icc_eq_nhdsWithin_Ici {a b : α} (h : a < b) : 𝓝[Icc a b] a = 𝓝[≥] a :=
   le_antisymm (nhdsWithin_mono _ Icc_subset_Ici_self) <|
     nhdsWithin_le_of_mem <| Icc_mem_nhdsWithin_Ici <| left_mem_Ico.2 h
 #align nhds_within_Icc_eq_nhds_within_Ici nhdsWithin_Icc_eq_nhdsWithin_Ici
+-/
 
+#print nhdsWithin_Ico_eq_nhdsWithin_Ici /-
 @[simp]
 theorem nhdsWithin_Ico_eq_nhdsWithin_Ici {a b : α} (h : a < b) : 𝓝[Ico a b] a = 𝓝[≥] a :=
   le_antisymm (nhdsWithin_mono _ fun x => And.left) <|
     nhdsWithin_le_of_mem <| Ico_mem_nhdsWithin_Ici <| left_mem_Ico.2 h
 #align nhds_within_Ico_eq_nhds_within_Ici nhdsWithin_Ico_eq_nhdsWithin_Ici
+-/
 
+#print continuousWithinAt_Icc_iff_Ici /-
 @[simp]
 theorem continuousWithinAt_Icc_iff_Ici [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Icc a b) a ↔ ContinuousWithinAt f (Ici a) a := by
   simp only [ContinuousWithinAt, nhdsWithin_Icc_eq_nhdsWithin_Ici h]
 #align continuous_within_at_Icc_iff_Ici continuousWithinAt_Icc_iff_Ici
+-/
 
+#print continuousWithinAt_Ico_iff_Ici /-
 @[simp]
 theorem continuousWithinAt_Ico_iff_Ici [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Ico a b) a ↔ ContinuousWithinAt f (Ici a) a := by
   simp only [ContinuousWithinAt, nhdsWithin_Ico_eq_nhdsWithin_Ici h]
 #align continuous_within_at_Ico_iff_Ici continuousWithinAt_Ico_iff_Ici
+-/
 
 /-!
 #### Left neighborhoods, point included
@@ -631,27 +713,35 @@ theorem Icc_mem_nhdsWithin_Iic {a b c : α} (H : b ∈ Ioc a c) : Icc a c ∈ 
 #align Icc_mem_nhds_within_Iic Icc_mem_nhdsWithin_Iic
 -/
 
+#print nhdsWithin_Icc_eq_nhdsWithin_Iic /-
 @[simp]
 theorem nhdsWithin_Icc_eq_nhdsWithin_Iic {a b : α} (h : a < b) : 𝓝[Icc a b] b = 𝓝[≤] b := by
   simpa only [dual_Icc] using nhdsWithin_Icc_eq_nhdsWithin_Ici h.dual
 #align nhds_within_Icc_eq_nhds_within_Iic nhdsWithin_Icc_eq_nhdsWithin_Iic
+-/
 
+#print nhdsWithin_Ioc_eq_nhdsWithin_Iic /-
 @[simp]
 theorem nhdsWithin_Ioc_eq_nhdsWithin_Iic {a b : α} (h : a < b) : 𝓝[Ioc a b] b = 𝓝[≤] b := by
   simpa only [dual_Ico] using nhdsWithin_Ico_eq_nhdsWithin_Ici h.dual
 #align nhds_within_Ioc_eq_nhds_within_Iic nhdsWithin_Ioc_eq_nhdsWithin_Iic
+-/
 
+#print continuousWithinAt_Icc_iff_Iic /-
 @[simp]
 theorem continuousWithinAt_Icc_iff_Iic [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Icc a b) b ↔ ContinuousWithinAt f (Iic b) b := by
   simp only [ContinuousWithinAt, nhdsWithin_Icc_eq_nhdsWithin_Iic h]
 #align continuous_within_at_Icc_iff_Iic continuousWithinAt_Icc_iff_Iic
+-/
 
+#print continuousWithinAt_Ioc_iff_Iic /-
 @[simp]
 theorem continuousWithinAt_Ioc_iff_Iic [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Ioc a b) b ↔ ContinuousWithinAt f (Iic b) b := by
   simp only [ContinuousWithinAt, nhdsWithin_Ioc_eq_nhdsWithin_Iic h]
 #align continuous_within_at_Ioc_iff_Iic continuousWithinAt_Ioc_iff_Iic
+-/
 
 end LinearOrder
 
@@ -663,11 +753,14 @@ section
 
 variable [TopologicalSpace β]
 
+#print lt_subset_interior_le /-
 theorem lt_subset_interior_le (hf : Continuous f) (hg : Continuous g) :
     { b | f b < g b } ⊆ interior { b | f b ≤ g b } :=
   (interior_maximal fun p => le_of_lt) <| isOpen_lt hf hg
 #align lt_subset_interior_le lt_subset_interior_le
+-/
 
+#print frontier_le_subset_eq /-
 theorem frontier_le_subset_eq (hf : Continuous f) (hg : Continuous g) :
     frontier { b | f b ≤ g b } ⊆ { b | f b = g b } :=
   by
@@ -676,6 +769,7 @@ theorem frontier_le_subset_eq (hf : Continuous f) (hg : Continuous g) :
   refine' le_antisymm hb₁ (closure_lt_subset_le hg hf _)
   convert hb₂ using 2; simp only [not_le.symm]; rfl
 #align frontier_le_subset_eq frontier_le_subset_eq
+-/
 
 #print frontier_Iic_subset /-
 theorem frontier_Iic_subset (a : α) : frontier (Iic a) ⊆ {a} :=
@@ -689,11 +783,14 @@ theorem frontier_Ici_subset (a : α) : frontier (Ici a) ⊆ {a} :=
 #align frontier_Ici_subset frontier_Ici_subset
 -/
 
+#print frontier_lt_subset_eq /-
 theorem frontier_lt_subset_eq (hf : Continuous f) (hg : Continuous g) :
     frontier { b | f b < g b } ⊆ { b | f b = g b } := by
   rw [← frontier_compl] <;> convert frontier_le_subset_eq hg hf <;> simp [ext_iff, eq_comm]
 #align frontier_lt_subset_eq frontier_lt_subset_eq
+-/
 
+#print continuous_if_le /-
 theorem continuous_if_le [TopologicalSpace γ] [∀ x, Decidable (f x ≤ g x)] {f' g' : β → γ}
     (hf : Continuous f) (hg : Continuous g) (hf' : ContinuousOn f' { x | f x ≤ g x })
     (hg' : ContinuousOn g' { x | g x ≤ f x }) (hfg : ∀ x, f x = g x → f' x = g' x) :
@@ -703,13 +800,17 @@ theorem continuous_if_le [TopologicalSpace γ] [∀ x, Decidable (f x ≤ g x)]
   · rwa [(isClosed_le hf hg).closure_eq]
   · simp only [not_le]; exact closure_lt_subset_le hg hf
 #align continuous_if_le continuous_if_le
+-/
 
+#print Continuous.if_le /-
 theorem Continuous.if_le [TopologicalSpace γ] [∀ x, Decidable (f x ≤ g x)] {f' g' : β → γ}
     (hf' : Continuous f') (hg' : Continuous g') (hf : Continuous f) (hg : Continuous g)
     (hfg : ∀ x, f x = g x → f' x = g' x) : Continuous fun x => if f x ≤ g x then f' x else g' x :=
   continuous_if_le hf hg hf'.ContinuousOn hg'.ContinuousOn hfg
 #align continuous.if_le Continuous.if_le
+-/
 
+#print Filter.Tendsto.eventually_lt /-
 theorem Filter.Tendsto.eventually_lt {l : Filter γ} {f g : γ → α} {y z : α} (hf : Tendsto f l (𝓝 y))
     (hg : Tendsto g l (𝓝 z)) (hyz : y < z) : ∀ᶠ x in l, f x < g x :=
   by
@@ -721,11 +822,14 @@ theorem Filter.Tendsto.eventually_lt {l : Filter γ} {f g : γ → α} {y z : α
     filter_upwards [hf (Iio_mem_nhds hyw), hg (Ioi_mem_nhds hwz)]
     exact fun x => lt_trans
 #align tendsto.eventually_lt Filter.Tendsto.eventually_lt
+-/
 
+#print ContinuousAt.eventually_lt /-
 theorem ContinuousAt.eventually_lt {x₀ : β} (hf : ContinuousAt f x₀) (hg : ContinuousAt g x₀)
     (hfg : f x₀ < g x₀) : ∀ᶠ x in 𝓝 x₀, f x < g x :=
   Filter.Tendsto.eventually_lt hf hg hfg
 #align continuous_at.eventually_lt ContinuousAt.eventually_lt
+-/
 
 @[continuity]
 theorem Continuous.min (hf : Continuous f) (hg : Continuous g) :
@@ -962,29 +1066,41 @@ theorem isOpen_iff_generate_intervals {s : Set α} :
 #align is_open_iff_generate_intervals isOpen_iff_generate_intervals
 -/
 
+#print isOpen_lt' /-
 theorem isOpen_lt' (a : α) : IsOpen { b : α | a < b } := by
   rw [@isOpen_iff_generate_intervals α _ _ t] <;> exact generate_open.basic _ ⟨a, Or.inl rfl⟩
 #align is_open_lt' isOpen_lt'
+-/
 
+#print isOpen_gt' /-
 theorem isOpen_gt' (a : α) : IsOpen { b : α | b < a } := by
   rw [@isOpen_iff_generate_intervals α _ _ t] <;> exact generate_open.basic _ ⟨a, Or.inr rfl⟩
 #align is_open_gt' isOpen_gt'
+-/
 
+#print lt_mem_nhds /-
 theorem lt_mem_nhds {a b : α} (h : a < b) : ∀ᶠ x in 𝓝 b, a < x :=
   IsOpen.mem_nhds (isOpen_lt' _) h
 #align lt_mem_nhds lt_mem_nhds
+-/
 
+#print le_mem_nhds /-
 theorem le_mem_nhds {a b : α} (h : a < b) : ∀ᶠ x in 𝓝 b, a ≤ x :=
   (𝓝 b).sets_of_superset (lt_mem_nhds h) fun b hb => le_of_lt hb
 #align le_mem_nhds le_mem_nhds
+-/
 
+#print gt_mem_nhds /-
 theorem gt_mem_nhds {a b : α} (h : a < b) : ∀ᶠ x in 𝓝 a, x < b :=
   IsOpen.mem_nhds (isOpen_gt' _) h
 #align gt_mem_nhds gt_mem_nhds
+-/
 
+#print ge_mem_nhds /-
 theorem ge_mem_nhds {a b : α} (h : a < b) : ∀ᶠ x in 𝓝 a, x ≤ b :=
   (𝓝 a).sets_of_superset (gt_mem_nhds h) fun b hb => le_of_lt hb
 #align ge_mem_nhds ge_mem_nhds
+-/
 
 theorem nhds_eq_order (a : α) : 𝓝 a = (⨅ b ∈ Iio a, 𝓟 (Ioi b)) ⊓ ⨅ b ∈ Ioi a, 𝓟 (Iio b) := by
   rw [t.topology_eq_generate_intervals, nhds_generate_from] <;>
@@ -1000,10 +1116,12 @@ theorem nhds_eq_order (a : α) : 𝓝 a = (⨅ b ∈ Iio a, 𝓟 (Ioi b)) ⊓ 
             | _, h, Or.inr rfl => inf_le_of_right_le <| iInf_le_of_le b <| iInf_le _ h)
 #align nhds_eq_order nhds_eq_order
 
+#print tendsto_order /-
 theorem tendsto_order {f : β → α} {a : α} {x : Filter β} :
     Tendsto f x (𝓝 a) ↔ (∀ a' < a, ∀ᶠ b in x, a' < f b) ∧ ∀ a' > a, ∀ᶠ b in x, f b < a' := by
   simp [nhds_eq_order a, tendsto_inf, tendsto_infi, tendsto_principal]
 #align tendsto_order tendsto_order
+-/
 
 #print tendstoIccClassNhds /-
 instance tendstoIccClassNhds (a : α) : TendstoIxxClass Icc (𝓝 a) (𝓝 a) :=
@@ -1035,6 +1153,7 @@ instance tendstoIooClassNhds (a : α) : TendstoIxxClass Ioo (𝓝 a) (𝓝 a) :=
 #align tendsto_Ioo_class_nhds tendstoIooClassNhds
 -/
 
+#print tendsto_of_tendsto_of_tendsto_of_le_of_le' /-
 /-- **Squeeze theorem** (also known as **sandwich theorem**). This version assumes that inequalities
 hold eventually for the filter. -/
 theorem tendsto_of_tendsto_of_tendsto_of_le_of_le' {f g h : β → α} {b : Filter β} {a : α}
@@ -1042,7 +1161,9 @@ theorem tendsto_of_tendsto_of_tendsto_of_le_of_le' {f g h : β → α} {b : Filt
     (hfh : ∀ᶠ b in b, f b ≤ h b) : Tendsto f b (𝓝 a) :=
   (hg.Icc hh).of_smallSets <| hgf.And hfh
 #align tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_of_tendsto_of_tendsto_of_le_of_le'
+-/
 
+#print tendsto_of_tendsto_of_tendsto_of_le_of_le /-
 /-- **Squeeze theorem** (also known as **sandwich theorem**). This version assumes that inequalities
 hold everywhere. -/
 theorem tendsto_of_tendsto_of_tendsto_of_le_of_le {f g h : β → α} {b : Filter β} {a : α}
@@ -1051,6 +1172,7 @@ theorem tendsto_of_tendsto_of_tendsto_of_le_of_le {f g h : β → α} {b : Filte
   tendsto_of_tendsto_of_tendsto_of_le_of_le' hg hh (eventually_of_forall hgf)
     (eventually_of_forall hfh)
 #align tendsto_of_tendsto_of_tendsto_of_le_of_le tendsto_of_tendsto_of_tendsto_of_le_of_le
+-/
 
 theorem nhds_order_unbounded {a : α} (hu : ∃ u, a < u) (hl : ∃ l, l < a) :
     𝓝 a = ⨅ (l) (h₂ : l < a) (u) (h₂ : a < u), 𝓟 (Ioo l u) :=
@@ -1061,6 +1183,7 @@ theorem nhds_order_unbounded {a : α} (hu : ∃ u, a < u) (hl : ∃ l, l < a) :
   rfl
 #align nhds_order_unbounded nhds_order_unbounded
 
+#print tendsto_order_unbounded /-
 theorem tendsto_order_unbounded {f : β → α} {a : α} {x : Filter β} (hu : ∃ u, a < u)
     (hl : ∃ l, l < a) (h : ∀ l u, l < a → a < u → ∀ᶠ b in x, l < f b ∧ f b < u) :
     Tendsto f x (𝓝 a) := by
@@ -1070,6 +1193,7 @@ theorem tendsto_order_unbounded {f : β → α} {a : α} {x : Filter β} (hu : 
         tendsto_infi.2 fun hl =>
           tendsto_infi.2 fun u => tendsto_infi.2 fun hu => tendsto_principal.2 <| h l u hl hu
 #align tendsto_order_unbounded tendsto_order_unbounded
+-/
 
 end Preorder
 
@@ -1131,6 +1255,7 @@ theorem induced_orderTopology' {α : Type u} {β : Type v} [Preorder α] [ta : T
       exact fun c hc => lt_of_lt_of_le (hf.2 hc) xb
 #align induced_order_topology' induced_orderTopology'
 
+#print induced_orderTopology /-
 theorem induced_orderTopology {α : Type u} {β : Type v} [Preorder α] [ta : TopologicalSpace β]
     [Preorder β] [OrderTopology β] (f : α → β) (hf : ∀ {x y}, f x < f y ↔ x < y)
     (H : ∀ {x y}, x < y → ∃ a, x < f a ∧ f a < y) : @OrderTopology _ (induced f ta) _ :=
@@ -1142,6 +1267,7 @@ theorem induced_orderTopology {α : Type u} {β : Type v} [Preorder α] [ta : To
     let ⟨b, ab, bx⟩ := H ax
     ⟨b, hf.1 ab, le_of_lt bx⟩
 #align induced_order_topology induced_orderTopology
+-/
 
 #print orderTopology_of_ordConnected /-
 /-- On an `ord_connected` subset of a linear order, the order topology for the restriction of the
@@ -1215,6 +1341,7 @@ theorem nhdsWithin_Iic_eq' [TopologicalSpace α] [Preorder α] [OrderTopology α
   simp only [nhdsWithin_Iic_eq'', biInf_inf ha, inf_principal, Ioi_inter_Iic]
 #align nhds_within_Iic_eq' nhdsWithin_Iic_eq'
 
+#print nhdsWithin_Ici_basis' /-
 theorem nhdsWithin_Ici_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopology α] {a : α}
     (ha : ∃ u, a < u) : (𝓝[≥] a).HasBasis (fun u => a < u) fun u => Ico a u :=
   (nhdsWithin_Ici_eq' ha).symm ▸
@@ -1224,23 +1351,30 @@ theorem nhdsWithin_Ici_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopol
           Ico_subset_Ico_right (min_le_right _ _)⟩)
       ha
 #align nhds_within_Ici_basis' nhdsWithin_Ici_basis'
+-/
 
+#print nhdsWithin_Iic_basis' /-
 theorem nhdsWithin_Iic_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopology α] {a : α}
     (ha : ∃ l, l < a) : (𝓝[≤] a).HasBasis (fun l => l < a) fun l => Ioc l a :=
   by
   convert@nhdsWithin_Ici_basis' αᵒᵈ _ _ _ (to_dual a) ha
   exact funext fun x => (@dual_Ico _ _ _ _).symm
 #align nhds_within_Iic_basis' nhdsWithin_Iic_basis'
+-/
 
+#print nhdsWithin_Ici_basis /-
 theorem nhdsWithin_Ici_basis [TopologicalSpace α] [LinearOrder α] [OrderTopology α] [NoMaxOrder α]
     (a : α) : (𝓝[≥] a).HasBasis (fun u => a < u) fun u => Ico a u :=
   nhdsWithin_Ici_basis' (exists_gt a)
 #align nhds_within_Ici_basis nhdsWithin_Ici_basis
+-/
 
+#print nhdsWithin_Iic_basis /-
 theorem nhdsWithin_Iic_basis [TopologicalSpace α] [LinearOrder α] [OrderTopology α] [NoMinOrder α]
     (a : α) : (𝓝[≤] a).HasBasis (fun l => l < a) fun l => Ioc l a :=
   nhdsWithin_Iic_basis' (exists_lt a)
 #align nhds_within_Iic_basis nhdsWithin_Iic_basis
+-/
 
 theorem nhds_top_order [TopologicalSpace α] [Preorder α] [OrderTop α] [OrderTopology α] :
     𝓝 (⊤ : α) = ⨅ (l) (h₂ : l < ⊤), 𝓟 (Ioi l) := by simp [nhds_eq_order (⊤ : α)]
@@ -1307,21 +1441,29 @@ section OrderClosedTopology
 
 variable [OrderClosedTopology α] {a b : α}
 
+#print eventually_le_nhds /-
 theorem eventually_le_nhds (hab : a < b) : ∀ᶠ x in 𝓝 a, x ≤ b :=
   eventually_iff.mpr (mem_nhds_iff.mpr ⟨Iio b, Iio_subset_Iic_self, isOpen_Iio, hab⟩)
 #align eventually_le_nhds eventually_le_nhds
+-/
 
+#print eventually_lt_nhds /-
 theorem eventually_lt_nhds (hab : a < b) : ∀ᶠ x in 𝓝 a, x < b :=
   eventually_iff.mpr (mem_nhds_iff.mpr ⟨Iio b, rfl.Subset, isOpen_Iio, hab⟩)
 #align eventually_lt_nhds eventually_lt_nhds
+-/
 
+#print eventually_ge_nhds /-
 theorem eventually_ge_nhds (hab : b < a) : ∀ᶠ x in 𝓝 a, b ≤ x :=
   eventually_iff.mpr (mem_nhds_iff.mpr ⟨Ioi b, Ioi_subset_Ici_self, isOpen_Ioi, hab⟩)
 #align eventually_ge_nhds eventually_ge_nhds
+-/
 
+#print eventually_gt_nhds /-
 theorem eventually_gt_nhds (hab : b < a) : ∀ᶠ x in 𝓝 a, b < x :=
   eventually_iff.mpr (mem_nhds_iff.mpr ⟨Ioi b, rfl.Subset, isOpen_Ioi, hab⟩)
 #align eventually_gt_nhds eventually_gt_nhds
+-/
 
 end OrderClosedTopology
 
@@ -1329,6 +1471,7 @@ section OrderTopology
 
 variable [OrderTopology α]
 
+#print order_separated /-
 theorem order_separated {a₁ a₂ : α} (h : a₁ < a₂) :
     ∃ u v : Set α, IsOpen u ∧ IsOpen v ∧ a₁ ∈ u ∧ a₂ ∈ v ∧ ∀ b₁ ∈ u, ∀ b₂ ∈ v, b₁ < b₂ :=
   match dense_or_discrete a₁ a₂ with
@@ -1343,6 +1486,7 @@ theorem order_separated {a₁ a₂ : α} (h : a₁ < a₂) :
         _ ≤ b₂ := h₁ _ hb₂
         ⟩
 #align order_separated order_separated
+-/
 
 #print OrderTopology.to_orderClosedTopology /-
 -- see Note [lower instance priority]
@@ -1414,6 +1558,7 @@ theorem exists_Icc_mem_subset_of_mem_nhds {a : α} {s : Set α} (hs : s ∈ 𝓝
 #align exists_Icc_mem_subset_of_mem_nhds exists_Icc_mem_subset_of_mem_nhds
 -/
 
+#print IsOpen.exists_Ioo_subset /-
 theorem IsOpen.exists_Ioo_subset [Nontrivial α] {s : Set α} (hs : IsOpen s) (h : s.Nonempty) :
     ∃ a b, a < b ∧ Ioo a b ⊆ s :=
   by
@@ -1428,6 +1573,7 @@ theorem IsOpen.exists_Ioo_subset [Nontrivial α] {s : Set α} (hs : IsOpen s) (h
       exists_Ioc_subset_of_mem_nhds (hs.mem_nhds hx) ⟨y, H⟩
     exact ⟨l, x, lx, Ioo_subset_Ioc_self.trans hl⟩
 #align is_open.exists_Ioo_subset IsOpen.exists_Ioo_subset
+-/
 
 theorem dense_of_exists_between [Nontrivial α] {s : Set α}
     (h : ∀ ⦃a b⦄, a < b → ∃ c ∈ s, a < c ∧ c < b) : Dense s :=
@@ -1446,6 +1592,7 @@ theorem dense_iff_exists_between [DenselyOrdered α] [Nontrivial α] {s : Set α
   ⟨fun h a b hab => h.exists_between hab, dense_of_exists_between⟩
 #align dense_iff_exists_between dense_iff_exists_between
 
+#print mem_nhds_iff_exists_Ioo_subset' /-
 /-- A set is a neighborhood of `a` if and only if it contains an interval `(l, u)` containing `a`,
 provided `a` is neither a bottom element nor a top element. -/
 theorem mem_nhds_iff_exists_Ioo_subset' {a : α} {s : Set α} (hl : ∃ l, l < a) (hu : ∃ u, a < u) :
@@ -1459,29 +1606,39 @@ theorem mem_nhds_iff_exists_Ioo_subset' {a : α} {s : Set α} (hl : ∃ l, l < a
   · rintro ⟨l, u, ha, h⟩
     apply mem_of_superset (Ioo_mem_nhds ha.1 ha.2) h
 #align mem_nhds_iff_exists_Ioo_subset' mem_nhds_iff_exists_Ioo_subset'
+-/
 
+#print mem_nhds_iff_exists_Ioo_subset /-
 /-- A set is a neighborhood of `a` if and only if it contains an interval `(l, u)` containing `a`.
 -/
 theorem mem_nhds_iff_exists_Ioo_subset [NoMaxOrder α] [NoMinOrder α] {a : α} {s : Set α} :
     s ∈ 𝓝 a ↔ ∃ l u, a ∈ Ioo l u ∧ Ioo l u ⊆ s :=
   mem_nhds_iff_exists_Ioo_subset' (exists_lt a) (exists_gt a)
 #align mem_nhds_iff_exists_Ioo_subset mem_nhds_iff_exists_Ioo_subset
+-/
 
+#print nhds_basis_Ioo' /-
 theorem nhds_basis_Ioo' {a : α} (hl : ∃ l, l < a) (hu : ∃ u, a < u) :
     (𝓝 a).HasBasis (fun b : α × α => b.1 < a ∧ a < b.2) fun b => Ioo b.1 b.2 :=
   ⟨fun s => (mem_nhds_iff_exists_Ioo_subset' hl hu).trans <| by simp⟩
 #align nhds_basis_Ioo' nhds_basis_Ioo'
+-/
 
+#print nhds_basis_Ioo /-
 theorem nhds_basis_Ioo [NoMaxOrder α] [NoMinOrder α] (a : α) :
     (𝓝 a).HasBasis (fun b : α × α => b.1 < a ∧ a < b.2) fun b => Ioo b.1 b.2 :=
   nhds_basis_Ioo' (exists_lt a) (exists_gt a)
 #align nhds_basis_Ioo nhds_basis_Ioo
+-/
 
+#print Filter.Eventually.exists_Ioo_subset /-
 theorem Filter.Eventually.exists_Ioo_subset [NoMaxOrder α] [NoMinOrder α] {a : α} {p : α → Prop}
     (hp : ∀ᶠ x in 𝓝 a, p x) : ∃ l u, a ∈ Ioo l u ∧ Ioo l u ⊆ { x | p x } :=
   mem_nhds_iff_exists_Ioo_subset.1 hp
 #align filter.eventually.exists_Ioo_subset Filter.Eventually.exists_Ioo_subset
+-/
 
+#print countable_of_isolated_right' /-
 /-- The set of points which are isolated on the right is countable when the space is
 second-countable. -/
 theorem countable_of_isolated_right' [SecondCountableTopology α] :
@@ -1543,7 +1700,9 @@ theorem countable_of_isolated_right' [SecondCountableTopology α] :
   · rw [H]; exact isOpen_Ioo
   exact subset.antisymm (Ioc_subset_Ioo_right (hy x hx.1)) fun u hu => ⟨hu.1, Hy _ _ hx.1 hu.2⟩
 #align countable_of_isolated_right countable_of_isolated_right'
+-/
 
+#print countable_of_isolated_left' /-
 /-- The set of points which are isolated on the left is countable when the space is
 second-countable. -/
 theorem countable_of_isolated_left' [SecondCountableTopology α] :
@@ -1555,6 +1714,7 @@ theorem countable_of_isolated_left' [SecondCountableTopology α] :
   simp_rw [this]
   rfl
 #align countable_of_isolated_left countable_of_isolated_left'
+-/
 
 /-- Consider a disjoint family of intervals `(x, y)` with `x < y` in a second-countable space.
 Then the family is countable.
@@ -1590,25 +1750,31 @@ e.g., `ι → ℝ`.
 variable {ι : Type _} {π : ι → Type _} [Finite ι] [∀ i, LinearOrder (π i)]
   [∀ i, TopologicalSpace (π i)] [∀ i, OrderTopology (π i)] {a b x : ∀ i, π i} {a' b' x' : ι → α}
 
+#print pi_Iic_mem_nhds /-
 theorem pi_Iic_mem_nhds (ha : ∀ i, x i < a i) : Iic a ∈ 𝓝 x :=
   pi_univ_Iic a ▸ set_pi_mem_nhds (Set.toFinite _) fun i _ => Iic_mem_nhds (ha _)
 #align pi_Iic_mem_nhds pi_Iic_mem_nhds
+-/
 
 theorem pi_Iic_mem_nhds' (ha : ∀ i, x' i < a' i) : Iic a' ∈ 𝓝 x' :=
   pi_Iic_mem_nhds ha
 #align pi_Iic_mem_nhds' pi_Iic_mem_nhds'
 
+#print pi_Ici_mem_nhds /-
 theorem pi_Ici_mem_nhds (ha : ∀ i, a i < x i) : Ici a ∈ 𝓝 x :=
   pi_univ_Ici a ▸ set_pi_mem_nhds (Set.toFinite _) fun i _ => Ici_mem_nhds (ha _)
 #align pi_Ici_mem_nhds pi_Ici_mem_nhds
+-/
 
 theorem pi_Ici_mem_nhds' (ha : ∀ i, a' i < x' i) : Ici a' ∈ 𝓝 x' :=
   pi_Ici_mem_nhds ha
 #align pi_Ici_mem_nhds' pi_Ici_mem_nhds'
 
+#print pi_Icc_mem_nhds /-
 theorem pi_Icc_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Icc a b ∈ 𝓝 x :=
   pi_univ_Icc a b ▸ set_pi_mem_nhds finite_univ fun i _ => Icc_mem_nhds (ha _) (hb _)
 #align pi_Icc_mem_nhds pi_Icc_mem_nhds
+-/
 
 theorem pi_Icc_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : Icc a' b' ∈ 𝓝 x' :=
   pi_Icc_mem_nhds ha hb
@@ -1616,49 +1782,59 @@ theorem pi_Icc_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : I
 
 variable [Nonempty ι]
 
+#print pi_Iio_mem_nhds /-
 theorem pi_Iio_mem_nhds (ha : ∀ i, x i < a i) : Iio a ∈ 𝓝 x :=
   by
   refine' mem_of_superset (set_pi_mem_nhds (Set.toFinite _) fun i _ => _) (pi_univ_Iio_subset a)
   exact Iio_mem_nhds (ha i)
 #align pi_Iio_mem_nhds pi_Iio_mem_nhds
+-/
 
 theorem pi_Iio_mem_nhds' (ha : ∀ i, x' i < a' i) : Iio a' ∈ 𝓝 x' :=
   pi_Iio_mem_nhds ha
 #align pi_Iio_mem_nhds' pi_Iio_mem_nhds'
 
+#print pi_Ioi_mem_nhds /-
 theorem pi_Ioi_mem_nhds (ha : ∀ i, a i < x i) : Ioi a ∈ 𝓝 x :=
   @pi_Iio_mem_nhds ι (fun i => (π i)ᵒᵈ) _ _ _ _ _ _ _ ha
 #align pi_Ioi_mem_nhds pi_Ioi_mem_nhds
+-/
 
 theorem pi_Ioi_mem_nhds' (ha : ∀ i, a' i < x' i) : Ioi a' ∈ 𝓝 x' :=
   pi_Ioi_mem_nhds ha
 #align pi_Ioi_mem_nhds' pi_Ioi_mem_nhds'
 
+#print pi_Ioc_mem_nhds /-
 theorem pi_Ioc_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Ioc a b ∈ 𝓝 x :=
   by
   refine' mem_of_superset (set_pi_mem_nhds (Set.toFinite _) fun i _ => _) (pi_univ_Ioc_subset a b)
   exact Ioc_mem_nhds (ha i) (hb i)
 #align pi_Ioc_mem_nhds pi_Ioc_mem_nhds
+-/
 
 theorem pi_Ioc_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : Ioc a' b' ∈ 𝓝 x' :=
   pi_Ioc_mem_nhds ha hb
 #align pi_Ioc_mem_nhds' pi_Ioc_mem_nhds'
 
+#print pi_Ico_mem_nhds /-
 theorem pi_Ico_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Ico a b ∈ 𝓝 x :=
   by
   refine' mem_of_superset (set_pi_mem_nhds (Set.toFinite _) fun i _ => _) (pi_univ_Ico_subset a b)
   exact Ico_mem_nhds (ha i) (hb i)
 #align pi_Ico_mem_nhds pi_Ico_mem_nhds
+-/
 
 theorem pi_Ico_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : Ico a' b' ∈ 𝓝 x' :=
   pi_Ico_mem_nhds ha hb
 #align pi_Ico_mem_nhds' pi_Ico_mem_nhds'
 
+#print pi_Ioo_mem_nhds /-
 theorem pi_Ioo_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Ioo a b ∈ 𝓝 x :=
   by
   refine' mem_of_superset (set_pi_mem_nhds (Set.toFinite _) fun i _ => _) (pi_univ_Ioo_subset a b)
   exact Ioo_mem_nhds (ha i) (hb i)
 #align pi_Ioo_mem_nhds pi_Ioo_mem_nhds
+-/
 
 theorem pi_Ioo_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : Ioo a' b' ∈ 𝓝 x' :=
   pi_Ioo_mem_nhds ha hb
@@ -1687,25 +1863,33 @@ theorem inf_nhds_atBot [NoMinOrder α] (x : α) : 𝓝 x ⊓ atBot = ⊥ :=
   @inf_nhds_atTop αᵒᵈ _ _ _ _ x
 #align inf_nhds_at_bot inf_nhds_atBot
 
+#print not_tendsto_nhds_of_tendsto_atTop /-
 theorem not_tendsto_nhds_of_tendsto_atTop [NoMaxOrder α] {F : Filter β} [NeBot F] {f : β → α}
     (hf : Tendsto f F atTop) (x : α) : ¬Tendsto f F (𝓝 x) :=
   hf.not_tendsto (disjoint_nhds_atTop x).symm
 #align not_tendsto_nhds_of_tendsto_at_top not_tendsto_nhds_of_tendsto_atTop
+-/
 
+#print not_tendsto_atTop_of_tendsto_nhds /-
 theorem not_tendsto_atTop_of_tendsto_nhds [NoMaxOrder α] {F : Filter β} [NeBot F] {f : β → α}
     {x : α} (hf : Tendsto f F (𝓝 x)) : ¬Tendsto f F atTop :=
   hf.not_tendsto (disjoint_nhds_atTop x)
 #align not_tendsto_at_top_of_tendsto_nhds not_tendsto_atTop_of_tendsto_nhds
+-/
 
+#print not_tendsto_nhds_of_tendsto_atBot /-
 theorem not_tendsto_nhds_of_tendsto_atBot [NoMinOrder α] {F : Filter β} [NeBot F] {f : β → α}
     (hf : Tendsto f F atBot) (x : α) : ¬Tendsto f F (𝓝 x) :=
   hf.not_tendsto (disjoint_nhds_atBot x).symm
 #align not_tendsto_nhds_of_tendsto_at_bot not_tendsto_nhds_of_tendsto_atBot
+-/
 
+#print not_tendsto_atBot_of_tendsto_nhds /-
 theorem not_tendsto_atBot_of_tendsto_nhds [NoMinOrder α] {F : Filter β} [NeBot F] {f : β → α}
     {x : α} (hf : Tendsto f F (𝓝 x)) : ¬Tendsto f F atBot :=
   hf.not_tendsto (disjoint_nhds_atBot x)
 #align not_tendsto_at_bot_of_tendsto_nhds not_tendsto_atBot_of_tendsto_nhds
+-/
 
 /-!
 ### Neighborhoods to the left and to the right on an `order_topology`
@@ -1886,11 +2070,14 @@ theorem mem_nhdsWithin_Ici_iff_exists_Ico_subset [NoMaxOrder α] {a : α} {s : S
   mem_nhdsWithin_Ici_iff_exists_Ico_subset' hu'
 #align mem_nhds_within_Ici_iff_exists_Ico_subset mem_nhdsWithin_Ici_iff_exists_Ico_subset
 
+#print nhdsWithin_Ici_basis_Ico /-
 theorem nhdsWithin_Ici_basis_Ico [NoMaxOrder α] (a : α) :
     (𝓝[≥] a).HasBasis (fun u => a < u) (Ico a) :=
   ⟨fun s => mem_nhdsWithin_Ici_iff_exists_Ico_subset⟩
 #align nhds_within_Ici_basis_Ico nhdsWithin_Ici_basis_Ico
+-/
 
+#print mem_nhdsWithin_Ici_iff_exists_Icc_subset /-
 /-- A set is a neighborhood of `a` within `[a, +∞)` if and only if it contains an interval `[a, u]`
 with `a < u`. -/
 theorem mem_nhdsWithin_Ici_iff_exists_Icc_subset [NoMaxOrder α] [DenselyOrdered α] {a : α}
@@ -1904,6 +2091,7 @@ theorem mem_nhdsWithin_Ici_iff_exists_Icc_subset [NoMaxOrder α] [DenselyOrdered
   · rintro ⟨u, au, as⟩
     exact ⟨u, au, subset.trans Ico_subset_Icc_self as⟩
 #align mem_nhds_within_Ici_iff_exists_Icc_subset mem_nhdsWithin_Ici_iff_exists_Icc_subset
+-/
 
 /-- The following statements are equivalent:
 
@@ -1946,6 +2134,7 @@ theorem mem_nhdsWithin_Iic_iff_exists_Ioc_subset [NoMinOrder α] {a : α} {s : S
   mem_nhdsWithin_Iic_iff_exists_Ioc_subset' hl'
 #align mem_nhds_within_Iic_iff_exists_Ioc_subset mem_nhdsWithin_Iic_iff_exists_Ioc_subset
 
+#print mem_nhdsWithin_Iic_iff_exists_Icc_subset /-
 /-- A set is a neighborhood of `a` within `(-∞, a]` if and only if it contains an interval `[l, a]`
 with `l < a`. -/
 theorem mem_nhdsWithin_Iic_iff_exists_Icc_subset [NoMinOrder α] [DenselyOrdered α] {a : α}
@@ -1955,6 +2144,7 @@ theorem mem_nhdsWithin_Iic_iff_exists_Icc_subset [NoMinOrder α] [DenselyOrdered
   simp_rw [show ∀ u : αᵒᵈ, @Icc αᵒᵈ _ a u = @Icc α _ u a from fun u => dual_Icc]
   rfl
 #align mem_nhds_within_Iic_iff_exists_Icc_subset mem_nhdsWithin_Iic_iff_exists_Icc_subset
+-/
 
 end OrderTopology
 
@@ -2290,6 +2480,7 @@ alias IsGLB.mem_of_isClosed ← IsClosed.isGLB_mem
 -/
 
 
+#print IsLUB.exists_seq_strictMono_tendsto_of_not_mem /-
 theorem IsLUB.exists_seq_strictMono_tendsto_of_not_mem {t : Set α} {x : α}
     [IsCountablyGenerated (𝓝 x)] (htx : IsLUB t x) (not_mem : x ∉ t) (ht : t.Nonempty) :
     ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n < x) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t :=
@@ -2327,7 +2518,9 @@ theorem IsLUB.exists_seq_strictMono_tendsto_of_not_mem {t : Set α} {x : α}
     · exact (hf 0 l hl).2.2.2
     · exact (hf n.succ _ (I n)).2.2.2
 #align is_lub.exists_seq_strict_mono_tendsto_of_not_mem IsLUB.exists_seq_strictMono_tendsto_of_not_mem
+-/
 
+#print IsLUB.exists_seq_monotone_tendsto /-
 theorem IsLUB.exists_seq_monotone_tendsto {t : Set α} {x : α} [IsCountablyGenerated (𝓝 x)]
     (htx : IsLUB t x) (ht : t.Nonempty) :
     ∃ u : ℕ → α, Monotone u ∧ (∀ n, u n ≤ x) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t :=
@@ -2337,7 +2530,9 @@ theorem IsLUB.exists_seq_monotone_tendsto {t : Set α} {x : α} [IsCountablyGene
   · rcases htx.exists_seq_strict_mono_tendsto_of_not_mem h ht with ⟨u, hu⟩
     exact ⟨u, hu.1.Monotone, fun n => (hu.2.1 n).le, hu.2.2⟩
 #align is_lub.exists_seq_monotone_tendsto IsLUB.exists_seq_monotone_tendsto
+-/
 
+#print exists_seq_strictMono_tendsto' /-
 theorem exists_seq_strictMono_tendsto' {α : Type _} [LinearOrder α] [TopologicalSpace α]
     [DenselyOrdered α] [OrderTopology α] [FirstCountableTopology α] {x y : α} (hy : y < x) :
     ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n ∈ Ioo y x) ∧ Tendsto u atTop (𝓝 x) :=
@@ -2347,7 +2542,9 @@ theorem exists_seq_strictMono_tendsto' {α : Type _} [LinearOrder α] [Topologic
   rcases(isLUB_Ioo hy).exists_seq_strictMono_tendsto_of_not_mem hx ht with ⟨u, hu⟩
   exact ⟨u, hu.1, hu.2.2.symm⟩
 #align exists_seq_strict_mono_tendsto' exists_seq_strictMono_tendsto'
+-/
 
+#print exists_seq_strictMono_tendsto /-
 theorem exists_seq_strictMono_tendsto [DenselyOrdered α] [NoMinOrder α] [FirstCountableTopology α]
     (x : α) : ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n < x) ∧ Tendsto u atTop (𝓝 x) :=
   by
@@ -2355,13 +2552,16 @@ theorem exists_seq_strictMono_tendsto [DenselyOrdered α] [NoMinOrder α] [First
   rcases exists_seq_strictMono_tendsto' hy with ⟨u, hu_mono, hu_mem, hux⟩
   exact ⟨u, hu_mono, fun n => (hu_mem n).2, hux⟩
 #align exists_seq_strict_mono_tendsto exists_seq_strictMono_tendsto
+-/
 
+#print exists_seq_strictMono_tendsto_nhdsWithin /-
 theorem exists_seq_strictMono_tendsto_nhdsWithin [DenselyOrdered α] [NoMinOrder α]
     [FirstCountableTopology α] (x : α) :
     ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n < x) ∧ Tendsto u atTop (𝓝[<] x) :=
   let ⟨u, hu, hx, h⟩ := exists_seq_strictMono_tendsto x
   ⟨u, hu, hx, tendsto_nhdsWithin_mono_right (range_subset_iff.2 hx) <| tendsto_nhdsWithin_range.2 h⟩
 #align exists_seq_strict_mono_tendsto_nhds_within exists_seq_strictMono_tendsto_nhdsWithin
+-/
 
 theorem exists_seq_tendsto_sSup {α : Type _} [ConditionallyCompleteLinearOrder α]
     [TopologicalSpace α] [OrderTopology α] [FirstCountableTopology α] {S : Set α} (hS : S.Nonempty)
@@ -2371,34 +2571,45 @@ theorem exists_seq_tendsto_sSup {α : Type _} [ConditionallyCompleteLinearOrder
   exact ⟨u, hu.1, hu.2.2⟩
 #align exists_seq_tendsto_Sup exists_seq_tendsto_sSup
 
+#print IsGLB.exists_seq_strictAnti_tendsto_of_not_mem /-
 theorem IsGLB.exists_seq_strictAnti_tendsto_of_not_mem {t : Set α} {x : α}
     [IsCountablyGenerated (𝓝 x)] (htx : IsGLB t x) (not_mem : x ∉ t) (ht : t.Nonempty) :
     ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, x < u n) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t :=
   @IsLUB.exists_seq_strictMono_tendsto_of_not_mem αᵒᵈ _ _ _ t x _ htx not_mem ht
 #align is_glb.exists_seq_strict_anti_tendsto_of_not_mem IsGLB.exists_seq_strictAnti_tendsto_of_not_mem
+-/
 
+#print IsGLB.exists_seq_antitone_tendsto /-
 theorem IsGLB.exists_seq_antitone_tendsto {t : Set α} {x : α} [IsCountablyGenerated (𝓝 x)]
     (htx : IsGLB t x) (ht : t.Nonempty) :
     ∃ u : ℕ → α, Antitone u ∧ (∀ n, x ≤ u n) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t :=
   @IsLUB.exists_seq_monotone_tendsto αᵒᵈ _ _ _ t x _ htx ht
 #align is_glb.exists_seq_antitone_tendsto IsGLB.exists_seq_antitone_tendsto
+-/
 
+#print exists_seq_strictAnti_tendsto' /-
 theorem exists_seq_strictAnti_tendsto' [DenselyOrdered α] [FirstCountableTopology α] {x y : α}
     (hy : x < y) : ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, u n ∈ Ioo x y) ∧ Tendsto u atTop (𝓝 x) := by
   simpa only [dual_Ioo] using exists_seq_strictMono_tendsto' (OrderDual.toDual_lt_toDual.2 hy)
 #align exists_seq_strict_anti_tendsto' exists_seq_strictAnti_tendsto'
+-/
 
+#print exists_seq_strictAnti_tendsto /-
 theorem exists_seq_strictAnti_tendsto [DenselyOrdered α] [NoMaxOrder α] [FirstCountableTopology α]
     (x : α) : ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, x < u n) ∧ Tendsto u atTop (𝓝 x) :=
   @exists_seq_strictMono_tendsto αᵒᵈ _ _ _ _ _ _ x
 #align exists_seq_strict_anti_tendsto exists_seq_strictAnti_tendsto
+-/
 
+#print exists_seq_strictAnti_tendsto_nhdsWithin /-
 theorem exists_seq_strictAnti_tendsto_nhdsWithin [DenselyOrdered α] [NoMaxOrder α]
     [FirstCountableTopology α] (x : α) :
     ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, x < u n) ∧ Tendsto u atTop (𝓝[>] x) :=
   @exists_seq_strictMono_tendsto_nhdsWithin αᵒᵈ _ _ _ _ _ _ _
 #align exists_seq_strict_anti_tendsto_nhds_within exists_seq_strictAnti_tendsto_nhdsWithin
+-/
 
+#print exists_seq_strictAnti_strictMono_tendsto /-
 theorem exists_seq_strictAnti_strictMono_tendsto [DenselyOrdered α] [FirstCountableTopology α]
     {x y : α} (h : x < y) :
     ∃ u v : ℕ → α,
@@ -2414,6 +2625,7 @@ theorem exists_seq_strictAnti_strictMono_tendsto [DenselyOrdered α] [FirstCount
     ⟨u, v, hu_anti, hv_mono, hu_mem, fun l => ⟨(hu_mem 0).1.trans (hv_mem l).1, (hv_mem l).2⟩,
       fun k l => (hu_anti.antitone (zero_le k)).trans_lt (hv_mem l).1, hux, hvy⟩
 #align exists_seq_strict_anti_strict_mono_tendsto exists_seq_strictAnti_strictMono_tendsto
+-/
 
 theorem exists_seq_tendsto_sInf {α : Type _} [ConditionallyCompleteLinearOrder α]
     [TopologicalSpace α] [OrderTopology α] [FirstCountableTopology α] {S : Set α} (hS : S.Nonempty)
@@ -2428,6 +2640,7 @@ section DenselyOrdered
 variable [TopologicalSpace α] [LinearOrder α] [OrderTopology α] [DenselyOrdered α] {a b : α}
   {s : Set α}
 
+#print closure_Ioi' /-
 /-- The closure of the interval `(a, +∞)` is the closed interval `[a, +∞)`, unless `a` is a top
 element. -/
 theorem closure_Ioi' {a : α} (h : (Ioi a).Nonempty) : closure (Ioi a) = Ici a :=
@@ -2437,25 +2650,33 @@ theorem closure_Ioi' {a : α} (h : (Ioi a).Nonempty) : closure (Ioi a) = Ici a :
   · rw [← diff_subset_closure_iff, Ici_diff_Ioi_same, singleton_subset_iff]
     exact is_glb_Ioi.mem_closure h
 #align closure_Ioi' closure_Ioi'
+-/
 
+#print closure_Ioi /-
 /-- The closure of the interval `(a, +∞)` is the closed interval `[a, +∞)`. -/
 @[simp]
 theorem closure_Ioi (a : α) [NoMaxOrder α] : closure (Ioi a) = Ici a :=
   closure_Ioi' nonempty_Ioi
 #align closure_Ioi closure_Ioi
+-/
 
+#print closure_Iio' /-
 /-- The closure of the interval `(-∞, a)` is the closed interval `(-∞, a]`, unless `a` is a bottom
 element. -/
 theorem closure_Iio' (h : (Iio a).Nonempty) : closure (Iio a) = Iic a :=
   @closure_Ioi' αᵒᵈ _ _ _ _ _ h
 #align closure_Iio' closure_Iio'
+-/
 
+#print closure_Iio /-
 /-- The closure of the interval `(-∞, a)` is the interval `(-∞, a]`. -/
 @[simp]
 theorem closure_Iio (a : α) [NoMinOrder α] : closure (Iio a) = Iic a :=
   closure_Iio' nonempty_Iio
 #align closure_Iio closure_Iio
+-/
 
+#print closure_Ioo /-
 /-- The closure of the open interval `(a, b)` is the closed interval `[a, b]`. -/
 @[simp]
 theorem closure_Ioo {a b : α} (hab : a ≠ b) : closure (Ioo a b) = Icc a b :=
@@ -2469,7 +2690,9 @@ theorem closure_Ioo {a b : α} (hab : a ≠ b) : closure (Ioo a b) = Icc a b :=
       exact ⟨(isGLB_Ioo hab).mem_closure hab', (isLUB_Ioo hab).mem_closure hab'⟩
     · rw [Icc_eq_empty_of_lt hab]; exact empty_subset _
 #align closure_Ioo closure_Ioo
+-/
 
+#print closure_Ioc /-
 /-- The closure of the interval `(a, b]` is the closed interval `[a, b]`. -/
 @[simp]
 theorem closure_Ioc {a b : α} (hab : a ≠ b) : closure (Ioc a b) = Icc a b :=
@@ -2479,7 +2702,9 @@ theorem closure_Ioc {a b : α} (hab : a ≠ b) : closure (Ioc a b) = Icc a b :=
   · apply subset.trans _ (closure_mono Ioo_subset_Ioc_self)
     rw [closure_Ioo hab]
 #align closure_Ioc closure_Ioc
+-/
 
+#print closure_Ico /-
 /-- The closure of the interval `[a, b)` is the closed interval `[a, b]`. -/
 @[simp]
 theorem closure_Ico {a b : α} (hab : a ≠ b) : closure (Ico a b) = Icc a b :=
@@ -2489,40 +2714,56 @@ theorem closure_Ico {a b : α} (hab : a ≠ b) : closure (Ico a b) = Icc a b :=
   · apply subset.trans _ (closure_mono Ioo_subset_Ico_self)
     rw [closure_Ioo hab]
 #align closure_Ico closure_Ico
+-/
 
+#print interior_Ici' /-
 @[simp]
 theorem interior_Ici' {a : α} (ha : (Iio a).Nonempty) : interior (Ici a) = Ioi a := by
   rw [← compl_Iio, interior_compl, closure_Iio' ha, compl_Iic]
 #align interior_Ici' interior_Ici'
+-/
 
+#print interior_Ici /-
 theorem interior_Ici [NoMinOrder α] {a : α} : interior (Ici a) = Ioi a :=
   interior_Ici' nonempty_Iio
 #align interior_Ici interior_Ici
+-/
 
+#print interior_Iic' /-
 @[simp]
 theorem interior_Iic' {a : α} (ha : (Ioi a).Nonempty) : interior (Iic a) = Iio a :=
   @interior_Ici' αᵒᵈ _ _ _ _ _ ha
 #align interior_Iic' interior_Iic'
+-/
 
+#print interior_Iic /-
 theorem interior_Iic [NoMaxOrder α] {a : α} : interior (Iic a) = Iio a :=
   interior_Iic' nonempty_Ioi
 #align interior_Iic interior_Iic
+-/
 
+#print interior_Icc /-
 @[simp]
 theorem interior_Icc [NoMinOrder α] [NoMaxOrder α] {a b : α} : interior (Icc a b) = Ioo a b := by
   rw [← Ici_inter_Iic, interior_inter, interior_Ici, interior_Iic, Ioi_inter_Iio]
 #align interior_Icc interior_Icc
+-/
 
+#print interior_Ico /-
 @[simp]
 theorem interior_Ico [NoMinOrder α] {a b : α} : interior (Ico a b) = Ioo a b := by
   rw [← Ici_inter_Iio, interior_inter, interior_Ici, interior_Iio, Ioi_inter_Iio]
 #align interior_Ico interior_Ico
+-/
 
+#print interior_Ioc /-
 @[simp]
 theorem interior_Ioc [NoMaxOrder α] {a b : α} : interior (Ioc a b) = Ioo a b := by
   rw [← Ioi_inter_Iic, interior_inter, interior_Ioi, interior_Iic, Ioi_inter_Iio]
 #align interior_Ioc interior_Ioc
+-/
 
+#print closure_interior_Icc /-
 theorem closure_interior_Icc {a b : α} (h : a ≠ b) : closure (interior (Icc a b)) = Icc a b :=
   (closure_minimal interior_subset isClosed_Icc).antisymm <|
     calc
@@ -2531,7 +2772,9 @@ theorem closure_interior_Icc {a b : α} (h : a ≠ b) : closure (interior (Icc a
         closure_mono (interior_maximal Ioo_subset_Icc_self isOpen_Ioo)
       
 #align closure_interior_Icc closure_interior_Icc
+-/
 
+#print Ioc_subset_closure_interior /-
 theorem Ioc_subset_closure_interior (a b : α) : Ioc a b ⊆ closure (interior (Ioc a b)) :=
   by
   rcases eq_or_ne a b with (rfl | h)
@@ -2544,83 +2787,118 @@ theorem Ioc_subset_closure_interior (a b : α) : Ioc a b ⊆ closure (interior (
         closure_mono (interior_maximal Ioo_subset_Ioc_self isOpen_Ioo)
       
 #align Ioc_subset_closure_interior Ioc_subset_closure_interior
+-/
 
+#print Ico_subset_closure_interior /-
 theorem Ico_subset_closure_interior (a b : α) : Ico a b ⊆ closure (interior (Ico a b)) := by
   simpa only [dual_Ioc] using Ioc_subset_closure_interior (OrderDual.toDual b) (OrderDual.toDual a)
 #align Ico_subset_closure_interior Ico_subset_closure_interior
+-/
 
+#print frontier_Ici' /-
 @[simp]
 theorem frontier_Ici' {a : α} (ha : (Iio a).Nonempty) : frontier (Ici a) = {a} := by
   simp [frontier, ha]
 #align frontier_Ici' frontier_Ici'
+-/
 
+#print frontier_Ici /-
 theorem frontier_Ici [NoMinOrder α] {a : α} : frontier (Ici a) = {a} :=
   frontier_Ici' nonempty_Iio
 #align frontier_Ici frontier_Ici
+-/
 
+#print frontier_Iic' /-
 @[simp]
 theorem frontier_Iic' {a : α} (ha : (Ioi a).Nonempty) : frontier (Iic a) = {a} := by
   simp [frontier, ha]
 #align frontier_Iic' frontier_Iic'
+-/
 
+#print frontier_Iic /-
 theorem frontier_Iic [NoMaxOrder α] {a : α} : frontier (Iic a) = {a} :=
   frontier_Iic' nonempty_Ioi
 #align frontier_Iic frontier_Iic
+-/
 
+#print frontier_Ioi' /-
 @[simp]
 theorem frontier_Ioi' {a : α} (ha : (Ioi a).Nonempty) : frontier (Ioi a) = {a} := by
   simp [frontier, closure_Ioi' ha, Iic_diff_Iio, Icc_self]
 #align frontier_Ioi' frontier_Ioi'
+-/
 
+#print frontier_Ioi /-
 theorem frontier_Ioi [NoMaxOrder α] {a : α} : frontier (Ioi a) = {a} :=
   frontier_Ioi' nonempty_Ioi
 #align frontier_Ioi frontier_Ioi
+-/
 
+#print frontier_Iio' /-
 @[simp]
 theorem frontier_Iio' {a : α} (ha : (Iio a).Nonempty) : frontier (Iio a) = {a} := by
   simp [frontier, closure_Iio' ha, Iic_diff_Iio, Icc_self]
 #align frontier_Iio' frontier_Iio'
+-/
 
+#print frontier_Iio /-
 theorem frontier_Iio [NoMinOrder α] {a : α} : frontier (Iio a) = {a} :=
   frontier_Iio' nonempty_Iio
 #align frontier_Iio frontier_Iio
+-/
 
+#print frontier_Icc /-
 @[simp]
 theorem frontier_Icc [NoMinOrder α] [NoMaxOrder α] {a b : α} (h : a ≤ b) :
     frontier (Icc a b) = {a, b} := by simp [frontier, h, Icc_diff_Ioo_same]
 #align frontier_Icc frontier_Icc
+-/
 
+#print frontier_Ioo /-
 @[simp]
 theorem frontier_Ioo {a b : α} (h : a < b) : frontier (Ioo a b) = {a, b} := by
   rw [frontier, closure_Ioo h.ne, interior_Ioo, Icc_diff_Ioo_same h.le]
 #align frontier_Ioo frontier_Ioo
+-/
 
+#print frontier_Ico /-
 @[simp]
 theorem frontier_Ico [NoMinOrder α] {a b : α} (h : a < b) : frontier (Ico a b) = {a, b} := by
   rw [frontier, closure_Ico h.ne, interior_Ico, Icc_diff_Ioo_same h.le]
 #align frontier_Ico frontier_Ico
+-/
 
+#print frontier_Ioc /-
 @[simp]
 theorem frontier_Ioc [NoMaxOrder α] {a b : α} (h : a < b) : frontier (Ioc a b) = {a, b} := by
   rw [frontier, closure_Ioc h.ne, interior_Ioc, Icc_diff_Ioo_same h.le]
 #align frontier_Ioc frontier_Ioc
+-/
 
+#print nhdsWithin_Ioi_neBot' /-
 theorem nhdsWithin_Ioi_neBot' {a b : α} (H₁ : (Ioi a).Nonempty) (H₂ : a ≤ b) : NeBot (𝓝[Ioi a] b) :=
   mem_closure_iff_nhdsWithin_neBot.1 <| by rwa [closure_Ioi' H₁]
 #align nhds_within_Ioi_ne_bot' nhdsWithin_Ioi_neBot'
+-/
 
+#print nhdsWithin_Ioi_neBot /-
 theorem nhdsWithin_Ioi_neBot [NoMaxOrder α] {a b : α} (H : a ≤ b) : NeBot (𝓝[Ioi a] b) :=
   nhdsWithin_Ioi_neBot' nonempty_Ioi H
 #align nhds_within_Ioi_ne_bot nhdsWithin_Ioi_neBot
+-/
 
+#print nhdsWithin_Ioi_self_neBot' /-
 theorem nhdsWithin_Ioi_self_neBot' {a : α} (H : (Ioi a).Nonempty) : NeBot (𝓝[>] a) :=
   nhdsWithin_Ioi_neBot' H (le_refl a)
 #align nhds_within_Ioi_self_ne_bot' nhdsWithin_Ioi_self_neBot'
+-/
 
+#print nhdsWithin_Ioi_self_neBot /-
 @[instance]
 theorem nhdsWithin_Ioi_self_neBot [NoMaxOrder α] (a : α) : NeBot (𝓝[>] a) :=
   nhdsWithin_Ioi_neBot (le_refl a)
 #align nhds_within_Ioi_self_ne_bot nhdsWithin_Ioi_self_neBot
+-/
 
 theorem Filter.Eventually.exists_gt [NoMaxOrder α] {a : α} {p : α → Prop} (h : ∀ᶠ x in 𝓝 a, p x) :
     ∃ b > a, p b := by
@@ -2628,43 +2906,59 @@ theorem Filter.Eventually.exists_gt [NoMaxOrder α] {a : α} {p : α → Prop} (
     ((h.filter_mono (@nhdsWithin_le_nhds _ _ a (Ioi a))).And self_mem_nhdsWithin).exists
 #align filter.eventually.exists_gt Filter.Eventually.exists_gt
 
+#print nhdsWithin_Iio_neBot' /-
 theorem nhdsWithin_Iio_neBot' {b c : α} (H₁ : (Iio c).Nonempty) (H₂ : b ≤ c) : NeBot (𝓝[Iio c] b) :=
   mem_closure_iff_nhdsWithin_neBot.1 <| by rwa [closure_Iio' H₁]
 #align nhds_within_Iio_ne_bot' nhdsWithin_Iio_neBot'
+-/
 
+#print nhdsWithin_Iio_neBot /-
 theorem nhdsWithin_Iio_neBot [NoMinOrder α] {a b : α} (H : a ≤ b) : NeBot (𝓝[Iio b] a) :=
   nhdsWithin_Iio_neBot' nonempty_Iio H
 #align nhds_within_Iio_ne_bot nhdsWithin_Iio_neBot
+-/
 
+#print nhdsWithin_Iio_self_neBot' /-
 theorem nhdsWithin_Iio_self_neBot' {b : α} (H : (Iio b).Nonempty) : NeBot (𝓝[<] b) :=
   nhdsWithin_Iio_neBot' H (le_refl b)
 #align nhds_within_Iio_self_ne_bot' nhdsWithin_Iio_self_neBot'
+-/
 
+#print nhdsWithin_Iio_self_neBot /-
 @[instance]
 theorem nhdsWithin_Iio_self_neBot [NoMinOrder α] (a : α) : NeBot (𝓝[<] a) :=
   nhdsWithin_Iio_neBot (le_refl a)
 #align nhds_within_Iio_self_ne_bot nhdsWithin_Iio_self_neBot
+-/
 
 theorem Filter.Eventually.exists_lt [NoMinOrder α] {a : α} {p : α → Prop} (h : ∀ᶠ x in 𝓝 a, p x) :
     ∃ b < a, p b :=
   @Filter.Eventually.exists_gt αᵒᵈ _ _ _ _ _ _ _ h
 #align filter.eventually.exists_lt Filter.Eventually.exists_lt
 
+#print right_nhdsWithin_Ico_neBot /-
 theorem right_nhdsWithin_Ico_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ico a b] b) :=
   (isLUB_Ico H).nhdsWithin_neBot (nonempty_Ico.2 H)
 #align right_nhds_within_Ico_ne_bot right_nhdsWithin_Ico_neBot
+-/
 
+#print left_nhdsWithin_Ioc_neBot /-
 theorem left_nhdsWithin_Ioc_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ioc a b] a) :=
   (isGLB_Ioc H).nhdsWithin_neBot (nonempty_Ioc.2 H)
 #align left_nhds_within_Ioc_ne_bot left_nhdsWithin_Ioc_neBot
+-/
 
+#print left_nhdsWithin_Ioo_neBot /-
 theorem left_nhdsWithin_Ioo_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ioo a b] a) :=
   (isGLB_Ioo H).nhdsWithin_neBot (nonempty_Ioo.2 H)
 #align left_nhds_within_Ioo_ne_bot left_nhdsWithin_Ioo_neBot
+-/
 
+#print right_nhdsWithin_Ioo_neBot /-
 theorem right_nhdsWithin_Ioo_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ioo a b] b) :=
   (isLUB_Ioo H).nhdsWithin_neBot (nonempty_Ioo.2 H)
 #align right_nhds_within_Ioo_ne_bot right_nhdsWithin_Ioo_neBot
+-/
 
 theorem comap_coe_nhdsWithin_Iio_of_Ioo_subset (hb : s ⊆ Iio b)
     (hs : s.Nonempty → ∃ a < b, Ioo a b ⊆ s) : comap (coe : s → α) (𝓝[<] b) = atTop :=
@@ -2711,97 +3005,129 @@ theorem map_coe_atBot_of_Ioo_subset (ha : s ⊆ Ioi a) (hs : ∀ b' > a, ∃ b >
   simpa only [OrderDual.exists, dual_Ioo] using hs b' hb'
 #align map_coe_at_bot_of_Ioo_subset map_coe_atBot_of_Ioo_subset
 
+#print comap_coe_Ioo_nhdsWithin_Iio /-
 /-- The `at_top` filter for an open interval `Ioo a b` comes from the left-neighbourhoods filter at
 the right endpoint in the ambient order. -/
 theorem comap_coe_Ioo_nhdsWithin_Iio (a b : α) : comap (coe : Ioo a b → α) (𝓝[<] b) = atTop :=
   comap_coe_nhdsWithin_Iio_of_Ioo_subset Ioo_subset_Iio_self fun h =>
     ⟨a, nonempty_Ioo.1 h, Subset.refl _⟩
 #align comap_coe_Ioo_nhds_within_Iio comap_coe_Ioo_nhdsWithin_Iio
+-/
 
+#print comap_coe_Ioo_nhdsWithin_Ioi /-
 /-- The `at_bot` filter for an open interval `Ioo a b` comes from the right-neighbourhoods filter at
 the left endpoint in the ambient order. -/
 theorem comap_coe_Ioo_nhdsWithin_Ioi (a b : α) : comap (coe : Ioo a b → α) (𝓝[>] a) = atBot :=
   comap_coe_nhdsWithin_Ioi_of_Ioo_subset Ioo_subset_Ioi_self fun h =>
     ⟨b, nonempty_Ioo.1 h, Subset.refl _⟩
 #align comap_coe_Ioo_nhds_within_Ioi comap_coe_Ioo_nhdsWithin_Ioi
+-/
 
+#print comap_coe_Ioi_nhdsWithin_Ioi /-
 theorem comap_coe_Ioi_nhdsWithin_Ioi (a : α) : comap (coe : Ioi a → α) (𝓝[>] a) = atBot :=
   comap_coe_nhdsWithin_Ioi_of_Ioo_subset (Subset.refl _) fun ⟨x, hx⟩ => ⟨x, hx, Ioo_subset_Ioi_self⟩
 #align comap_coe_Ioi_nhds_within_Ioi comap_coe_Ioi_nhdsWithin_Ioi
+-/
 
+#print comap_coe_Iio_nhdsWithin_Iio /-
 theorem comap_coe_Iio_nhdsWithin_Iio (a : α) : comap (coe : Iio a → α) (𝓝[<] a) = atTop :=
   @comap_coe_Ioi_nhdsWithin_Ioi αᵒᵈ _ _ _ _ a
 #align comap_coe_Iio_nhds_within_Iio comap_coe_Iio_nhdsWithin_Iio
+-/
 
+#print map_coe_Ioo_atTop /-
 @[simp]
 theorem map_coe_Ioo_atTop {a b : α} (h : a < b) : map (coe : Ioo a b → α) atTop = 𝓝[<] b :=
   map_coe_atTop_of_Ioo_subset Ioo_subset_Iio_self fun _ _ => ⟨_, h, Subset.refl _⟩
 #align map_coe_Ioo_at_top map_coe_Ioo_atTop
+-/
 
+#print map_coe_Ioo_atBot /-
 @[simp]
 theorem map_coe_Ioo_atBot {a b : α} (h : a < b) : map (coe : Ioo a b → α) atBot = 𝓝[>] a :=
   map_coe_atBot_of_Ioo_subset Ioo_subset_Ioi_self fun _ _ => ⟨_, h, Subset.refl _⟩
 #align map_coe_Ioo_at_bot map_coe_Ioo_atBot
+-/
 
+#print map_coe_Ioi_atBot /-
 @[simp]
 theorem map_coe_Ioi_atBot (a : α) : map (coe : Ioi a → α) atBot = 𝓝[>] a :=
   map_coe_atBot_of_Ioo_subset (Subset.refl _) fun b hb => ⟨b, hb, Ioo_subset_Ioi_self⟩
 #align map_coe_Ioi_at_bot map_coe_Ioi_atBot
+-/
 
+#print map_coe_Iio_atTop /-
 @[simp]
 theorem map_coe_Iio_atTop (a : α) : map (coe : Iio a → α) atTop = 𝓝[<] a :=
   @map_coe_Ioi_atBot αᵒᵈ _ _ _ _ _
 #align map_coe_Iio_at_top map_coe_Iio_atTop
+-/
 
 variable {l : Filter β} {f : α → β}
 
+#print tendsto_comp_coe_Ioo_atTop /-
 @[simp]
 theorem tendsto_comp_coe_Ioo_atTop (h : a < b) :
     Tendsto (fun x : Ioo a b => f x) atTop l ↔ Tendsto f (𝓝[<] b) l := by
   rw [← map_coe_Ioo_atTop h, tendsto_map'_iff]
 #align tendsto_comp_coe_Ioo_at_top tendsto_comp_coe_Ioo_atTop
+-/
 
+#print tendsto_comp_coe_Ioo_atBot /-
 @[simp]
 theorem tendsto_comp_coe_Ioo_atBot (h : a < b) :
     Tendsto (fun x : Ioo a b => f x) atBot l ↔ Tendsto f (𝓝[>] a) l := by
   rw [← map_coe_Ioo_atBot h, tendsto_map'_iff]
 #align tendsto_comp_coe_Ioo_at_bot tendsto_comp_coe_Ioo_atBot
+-/
 
+#print tendsto_comp_coe_Ioi_atBot /-
 @[simp]
 theorem tendsto_comp_coe_Ioi_atBot :
     Tendsto (fun x : Ioi a => f x) atBot l ↔ Tendsto f (𝓝[>] a) l := by
   rw [← map_coe_Ioi_atBot, tendsto_map'_iff]
 #align tendsto_comp_coe_Ioi_at_bot tendsto_comp_coe_Ioi_atBot
+-/
 
+#print tendsto_comp_coe_Iio_atTop /-
 @[simp]
 theorem tendsto_comp_coe_Iio_atTop :
     Tendsto (fun x : Iio a => f x) atTop l ↔ Tendsto f (𝓝[<] a) l := by
   rw [← map_coe_Iio_atTop, tendsto_map'_iff]
 #align tendsto_comp_coe_Iio_at_top tendsto_comp_coe_Iio_atTop
+-/
 
+#print tendsto_Ioo_atTop /-
 @[simp]
 theorem tendsto_Ioo_atTop {f : β → Ioo a b} :
     Tendsto f l atTop ↔ Tendsto (fun x => (f x : α)) l (𝓝[<] b) := by
   rw [← comap_coe_Ioo_nhdsWithin_Iio, tendsto_comap_iff]
 #align tendsto_Ioo_at_top tendsto_Ioo_atTop
+-/
 
+#print tendsto_Ioo_atBot /-
 @[simp]
 theorem tendsto_Ioo_atBot {f : β → Ioo a b} :
     Tendsto f l atBot ↔ Tendsto (fun x => (f x : α)) l (𝓝[>] a) := by
   rw [← comap_coe_Ioo_nhdsWithin_Ioi, tendsto_comap_iff]
 #align tendsto_Ioo_at_bot tendsto_Ioo_atBot
+-/
 
+#print tendsto_Ioi_atBot /-
 @[simp]
 theorem tendsto_Ioi_atBot {f : β → Ioi a} :
     Tendsto f l atBot ↔ Tendsto (fun x => (f x : α)) l (𝓝[>] a) := by
   rw [← comap_coe_Ioi_nhdsWithin_Ioi, tendsto_comap_iff]
 #align tendsto_Ioi_at_bot tendsto_Ioi_atBot
+-/
 
+#print tendsto_Iio_atTop /-
 @[simp]
 theorem tendsto_Iio_atTop {f : β → Iio a} :
     Tendsto f l atTop ↔ Tendsto (fun x => (f x : α)) l (𝓝[<] a) := by
   rw [← comap_coe_Iio_nhdsWithin_Iio, tendsto_comap_iff]
 #align tendsto_Iio_at_top tendsto_Iio_atTop
+-/
 
 instance (x : α) [Nontrivial α] : NeBot (𝓝[≠] x) :=
   by
@@ -2833,6 +3159,7 @@ theorem Dense.exists_countable_dense_subset_no_bot_top [Nontrivial α] {s : Set
 
 variable (α)
 
+#print exists_countable_dense_no_bot_top /-
 /-- If `α` is a nontrivial separable dense linear order, then there exists a
 countable dense set `s : set α` that contains neither top nor bottom elements of `α`.
 For a dense set containing both bot and top elements, see
@@ -2841,6 +3168,7 @@ theorem exists_countable_dense_no_bot_top [SeparableSpace α] [Nontrivial α] :
     ∃ s : Set α, s.Countable ∧ Dense s ∧ (∀ x, IsBot x → x ∉ s) ∧ ∀ x, IsTop x → x ∉ s := by
   simpa using dense_univ.exists_countable_dense_subset_no_bot_top
 #align exists_countable_dense_no_bot_top exists_countable_dense_no_bot_top
+-/
 
 end DenselyOrdered
 
@@ -3116,13 +3444,17 @@ section LinearOrderedAddCommGroup
 
 variable [LinearOrder α] [Zero α] [TopologicalSpace α] [OrderTopology α]
 
+#print eventually_nhdsWithin_pos_mem_Ioo /-
 theorem eventually_nhdsWithin_pos_mem_Ioo {ε : α} (h : 0 < ε) : ∀ᶠ x in 𝓝[>] 0, x ∈ Ioo 0 ε :=
   Ioo_mem_nhdsWithin_Ioi (left_mem_Ico.2 h)
 #align eventually_nhds_within_pos_mem_Ioo eventually_nhdsWithin_pos_mem_Ioo
+-/
 
+#print eventually_nhdsWithin_pos_mem_Ioc /-
 theorem eventually_nhdsWithin_pos_mem_Ioc {ε : α} (h : 0 < ε) : ∀ᶠ x in 𝓝[>] 0, x ∈ Ioc 0 ε :=
   Ioc_mem_nhdsWithin_Ioi (left_mem_Ico.2 h)
 #align eventually_nhds_within_pos_mem_Ioc eventually_nhdsWithin_pos_mem_Ioc
+-/
 
 end LinearOrderedAddCommGroup
 

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

@@ -136,33 +136,15 @@ instance {p : α → Prop} : OrderClosedTopology (Subtype p) :=
 
 end Subtype
 
-/- warning: is_closed_le_prod -> isClosed_le_prod is a dubious translation:
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-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2], IsClosed.{u1} (Prod.{u1, u1} α α) (instTopologicalSpaceProd.{u1, u1} α α _inst_1 _inst_1) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)))
-Case conversion may be inaccurate. Consider using '#align is_closed_le_prod isClosed_le_prodₓ'. -/
 theorem isClosed_le_prod : IsClosed { p : α × α | p.1 ≤ p.2 } :=
   t.isClosed_le'
 #align is_closed_le_prod isClosed_le_prod
 
-/- warning: is_closed_le -> isClosed_le is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_closed_le isClosed_leₓ'. -/
 theorem isClosed_le [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
     IsClosed { b | f b ≤ g b } :=
   continuous_iff_isClosed.mp (hf.prod_mk hg) _ isClosed_le_prod
 #align is_closed_le isClosed_le
 
-/- warning: is_closed_le' -> isClosed_le' is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_closed_le' isClosed_le'ₓ'. -/
 theorem isClosed_le' (a : α) : IsClosed { b | b ≤ a } :=
   isClosed_le continuous_id continuous_const
 #align is_closed_le' isClosed_le'
@@ -173,12 +155,6 @@ theorem isClosed_Iic {a : α} : IsClosed (Iic a) :=
 #align is_closed_Iic isClosed_Iic
 -/
 
-/- warning: is_closed_ge' -> isClosed_ge' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] (a : α), IsClosed.{u1} α _inst_1 (setOf.{u1} α (fun (b : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a b))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_closed_ge' isClosed_ge'ₓ'. -/
 theorem isClosed_ge' (a : α) : IsClosed { b | a ≤ b } :=
   isClosed_le continuous_const continuous_id
 #align is_closed_ge' isClosed_ge'
@@ -219,12 +195,6 @@ theorem closure_Ici (a : α) : closure (Ici a) = Ici a :=
 #align closure_Ici closure_Ici
 -/
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align le_of_tendsto_of_tendsto le_of_tendsto_of_tendstoₓ'. -/
 theorem le_of_tendsto_of_tendsto {f g : β → α} {b : Filter β} {a₁ a₂ : α} [NeBot b]
     (hf : Tendsto f b (𝓝 a₁)) (hg : Tendsto g b (𝓝 a₂)) (h : f ≤ᶠ[b] g) : a₁ ≤ a₂ :=
   have : Tendsto (fun b => (f b, g b)) b (𝓝 (a₁, a₂)) := by
@@ -232,99 +202,45 @@ theorem le_of_tendsto_of_tendsto {f g : β → α} {b : Filter β} {a₁ a₂ :
   show (a₁, a₂) ∈ { p : α × α | p.1 ≤ p.2 } from t.isClosed_le'.mem_of_tendsto this h
 #align le_of_tendsto_of_tendsto le_of_tendsto_of_tendsto
 
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-Case conversion may be inaccurate. Consider using '#align tendsto_le_of_eventually_le tendsto_le_of_eventuallyLEₓ'. -/
 alias le_of_tendsto_of_tendsto ← tendsto_le_of_eventuallyLE
 #align tendsto_le_of_eventually_le tendsto_le_of_eventuallyLE
 
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-Case conversion may be inaccurate. Consider using '#align le_of_tendsto_of_tendsto' le_of_tendsto_of_tendsto'ₓ'. -/
 theorem le_of_tendsto_of_tendsto' {f g : β → α} {b : Filter β} {a₁ a₂ : α} [NeBot b]
     (hf : Tendsto f b (𝓝 a₁)) (hg : Tendsto g b (𝓝 a₂)) (h : ∀ x, f x ≤ g x) : a₁ ≤ a₂ :=
   le_of_tendsto_of_tendsto hf hg (eventually_of_forall h)
 #align le_of_tendsto_of_tendsto' le_of_tendsto_of_tendsto'
 
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-Case conversion may be inaccurate. Consider using '#align le_of_tendsto le_of_tendstoₓ'. -/
 theorem le_of_tendsto {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
     (h : ∀ᶠ c in x, f c ≤ b) : a ≤ b :=
   le_of_tendsto_of_tendsto limUnder tendsto_const_nhds h
 #align le_of_tendsto le_of_tendsto
 
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-Case conversion may be inaccurate. Consider using '#align le_of_tendsto' le_of_tendsto'ₓ'. -/
 theorem le_of_tendsto' {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
     (h : ∀ c, f c ≤ b) : a ≤ b :=
   le_of_tendsto limUnder (eventually_of_forall h)
 #align le_of_tendsto' le_of_tendsto'
 
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-Case conversion may be inaccurate. Consider using '#align ge_of_tendsto ge_of_tendstoₓ'. -/
 theorem ge_of_tendsto {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
     (h : ∀ᶠ c in x, b ≤ f c) : b ≤ a :=
   le_of_tendsto_of_tendsto tendsto_const_nhds limUnder h
 #align ge_of_tendsto ge_of_tendsto
 
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-Case conversion may be inaccurate. Consider using '#align ge_of_tendsto' ge_of_tendsto'ₓ'. -/
 theorem ge_of_tendsto' {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
     (h : ∀ c, b ≤ f c) : b ≤ a :=
   ge_of_tendsto limUnder (eventually_of_forall h)
 #align ge_of_tendsto' ge_of_tendsto'
 
-/- warning: closure_le_eq -> closure_le_eq is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align closure_le_eq closure_le_eqₓ'. -/
 @[simp]
 theorem closure_le_eq [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
     closure { b | f b ≤ g b } = { b | f b ≤ g b } :=
   (isClosed_le hf hg).closure_eq
 #align closure_le_eq closure_le_eq
 
-/- warning: closure_lt_subset_le -> closure_lt_subset_le is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align closure_lt_subset_le closure_lt_subset_leₓ'. -/
 theorem closure_lt_subset_le [TopologicalSpace β] {f g : β → α} (hf : Continuous f)
     (hg : Continuous g) : closure { b | f b < g b } ⊆ { b | f b ≤ g b } :=
   (closure_minimal fun x => le_of_lt) <| isClosed_le hf hg
 #align closure_lt_subset_le closure_lt_subset_le
 
-/- warning: continuous_within_at.closure_le -> ContinuousWithinAt.closure_le is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align continuous_within_at.closure_le ContinuousWithinAt.closure_leₓ'. -/
 theorem ContinuousWithinAt.closure_le [TopologicalSpace β] {f g : β → α} {s : Set β} {x : β}
     (hx : x ∈ closure s) (hf : ContinuousWithinAt f s x) (hg : ContinuousWithinAt g s x)
     (h : ∀ y ∈ s, f y ≤ g y) : f x ≤ g x :=
@@ -332,12 +248,6 @@ theorem ContinuousWithinAt.closure_le [TopologicalSpace β] {f g : β → α} {s
     OrderClosedTopology.isClosed_le'.closure_subset ((hf.Prod hg).mem_closure hx h)
 #align continuous_within_at.closure_le ContinuousWithinAt.closure_le
 
-/- warning: is_closed.is_closed_le -> IsClosed.isClosed_le is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_closed.is_closed_le IsClosed.isClosed_leₓ'. -/
 /-- If `s` is a closed set and two functions `f` and `g` are continuous on `s`,
 then the set `{x ∈ s | f x ≤ g x}` is a closed set. -/
 theorem IsClosed.isClosed_le [TopologicalSpace β] {f g : β → α} {s : Set β} (hs : IsClosed s)
@@ -345,12 +255,6 @@ theorem IsClosed.isClosed_le [TopologicalSpace β] {f g : β → α} {s : Set β
   (hf.Prod hg).preimage_closed_of_closed hs OrderClosedTopology.isClosed_le'
 #align is_closed.is_closed_le IsClosed.isClosed_le
 
-/- warning: le_on_closure -> le_on_closure is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align le_on_closure le_on_closureₓ'. -/
 theorem le_on_closure [TopologicalSpace β] {f g : β → α} {s : Set β} (h : ∀ x ∈ s, f x ≤ g x)
     (hf : ContinuousOn f (closure s)) (hg : ContinuousOn g (closure s)) ⦃x⦄ (hx : x ∈ closure s) :
     f x ≤ g x :=
@@ -358,23 +262,11 @@ theorem le_on_closure [TopologicalSpace β] {f g : β → α} {s : Set β} (h :
   (closure_minimal this (isClosed_closure.isClosed_le hf hg) hx).2
 #align le_on_closure le_on_closure
 
-/- warning: is_closed.epigraph -> IsClosed.epigraph is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_closed.epigraph IsClosed.epigraphₓ'. -/
 theorem IsClosed.epigraph [TopologicalSpace β] {f : β → α} {s : Set β} (hs : IsClosed s)
     (hf : ContinuousOn f s) : IsClosed { p : β × α | p.1 ∈ s ∧ f p.1 ≤ p.2 } :=
   (hs.Preimage continuous_fst).isClosed_le (hf.comp continuousOn_fst Subset.rfl) continuousOn_snd
 #align is_closed.epigraph IsClosed.epigraph
 
-/- warning: is_closed.hypograph -> IsClosed.hypograph is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {s : Set.{u2} β}, (IsClosed.{u2} β _inst_3 s) -> (ContinuousOn.{u2, u1} β α _inst_3 _inst_1 f s) -> (IsClosed.{max u2 u1} (Prod.{u2, u1} β α) (Prod.topologicalSpace.{u2, u1} β α _inst_3 _inst_1) (setOf.{max u2 u1} (Prod.{u2, u1} β α) (fun (p : Prod.{u2, u1} β α) => And (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) (Prod.fst.{u2, u1} β α p) s) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (Prod.snd.{u2, u1} β α p) (f (Prod.fst.{u2, u1} β α p))))))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_closed.hypograph IsClosed.hypographₓ'. -/
 theorem IsClosed.hypograph [TopologicalSpace β] {f : β → α} {s : Set β} (hs : IsClosed s)
     (hf : ContinuousOn f s) : IsClosed { p : β × α | p.1 ∈ s ∧ p.2 ≤ f p.1 } :=
   (hs.Preimage continuous_fst).isClosed_le continuousOn_snd (hf.comp continuousOn_fst Subset.rfl)
@@ -382,12 +274,6 @@ theorem IsClosed.hypograph [TopologicalSpace β] {f : β → α} {s : Set β} (h
 
 omit t
 
-/- warning: nhds_within_Ici_ne_bot -> nhdsWithin_Ici_neBot is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ici.{u1} α _inst_2 a)))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align nhds_within_Ici_ne_bot nhdsWithin_Ici_neBotₓ'. -/
 theorem nhdsWithin_Ici_neBot {a b : α} (H₂ : a ≤ b) : NeBot (𝓝[Ici a] b) :=
   nhdsWithin_neBot_of_mem H₂
 #align nhds_within_Ici_ne_bot nhdsWithin_Ici_neBot
@@ -399,12 +285,6 @@ theorem nhdsWithin_Ici_self_neBot (a : α) : NeBot (𝓝[≥] a) :=
 #align nhds_within_Ici_self_ne_bot nhdsWithin_Ici_self_neBot
 -/
 
-/- warning: nhds_within_Iic_ne_bot -> nhdsWithin_Iic_neBot is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align nhds_within_Iic_ne_bot nhdsWithin_Iic_neBotₓ'. -/
 theorem nhdsWithin_Iic_neBot {a b : α} (H : a ≤ b) : NeBot (𝓝[Iic b] a) :=
   nhdsWithin_neBot_of_mem H
 #align nhds_within_Iic_ne_bot nhdsWithin_Iic_neBot
@@ -439,24 +319,12 @@ section LinearOrder
 
 variable [TopologicalSpace α] [LinearOrder α] [OrderClosedTopology α]
 
-/- warning: is_open_lt_prod -> isOpen_lt_prod is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))], IsOpen.{u1} (Prod.{u1, u1} α α) (instTopologicalSpaceProd.{u1, u1} α α _inst_1 _inst_1) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)))
-Case conversion may be inaccurate. Consider using '#align is_open_lt_prod isOpen_lt_prodₓ'. -/
 theorem isOpen_lt_prod : IsOpen { p : α × α | p.1 < p.2 } :=
   by
   simp_rw [← isClosed_compl_iff, compl_set_of, not_lt]
   exact isClosed_le continuous_snd continuous_fst
 #align is_open_lt_prod isOpen_lt_prod
 
-/- warning: is_open_lt -> isOpen_lt is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align is_open_lt isOpen_ltₓ'. -/
 theorem isOpen_lt [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
     IsOpen { b | f b < g b } := by
   simp [lt_iff_not_ge, -not_le] <;> exact (isClosed_le hg hf).isOpen_compl
@@ -509,125 +377,53 @@ theorem Ioo_subset_closure_interior : Ioo a b ⊆ closure (interior (Ioo a b)) :
 #align Ioo_subset_closure_interior Ioo_subset_closure_interior
 -/
 
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 theorem Iio_mem_nhds {a b : α} (h : a < b) : Iio b ∈ 𝓝 a :=
   IsOpen.mem_nhds isOpen_Iio h
 #align Iio_mem_nhds Iio_mem_nhds
 
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 theorem Ioi_mem_nhds {a b : α} (h : a < b) : Ioi a ∈ 𝓝 b :=
   IsOpen.mem_nhds isOpen_Ioi h
 #align Ioi_mem_nhds Ioi_mem_nhds
 
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 theorem Iic_mem_nhds {a b : α} (h : a < b) : Iic b ∈ 𝓝 a :=
   mem_of_superset (Iio_mem_nhds h) Iio_subset_Iic_self
 #align Iic_mem_nhds Iic_mem_nhds
 
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 theorem Ici_mem_nhds {a b : α} (h : a < b) : Ici a ∈ 𝓝 b :=
   mem_of_superset (Ioi_mem_nhds h) Ioi_subset_Ici_self
 #align Ici_mem_nhds Ici_mem_nhds
 
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 theorem Ioo_mem_nhds {a b x : α} (ha : a < x) (hb : x < b) : Ioo a b ∈ 𝓝 x :=
   IsOpen.mem_nhds isOpen_Ioo ⟨ha, hb⟩
 #align Ioo_mem_nhds Ioo_mem_nhds
 
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 theorem Ioc_mem_nhds {a b x : α} (ha : a < x) (hb : x < b) : Ioc a b ∈ 𝓝 x :=
   mem_of_superset (Ioo_mem_nhds ha hb) Ioo_subset_Ioc_self
 #align Ioc_mem_nhds Ioc_mem_nhds
 
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 theorem Ico_mem_nhds {a b x : α} (ha : a < x) (hb : x < b) : Ico a b ∈ 𝓝 x :=
   mem_of_superset (Ioo_mem_nhds ha hb) Ioo_subset_Ico_self
 #align Ico_mem_nhds Ico_mem_nhds
 
-/- warning: Icc_mem_nhds -> Icc_mem_nhds is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α} {x : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a x) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x b) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) (nhds.{u1} α _inst_1 x))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α} {x : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a x) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x b) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) (nhds.{u1} α _inst_1 x))
-Case conversion may be inaccurate. Consider using '#align Icc_mem_nhds Icc_mem_nhdsₓ'. -/
 theorem Icc_mem_nhds {a b x : α} (ha : a < x) (hb : x < b) : Icc a b ∈ 𝓝 x :=
   mem_of_superset (Ioo_mem_nhds ha hb) Ioo_subset_Icc_self
 #align Icc_mem_nhds Icc_mem_nhds
 
-/- warning: eventually_lt_of_tendsto_lt -> eventually_lt_of_tendsto_lt is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align eventually_lt_of_tendsto_lt eventually_lt_of_tendsto_ltₓ'. -/
 theorem eventually_lt_of_tendsto_lt {l : Filter γ} {f : γ → α} {u v : α} (hv : v < u)
     (h : Filter.Tendsto f l (𝓝 v)) : ∀ᶠ a in l, f a < u :=
   tendsto_nhds.1 h (· < u) isOpen_Iio hv
 #align eventually_lt_of_tendsto_lt eventually_lt_of_tendsto_lt
 
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-but is expected to have type
-  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {l : Filter.{u2} γ} {f : γ -> α} {u : α} {v : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) u v) -> (Filter.Tendsto.{u2, u1} γ α f l (nhds.{u1} α _inst_1 v)) -> (Filter.Eventually.{u2} γ (fun (a : γ) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) u (f a)) l)
-Case conversion may be inaccurate. Consider using '#align eventually_gt_of_tendsto_gt eventually_gt_of_tendsto_gtₓ'. -/
 theorem eventually_gt_of_tendsto_gt {l : Filter γ} {f : γ → α} {u v : α} (hv : u < v)
     (h : Filter.Tendsto f l (𝓝 v)) : ∀ᶠ a in l, u < f a :=
   tendsto_nhds.1 h (· > u) isOpen_Ioi hv
 #align eventually_gt_of_tendsto_gt eventually_gt_of_tendsto_gt
 
-/- warning: eventually_le_of_tendsto_lt -> eventually_le_of_tendsto_lt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {l : Filter.{u2} γ} {f : γ -> α} {u : α} {v : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) v u) -> (Filter.Tendsto.{u2, u1} γ α f l (nhds.{u1} α _inst_1 v)) -> (Filter.Eventually.{u2} γ (fun (a : γ) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f a) u) l)
-but is expected to have type
-  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {l : Filter.{u2} γ} {f : γ -> α} {u : α} {v : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) v u) -> (Filter.Tendsto.{u2, u1} γ α f l (nhds.{u1} α _inst_1 v)) -> (Filter.Eventually.{u2} γ (fun (a : γ) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f a) u) l)
-Case conversion may be inaccurate. Consider using '#align eventually_le_of_tendsto_lt eventually_le_of_tendsto_ltₓ'. -/
 theorem eventually_le_of_tendsto_lt {l : Filter γ} {f : γ → α} {u v : α} (hv : v < u)
     (h : Tendsto f l (𝓝 v)) : ∀ᶠ a in l, f a ≤ u :=
   (eventually_lt_of_tendsto_lt hv h).mono fun v => le_of_lt
 #align eventually_le_of_tendsto_lt eventually_le_of_tendsto_lt
 
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-lean 3 declaration is
-  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {l : Filter.{u2} γ} {f : γ -> α} {u : α} {v : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) u v) -> (Filter.Tendsto.{u2, u1} γ α f l (nhds.{u1} α _inst_1 v)) -> (Filter.Eventually.{u2} γ (fun (a : γ) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) u (f a)) l)
-but is expected to have type
-  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {l : Filter.{u2} γ} {f : γ -> α} {u : α} {v : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) u v) -> (Filter.Tendsto.{u2, u1} γ α f l (nhds.{u1} α _inst_1 v)) -> (Filter.Eventually.{u2} γ (fun (a : γ) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) u (f a)) l)
-Case conversion may be inaccurate. Consider using '#align eventually_ge_of_tendsto_gt eventually_ge_of_tendsto_gtₓ'. -/
 theorem eventually_ge_of_tendsto_gt {l : Filter γ} {f : γ → α} {u v : α} (hv : u < v)
     (h : Tendsto f l (𝓝 v)) : ∀ᶠ a in l, u ≤ f a :=
   (eventually_gt_of_tendsto_gt hv h).mono fun v => le_of_lt
@@ -675,48 +471,24 @@ theorem Icc_mem_nhdsWithin_Ioi {a b c : α} (H : b ∈ Ico a c) : Icc a c ∈ 
 #align Icc_mem_nhds_within_Ioi Icc_mem_nhdsWithin_Ioi
 -/
 
-/- warning: nhds_within_Ioc_eq_nhds_within_Ioi -> nhdsWithin_Ioc_eq_nhdsWithin_Ioi is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
-Case conversion may be inaccurate. Consider using '#align nhds_within_Ioc_eq_nhds_within_Ioi nhdsWithin_Ioc_eq_nhdsWithin_Ioiₓ'. -/
 @[simp]
 theorem nhdsWithin_Ioc_eq_nhdsWithin_Ioi {a b : α} (h : a < b) : 𝓝[Ioc a b] a = 𝓝[>] a :=
   le_antisymm (nhdsWithin_mono _ Ioc_subset_Ioi_self) <|
     nhdsWithin_le_of_mem <| Ioc_mem_nhdsWithin_Ioi <| left_mem_Ico.2 h
 #align nhds_within_Ioc_eq_nhds_within_Ioi nhdsWithin_Ioc_eq_nhdsWithin_Ioi
 
-/- warning: nhds_within_Ioo_eq_nhds_within_Ioi -> nhdsWithin_Ioo_eq_nhdsWithin_Ioi is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
-Case conversion may be inaccurate. Consider using '#align nhds_within_Ioo_eq_nhds_within_Ioi nhdsWithin_Ioo_eq_nhdsWithin_Ioiₓ'. -/
 @[simp]
 theorem nhdsWithin_Ioo_eq_nhdsWithin_Ioi {a b : α} (h : a < b) : 𝓝[Ioo a b] a = 𝓝[>] a :=
   le_antisymm (nhdsWithin_mono _ Ioo_subset_Ioi_self) <|
     nhdsWithin_le_of_mem <| Ioo_mem_nhdsWithin_Ioi <| left_mem_Ico.2 h
 #align nhds_within_Ioo_eq_nhds_within_Ioi nhdsWithin_Ioo_eq_nhdsWithin_Ioi
 
-/- warning: continuous_within_at_Ioc_iff_Ioi -> continuousWithinAt_Ioc_iff_Ioi is a dubious translation:
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 @[simp]
 theorem continuousWithinAt_Ioc_iff_Ioi [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Ioc a b) a ↔ ContinuousWithinAt f (Ioi a) a := by
   simp only [ContinuousWithinAt, nhdsWithin_Ioc_eq_nhdsWithin_Ioi h]
 #align continuous_within_at_Ioc_iff_Ioi continuousWithinAt_Ioc_iff_Ioi
 
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-Case conversion may be inaccurate. Consider using '#align continuous_within_at_Ioo_iff_Ioi continuousWithinAt_Ioo_iff_Ioiₓ'. -/
 @[simp]
 theorem continuousWithinAt_Ioo_iff_Ioi [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Ioo a b) a ↔ ContinuousWithinAt f (Ioi a) a := by
@@ -753,46 +525,22 @@ theorem Icc_mem_nhdsWithin_Iio {a b c : α} (H : b ∈ Ioc a c) : Icc a c ∈ 
 #align Icc_mem_nhds_within_Iio Icc_mem_nhdsWithin_Iio
 -/
 
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 @[simp]
 theorem nhdsWithin_Ico_eq_nhdsWithin_Iio {a b : α} (h : a < b) : 𝓝[Ico a b] b = 𝓝[<] b := by
   simpa only [dual_Ioc] using nhdsWithin_Ioc_eq_nhdsWithin_Ioi h.dual
 #align nhds_within_Ico_eq_nhds_within_Iio nhdsWithin_Ico_eq_nhdsWithin_Iio
 
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-Case conversion may be inaccurate. Consider using '#align nhds_within_Ioo_eq_nhds_within_Iio nhdsWithin_Ioo_eq_nhdsWithin_Iioₓ'. -/
 @[simp]
 theorem nhdsWithin_Ioo_eq_nhdsWithin_Iio {a b : α} (h : a < b) : 𝓝[Ioo a b] b = 𝓝[<] b := by
   simpa only [dual_Ioo] using nhdsWithin_Ioo_eq_nhdsWithin_Ioi h.dual
 #align nhds_within_Ioo_eq_nhds_within_Iio nhdsWithin_Ioo_eq_nhdsWithin_Iio
 
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-Case conversion may be inaccurate. Consider using '#align continuous_within_at_Ico_iff_Iio continuousWithinAt_Ico_iff_Iioₓ'. -/
 @[simp]
 theorem continuousWithinAt_Ico_iff_Iio {a b : α} {f : α → γ} (h : a < b) :
     ContinuousWithinAt f (Ico a b) b ↔ ContinuousWithinAt f (Iio b) b := by
   simp only [ContinuousWithinAt, nhdsWithin_Ico_eq_nhdsWithin_Iio h]
 #align continuous_within_at_Ico_iff_Iio continuousWithinAt_Ico_iff_Iio
 
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-Case conversion may be inaccurate. Consider using '#align continuous_within_at_Ioo_iff_Iio continuousWithinAt_Ioo_iff_Iioₓ'. -/
 @[simp]
 theorem continuousWithinAt_Ioo_iff_Iio {a b : α} {f : α → γ} (h : a < b) :
     ContinuousWithinAt f (Ioo a b) b ↔ ContinuousWithinAt f (Iio b) b := by
@@ -829,48 +577,24 @@ theorem Icc_mem_nhdsWithin_Ici {a b c : α} (H : b ∈ Ico a c) : Icc a c ∈ 
 #align Icc_mem_nhds_within_Ici Icc_mem_nhdsWithin_Ici
 -/
 
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 @[simp]
 theorem nhdsWithin_Icc_eq_nhdsWithin_Ici {a b : α} (h : a < b) : 𝓝[Icc a b] a = 𝓝[≥] a :=
   le_antisymm (nhdsWithin_mono _ Icc_subset_Ici_self) <|
     nhdsWithin_le_of_mem <| Icc_mem_nhdsWithin_Ici <| left_mem_Ico.2 h
 #align nhds_within_Icc_eq_nhds_within_Ici nhdsWithin_Icc_eq_nhdsWithin_Ici
 
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 @[simp]
 theorem nhdsWithin_Ico_eq_nhdsWithin_Ici {a b : α} (h : a < b) : 𝓝[Ico a b] a = 𝓝[≥] a :=
   le_antisymm (nhdsWithin_mono _ fun x => And.left) <|
     nhdsWithin_le_of_mem <| Ico_mem_nhdsWithin_Ici <| left_mem_Ico.2 h
 #align nhds_within_Ico_eq_nhds_within_Ici nhdsWithin_Ico_eq_nhdsWithin_Ici
 
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 @[simp]
 theorem continuousWithinAt_Icc_iff_Ici [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Icc a b) a ↔ ContinuousWithinAt f (Ici a) a := by
   simp only [ContinuousWithinAt, nhdsWithin_Icc_eq_nhdsWithin_Ici h]
 #align continuous_within_at_Icc_iff_Ici continuousWithinAt_Icc_iff_Ici
 
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 @[simp]
 theorem continuousWithinAt_Ico_iff_Ici [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Ico a b) a ↔ ContinuousWithinAt f (Ici a) a := by
@@ -907,46 +631,22 @@ theorem Icc_mem_nhdsWithin_Iic {a b c : α} (H : b ∈ Ioc a c) : Icc a c ∈ 
 #align Icc_mem_nhds_within_Iic Icc_mem_nhdsWithin_Iic
 -/
 
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 @[simp]
 theorem nhdsWithin_Icc_eq_nhdsWithin_Iic {a b : α} (h : a < b) : 𝓝[Icc a b] b = 𝓝[≤] b := by
   simpa only [dual_Icc] using nhdsWithin_Icc_eq_nhdsWithin_Ici h.dual
 #align nhds_within_Icc_eq_nhds_within_Iic nhdsWithin_Icc_eq_nhdsWithin_Iic
 
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 @[simp]
 theorem nhdsWithin_Ioc_eq_nhdsWithin_Iic {a b : α} (h : a < b) : 𝓝[Ioc a b] b = 𝓝[≤] b := by
   simpa only [dual_Ico] using nhdsWithin_Ico_eq_nhdsWithin_Ici h.dual
 #align nhds_within_Ioc_eq_nhds_within_Iic nhdsWithin_Ioc_eq_nhdsWithin_Iic
 
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 @[simp]
 theorem continuousWithinAt_Icc_iff_Iic [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Icc a b) b ↔ ContinuousWithinAt f (Iic b) b := by
   simp only [ContinuousWithinAt, nhdsWithin_Icc_eq_nhdsWithin_Iic h]
 #align continuous_within_at_Icc_iff_Iic continuousWithinAt_Icc_iff_Iic
 
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-Case conversion may be inaccurate. Consider using '#align continuous_within_at_Ioc_iff_Iic continuousWithinAt_Ioc_iff_Iicₓ'. -/
 @[simp]
 theorem continuousWithinAt_Ioc_iff_Iic [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Ioc a b) b ↔ ContinuousWithinAt f (Iic b) b := by
@@ -963,23 +663,11 @@ section
 
 variable [TopologicalSpace β]
 
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-Case conversion may be inaccurate. Consider using '#align lt_subset_interior_le lt_subset_interior_leₓ'. -/
 theorem lt_subset_interior_le (hf : Continuous f) (hg : Continuous g) :
     { b | f b < g b } ⊆ interior { b | f b ≤ g b } :=
   (interior_maximal fun p => le_of_lt) <| isOpen_lt hf hg
 #align lt_subset_interior_le lt_subset_interior_le
 
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-Case conversion may be inaccurate. Consider using '#align frontier_le_subset_eq frontier_le_subset_eqₓ'. -/
 theorem frontier_le_subset_eq (hf : Continuous f) (hg : Continuous g) :
     frontier { b | f b ≤ g b } ⊆ { b | f b = g b } :=
   by
@@ -1001,20 +689,11 @@ theorem frontier_Ici_subset (a : α) : frontier (Ici a) ⊆ {a} :=
 #align frontier_Ici_subset frontier_Ici_subset
 -/
 
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-Case conversion may be inaccurate. Consider using '#align frontier_lt_subset_eq frontier_lt_subset_eqₓ'. -/
 theorem frontier_lt_subset_eq (hf : Continuous f) (hg : Continuous g) :
     frontier { b | f b < g b } ⊆ { b | f b = g b } := by
   rw [← frontier_compl] <;> convert frontier_le_subset_eq hg hf <;> simp [ext_iff, eq_comm]
 #align frontier_lt_subset_eq frontier_lt_subset_eq
 
-/- warning: continuous_if_le -> continuous_if_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_if_le continuous_if_leₓ'. -/
 theorem continuous_if_le [TopologicalSpace γ] [∀ x, Decidable (f x ≤ g x)] {f' g' : β → γ}
     (hf : Continuous f) (hg : Continuous g) (hf' : ContinuousOn f' { x | f x ≤ g x })
     (hg' : ContinuousOn g' { x | g x ≤ f x }) (hfg : ∀ x, f x = g x → f' x = g' x) :
@@ -1025,21 +704,12 @@ theorem continuous_if_le [TopologicalSpace γ] [∀ x, Decidable (f x ≤ g x)]
   · simp only [not_le]; exact closure_lt_subset_le hg hf
 #align continuous_if_le continuous_if_le
 
-/- warning: continuous.if_le -> Continuous.if_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous.if_le Continuous.if_leₓ'. -/
 theorem Continuous.if_le [TopologicalSpace γ] [∀ x, Decidable (f x ≤ g x)] {f' g' : β → γ}
     (hf' : Continuous f') (hg' : Continuous g') (hf : Continuous f) (hg : Continuous g)
     (hfg : ∀ x, f x = g x → f' x = g' x) : Continuous fun x => if f x ≤ g x then f' x else g' x :=
   continuous_if_le hf hg hf'.ContinuousOn hg'.ContinuousOn hfg
 #align continuous.if_le Continuous.if_le
 
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-Case conversion may be inaccurate. Consider using '#align tendsto.eventually_lt Filter.Tendsto.eventually_ltₓ'. -/
 theorem Filter.Tendsto.eventually_lt {l : Filter γ} {f g : γ → α} {y z : α} (hf : Tendsto f l (𝓝 y))
     (hg : Tendsto g l (𝓝 z)) (hyz : y < z) : ∀ᶠ x in l, f x < g x :=
   by
@@ -1052,35 +722,17 @@ theorem Filter.Tendsto.eventually_lt {l : Filter γ} {f g : γ → α} {y z : α
     exact fun x => lt_trans
 #align tendsto.eventually_lt Filter.Tendsto.eventually_lt
 
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-Case conversion may be inaccurate. Consider using '#align continuous_at.eventually_lt ContinuousAt.eventually_ltₓ'. -/
 theorem ContinuousAt.eventually_lt {x₀ : β} (hf : ContinuousAt f x₀) (hg : ContinuousAt g x₀)
     (hfg : f x₀ < g x₀) : ∀ᶠ x in 𝓝 x₀, f x < g x :=
   Filter.Tendsto.eventually_lt hf hg hfg
 #align continuous_at.eventually_lt ContinuousAt.eventually_lt
 
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-Case conversion may be inaccurate. Consider using '#align continuous.min Continuous.minₓ'. -/
 @[continuity]
 theorem Continuous.min (hf : Continuous f) (hg : Continuous g) :
     Continuous fun b => min (f b) (g b) := by simp only [min_def];
   exact hf.if_le hg hf hg fun x => id
 #align continuous.min Continuous.min
 
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-Case conversion may be inaccurate. Consider using '#align continuous.max Continuous.maxₓ'. -/
 @[continuity]
 theorem Continuous.max (hf : Continuous f) (hg : Continuous g) :
     Continuous fun b => max (f b) (g b) :=
@@ -1089,75 +741,33 @@ theorem Continuous.max (hf : Continuous f) (hg : Continuous g) :
 
 end
 
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-Case conversion may be inaccurate. Consider using '#align continuous_min continuous_minₓ'. -/
 theorem continuous_min : Continuous fun p : α × α => min p.1 p.2 :=
   continuous_fst.min continuous_snd
 #align continuous_min continuous_min
 
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 theorem continuous_max : Continuous fun p : α × α => max p.1 p.2 :=
   continuous_fst.max continuous_snd
 #align continuous_max continuous_max
 
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-Case conversion may be inaccurate. Consider using '#align filter.tendsto.max Filter.Tendsto.maxₓ'. -/
 theorem Filter.Tendsto.max {b : Filter β} {a₁ a₂ : α} (hf : Tendsto f b (𝓝 a₁))
     (hg : Tendsto g b (𝓝 a₂)) : Tendsto (fun b => max (f b) (g b)) b (𝓝 (max a₁ a₂)) :=
   (continuous_max.Tendsto (a₁, a₂)).comp (hf.prod_mk_nhds hg)
 #align filter.tendsto.max Filter.Tendsto.max
 
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-Case conversion may be inaccurate. Consider using '#align filter.tendsto.min Filter.Tendsto.minₓ'. -/
 theorem Filter.Tendsto.min {b : Filter β} {a₁ a₂ : α} (hf : Tendsto f b (𝓝 a₁))
     (hg : Tendsto g b (𝓝 a₂)) : Tendsto (fun b => min (f b) (g b)) b (𝓝 (min a₁ a₂)) :=
   (continuous_min.Tendsto (a₁, a₂)).comp (hf.prod_mk_nhds hg)
 #align filter.tendsto.min Filter.Tendsto.min
 
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-Case conversion may be inaccurate. Consider using '#align filter.tendsto.max_right Filter.Tendsto.max_rightₓ'. -/
 theorem Filter.Tendsto.max_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
     Tendsto (fun i => max a (f i)) l (𝓝 a) := by
   convert((continuous_max.comp (@Continuous.Prod.mk α α _ _ a)).Tendsto a).comp h; simp
 #align filter.tendsto.max_right Filter.Tendsto.max_right
 
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-Case conversion may be inaccurate. Consider using '#align filter.tendsto.max_left Filter.Tendsto.max_leftₓ'. -/
 theorem Filter.Tendsto.max_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
     Tendsto (fun i => max (f i) a) l (𝓝 a) := by simp_rw [max_comm _ a]; exact h.max_right
 #align filter.tendsto.max_left Filter.Tendsto.max_left
 
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-Case conversion may be inaccurate. Consider using '#align filter.tendsto_nhds_max_right Filter.tendsto_nhds_max_rightₓ'. -/
 theorem Filter.tendsto_nhds_max_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝[>] a)) :
     Tendsto (fun i => max a (f i)) l (𝓝[>] a) :=
   by
@@ -1165,107 +775,47 @@ theorem Filter.tendsto_nhds_max_right {l : Filter β} {a : α} (h : Tendsto f l
   exact tendsto_nhds_within_iff.mpr ⟨h₁.max_right, h₂.mono fun i hi => lt_max_of_lt_right hi⟩
 #align filter.tendsto_nhds_max_right Filter.tendsto_nhds_max_right
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align filter.tendsto_nhds_max_left Filter.tendsto_nhds_max_leftₓ'. -/
 theorem Filter.tendsto_nhds_max_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝[>] a)) :
     Tendsto (fun i => max (f i) a) l (𝓝[>] a) := by simp_rw [max_comm _ a];
   exact Filter.tendsto_nhds_max_right h
 #align filter.tendsto_nhds_max_left Filter.tendsto_nhds_max_left
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align filter.tendsto.min_right Filter.Tendsto.min_rightₓ'. -/
 theorem Filter.Tendsto.min_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
     Tendsto (fun i => min a (f i)) l (𝓝 a) :=
   @Filter.Tendsto.max_right αᵒᵈ β _ _ _ f l a h
 #align filter.tendsto.min_right Filter.Tendsto.min_right
 
-/- warning: filter.tendsto.min_left -> Filter.Tendsto.min_left is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {f : β -> α} {l : Filter.{u2} β} {a : α}, (Filter.Tendsto.{u2, u1} β α f l (nhds.{u1} α _inst_1 a)) -> (Filter.Tendsto.{u2, u1} β α (fun (i : β) => LinearOrder.min.{u1} α _inst_2 (f i) a) l (nhds.{u1} α _inst_1 a))
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {f : β -> α} {l : Filter.{u2} β} {a : α}, (Filter.Tendsto.{u2, u1} β α f l (nhds.{u1} α _inst_1 a)) -> (Filter.Tendsto.{u2, u1} β α (fun (i : β) => Min.min.{u1} α (LinearOrder.toMin.{u1} α _inst_2) (f i) a) l (nhds.{u1} α _inst_1 a))
-Case conversion may be inaccurate. Consider using '#align filter.tendsto.min_left Filter.Tendsto.min_leftₓ'. -/
 theorem Filter.Tendsto.min_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
     Tendsto (fun i => min (f i) a) l (𝓝 a) :=
   @Filter.Tendsto.max_left αᵒᵈ β _ _ _ f l a h
 #align filter.tendsto.min_left Filter.Tendsto.min_left
 
-/- warning: filter.tendsto_nhds_min_right -> Filter.tendsto_nhds_min_right is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {f : β -> α} {l : Filter.{u2} β} {a : α}, (Filter.Tendsto.{u2, u1} β α f l (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) -> (Filter.Tendsto.{u2, u1} β α (fun (i : β) => LinearOrder.min.{u1} α _inst_2 a (f i)) l (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
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-Case conversion may be inaccurate. Consider using '#align filter.tendsto_nhds_min_right Filter.tendsto_nhds_min_rightₓ'. -/
 theorem Filter.tendsto_nhds_min_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝[<] a)) :
     Tendsto (fun i => min a (f i)) l (𝓝[<] a) :=
   @Filter.tendsto_nhds_max_right αᵒᵈ β _ _ _ f l a h
 #align filter.tendsto_nhds_min_right Filter.tendsto_nhds_min_right
 
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-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {f : β -> α} {l : Filter.{u2} β} {a : α}, (Filter.Tendsto.{u2, u1} β α f l (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) -> (Filter.Tendsto.{u2, u1} β α (fun (i : β) => LinearOrder.min.{u1} α _inst_2 (f i) a) l (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {f : β -> α} {l : Filter.{u2} β} {a : α}, (Filter.Tendsto.{u2, u1} β α f l (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) -> (Filter.Tendsto.{u2, u1} β α (fun (i : β) => Min.min.{u1} α (LinearOrder.toMin.{u1} α _inst_2) (f i) a) l (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
-Case conversion may be inaccurate. Consider using '#align filter.tendsto_nhds_min_left Filter.tendsto_nhds_min_leftₓ'. -/
 theorem Filter.tendsto_nhds_min_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝[<] a)) :
     Tendsto (fun i => min (f i) a) l (𝓝[<] a) :=
   @Filter.tendsto_nhds_max_left αᵒᵈ β _ _ _ f l a h
 #align filter.tendsto_nhds_min_left Filter.tendsto_nhds_min_left
 
-/- warning: dense.exists_lt -> Dense.exists_lt is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) y x)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) y x)))
-Case conversion may be inaccurate. Consider using '#align dense.exists_lt Dense.exists_ltₓ'. -/
 theorem Dense.exists_lt [NoMinOrder α] {s : Set α} (hs : Dense s) (x : α) : ∃ y ∈ s, y < x :=
   hs.exists_mem_open isOpen_Iio (exists_lt x)
 #align dense.exists_lt Dense.exists_lt
 
-/- warning: dense.exists_gt -> Dense.exists_gt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x y)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x y)))
-Case conversion may be inaccurate. Consider using '#align dense.exists_gt Dense.exists_gtₓ'. -/
 theorem Dense.exists_gt [NoMaxOrder α] {s : Set α} (hs : Dense s) (x : α) : ∃ y ∈ s, x < y :=
   hs.OrderDual.exists_lt x
 #align dense.exists_gt Dense.exists_gt
 
-/- warning: dense.exists_le -> Dense.exists_le is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) y x)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) y x)))
-Case conversion may be inaccurate. Consider using '#align dense.exists_le Dense.exists_leₓ'. -/
 theorem Dense.exists_le [NoMinOrder α] {s : Set α} (hs : Dense s) (x : α) : ∃ y ∈ s, y ≤ x :=
   (hs.exists_lt x).imp fun y hy => ⟨hy.fst, hy.snd.le⟩
 #align dense.exists_le Dense.exists_le
 
-/- warning: dense.exists_ge -> Dense.exists_ge is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x y)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x y)))
-Case conversion may be inaccurate. Consider using '#align dense.exists_ge Dense.exists_geₓ'. -/
 theorem Dense.exists_ge [NoMaxOrder α] {s : Set α} (hs : Dense s) (x : α) : ∃ y ∈ s, x ≤ y :=
   hs.OrderDual.exists_le x
 #align dense.exists_ge Dense.exists_ge
 
-/- warning: dense.exists_le' -> Dense.exists_le' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), (IsBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s)) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) y x)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), (IsBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) y x)))
-Case conversion may be inaccurate. Consider using '#align dense.exists_le' Dense.exists_le'ₓ'. -/
 theorem Dense.exists_le' {s : Set α} (hs : Dense s) (hbot : ∀ x, IsBot x → x ∈ s) (x : α) :
     ∃ y ∈ s, y ≤ x := by
   by_cases hx : IsBot x
@@ -1275,23 +825,11 @@ theorem Dense.exists_le' {s : Set α} (hs : Dense s) (hbot : ∀ x, IsBot x →
     exact ⟨y, hys, hy.le⟩
 #align dense.exists_le' Dense.exists_le'
 
-/- warning: dense.exists_ge' -> Dense.exists_ge' is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), (IsTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s)) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x y)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), (IsTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x y)))
-Case conversion may be inaccurate. Consider using '#align dense.exists_ge' Dense.exists_ge'ₓ'. -/
 theorem Dense.exists_ge' {s : Set α} (hs : Dense s) (htop : ∀ x, IsTop x → x ∈ s) (x : α) :
     ∃ y ∈ s, x ≤ y :=
   hs.OrderDual.exists_le' htop x
 #align dense.exists_ge' Dense.exists_ge'
 
-/- warning: dense.exists_between -> Dense.exists_between is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall {x : α} {y : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x y) -> (Exists.{succ u1} α (fun (z : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) z s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) z s) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) z (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) x y)))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall {x : α} {y : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x y) -> (Exists.{succ u1} α (fun (z : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) z s) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) z (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) x y)))))
-Case conversion may be inaccurate. Consider using '#align dense.exists_between Dense.exists_betweenₓ'. -/
 theorem Dense.exists_between [DenselyOrdered α] {s : Set α} (hs : Dense s) {x y : α} (h : x < y) :
     ∃ z ∈ s, z ∈ Ioo x y :=
   hs.exists_mem_open isOpen_Ioo (nonempty_Ioo.2 h)
@@ -1424,72 +962,30 @@ theorem isOpen_iff_generate_intervals {s : Set α} :
 #align is_open_iff_generate_intervals isOpen_iff_generate_intervals
 -/
 
-/- warning: is_open_lt' -> isOpen_lt' is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_open_lt' isOpen_lt'ₓ'. -/
 theorem isOpen_lt' (a : α) : IsOpen { b : α | a < b } := by
   rw [@isOpen_iff_generate_intervals α _ _ t] <;> exact generate_open.basic _ ⟨a, Or.inl rfl⟩
 #align is_open_lt' isOpen_lt'
 
-/- warning: is_open_gt' -> isOpen_gt' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), IsOpen.{u1} α _inst_1 (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b a))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_open_gt' isOpen_gt'ₓ'. -/
 theorem isOpen_gt' (a : α) : IsOpen { b : α | b < a } := by
   rw [@isOpen_iff_generate_intervals α _ _ t] <;> exact generate_open.basic _ ⟨a, Or.inr rfl⟩
 #align is_open_gt' isOpen_gt'
 
-/- warning: lt_mem_nhds -> lt_mem_nhds is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a x) (nhds.{u1} α _inst_1 b))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align lt_mem_nhds lt_mem_nhdsₓ'. -/
 theorem lt_mem_nhds {a b : α} (h : a < b) : ∀ᶠ x in 𝓝 b, a < x :=
   IsOpen.mem_nhds (isOpen_lt' _) h
 #align lt_mem_nhds lt_mem_nhds
 
-/- warning: le_mem_nhds -> le_mem_nhds is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a x) (nhds.{u1} α _inst_1 b))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align le_mem_nhds le_mem_nhdsₓ'. -/
 theorem le_mem_nhds {a b : α} (h : a < b) : ∀ᶠ x in 𝓝 b, a ≤ x :=
   (𝓝 b).sets_of_superset (lt_mem_nhds h) fun b hb => le_of_lt hb
 #align le_mem_nhds le_mem_nhds
 
-/- warning: gt_mem_nhds -> gt_mem_nhds is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) x b) (nhds.{u1} α _inst_1 a))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align gt_mem_nhds gt_mem_nhdsₓ'. -/
 theorem gt_mem_nhds {a b : α} (h : a < b) : ∀ᶠ x in 𝓝 a, x < b :=
   IsOpen.mem_nhds (isOpen_gt' _) h
 #align gt_mem_nhds gt_mem_nhds
 
-/- warning: ge_mem_nhds -> ge_mem_nhds is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) x b) (nhds.{u1} α _inst_1 a))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x b) (nhds.{u1} α _inst_1 a))
-Case conversion may be inaccurate. Consider using '#align ge_mem_nhds ge_mem_nhdsₓ'. -/
 theorem ge_mem_nhds {a b : α} (h : a < b) : ∀ᶠ x in 𝓝 a, x ≤ b :=
   (𝓝 a).sets_of_superset (gt_mem_nhds h) fun b hb => le_of_lt hb
 #align ge_mem_nhds ge_mem_nhds
 
-/- warning: nhds_eq_order -> nhds_eq_order is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nhds_eq_order nhds_eq_orderₓ'. -/
 theorem nhds_eq_order (a : α) : 𝓝 a = (⨅ b ∈ Iio a, 𝓟 (Ioi b)) ⊓ ⨅ b ∈ Ioi a, 𝓟 (Iio b) := by
   rw [t.topology_eq_generate_intervals, nhds_generate_from] <;>
     exact
@@ -1504,12 +1000,6 @@ theorem nhds_eq_order (a : α) : 𝓝 a = (⨅ b ∈ Iio a, 𝓟 (Ioi b)) ⊓ 
             | _, h, Or.inr rfl => inf_le_of_right_le <| iInf_le_of_le b <| iInf_le _ h)
 #align nhds_eq_order nhds_eq_order
 
-/- warning: tendsto_order -> tendsto_order is a dubious translation:
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-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {a : α} {x : Filter.{u2} β}, Iff (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) (And (forall (a' : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a' a) -> (Filter.Eventually.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a' (f b)) x)) (forall (a' : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α _inst_2) a' a) -> (Filter.Eventually.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (f b) a') x)))
-Case conversion may be inaccurate. Consider using '#align tendsto_order tendsto_orderₓ'. -/
 theorem tendsto_order {f : β → α} {a : α} {x : Filter β} :
     Tendsto f x (𝓝 a) ↔ (∀ a' < a, ∀ᶠ b in x, a' < f b) ∧ ∀ a' > a, ∀ᶠ b in x, f b < a' := by
   simp [nhds_eq_order a, tendsto_inf, tendsto_infi, tendsto_principal]
@@ -1545,12 +1035,6 @@ instance tendstoIooClassNhds (a : α) : TendstoIxxClass Ioo (𝓝 a) (𝓝 a) :=
 #align tendsto_Ioo_class_nhds tendstoIooClassNhds
 -/
 
-/- warning: tendsto_of_tendsto_of_tendsto_of_le_of_le' -> tendsto_of_tendsto_of_tendsto_of_le_of_le' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_of_tendsto_of_tendsto_of_le_of_le'ₓ'. -/
 /-- **Squeeze theorem** (also known as **sandwich theorem**). This version assumes that inequalities
 hold eventually for the filter. -/
 theorem tendsto_of_tendsto_of_tendsto_of_le_of_le' {f g h : β → α} {b : Filter β} {a : α}
@@ -1559,12 +1043,6 @@ theorem tendsto_of_tendsto_of_tendsto_of_le_of_le' {f g h : β → α} {b : Filt
   (hg.Icc hh).of_smallSets <| hgf.And hfh
 #align tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_of_tendsto_of_tendsto_of_le_of_le'
 
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-Case conversion may be inaccurate. Consider using '#align tendsto_of_tendsto_of_tendsto_of_le_of_le tendsto_of_tendsto_of_tendsto_of_le_of_leₓ'. -/
 /-- **Squeeze theorem** (also known as **sandwich theorem**). This version assumes that inequalities
 hold everywhere. -/
 theorem tendsto_of_tendsto_of_tendsto_of_le_of_le {f g h : β → α} {b : Filter β} {a : α}
@@ -1574,12 +1052,6 @@ theorem tendsto_of_tendsto_of_tendsto_of_le_of_le {f g h : β → α} {b : Filte
     (eventually_of_forall hfh)
 #align tendsto_of_tendsto_of_tendsto_of_le_of_le tendsto_of_tendsto_of_tendsto_of_le_of_le
 
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-Case conversion may be inaccurate. Consider using '#align nhds_order_unbounded nhds_order_unboundedₓ'. -/
 theorem nhds_order_unbounded {a : α} (hu : ∃ u, a < u) (hl : ∃ l, l < a) :
     𝓝 a = ⨅ (l) (h₂ : l < a) (u) (h₂ : a < u), 𝓟 (Ioo l u) :=
   by
@@ -1589,12 +1061,6 @@ theorem nhds_order_unbounded {a : α} (hu : ∃ u, a < u) (hl : ∃ l, l < a) :
   rfl
 #align nhds_order_unbounded nhds_order_unbounded
 
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 theorem tendsto_order_unbounded {f : β → α} {a : α} {x : Filter β} (hu : ∃ u, a < u)
     (hl : ∃ l, l < a) (h : ∀ l u, l < a → a < u → ∀ᶠ b in x, l < f b ∧ f b < u) :
     Tendsto f x (𝓝 a) := by
@@ -1630,12 +1096,6 @@ instance tendstoIccClassNhdsPi {ι : Type _} {α : ι → Type _} [∀ i, Preord
 #align tendsto_Icc_class_nhds_pi tendstoIccClassNhdsPi
 -/
 
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-Case conversion may be inaccurate. Consider using '#align induced_order_topology' induced_orderTopology'ₓ'. -/
 theorem induced_orderTopology' {α : Type u} {β : Type v} [Preorder α] [ta : TopologicalSpace β]
     [Preorder β] [OrderTopology β] (f : α → β) (hf : ∀ {x y}, f x < f y ↔ x < y)
     (H₁ : ∀ {a x}, x < f a → ∃ b < a, x ≤ f b) (H₂ : ∀ {a x}, f a < x → ∃ b > a, f b ≤ x) :
@@ -1671,12 +1131,6 @@ theorem induced_orderTopology' {α : Type u} {β : Type v} [Preorder α] [ta : T
       exact fun c hc => lt_of_lt_of_le (hf.2 hc) xb
 #align induced_order_topology' induced_orderTopology'
 
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-Case conversion may be inaccurate. Consider using '#align induced_order_topology induced_orderTopologyₓ'. -/
 theorem induced_orderTopology {α : Type u} {β : Type v} [Preorder α] [ta : TopologicalSpace β]
     [Preorder β] [OrderTopology β] (f : α → β) (hf : ∀ {x y}, f x < f y ↔ x < y)
     (H : ∀ {x y}, x < y → ∃ a, x < f a ∧ f a < y) : @OrderTopology _ (induced f ta) _ :=
@@ -1738,12 +1192,6 @@ instance orderTopology_of_ordConnected {α : Type u} [ta : TopologicalSpace α]
 #align order_topology_of_ord_connected orderTopology_of_ordConnected
 -/
 
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-Case conversion may be inaccurate. Consider using '#align nhds_within_Ici_eq'' nhdsWithin_Ici_eq''ₓ'. -/
 theorem nhdsWithin_Ici_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology α] (a : α) :
     𝓝[≥] a = (⨅ (u) (hu : a < u), 𝓟 (Iio u)) ⊓ 𝓟 (Ici a) :=
   by
@@ -1752,45 +1200,21 @@ theorem nhdsWithin_Ici_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology 
   exact inf_le_right.trans (le_iInf₂ fun l hl => principal_mono.2 <| Ici_subset_Ioi.2 hl)
 #align nhds_within_Ici_eq'' nhdsWithin_Ici_eq''
 
-/- warning: nhds_within_Iic_eq'' -> nhdsWithin_Iic_eq'' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nhds_within_Iic_eq'' nhdsWithin_Iic_eq''ₓ'. -/
 theorem nhdsWithin_Iic_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology α] (a : α) :
     𝓝[≤] a = (⨅ l < a, 𝓟 (Ioi l)) ⊓ 𝓟 (Iic a) :=
   nhdsWithin_Ici_eq'' (toDual a)
 #align nhds_within_Iic_eq'' nhdsWithin_Iic_eq''
 
-/- warning: nhds_within_Ici_eq' -> nhdsWithin_Ici_eq' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nhds_within_Ici_eq' nhdsWithin_Ici_eq'ₓ'. -/
 theorem nhdsWithin_Ici_eq' [TopologicalSpace α] [Preorder α] [OrderTopology α] {a : α}
     (ha : ∃ u, a < u) : 𝓝[≥] a = ⨅ (u) (hu : a < u), 𝓟 (Ico a u) := by
   simp only [nhdsWithin_Ici_eq'', biInf_inf ha, inf_principal, Iio_inter_Ici]
 #align nhds_within_Ici_eq' nhdsWithin_Ici_eq'
 
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-Case conversion may be inaccurate. Consider using '#align nhds_within_Iic_eq' nhdsWithin_Iic_eq'ₓ'. -/
 theorem nhdsWithin_Iic_eq' [TopologicalSpace α] [Preorder α] [OrderTopology α] {a : α}
     (ha : ∃ l, l < a) : 𝓝[≤] a = ⨅ l < a, 𝓟 (Ioc l a) := by
   simp only [nhdsWithin_Iic_eq'', biInf_inf ha, inf_principal, Ioi_inter_Iic]
 #align nhds_within_Iic_eq' nhdsWithin_Iic_eq'
 
-/- warning: nhds_within_Ici_basis' -> nhdsWithin_Ici_basis' is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u)) -> (Filter.HasBasis.{u1, succ u1} α α (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (u : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u) (fun (u : α) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u))
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-Case conversion may be inaccurate. Consider using '#align nhds_within_Ici_basis' nhdsWithin_Ici_basis'ₓ'. -/
 theorem nhdsWithin_Ici_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopology α] {a : α}
     (ha : ∃ u, a < u) : (𝓝[≥] a).HasBasis (fun u => a < u) fun u => Ico a u :=
   (nhdsWithin_Ici_eq' ha).symm ▸
@@ -1801,12 +1225,6 @@ theorem nhdsWithin_Ici_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopol
       ha
 #align nhds_within_Ici_basis' nhdsWithin_Ici_basis'
 
-/- warning: nhds_within_Iic_basis' -> nhdsWithin_Iic_basis' is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α}, (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a)) -> (Filter.HasBasis.{u1, succ u1} α α (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (l : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a) (fun (l : α) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a))
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-Case conversion may be inaccurate. Consider using '#align nhds_within_Iic_basis' nhdsWithin_Iic_basis'ₓ'. -/
 theorem nhdsWithin_Iic_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopology α] {a : α}
     (ha : ∃ l, l < a) : (𝓝[≤] a).HasBasis (fun l => l < a) fun l => Ioc l a :=
   by
@@ -1814,54 +1232,24 @@ theorem nhdsWithin_Iic_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopol
   exact funext fun x => (@dual_Ico _ _ _ _).symm
 #align nhds_within_Iic_basis' nhdsWithin_Iic_basis'
 
-/- warning: nhds_within_Ici_basis -> nhdsWithin_Ici_basis is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α), Filter.HasBasis.{u1, succ u1} α α (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (u : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u) (fun (u : α) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u)
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-Case conversion may be inaccurate. Consider using '#align nhds_within_Ici_basis nhdsWithin_Ici_basisₓ'. -/
 theorem nhdsWithin_Ici_basis [TopologicalSpace α] [LinearOrder α] [OrderTopology α] [NoMaxOrder α]
     (a : α) : (𝓝[≥] a).HasBasis (fun u => a < u) fun u => Ico a u :=
   nhdsWithin_Ici_basis' (exists_gt a)
 #align nhds_within_Ici_basis nhdsWithin_Ici_basis
 
-/- warning: nhds_within_Iic_basis -> nhdsWithin_Iic_basis is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α), Filter.HasBasis.{u1, succ u1} α α (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (l : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a) (fun (l : α) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a)
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-Case conversion may be inaccurate. Consider using '#align nhds_within_Iic_basis nhdsWithin_Iic_basisₓ'. -/
 theorem nhdsWithin_Iic_basis [TopologicalSpace α] [LinearOrder α] [OrderTopology α] [NoMinOrder α]
     (a : α) : (𝓝[≤] a).HasBasis (fun l => l < a) fun l => Ioc l a :=
   nhdsWithin_Iic_basis' (exists_lt a)
 #align nhds_within_Iic_basis nhdsWithin_Iic_basis
 
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-Case conversion may be inaccurate. Consider using '#align nhds_top_order nhds_top_orderₓ'. -/
 theorem nhds_top_order [TopologicalSpace α] [Preorder α] [OrderTop α] [OrderTopology α] :
     𝓝 (⊤ : α) = ⨅ (l) (h₂ : l < ⊤), 𝓟 (Ioi l) := by simp [nhds_eq_order (⊤ : α)]
 #align nhds_top_order nhds_top_order
 
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-Case conversion may be inaccurate. Consider using '#align nhds_bot_order nhds_bot_orderₓ'. -/
 theorem nhds_bot_order [TopologicalSpace α] [Preorder α] [OrderBot α] [OrderTopology α] :
     𝓝 (⊥ : α) = ⨅ (l) (h₂ : ⊥ < l), 𝓟 (Iio l) := by simp [nhds_eq_order (⊥ : α)]
 #align nhds_bot_order nhds_bot_order
 
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-Case conversion may be inaccurate. Consider using '#align nhds_top_basis nhds_top_basisₓ'. -/
 theorem nhds_top_basis [TopologicalSpace α] [LinearOrder α] [OrderTop α] [OrderTopology α]
     [Nontrivial α] : (𝓝 ⊤).HasBasis (fun a : α => a < ⊤) fun a : α => Ioi a :=
   by
@@ -1869,23 +1257,11 @@ theorem nhds_top_basis [TopologicalSpace α] [LinearOrder α] [OrderTop α] [Ord
   simpa only [Iic_top, nhdsWithin_univ, Ioc_top] using nhdsWithin_Iic_basis' this
 #align nhds_top_basis nhds_top_basis
 
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-Case conversion may be inaccurate. Consider using '#align nhds_bot_basis nhds_bot_basisₓ'. -/
 theorem nhds_bot_basis [TopologicalSpace α] [LinearOrder α] [OrderBot α] [OrderTopology α]
     [Nontrivial α] : (𝓝 ⊥).HasBasis (fun a : α => ⊥ < a) fun a : α => Iio a :=
   @nhds_top_basis αᵒᵈ _ _ _ _ _
 #align nhds_bot_basis nhds_bot_basis
 
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : Nontrivial.{u1} α] [_inst_6 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3))) (fun (a : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3))) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))
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-Case conversion may be inaccurate. Consider using '#align nhds_top_basis_Ici nhds_top_basis_Iciₓ'. -/
 theorem nhds_top_basis_Ici [TopologicalSpace α] [LinearOrder α] [OrderTop α] [OrderTopology α]
     [Nontrivial α] [DenselyOrdered α] : (𝓝 ⊤).HasBasis (fun a : α => a < ⊤) Ici :=
   nhds_top_basis.to_hasBasis
@@ -1895,23 +1271,11 @@ theorem nhds_top_basis_Ici [TopologicalSpace α] [LinearOrder α] [OrderTop α]
     fun a ha => ⟨a, ha, Ioi_subset_Ici_self⟩
 #align nhds_top_basis_Ici nhds_top_basis_Ici
 
-/- warning: nhds_bot_basis_Iic -> nhds_bot_basis_Iic is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nhds_bot_basis_Iic nhds_bot_basis_Iicₓ'. -/
 theorem nhds_bot_basis_Iic [TopologicalSpace α] [LinearOrder α] [OrderBot α] [OrderTopology α]
     [Nontrivial α] [DenselyOrdered α] : (𝓝 ⊥).HasBasis (fun a : α => ⊥ < a) Iic :=
   @nhds_top_basis_Ici αᵒᵈ _ _ _ _ _ _
 #align nhds_bot_basis_Iic nhds_bot_basis_Iic
 
-/- warning: tendsto_nhds_top_mono -> tendsto_nhds_top_mono is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align tendsto_nhds_top_mono tendsto_nhds_top_monoₓ'. -/
 theorem tendsto_nhds_top_mono [TopologicalSpace β] [Preorder β] [OrderTop β] [OrderTopology β]
     {l : Filter α} {f g : α → β} (hf : Tendsto f l (𝓝 ⊤)) (hg : f ≤ᶠ[l] g) : Tendsto g l (𝓝 ⊤) :=
   by
@@ -1920,34 +1284,16 @@ theorem tendsto_nhds_top_mono [TopologicalSpace β] [Preorder β] [OrderTop β]
   filter_upwards [hf x hx, hg]with _ using lt_of_lt_of_le
 #align tendsto_nhds_top_mono tendsto_nhds_top_mono
 
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-Case conversion may be inaccurate. Consider using '#align tendsto_nhds_bot_mono tendsto_nhds_bot_monoₓ'. -/
 theorem tendsto_nhds_bot_mono [TopologicalSpace β] [Preorder β] [OrderBot β] [OrderTopology β]
     {l : Filter α} {f g : α → β} (hf : Tendsto f l (𝓝 ⊥)) (hg : g ≤ᶠ[l] f) : Tendsto g l (𝓝 ⊥) :=
   @tendsto_nhds_top_mono α βᵒᵈ _ _ _ _ _ _ _ hf hg
 #align tendsto_nhds_bot_mono tendsto_nhds_bot_mono
 
-/- warning: tendsto_nhds_top_mono' -> tendsto_nhds_top_mono' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align tendsto_nhds_top_mono' tendsto_nhds_top_mono'ₓ'. -/
 theorem tendsto_nhds_top_mono' [TopologicalSpace β] [Preorder β] [OrderTop β] [OrderTopology β]
     {l : Filter α} {f g : α → β} (hf : Tendsto f l (𝓝 ⊤)) (hg : f ≤ g) : Tendsto g l (𝓝 ⊤) :=
   tendsto_nhds_top_mono hf (eventually_of_forall hg)
 #align tendsto_nhds_top_mono' tendsto_nhds_top_mono'
 
-/- warning: tendsto_nhds_bot_mono' -> tendsto_nhds_bot_mono' is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align tendsto_nhds_bot_mono' tendsto_nhds_bot_mono'ₓ'. -/
 theorem tendsto_nhds_bot_mono' [TopologicalSpace β] [Preorder β] [OrderBot β] [OrderTopology β]
     {l : Filter α} {f g : α → β} (hf : Tendsto f l (𝓝 ⊥)) (hg : g ≤ f) : Tendsto g l (𝓝 ⊥) :=
   tendsto_nhds_bot_mono hf (eventually_of_forall hg)
@@ -1961,42 +1307,18 @@ section OrderClosedTopology
 
 variable [OrderClosedTopology α] {a b : α}
 
-/- warning: eventually_le_nhds -> eventually_le_nhds is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x b) (nhds.{u1} α _inst_1 a))
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-Case conversion may be inaccurate. Consider using '#align eventually_le_nhds eventually_le_nhdsₓ'. -/
 theorem eventually_le_nhds (hab : a < b) : ∀ᶠ x in 𝓝 a, x ≤ b :=
   eventually_iff.mpr (mem_nhds_iff.mpr ⟨Iio b, Iio_subset_Iic_self, isOpen_Iio, hab⟩)
 #align eventually_le_nhds eventually_le_nhds
 
-/- warning: eventually_lt_nhds -> eventually_lt_nhds is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x b) (nhds.{u1} α _inst_1 a))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x b) (nhds.{u1} α _inst_1 a))
-Case conversion may be inaccurate. Consider using '#align eventually_lt_nhds eventually_lt_nhdsₓ'. -/
 theorem eventually_lt_nhds (hab : a < b) : ∀ᶠ x in 𝓝 a, x < b :=
   eventually_iff.mpr (mem_nhds_iff.mpr ⟨Iio b, rfl.Subset, isOpen_Iio, hab⟩)
 #align eventually_lt_nhds eventually_lt_nhds
 
-/- warning: eventually_ge_nhds -> eventually_ge_nhds is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) -> (Filter.Eventually.{u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b x) (nhds.{u1} α _inst_1 a))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b a) -> (Filter.Eventually.{u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b x) (nhds.{u1} α _inst_1 a))
-Case conversion may be inaccurate. Consider using '#align eventually_ge_nhds eventually_ge_nhdsₓ'. -/
 theorem eventually_ge_nhds (hab : b < a) : ∀ᶠ x in 𝓝 a, b ≤ x :=
   eventually_iff.mpr (mem_nhds_iff.mpr ⟨Ioi b, Ioi_subset_Ici_self, isOpen_Ioi, hab⟩)
 #align eventually_ge_nhds eventually_ge_nhds
 
-/- warning: eventually_gt_nhds -> eventually_gt_nhds is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b x) (nhds.{u1} α _inst_1 a))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b a) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b x) (nhds.{u1} α _inst_1 a))
-Case conversion may be inaccurate. Consider using '#align eventually_gt_nhds eventually_gt_nhdsₓ'. -/
 theorem eventually_gt_nhds (hab : b < a) : ∀ᶠ x in 𝓝 a, b < x :=
   eventually_iff.mpr (mem_nhds_iff.mpr ⟨Ioi b, rfl.Subset, isOpen_Ioi, hab⟩)
 #align eventually_gt_nhds eventually_gt_nhds
@@ -2007,12 +1329,6 @@ section OrderTopology
 
 variable [OrderTopology α]
 
-/- warning: order_separated -> order_separated is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a₁ : α} {a₂ : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a₁ a₂) -> (Exists.{succ u1} (Set.{u1} α) (fun (u : Set.{u1} α) => Exists.{succ u1} (Set.{u1} α) (fun (v : Set.{u1} α) => And (IsOpen.{u1} α _inst_1 u) (And (IsOpen.{u1} α _inst_1 v) (And (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a₁ u) (And (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a₂ v) (forall (b₁ : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b₁ u) -> (forall (b₂ : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b₂ v) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b₁ b₂)))))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a₁ : α} {a₂ : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a₁ a₂) -> (Exists.{succ u1} (Set.{u1} α) (fun (u : Set.{u1} α) => Exists.{succ u1} (Set.{u1} α) (fun (v : Set.{u1} α) => And (IsOpen.{u1} α _inst_1 u) (And (IsOpen.{u1} α _inst_1 v) (And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a₁ u) (And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a₂ v) (forall (b₁ : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b₁ u) -> (forall (b₂ : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b₂ v) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b₁ b₂)))))))))
-Case conversion may be inaccurate. Consider using '#align order_separated order_separatedₓ'. -/
 theorem order_separated {a₁ a₂ : α} (h : a₁ < a₂) :
     ∃ u v : Set α, IsOpen u ∧ IsOpen v ∧ a₁ ∈ u ∧ a₂ ∈ v ∧ ∀ b₁ ∈ u, ∀ b₂ ∈ v, b₁ < b₂ :=
   match dense_or_discrete a₁ a₂ with
@@ -2040,23 +1356,11 @@ instance (priority := 100) OrderTopology.to_orderClosedTopology : OrderClosedTop
 #align order_topology.to_order_closed_topology OrderTopology.to_orderClosedTopology
 -/
 
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a)) -> (Exists.{succ u1} α (fun (l : α) => Exists.{0} (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a) (fun (H : LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l a)) -> (Exists.{succ u1} α (fun (l : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l a) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s)))
-Case conversion may be inaccurate. Consider using '#align exists_Ioc_subset_of_mem_nhds exists_Ioc_subset_of_mem_nhdsₓ'. -/
 theorem exists_Ioc_subset_of_mem_nhds {a : α} {s : Set α} (hs : s ∈ 𝓝 a) (h : ∃ l, l < a) :
     ∃ l < a, Ioc l a ⊆ s :=
   (nhdsWithin_Iic_basis' h).mem_iff.mp (nhdsWithin_le_nhds hs)
 #align exists_Ioc_subset_of_mem_nhds exists_Ioc_subset_of_mem_nhds
 
-/- warning: exists_Ioc_subset_of_mem_nhds' -> exists_Ioc_subset_of_mem_nhds' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (forall {l : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a) -> (Exists.{succ u1} α (fun (l' : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l' (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l' (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l' a) s))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (forall {l : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l a) -> (Exists.{succ u1} α (fun (l' : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l' (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l' a) s))))
-Case conversion may be inaccurate. Consider using '#align exists_Ioc_subset_of_mem_nhds' exists_Ioc_subset_of_mem_nhds'ₓ'. -/
 theorem exists_Ioc_subset_of_mem_nhds' {a : α} {s : Set α} (hs : s ∈ 𝓝 a) {l : α} (hl : l < a) :
     ∃ l' ∈ Ico l a, Ioc l' a ⊆ s :=
   let ⟨l', hl'a, hl's⟩ := exists_Ioc_subset_of_mem_nhds hs ⟨l, hl⟩
@@ -2064,24 +1368,12 @@ theorem exists_Ioc_subset_of_mem_nhds' {a : α} {s : Set α} (hs : s ∈ 𝓝 a)
     (Ioc_subset_Ioc_left <| le_max_right _ _).trans hl's⟩
 #align exists_Ioc_subset_of_mem_nhds' exists_Ioc_subset_of_mem_nhds'
 
-/- warning: exists_Ico_subset_of_mem_nhds' -> exists_Ico_subset_of_mem_nhds' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (forall {u : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u) -> (Exists.{succ u1} α (fun (u' : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u' (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u' (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u') s))))
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-Case conversion may be inaccurate. Consider using '#align exists_Ico_subset_of_mem_nhds' exists_Ico_subset_of_mem_nhds'ₓ'. -/
 theorem exists_Ico_subset_of_mem_nhds' {a : α} {s : Set α} (hs : s ∈ 𝓝 a) {u : α} (hu : a < u) :
     ∃ u' ∈ Ioc a u, Ico a u' ⊆ s := by
   simpa only [OrderDual.exists, exists_prop, dual_Ico, dual_Ioc] using
     exists_Ioc_subset_of_mem_nhds' (show of_dual ⁻¹' s ∈ 𝓝 (to_dual a) from hs) hu.dual
 #align exists_Ico_subset_of_mem_nhds' exists_Ico_subset_of_mem_nhds'
 
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-Case conversion may be inaccurate. Consider using '#align exists_Ico_subset_of_mem_nhds exists_Ico_subset_of_mem_nhdsₓ'. -/
 theorem exists_Ico_subset_of_mem_nhds {a : α} {s : Set α} (hs : s ∈ 𝓝 a) (h : ∃ u, a < u) :
     ∃ (u : _)(_ : a < u), Ico a u ⊆ s :=
   let ⟨l', hl'⟩ := h
@@ -2089,12 +1381,6 @@ theorem exists_Ico_subset_of_mem_nhds {a : α} {s : Set α} (hs : s ∈ 𝓝 a)
   ⟨l, hl.fst.1, hl.snd⟩
 #align exists_Ico_subset_of_mem_nhds exists_Ico_subset_of_mem_nhds
 
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-Case conversion may be inaccurate. Consider using '#align exists_Icc_mem_subset_of_mem_nhds_within_Ici exists_Icc_mem_subset_of_mem_nhdsWithin_Iciₓ'. -/
 theorem exists_Icc_mem_subset_of_mem_nhdsWithin_Ici {a : α} {s : Set α} (hs : s ∈ 𝓝[≥] a) :
     ∃ (b : _)(_ : a ≤ b), Icc a b ∈ 𝓝[≥] a ∧ Icc a b ⊆ s :=
   by
@@ -2108,12 +1394,6 @@ theorem exists_Icc_mem_subset_of_mem_nhdsWithin_Ici {a : α} {s : Set α} (hs :
       exact (Icc_subset_Ico_right hcb).trans hbs
 #align exists_Icc_mem_subset_of_mem_nhds_within_Ici exists_Icc_mem_subset_of_mem_nhdsWithin_Ici
 
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-Case conversion may be inaccurate. Consider using '#align exists_Icc_mem_subset_of_mem_nhds_within_Iic exists_Icc_mem_subset_of_mem_nhdsWithin_Iicₓ'. -/
 theorem exists_Icc_mem_subset_of_mem_nhdsWithin_Iic {a : α} {s : Set α} (hs : s ∈ 𝓝[≤] a) :
     ∃ b ≤ a, Icc b a ∈ 𝓝[≤] a ∧ Icc b a ⊆ s := by
   simpa only [dual_Icc, to_dual.surjective.exists] using
@@ -2134,12 +1414,6 @@ theorem exists_Icc_mem_subset_of_mem_nhds {a : α} {s : Set α} (hs : s ∈ 𝓝
 #align exists_Icc_mem_subset_of_mem_nhds exists_Icc_mem_subset_of_mem_nhds
 -/
 
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-Case conversion may be inaccurate. Consider using '#align is_open.exists_Ioo_subset IsOpen.exists_Ioo_subsetₓ'. -/
 theorem IsOpen.exists_Ioo_subset [Nontrivial α] {s : Set α} (hs : IsOpen s) (h : s.Nonempty) :
     ∃ a b, a < b ∧ Ioo a b ⊆ s :=
   by
@@ -2155,12 +1429,6 @@ theorem IsOpen.exists_Ioo_subset [Nontrivial α] {s : Set α} (hs : IsOpen s) (h
     exact ⟨l, x, lx, Ioo_subset_Ioc_self.trans hl⟩
 #align is_open.exists_Ioo_subset IsOpen.exists_Ioo_subset
 
-/- warning: dense_of_exists_between -> dense_of_exists_between is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : Nontrivial.{u1} α] {s : Set.{u1} α}, (forall {{a : α}} {{b : α}}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Exists.{succ u1} α (fun (c : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a c) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) c b))))) -> (Dense.{u1} α _inst_1 s)
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : Nontrivial.{u1} α] {s : Set.{u1} α}, (forall {{a : α}} {{b : α}}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Exists.{succ u1} α (fun (c : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c s) (And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a c) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) c b))))) -> (Dense.{u1} α _inst_1 s)
-Case conversion may be inaccurate. Consider using '#align dense_of_exists_between dense_of_exists_betweenₓ'. -/
 theorem dense_of_exists_between [Nontrivial α] {s : Set α}
     (h : ∀ ⦃a b⦄, a < b → ∃ c ∈ s, a < c ∧ c < b) : Dense s :=
   by
@@ -2170,12 +1438,6 @@ theorem dense_of_exists_between [Nontrivial α] {s : Set α}
   exact ⟨x, ⟨H hx, xs⟩⟩
 #align dense_of_exists_between dense_of_exists_between
 
-/- warning: dense_iff_exists_between -> dense_iff_exists_between is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : Nontrivial.{u1} α] {s : Set.{u1} α}, Iff (Dense.{u1} α _inst_1 s) (forall (a : α) (b : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Exists.{succ u1} α (fun (c : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c s) (And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a c) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) c b)))))
-Case conversion may be inaccurate. Consider using '#align dense_iff_exists_between dense_iff_exists_betweenₓ'. -/
 /-- A set in a nontrivial densely linear ordered type is dense in the sense of topology if and only
 if for any `a < b` there exists `c ∈ s`, `a < c < b`. Each implication requires less typeclass
 assumptions. -/
@@ -2184,12 +1446,6 @@ theorem dense_iff_exists_between [DenselyOrdered α] [Nontrivial α] {s : Set α
   ⟨fun h a b hab => h.exists_between hab, dense_of_exists_between⟩
 #align dense_iff_exists_between dense_iff_exists_between
 
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-Case conversion may be inaccurate. Consider using '#align mem_nhds_iff_exists_Ioo_subset' mem_nhds_iff_exists_Ioo_subset'ₓ'. -/
 /-- A set is a neighborhood of `a` if and only if it contains an interval `(l, u)` containing `a`,
 provided `a` is neither a bottom element nor a top element. -/
 theorem mem_nhds_iff_exists_Ioo_subset' {a : α} {s : Set α} (hl : ∃ l, l < a) (hu : ∃ u, a < u) :
@@ -2204,12 +1460,6 @@ theorem mem_nhds_iff_exists_Ioo_subset' {a : α} {s : Set α} (hl : ∃ l, l < a
     apply mem_of_superset (Ioo_mem_nhds ha.1 ha.2) h
 #align mem_nhds_iff_exists_Ioo_subset' mem_nhds_iff_exists_Ioo_subset'
 
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-Case conversion may be inaccurate. Consider using '#align mem_nhds_iff_exists_Ioo_subset mem_nhds_iff_exists_Ioo_subsetₓ'. -/
 /-- A set is a neighborhood of `a` if and only if it contains an interval `(l, u)` containing `a`.
 -/
 theorem mem_nhds_iff_exists_Ioo_subset [NoMaxOrder α] [NoMinOrder α] {a : α} {s : Set α} :
@@ -2217,45 +1467,21 @@ theorem mem_nhds_iff_exists_Ioo_subset [NoMaxOrder α] [NoMinOrder α] {a : α}
   mem_nhds_iff_exists_Ioo_subset' (exists_lt a) (exists_gt a)
 #align mem_nhds_iff_exists_Ioo_subset mem_nhds_iff_exists_Ioo_subset
 
-/- warning: nhds_basis_Ioo' -> nhds_basis_Ioo' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nhds_basis_Ioo' nhds_basis_Ioo'ₓ'. -/
 theorem nhds_basis_Ioo' {a : α} (hl : ∃ l, l < a) (hu : ∃ u, a < u) :
     (𝓝 a).HasBasis (fun b : α × α => b.1 < a ∧ a < b.2) fun b => Ioo b.1 b.2 :=
   ⟨fun s => (mem_nhds_iff_exists_Ioo_subset' hl hu).trans <| by simp⟩
 #align nhds_basis_Ioo' nhds_basis_Ioo'
 
-/- warning: nhds_basis_Ioo -> nhds_basis_Ioo is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α), Filter.HasBasis.{u1, succ u1} α (Prod.{u1, u1} α α) (nhds.{u1} α _inst_1 a) (fun (b : Prod.{u1, u1} α α) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (Prod.fst.{u1, u1} α α b) a) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a (Prod.snd.{u1, u1} α α b))) (fun (b : Prod.{u1, u1} α α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (Prod.fst.{u1, u1} α α b) (Prod.snd.{u1, u1} α α b))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α), Filter.HasBasis.{u1, succ u1} α (Prod.{u1, u1} α α) (nhds.{u1} α _inst_1 a) (fun (b : Prod.{u1, u1} α α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (Prod.fst.{u1, u1} α α b) a) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a (Prod.snd.{u1, u1} α α b))) (fun (b : Prod.{u1, u1} α α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (Prod.fst.{u1, u1} α α b) (Prod.snd.{u1, u1} α α b))
-Case conversion may be inaccurate. Consider using '#align nhds_basis_Ioo nhds_basis_Iooₓ'. -/
 theorem nhds_basis_Ioo [NoMaxOrder α] [NoMinOrder α] (a : α) :
     (𝓝 a).HasBasis (fun b : α × α => b.1 < a ∧ a < b.2) fun b => Ioo b.1 b.2 :=
   nhds_basis_Ioo' (exists_lt a) (exists_gt a)
 #align nhds_basis_Ioo nhds_basis_Ioo
 
-/- warning: filter.eventually.exists_Ioo_subset -> Filter.Eventually.exists_Ioo_subset is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align filter.eventually.exists_Ioo_subset Filter.Eventually.exists_Ioo_subsetₓ'. -/
 theorem Filter.Eventually.exists_Ioo_subset [NoMaxOrder α] [NoMinOrder α] {a : α} {p : α → Prop}
     (hp : ∀ᶠ x in 𝓝 a, p x) : ∃ l u, a ∈ Ioo l u ∧ Ioo l u ⊆ { x | p x } :=
   mem_nhds_iff_exists_Ioo_subset.1 hp
 #align filter.eventually.exists_Ioo_subset Filter.Eventually.exists_Ioo_subset
 
-/- warning: countable_of_isolated_right -> countable_of_isolated_right' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align countable_of_isolated_right countable_of_isolated_right'ₓ'. -/
 /-- The set of points which are isolated on the right is countable when the space is
 second-countable. -/
 theorem countable_of_isolated_right' [SecondCountableTopology α] :
@@ -2318,12 +1544,6 @@ theorem countable_of_isolated_right' [SecondCountableTopology α] :
   exact subset.antisymm (Ioc_subset_Ioo_right (hy x hx.1)) fun u hu => ⟨hu.1, Hy _ _ hx.1 hu.2⟩
 #align countable_of_isolated_right countable_of_isolated_right'
 
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-Case conversion may be inaccurate. Consider using '#align countable_of_isolated_left countable_of_isolated_left'ₓ'. -/
 /-- The set of points which are isolated on the left is countable when the space is
 second-countable. -/
 theorem countable_of_isolated_left' [SecondCountableTopology α] :
@@ -2336,12 +1556,6 @@ theorem countable_of_isolated_left' [SecondCountableTopology α] :
   rfl
 #align countable_of_isolated_left countable_of_isolated_left'
 
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-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint.countable_of_Ioo Set.PairwiseDisjoint.countable_of_Iooₓ'. -/
 /-- Consider a disjoint family of intervals `(x, y)` with `x < y` in a second-countable space.
 Then the family is countable.
 This is not a straightforward consequence of second-countability as some of these intervals might be
@@ -2376,184 +1590,82 @@ e.g., `ι → ℝ`.
 variable {ι : Type _} {π : ι → Type _} [Finite ι] [∀ i, LinearOrder (π i)]
   [∀ i, TopologicalSpace (π i)] [∀ i, OrderTopology (π i)] {a b x : ∀ i, π i} {a' b' x' : ι → α}
 
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 theorem pi_Iic_mem_nhds (ha : ∀ i, x i < a i) : Iic a ∈ 𝓝 x :=
   pi_univ_Iic a ▸ set_pi_mem_nhds (Set.toFinite _) fun i _ => Iic_mem_nhds (ha _)
 #align pi_Iic_mem_nhds pi_Iic_mem_nhds
 
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 theorem pi_Iic_mem_nhds' (ha : ∀ i, x' i < a' i) : Iic a' ∈ 𝓝 x' :=
   pi_Iic_mem_nhds ha
 #align pi_Iic_mem_nhds' pi_Iic_mem_nhds'
 
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 theorem pi_Ici_mem_nhds (ha : ∀ i, a i < x i) : Ici a ∈ 𝓝 x :=
   pi_univ_Ici a ▸ set_pi_mem_nhds (Set.toFinite _) fun i _ => Ici_mem_nhds (ha _)
 #align pi_Ici_mem_nhds pi_Ici_mem_nhds
 
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 theorem pi_Ici_mem_nhds' (ha : ∀ i, a' i < x' i) : Ici a' ∈ 𝓝 x' :=
   pi_Ici_mem_nhds ha
 #align pi_Ici_mem_nhds' pi_Ici_mem_nhds'
 
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 theorem pi_Icc_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Icc a b ∈ 𝓝 x :=
   pi_univ_Icc a b ▸ set_pi_mem_nhds finite_univ fun i _ => Icc_mem_nhds (ha _) (hb _)
 #align pi_Icc_mem_nhds pi_Icc_mem_nhds
 
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-Case conversion may be inaccurate. Consider using '#align pi_Icc_mem_nhds' pi_Icc_mem_nhds'ₓ'. -/
 theorem pi_Icc_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : Icc a' b' ∈ 𝓝 x' :=
   pi_Icc_mem_nhds ha hb
 #align pi_Icc_mem_nhds' pi_Icc_mem_nhds'
 
 variable [Nonempty ι]
 
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-Case conversion may be inaccurate. Consider using '#align pi_Iio_mem_nhds pi_Iio_mem_nhdsₓ'. -/
 theorem pi_Iio_mem_nhds (ha : ∀ i, x i < a i) : Iio a ∈ 𝓝 x :=
   by
   refine' mem_of_superset (set_pi_mem_nhds (Set.toFinite _) fun i _ => _) (pi_univ_Iio_subset a)
   exact Iio_mem_nhds (ha i)
 #align pi_Iio_mem_nhds pi_Iio_mem_nhds
 
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-Case conversion may be inaccurate. Consider using '#align pi_Iio_mem_nhds' pi_Iio_mem_nhds'ₓ'. -/
 theorem pi_Iio_mem_nhds' (ha : ∀ i, x' i < a' i) : Iio a' ∈ 𝓝 x' :=
   pi_Iio_mem_nhds ha
 #align pi_Iio_mem_nhds' pi_Iio_mem_nhds'
 
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-Case conversion may be inaccurate. Consider using '#align pi_Ioi_mem_nhds pi_Ioi_mem_nhdsₓ'. -/
 theorem pi_Ioi_mem_nhds (ha : ∀ i, a i < x i) : Ioi a ∈ 𝓝 x :=
   @pi_Iio_mem_nhds ι (fun i => (π i)ᵒᵈ) _ _ _ _ _ _ _ ha
 #align pi_Ioi_mem_nhds pi_Ioi_mem_nhds
 
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 theorem pi_Ioi_mem_nhds' (ha : ∀ i, a' i < x' i) : Ioi a' ∈ 𝓝 x' :=
   pi_Ioi_mem_nhds ha
 #align pi_Ioi_mem_nhds' pi_Ioi_mem_nhds'
 
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-Case conversion may be inaccurate. Consider using '#align pi_Ioc_mem_nhds pi_Ioc_mem_nhdsₓ'. -/
 theorem pi_Ioc_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Ioc a b ∈ 𝓝 x :=
   by
   refine' mem_of_superset (set_pi_mem_nhds (Set.toFinite _) fun i _ => _) (pi_univ_Ioc_subset a b)
   exact Ioc_mem_nhds (ha i) (hb i)
 #align pi_Ioc_mem_nhds pi_Ioc_mem_nhds
 
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 theorem pi_Ioc_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : Ioc a' b' ∈ 𝓝 x' :=
   pi_Ioc_mem_nhds ha hb
 #align pi_Ioc_mem_nhds' pi_Ioc_mem_nhds'
 
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-Case conversion may be inaccurate. Consider using '#align pi_Ico_mem_nhds pi_Ico_mem_nhdsₓ'. -/
 theorem pi_Ico_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Ico a b ∈ 𝓝 x :=
   by
   refine' mem_of_superset (set_pi_mem_nhds (Set.toFinite _) fun i _ => _) (pi_univ_Ico_subset a b)
   exact Ico_mem_nhds (ha i) (hb i)
 #align pi_Ico_mem_nhds pi_Ico_mem_nhds
 
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 theorem pi_Ico_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : Ico a' b' ∈ 𝓝 x' :=
   pi_Ico_mem_nhds ha hb
 #align pi_Ico_mem_nhds' pi_Ico_mem_nhds'
 
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 theorem pi_Ioo_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Ioo a b ∈ 𝓝 x :=
   by
   refine' mem_of_superset (set_pi_mem_nhds (Set.toFinite _) fun i _ => _) (pi_univ_Ioo_subset a b)
   exact Ioo_mem_nhds (ha i) (hb i)
 #align pi_Ioo_mem_nhds pi_Ioo_mem_nhds
 
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 theorem pi_Ioo_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : Ioo a' b' ∈ 𝓝 x' :=
   pi_Ioo_mem_nhds ha hb
 #align pi_Ioo_mem_nhds' pi_Ioo_mem_nhds'
 
 end Pi
 
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 theorem disjoint_nhds_atTop [NoMaxOrder α] (x : α) : Disjoint (𝓝 x) atTop :=
   by
   rcases exists_gt x with ⟨y, hy : x < y⟩
@@ -2561,77 +1673,35 @@ theorem disjoint_nhds_atTop [NoMaxOrder α] (x : α) : Disjoint (𝓝 x) atTop :
   exact disjoint_left.mpr fun z => not_le.2
 #align disjoint_nhds_at_top disjoint_nhds_atTop
 
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 @[simp]
 theorem inf_nhds_atTop [NoMaxOrder α] (x : α) : 𝓝 x ⊓ atTop = ⊥ :=
   disjoint_iff.1 (disjoint_nhds_atTop x)
 #align inf_nhds_at_top inf_nhds_atTop
 
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 theorem disjoint_nhds_atBot [NoMinOrder α] (x : α) : Disjoint (𝓝 x) atBot :=
   @disjoint_nhds_atTop αᵒᵈ _ _ _ _ x
 #align disjoint_nhds_at_bot disjoint_nhds_atBot
 
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 @[simp]
 theorem inf_nhds_atBot [NoMinOrder α] (x : α) : 𝓝 x ⊓ atBot = ⊥ :=
   @inf_nhds_atTop αᵒᵈ _ _ _ _ x
 #align inf_nhds_at_bot inf_nhds_atBot
 
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-Case conversion may be inaccurate. Consider using '#align not_tendsto_nhds_of_tendsto_at_top not_tendsto_nhds_of_tendsto_atTopₓ'. -/
 theorem not_tendsto_nhds_of_tendsto_atTop [NoMaxOrder α] {F : Filter β} [NeBot F] {f : β → α}
     (hf : Tendsto f F atTop) (x : α) : ¬Tendsto f F (𝓝 x) :=
   hf.not_tendsto (disjoint_nhds_atTop x).symm
 #align not_tendsto_nhds_of_tendsto_at_top not_tendsto_nhds_of_tendsto_atTop
 
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 theorem not_tendsto_atTop_of_tendsto_nhds [NoMaxOrder α] {F : Filter β} [NeBot F] {f : β → α}
     {x : α} (hf : Tendsto f F (𝓝 x)) : ¬Tendsto f F atTop :=
   hf.not_tendsto (disjoint_nhds_atTop x)
 #align not_tendsto_at_top_of_tendsto_nhds not_tendsto_atTop_of_tendsto_nhds
 
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-Case conversion may be inaccurate. Consider using '#align not_tendsto_nhds_of_tendsto_at_bot not_tendsto_nhds_of_tendsto_atBotₓ'. -/
 theorem not_tendsto_nhds_of_tendsto_atBot [NoMinOrder α] {F : Filter β} [NeBot F] {f : β → α}
     (hf : Tendsto f F atBot) (x : α) : ¬Tendsto f F (𝓝 x) :=
   hf.not_tendsto (disjoint_nhds_atBot x).symm
 #align not_tendsto_nhds_of_tendsto_at_bot not_tendsto_nhds_of_tendsto_atBot
 
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-Case conversion may be inaccurate. Consider using '#align not_tendsto_at_bot_of_tendsto_nhds not_tendsto_atBot_of_tendsto_nhdsₓ'. -/
 theorem not_tendsto_atBot_of_tendsto_nhds [NoMinOrder α] {F : Filter β} [NeBot F] {f : β → α}
     {x : α} (hf : Tendsto f F (𝓝 x)) : ¬Tendsto f F atBot :=
   hf.not_tendsto (disjoint_nhds_atBot x)
@@ -2645,12 +1715,6 @@ In an `order_topology`, such neighborhoods can be characterized as the sets cont
 intervals to the right or to the left of `a`. We give now these characterizations. -/
 
 
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 -- NB: If you extend the list, append to the end please to avoid breaking the API
 /-- The following statements are equivalent:
 
@@ -2687,23 +1751,11 @@ theorem TFAE_mem_nhdsWithin_Ioi {a b : α} (hab : a < b) (s : Set α) :
   tfae_finish
 #align tfae_mem_nhds_within_Ioi TFAE_mem_nhdsWithin_Ioi
 
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-Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Ioi_iff_exists_mem_Ioc_Ioo_subset mem_nhdsWithin_Ioi_iff_exists_mem_Ioc_Ioo_subsetₓ'. -/
 theorem mem_nhdsWithin_Ioi_iff_exists_mem_Ioc_Ioo_subset {a u' : α} {s : Set α} (hu' : a < u') :
     s ∈ 𝓝[>] a ↔ ∃ u ∈ Ioc a u', Ioo a u ⊆ s :=
   (TFAE_mem_nhdsWithin_Ioi hu' s).out 0 3
 #align mem_nhds_within_Ioi_iff_exists_mem_Ioc_Ioo_subset mem_nhdsWithin_Ioi_iff_exists_mem_Ioc_Ioo_subset
 
-/- warning: mem_nhds_within_Ioi_iff_exists_Ioo_subset' -> mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Ioi_iff_exists_Ioo_subset' mem_nhdsWithin_Ioi_iff_exists_Ioo_subset'ₓ'. -/
 /-- A set is a neighborhood of `a` within `(a, +∞)` if and only if it contains an interval `(a, u)`
 with `a < u < u'`, provided `a` is not a top element. -/
 theorem mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' {a u' : α} {s : Set α} (hu' : a < u') :
@@ -2711,12 +1763,6 @@ theorem mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' {a u' : α} {s : Set α} (hu'
   (TFAE_mem_nhdsWithin_Ioi hu' s).out 0 4
 #align mem_nhds_within_Ioi_iff_exists_Ioo_subset' mem_nhdsWithin_Ioi_iff_exists_Ioo_subset'
 
-/- warning: mem_nhds_within_Ioi_iff_exists_Ioo_subset -> mem_nhdsWithin_Ioi_iff_exists_Ioo_subset is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Ioi_iff_exists_Ioo_subset mem_nhdsWithin_Ioi_iff_exists_Ioo_subsetₓ'. -/
 /-- A set is a neighborhood of `a` within `(a, +∞)` if and only if it contains an interval `(a, u)`
 with `a < u`. -/
 theorem mem_nhdsWithin_Ioi_iff_exists_Ioo_subset [NoMaxOrder α] {a : α} {s : Set α} :
@@ -2725,12 +1771,6 @@ theorem mem_nhdsWithin_Ioi_iff_exists_Ioo_subset [NoMaxOrder α] {a : α} {s : S
   mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' hu'
 #align mem_nhds_within_Ioi_iff_exists_Ioo_subset mem_nhdsWithin_Ioi_iff_exists_Ioo_subset
 
-/- warning: mem_nhds_within_Ioi_iff_exists_Ioc_subset -> mem_nhdsWithin_Ioi_iff_exists_Ioc_subset is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (u : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u) s)))
-Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Ioi_iff_exists_Ioc_subset mem_nhdsWithin_Ioi_iff_exists_Ioc_subsetₓ'. -/
 /-- A set is a neighborhood of `a` within `(a, +∞)` if and only if it contains an interval `(a, u]`
 with `a < u`. -/
 theorem mem_nhdsWithin_Ioi_iff_exists_Ioc_subset [NoMaxOrder α] [DenselyOrdered α] {a : α}
@@ -2745,12 +1785,6 @@ theorem mem_nhdsWithin_Ioi_iff_exists_Ioc_subset [NoMaxOrder α] [DenselyOrdered
     exact ⟨u, au, subset.trans Ioo_subset_Ioc_self as⟩
 #align mem_nhds_within_Ioi_iff_exists_Ioc_subset mem_nhdsWithin_Ioi_iff_exists_Ioc_subset
 
-/- warning: tfae_mem_nhds_within_Iio -> TFAE_mem_nhdsWithin_Iio is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (forall (s : Set.{u1} α), List.TFAE (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) l b) s))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) l b) s))) (List.nil.{0} Prop)))))))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (forall (s : Set.{u1} α), List.TFAE (List.cons.{0} Prop (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b))) (List.cons.{0} Prop (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (List.cons.{0} Prop (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l b) s))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l b) s))) (List.nil.{0} Prop)))))))
-Case conversion may be inaccurate. Consider using '#align tfae_mem_nhds_within_Iio TFAE_mem_nhdsWithin_Iioₓ'. -/
 /-- The following statements are equivalent:
 
 0. `s` is a neighborhood of `b` within `(-∞, b)`
@@ -2772,23 +1806,11 @@ theorem TFAE_mem_nhdsWithin_Iio {a b : α} (h : a < b) (s : Set α) :
     TFAE_mem_nhdsWithin_Ioi h.dual (of_dual ⁻¹' s)
 #align tfae_mem_nhds_within_Iio TFAE_mem_nhdsWithin_Iio
 
-/- warning: mem_nhds_within_Iio_iff_exists_mem_Ico_Ioo_subset -> mem_nhdsWithin_Iio_iff_exists_mem_Ico_Ioo_subset is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l' a) -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l' a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l' a)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s))))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l' a) -> (Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l' a)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s))))
-Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Iio_iff_exists_mem_Ico_Ioo_subset mem_nhdsWithin_Iio_iff_exists_mem_Ico_Ioo_subsetₓ'. -/
 theorem mem_nhdsWithin_Iio_iff_exists_mem_Ico_Ioo_subset {a l' : α} {s : Set α} (hl' : l' < a) :
     s ∈ 𝓝[<] a ↔ ∃ l ∈ Ico l' a, Ioo l a ⊆ s :=
   (TFAE_mem_nhdsWithin_Iio hl' s).out 0 3
 #align mem_nhds_within_Iio_iff_exists_mem_Ico_Ioo_subset mem_nhdsWithin_Iio_iff_exists_mem_Ico_Ioo_subset
 
-/- warning: mem_nhds_within_Iio_iff_exists_Ioo_subset' -> mem_nhdsWithin_Iio_iff_exists_Ioo_subset' is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l' a) -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s))))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l' a) -> (Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s))))
-Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Iio_iff_exists_Ioo_subset' mem_nhdsWithin_Iio_iff_exists_Ioo_subset'ₓ'. -/
 /-- A set is a neighborhood of `a` within `(-∞, a)` if and only if it contains an interval `(l, a)`
 with `l < a`, provided `a` is not a bottom element. -/
 theorem mem_nhdsWithin_Iio_iff_exists_Ioo_subset' {a l' : α} {s : Set α} (hl' : l' < a) :
@@ -2796,12 +1818,6 @@ theorem mem_nhdsWithin_Iio_iff_exists_Ioo_subset' {a l' : α} {s : Set α} (hl'
   (TFAE_mem_nhdsWithin_Iio hl' s).out 0 4
 #align mem_nhds_within_Iio_iff_exists_Ioo_subset' mem_nhdsWithin_Iio_iff_exists_Ioo_subset'
 
-/- warning: mem_nhds_within_Iio_iff_exists_Ioo_subset -> mem_nhdsWithin_Iio_iff_exists_Ioo_subset is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s)))
-Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Iio_iff_exists_Ioo_subset mem_nhdsWithin_Iio_iff_exists_Ioo_subsetₓ'. -/
 /-- A set is a neighborhood of `a` within `(-∞, a)` if and only if it contains an interval `(l, a)`
 with `l < a`. -/
 theorem mem_nhdsWithin_Iio_iff_exists_Ioo_subset [NoMinOrder α] {a : α} {s : Set α} :
@@ -2810,12 +1826,6 @@ theorem mem_nhdsWithin_Iio_iff_exists_Ioo_subset [NoMinOrder α] {a : α} {s : S
   mem_nhdsWithin_Iio_iff_exists_Ioo_subset' hl'
 #align mem_nhds_within_Iio_iff_exists_Ioo_subset mem_nhdsWithin_Iio_iff_exists_Ioo_subset
 
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-Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Iio_iff_exists_Ico_subset mem_nhdsWithin_Iio_iff_exists_Ico_subsetₓ'. -/
 /-- A set is a neighborhood of `a` within `(-∞, a)` if and only if it contains an interval `[l, a)`
 with `l < a`. -/
 theorem mem_nhdsWithin_Iio_iff_exists_Ico_subset [NoMinOrder α] [DenselyOrdered α] {a : α}
@@ -2825,12 +1835,6 @@ theorem mem_nhdsWithin_Iio_iff_exists_Ico_subset [NoMinOrder α] [DenselyOrdered
   simpa only [OrderDual.exists, exists_prop, dual_Ioc] using this
 #align mem_nhds_within_Iio_iff_exists_Ico_subset mem_nhdsWithin_Iio_iff_exists_Ico_subset
 
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-Case conversion may be inaccurate. Consider using '#align tfae_mem_nhds_within_Ici TFAE_mem_nhdsWithin_Iciₓ'. -/
 /-- The following statements are equivalent:
 
 0. `s` is a neighborhood of `a` within `[a, +∞)`
@@ -2862,23 +1866,11 @@ theorem TFAE_mem_nhdsWithin_Ici {a b : α} (hab : a < b) (s : Set α) :
   tfae_finish
 #align tfae_mem_nhds_within_Ici TFAE_mem_nhdsWithin_Ici
 
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-Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Ici_iff_exists_mem_Ioc_Ico_subset mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subsetₓ'. -/
 theorem mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subset {a u' : α} {s : Set α} (hu' : a < u') :
     s ∈ 𝓝[≥] a ↔ ∃ u ∈ Ioc a u', Ico a u ⊆ s :=
   (TFAE_mem_nhdsWithin_Ici hu' s).out 0 3 (by norm_num) (by norm_num)
 #align mem_nhds_within_Ici_iff_exists_mem_Ioc_Ico_subset mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subset
 
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-Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Ici_iff_exists_Ico_subset' mem_nhdsWithin_Ici_iff_exists_Ico_subset'ₓ'. -/
 /-- A set is a neighborhood of `a` within `[a, +∞)` if and only if it contains an interval `[a, u)`
 with `a < u < u'`, provided `a` is not a top element. -/
 theorem mem_nhdsWithin_Ici_iff_exists_Ico_subset' {a u' : α} {s : Set α} (hu' : a < u') :
@@ -2886,12 +1878,6 @@ theorem mem_nhdsWithin_Ici_iff_exists_Ico_subset' {a u' : α} {s : Set α} (hu'
   (TFAE_mem_nhdsWithin_Ici hu' s).out 0 4 (by norm_num) (by norm_num)
 #align mem_nhds_within_Ici_iff_exists_Ico_subset' mem_nhdsWithin_Ici_iff_exists_Ico_subset'
 
-/- warning: mem_nhds_within_Ici_iff_exists_Ico_subset -> mem_nhdsWithin_Ici_iff_exists_Ico_subset is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s)))
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-Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Ici_iff_exists_Ico_subset mem_nhdsWithin_Ici_iff_exists_Ico_subsetₓ'. -/
 /-- A set is a neighborhood of `a` within `[a, +∞)` if and only if it contains an interval `[a, u)`
 with `a < u`. -/
 theorem mem_nhdsWithin_Ici_iff_exists_Ico_subset [NoMaxOrder α] {a : α} {s : Set α} :
@@ -2900,23 +1886,11 @@ theorem mem_nhdsWithin_Ici_iff_exists_Ico_subset [NoMaxOrder α] {a : α} {s : S
   mem_nhdsWithin_Ici_iff_exists_Ico_subset' hu'
 #align mem_nhds_within_Ici_iff_exists_Ico_subset mem_nhdsWithin_Ici_iff_exists_Ico_subset
 
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-Case conversion may be inaccurate. Consider using '#align nhds_within_Ici_basis_Ico nhdsWithin_Ici_basis_Icoₓ'. -/
 theorem nhdsWithin_Ici_basis_Ico [NoMaxOrder α] (a : α) :
     (𝓝[≥] a).HasBasis (fun u => a < u) (Ico a) :=
   ⟨fun s => mem_nhdsWithin_Ici_iff_exists_Ico_subset⟩
 #align nhds_within_Ici_basis_Ico nhdsWithin_Ici_basis_Ico
 
-/- warning: mem_nhds_within_Ici_iff_exists_Icc_subset -> mem_nhdsWithin_Ici_iff_exists_Icc_subset is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (u : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a u) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u) s)))
-Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Ici_iff_exists_Icc_subset mem_nhdsWithin_Ici_iff_exists_Icc_subsetₓ'. -/
 /-- A set is a neighborhood of `a` within `[a, +∞)` if and only if it contains an interval `[a, u]`
 with `a < u`. -/
 theorem mem_nhdsWithin_Ici_iff_exists_Icc_subset [NoMaxOrder α] [DenselyOrdered α] {a : α}
@@ -2931,12 +1905,6 @@ theorem mem_nhdsWithin_Ici_iff_exists_Icc_subset [NoMaxOrder α] [DenselyOrdered
     exact ⟨u, au, subset.trans Ico_subset_Icc_self as⟩
 #align mem_nhds_within_Ici_iff_exists_Icc_subset mem_nhdsWithin_Ici_iff_exists_Icc_subset
 
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-Case conversion may be inaccurate. Consider using '#align tfae_mem_nhds_within_Iic TFAE_mem_nhdsWithin_Iicₓ'. -/
 /-- The following statements are equivalent:
 
 0. `s` is a neighborhood of `b` within `(-∞, b]`
@@ -2958,23 +1926,11 @@ theorem TFAE_mem_nhdsWithin_Iic {a b : α} (h : a < b) (s : Set α) :
     TFAE_mem_nhdsWithin_Ici h.dual (of_dual ⁻¹' s)
 #align tfae_mem_nhds_within_Iic TFAE_mem_nhdsWithin_Iic
 
-/- warning: mem_nhds_within_Iic_iff_exists_mem_Ico_Ioc_subset -> mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subset is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l' a) -> (Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l' a)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s))))
-Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Iic_iff_exists_mem_Ico_Ioc_subset mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subsetₓ'. -/
 theorem mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subset {a l' : α} {s : Set α} (hl' : l' < a) :
     s ∈ 𝓝[≤] a ↔ ∃ l ∈ Ico l' a, Ioc l a ⊆ s :=
   (TFAE_mem_nhdsWithin_Iic hl' s).out 0 3 (by norm_num) (by norm_num)
 #align mem_nhds_within_Iic_iff_exists_mem_Ico_Ioc_subset mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subset
 
-/- warning: mem_nhds_within_Iic_iff_exists_Ioc_subset' -> mem_nhdsWithin_Iic_iff_exists_Ioc_subset' is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l' a) -> (Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s))))
-Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Iic_iff_exists_Ioc_subset' mem_nhdsWithin_Iic_iff_exists_Ioc_subset'ₓ'. -/
 /-- A set is a neighborhood of `a` within `(-∞, a]` if and only if it contains an interval `(l, a]`
 with `l < a`, provided `a` is not a bottom element. -/
 theorem mem_nhdsWithin_Iic_iff_exists_Ioc_subset' {a l' : α} {s : Set α} (hl' : l' < a) :
@@ -2982,12 +1938,6 @@ theorem mem_nhdsWithin_Iic_iff_exists_Ioc_subset' {a l' : α} {s : Set α} (hl'
   (TFAE_mem_nhdsWithin_Iic hl' s).out 0 4 (by norm_num) (by norm_num)
 #align mem_nhds_within_Iic_iff_exists_Ioc_subset' mem_nhdsWithin_Iic_iff_exists_Ioc_subset'
 
-/- warning: mem_nhds_within_Iic_iff_exists_Ioc_subset -> mem_nhdsWithin_Iic_iff_exists_Ioc_subset is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s)))
-Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Iic_iff_exists_Ioc_subset mem_nhdsWithin_Iic_iff_exists_Ioc_subsetₓ'. -/
 /-- A set is a neighborhood of `a` within `(-∞, a]` if and only if it contains an interval `(l, a]`
 with `l < a`. -/
 theorem mem_nhdsWithin_Iic_iff_exists_Ioc_subset [NoMinOrder α] {a : α} {s : Set α} :
@@ -2996,12 +1946,6 @@ theorem mem_nhdsWithin_Iic_iff_exists_Ioc_subset [NoMinOrder α] {a : α} {s : S
   mem_nhdsWithin_Iic_iff_exists_Ioc_subset' hl'
 #align mem_nhds_within_Iic_iff_exists_Ioc_subset mem_nhdsWithin_Iic_iff_exists_Ioc_subset
 
-/- warning: mem_nhds_within_Iic_iff_exists_Icc_subset -> mem_nhdsWithin_Iic_iff_exists_Icc_subset is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (l : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l a) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s)))
-Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Iic_iff_exists_Icc_subset mem_nhdsWithin_Iic_iff_exists_Icc_subsetₓ'. -/
 /-- A set is a neighborhood of `a` within `(-∞, a]` if and only if it contains an interval `[l, a]`
 with `l < a`. -/
 theorem mem_nhdsWithin_Iic_iff_exists_Icc_subset [NoMinOrder α] [DenselyOrdered α] {a : α}
@@ -3022,12 +1966,6 @@ variable [TopologicalSpace α] [LinearOrderedAddCommGroup α] [OrderTopology α]
 
 variable {l : Filter β} {f g : β → α}
 
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-Case conversion may be inaccurate. Consider using '#align nhds_eq_infi_abs_sub nhds_eq_iInf_abs_subₓ'. -/
 theorem nhds_eq_iInf_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r } :=
   by
   simp only [le_antisymm_iff, nhds_eq_order, le_inf_iff, le_iInf_iff, le_principal_iff, mem_Ioi,
@@ -3044,12 +1982,6 @@ theorem nhds_eq_iInf_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| <
     exact mem_infi_of_mem (b - a) (mem_infi_of_mem (sub_pos.2 hb) (by simp [Iio]))
 #align nhds_eq_infi_abs_sub nhds_eq_iInf_abs_sub
 
-/- warning: order_topology_of_nhds_abs -> orderTopology_of_nhds_abs is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align order_topology_of_nhds_abs orderTopology_of_nhds_absₓ'. -/
 theorem orderTopology_of_nhds_abs {α : Type _} [TopologicalSpace α] [LinearOrderedAddCommGroup α]
     (h_nhds : ∀ a : α, 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r }) : OrderTopology α :=
   by
@@ -3059,34 +1991,16 @@ theorem orderTopology_of_nhds_abs {α : Type _} [TopologicalSpace α] [LinearOrd
   exact (nhds_eq_iInf_abs_sub a).symm
 #align order_topology_of_nhds_abs orderTopology_of_nhds_abs
 
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-Case conversion may be inaccurate. Consider using '#align linear_ordered_add_comm_group.tendsto_nhds LinearOrderedAddCommGroup.tendsto_nhdsₓ'. -/
 theorem LinearOrderedAddCommGroup.tendsto_nhds {x : Filter β} {a : α} :
     Tendsto f x (𝓝 a) ↔ ∀ ε > (0 : α), ∀ᶠ b in x, |f b - a| < ε := by
   simp [nhds_eq_iInf_abs_sub, abs_sub_comm a]
 #align linear_ordered_add_comm_group.tendsto_nhds LinearOrderedAddCommGroup.tendsto_nhds
 
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-Case conversion may be inaccurate. Consider using '#align eventually_abs_sub_lt eventually_abs_sub_ltₓ'. -/
 theorem eventually_abs_sub_lt (a : α) {ε : α} (hε : 0 < ε) : ∀ᶠ x in 𝓝 a, |x - a| < ε :=
   (nhds_eq_iInf_abs_sub a).symm ▸
     mem_iInf_of_mem ε (mem_iInf_of_mem hε <| by simp only [abs_sub_comm, mem_principal_self])
 #align eventually_abs_sub_lt eventually_abs_sub_lt
 
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-Case conversion may be inaccurate. Consider using '#align filter.tendsto.add_at_top Filter.Tendsto.add_atTopₓ'. -/
 /-- In a linearly ordered additive commutative group with the order topology, if `f` tends to `C`
 and `g` tends to `at_top` then `f + g` tends to `at_top`. -/
 theorem Filter.Tendsto.add_atTop {C : α} (hf : Tendsto f l (𝓝 C)) (hg : Tendsto g l atTop) :
@@ -3098,12 +2012,6 @@ theorem Filter.Tendsto.add_atTop {C : α} (hf : Tendsto f l (𝓝 C)) (hg : Tend
   exact (hf.eventually (lt_mem_nhds hC')).mono fun x => le_of_lt
 #align filter.tendsto.add_at_top Filter.Tendsto.add_atTop
 
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-Case conversion may be inaccurate. Consider using '#align filter.tendsto.add_at_bot Filter.Tendsto.add_atBotₓ'. -/
 /-- In a linearly ordered additive commutative group with the order topology, if `f` tends to `C`
 and `g` tends to `at_bot` then `f + g` tends to `at_bot`. -/
 theorem Filter.Tendsto.add_atBot {C : α} (hf : Tendsto f l (𝓝 C)) (hg : Tendsto g l atBot) :
@@ -3111,12 +2019,6 @@ theorem Filter.Tendsto.add_atBot {C : α} (hf : Tendsto f l (𝓝 C)) (hg : Tend
   @Filter.Tendsto.add_atTop αᵒᵈ _ _ _ _ _ _ _ _ hf hg
 #align filter.tendsto.add_at_bot Filter.Tendsto.add_atBot
 
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-Case conversion may be inaccurate. Consider using '#align filter.tendsto.at_top_add Filter.Tendsto.atTop_addₓ'. -/
 /-- In a linearly ordered additive commutative group with the order topology, if `f` tends to
 `at_top` and `g` tends to `C` then `f + g` tends to `at_top`. -/
 theorem Filter.Tendsto.atTop_add {C : α} (hf : Tendsto f l atTop) (hg : Tendsto g l (𝓝 C)) :
@@ -3124,12 +2026,6 @@ theorem Filter.Tendsto.atTop_add {C : α} (hf : Tendsto f l atTop) (hg : Tendsto
   exact hg.add_at_top hf
 #align filter.tendsto.at_top_add Filter.Tendsto.atTop_add
 
-/- warning: filter.tendsto.at_bot_add -> Filter.Tendsto.atBot_add is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] {l : Filter.{u2} β} {f : β -> α} {g : β -> α} {C : α}, (Filter.Tendsto.{u2, u1} β α f l (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) -> (Filter.Tendsto.{u2, u1} β α g l (nhds.{u1} α _inst_1 C)) -> (Filter.Tendsto.{u2, u1} β α (fun (x : β) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))) (f x) (g x)) l (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))
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-Case conversion may be inaccurate. Consider using '#align filter.tendsto.at_bot_add Filter.Tendsto.atBot_addₓ'. -/
 /-- In a linearly ordered additive commutative group with the order topology, if `f` tends to
 `at_bot` and `g` tends to `C` then `f + g` tends to `at_bot`. -/
 theorem Filter.Tendsto.atBot_add {C : α} (hf : Tendsto f l atBot) (hg : Tendsto g l (𝓝 C)) :
@@ -3137,12 +2033,6 @@ theorem Filter.Tendsto.atBot_add {C : α} (hf : Tendsto f l atBot) (hg : Tendsto
   exact hg.add_at_bot hf
 #align filter.tendsto.at_bot_add Filter.Tendsto.atBot_add
 
-/- warning: nhds_basis_Ioo_pos -> nhds_basis_Ioo_pos is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] (a : α), Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 a) (fun (ε : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) ε) (fun (ε : α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) a ε) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))) a ε))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] (_inst_5 : α), Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 _inst_5) (fun (ε : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))) ε) (fun (ε : α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) _inst_5 ε) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))) _inst_5 ε))
-Case conversion may be inaccurate. Consider using '#align nhds_basis_Ioo_pos nhds_basis_Ioo_posₓ'. -/
 theorem nhds_basis_Ioo_pos [NoMinOrder α] [NoMaxOrder α] (a : α) :
     (𝓝 a).HasBasis (fun ε : α => (0 : α) < ε) fun ε => Ioo (a - ε) (a + ε) :=
   ⟨by
@@ -3158,12 +2048,6 @@ theorem nhds_basis_Ioo_pos [NoMinOrder α] [NoMaxOrder α] (a : α) :
       exact ⟨(a - ε, a + ε), by simp [ε_pos], h⟩⟩
 #align nhds_basis_Ioo_pos nhds_basis_Ioo_pos
 
-/- warning: nhds_basis_abs_sub_lt -> nhds_basis_abs_sub_lt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] (a : α), Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 a) (fun (ε : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) ε) (fun (ε : α) => setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) b a)) ε))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] (_inst_5 : α), Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 _inst_5) (fun (ε : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))) ε) (fun (ε : α) => setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) b _inst_5)) ε))
-Case conversion may be inaccurate. Consider using '#align nhds_basis_abs_sub_lt nhds_basis_abs_sub_ltₓ'. -/
 theorem nhds_basis_abs_sub_lt [NoMinOrder α] [NoMaxOrder α] (a : α) :
     (𝓝 a).HasBasis (fun ε : α => (0 : α) < ε) fun ε => { b | |b - a| < ε } :=
   by
@@ -3175,12 +2059,6 @@ theorem nhds_basis_abs_sub_lt [NoMinOrder α] [NoMaxOrder α] (a : α) :
 
 variable (α)
 
-/- warning: nhds_basis_zero_abs_sub_lt -> nhds_basis_zero_abs_sub_lt is a dubious translation:
-lean 3 declaration is
-  forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) (fun (ε : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) ε) (fun (ε : α) => setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) b) ε))
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-  forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) (fun (ε : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))) ε) (fun (ε : α) => setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) b) ε))
-Case conversion may be inaccurate. Consider using '#align nhds_basis_zero_abs_sub_lt nhds_basis_zero_abs_sub_ltₓ'. -/
 theorem nhds_basis_zero_abs_sub_lt [NoMinOrder α] [NoMaxOrder α] :
     (𝓝 (0 : α)).HasBasis (fun ε : α => (0 : α) < ε) fun ε => { b | |b| < ε } := by
   simpa using nhds_basis_abs_sub_lt (0 : α)
@@ -3188,12 +2066,6 @@ theorem nhds_basis_zero_abs_sub_lt [NoMinOrder α] [NoMaxOrder α] :
 
 variable {α}
 
-/- warning: nhds_basis_Ioo_pos_of_pos -> nhds_basis_Ioo_pos_of_pos is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align nhds_basis_Ioo_pos_of_pos nhds_basis_Ioo_pos_of_posₓ'. -/
 /-- If `a` is positive we can form a basis from only nonnegative `Ioo` intervals -/
 theorem nhds_basis_Ioo_pos_of_pos [NoMinOrder α] [NoMaxOrder α] {a : α} (ha : 0 < a) :
     (𝓝 a).HasBasis (fun ε : α => (0 : α) < ε ∧ ε ≤ a) fun ε => Ioo (a - ε) (a + ε) :=
@@ -3213,22 +2085,10 @@ theorem nhds_basis_Ioo_pos_of_pos [NoMinOrder α] [NoMaxOrder α] {a : α} (ha :
 
 end LinearOrderedAddCommGroup
 
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-Case conversion may be inaccurate. Consider using '#align preimage_neg preimage_negₓ'. -/
 theorem preimage_neg [AddGroup α] : preimage (Neg.neg : α → α) = image (Neg.neg : α → α) :=
   (image_eq_preimage_of_inverse neg_neg neg_neg).symm
 #align preimage_neg preimage_neg
 
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 theorem Filter.map_neg_eq_comap_neg [AddGroup α] :
     map (Neg.neg : α → α) = comap (Neg.neg : α → α) :=
   funext fun f => map_eq_comap_of_inverse (funext neg_neg) (funext neg_neg)
@@ -3298,12 +2158,6 @@ theorem IsGLB.nhdsWithin_neBot : ∀ {a : α} {s : Set α}, IsGLB s a → s.None
 #align is_glb.nhds_within_ne_bot IsGLB.nhdsWithin_neBot
 -/
 
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 theorem isLUB_of_mem_nhds {s : Set α} {a : α} {f : Filter α} (hsa : a ∈ upperBounds s) (hsf : s ∈ f)
     [NeBot (f ⊓ 𝓝 a)] : IsLUB s a :=
   ⟨hsa, fun b hb =>
@@ -3323,12 +2177,6 @@ theorem isLUB_of_mem_closure {s : Set α} {a : α} (hsa : a ∈ upperBounds s) (
 #align is_lub_of_mem_closure isLUB_of_mem_closure
 -/
 
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-Case conversion may be inaccurate. Consider using '#align is_glb_of_mem_nhds isGLB_of_mem_nhdsₓ'. -/
 theorem isGLB_of_mem_nhds :
     ∀ {s : Set α} {a : α} {f : Filter α}, a ∈ lowerBounds s → s ∈ f → NeBot (f ⊓ 𝓝 a) → IsGLB s a :=
   @isLUB_of_mem_nhds αᵒᵈ _ _ _
@@ -3442,12 +2290,6 @@ alias IsGLB.mem_of_isClosed ← IsClosed.isGLB_mem
 -/
 
 
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-Case conversion may be inaccurate. Consider using '#align is_lub.exists_seq_strict_mono_tendsto_of_not_mem IsLUB.exists_seq_strictMono_tendsto_of_not_memₓ'. -/
 theorem IsLUB.exists_seq_strictMono_tendsto_of_not_mem {t : Set α} {x : α}
     [IsCountablyGenerated (𝓝 x)] (htx : IsLUB t x) (not_mem : x ∉ t) (ht : t.Nonempty) :
     ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n < x) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t :=
@@ -3486,12 +2328,6 @@ theorem IsLUB.exists_seq_strictMono_tendsto_of_not_mem {t : Set α} {x : α}
     · exact (hf n.succ _ (I n)).2.2.2
 #align is_lub.exists_seq_strict_mono_tendsto_of_not_mem IsLUB.exists_seq_strictMono_tendsto_of_not_mem
 
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-Case conversion may be inaccurate. Consider using '#align is_lub.exists_seq_monotone_tendsto IsLUB.exists_seq_monotone_tendstoₓ'. -/
 theorem IsLUB.exists_seq_monotone_tendsto {t : Set α} {x : α} [IsCountablyGenerated (𝓝 x)]
     (htx : IsLUB t x) (ht : t.Nonempty) :
     ∃ u : ℕ → α, Monotone u ∧ (∀ n, u n ≤ x) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t :=
@@ -3502,12 +2338,6 @@ theorem IsLUB.exists_seq_monotone_tendsto {t : Set α} {x : α} [IsCountablyGene
     exact ⟨u, hu.1.Monotone, fun n => (hu.2.1 n).le, hu.2.2⟩
 #align is_lub.exists_seq_monotone_tendsto IsLUB.exists_seq_monotone_tendsto
 
-/- warning: exists_seq_strict_mono_tendsto' -> exists_seq_strictMono_tendsto' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align exists_seq_strict_mono_tendsto' exists_seq_strictMono_tendsto'ₓ'. -/
 theorem exists_seq_strictMono_tendsto' {α : Type _} [LinearOrder α] [TopologicalSpace α]
     [DenselyOrdered α] [OrderTopology α] [FirstCountableTopology α] {x y : α} (hy : y < x) :
     ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n ∈ Ioo y x) ∧ Tendsto u atTop (𝓝 x) :=
@@ -3518,12 +2348,6 @@ theorem exists_seq_strictMono_tendsto' {α : Type _} [LinearOrder α] [Topologic
   exact ⟨u, hu.1, hu.2.2.symm⟩
 #align exists_seq_strict_mono_tendsto' exists_seq_strictMono_tendsto'
 
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-Case conversion may be inaccurate. Consider using '#align exists_seq_strict_mono_tendsto exists_seq_strictMono_tendstoₓ'. -/
 theorem exists_seq_strictMono_tendsto [DenselyOrdered α] [NoMinOrder α] [FirstCountableTopology α]
     (x : α) : ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n < x) ∧ Tendsto u atTop (𝓝 x) :=
   by
@@ -3532,12 +2356,6 @@ theorem exists_seq_strictMono_tendsto [DenselyOrdered α] [NoMinOrder α] [First
   exact ⟨u, hu_mono, fun n => (hu_mem n).2, hux⟩
 #align exists_seq_strict_mono_tendsto exists_seq_strictMono_tendsto
 
-/- warning: exists_seq_strict_mono_tendsto_nhds_within -> exists_seq_strictMono_tendsto_nhdsWithin is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] [_inst_7 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))))] [_inst_8 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))))] [_inst_9 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_1] (x : α), Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictMono.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) u) (And (forall (n : Nat), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))) (u n) x) (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhdsWithin.{u1} α _inst_1 x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) x)))))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))] [_inst_7 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))))] [_inst_8 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))))] [_inst_9 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_1] (x : α), Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictMono.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) u) (And (forall (n : Nat), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))) (u n) x) (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhdsWithin.{u1} α _inst_1 x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) x)))))
-Case conversion may be inaccurate. Consider using '#align exists_seq_strict_mono_tendsto_nhds_within exists_seq_strictMono_tendsto_nhdsWithinₓ'. -/
 theorem exists_seq_strictMono_tendsto_nhdsWithin [DenselyOrdered α] [NoMinOrder α]
     [FirstCountableTopology α] (x : α) :
     ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n < x) ∧ Tendsto u atTop (𝓝[<] x) :=
@@ -3545,12 +2363,6 @@ theorem exists_seq_strictMono_tendsto_nhdsWithin [DenselyOrdered α] [NoMinOrder
   ⟨u, hu, hx, tendsto_nhdsWithin_mono_right (range_subset_iff.2 hx) <| tendsto_nhdsWithin_range.2 h⟩
 #align exists_seq_strict_mono_tendsto_nhds_within exists_seq_strictMono_tendsto_nhdsWithin
 
-/- warning: exists_seq_tendsto_Sup -> exists_seq_tendsto_sSup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align exists_seq_tendsto_Sup exists_seq_tendsto_sSupₓ'. -/
 theorem exists_seq_tendsto_sSup {α : Type _} [ConditionallyCompleteLinearOrder α]
     [TopologicalSpace α] [OrderTopology α] [FirstCountableTopology α] {S : Set α} (hS : S.Nonempty)
     (hS' : BddAbove S) : ∃ u : ℕ → α, Monotone u ∧ Tendsto u atTop (𝓝 (sSup S)) ∧ ∀ n, u n ∈ S :=
@@ -3559,67 +2371,34 @@ theorem exists_seq_tendsto_sSup {α : Type _} [ConditionallyCompleteLinearOrder
   exact ⟨u, hu.1, hu.2.2⟩
 #align exists_seq_tendsto_Sup exists_seq_tendsto_sSup
 
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-Case conversion may be inaccurate. Consider using '#align is_glb.exists_seq_strict_anti_tendsto_of_not_mem IsGLB.exists_seq_strictAnti_tendsto_of_not_memₓ'. -/
 theorem IsGLB.exists_seq_strictAnti_tendsto_of_not_mem {t : Set α} {x : α}
     [IsCountablyGenerated (𝓝 x)] (htx : IsGLB t x) (not_mem : x ∉ t) (ht : t.Nonempty) :
     ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, x < u n) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t :=
   @IsLUB.exists_seq_strictMono_tendsto_of_not_mem αᵒᵈ _ _ _ t x _ htx not_mem ht
 #align is_glb.exists_seq_strict_anti_tendsto_of_not_mem IsGLB.exists_seq_strictAnti_tendsto_of_not_mem
 
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 theorem IsGLB.exists_seq_antitone_tendsto {t : Set α} {x : α} [IsCountablyGenerated (𝓝 x)]
     (htx : IsGLB t x) (ht : t.Nonempty) :
     ∃ u : ℕ → α, Antitone u ∧ (∀ n, x ≤ u n) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t :=
   @IsLUB.exists_seq_monotone_tendsto αᵒᵈ _ _ _ t x _ htx ht
 #align is_glb.exists_seq_antitone_tendsto IsGLB.exists_seq_antitone_tendsto
 
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-Case conversion may be inaccurate. Consider using '#align exists_seq_strict_anti_tendsto' exists_seq_strictAnti_tendsto'ₓ'. -/
 theorem exists_seq_strictAnti_tendsto' [DenselyOrdered α] [FirstCountableTopology α] {x y : α}
     (hy : x < y) : ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, u n ∈ Ioo x y) ∧ Tendsto u atTop (𝓝 x) := by
   simpa only [dual_Ioo] using exists_seq_strictMono_tendsto' (OrderDual.toDual_lt_toDual.2 hy)
 #align exists_seq_strict_anti_tendsto' exists_seq_strictAnti_tendsto'
 
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-Case conversion may be inaccurate. Consider using '#align exists_seq_strict_anti_tendsto exists_seq_strictAnti_tendstoₓ'. -/
 theorem exists_seq_strictAnti_tendsto [DenselyOrdered α] [NoMaxOrder α] [FirstCountableTopology α]
     (x : α) : ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, x < u n) ∧ Tendsto u atTop (𝓝 x) :=
   @exists_seq_strictMono_tendsto αᵒᵈ _ _ _ _ _ _ x
 #align exists_seq_strict_anti_tendsto exists_seq_strictAnti_tendsto
 
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] [_inst_7 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))))] [_inst_8 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))))] [_inst_9 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_1] (x : α), Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictAnti.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) u) (And (forall (n : Nat), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))) x (u n)) (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhdsWithin.{u1} α _inst_1 x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) x)))))
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-Case conversion may be inaccurate. Consider using '#align exists_seq_strict_anti_tendsto_nhds_within exists_seq_strictAnti_tendsto_nhdsWithinₓ'. -/
 theorem exists_seq_strictAnti_tendsto_nhdsWithin [DenselyOrdered α] [NoMaxOrder α]
     [FirstCountableTopology α] (x : α) :
     ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, x < u n) ∧ Tendsto u atTop (𝓝[>] x) :=
   @exists_seq_strictMono_tendsto_nhdsWithin αᵒᵈ _ _ _ _ _ _ _
 #align exists_seq_strict_anti_tendsto_nhds_within exists_seq_strictAnti_tendsto_nhdsWithin
 
-/- warning: exists_seq_strict_anti_strict_mono_tendsto -> exists_seq_strictAnti_strictMono_tendsto is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align exists_seq_strict_anti_strict_mono_tendsto exists_seq_strictAnti_strictMono_tendstoₓ'. -/
 theorem exists_seq_strictAnti_strictMono_tendsto [DenselyOrdered α] [FirstCountableTopology α]
     {x y : α} (h : x < y) :
     ∃ u v : ℕ → α,
@@ -3636,12 +2415,6 @@ theorem exists_seq_strictAnti_strictMono_tendsto [DenselyOrdered α] [FirstCount
       fun k l => (hu_anti.antitone (zero_le k)).trans_lt (hv_mem l).1, hux, hvy⟩
 #align exists_seq_strict_anti_strict_mono_tendsto exists_seq_strictAnti_strictMono_tendsto
 
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-Case conversion may be inaccurate. Consider using '#align exists_seq_tendsto_Inf exists_seq_tendsto_sInfₓ'. -/
 theorem exists_seq_tendsto_sInf {α : Type _} [ConditionallyCompleteLinearOrder α]
     [TopologicalSpace α] [OrderTopology α] [FirstCountableTopology α] {S : Set α} (hS : S.Nonempty)
     (hS' : BddBelow S) : ∃ u : ℕ → α, Antitone u ∧ Tendsto u atTop (𝓝 (sInf S)) ∧ ∀ n, u n ∈ S :=
@@ -3655,12 +2428,6 @@ section DenselyOrdered
 variable [TopologicalSpace α] [LinearOrder α] [OrderTopology α] [DenselyOrdered α] {a b : α}
   {s : Set α}
 
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-Case conversion may be inaccurate. Consider using '#align closure_Ioi' closure_Ioi'ₓ'. -/
 /-- The closure of the interval `(a, +∞)` is the closed interval `[a, +∞)`, unless `a` is a top
 element. -/
 theorem closure_Ioi' {a : α} (h : (Ioi a).Nonempty) : closure (Ioi a) = Ici a :=
@@ -3671,48 +2438,24 @@ theorem closure_Ioi' {a : α} (h : (Ioi a).Nonempty) : closure (Ioi a) = Ici a :
     exact is_glb_Ioi.mem_closure h
 #align closure_Ioi' closure_Ioi'
 
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 /-- The closure of the interval `(a, +∞)` is the closed interval `[a, +∞)`. -/
 @[simp]
 theorem closure_Ioi (a : α) [NoMaxOrder α] : closure (Ioi a) = Ici a :=
   closure_Ioi' nonempty_Ioi
 #align closure_Ioi closure_Ioi
 
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 /-- The closure of the interval `(-∞, a)` is the closed interval `(-∞, a]`, unless `a` is a bottom
 element. -/
 theorem closure_Iio' (h : (Iio a).Nonempty) : closure (Iio a) = Iic a :=
   @closure_Ioi' αᵒᵈ _ _ _ _ _ h
 #align closure_Iio' closure_Iio'
 
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 /-- The closure of the interval `(-∞, a)` is the interval `(-∞, a]`. -/
 @[simp]
 theorem closure_Iio (a : α) [NoMinOrder α] : closure (Iio a) = Iic a :=
   closure_Iio' nonempty_Iio
 #align closure_Iio closure_Iio
 
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 /-- The closure of the open interval `(a, b)` is the closed interval `[a, b]`. -/
 @[simp]
 theorem closure_Ioo {a b : α} (hab : a ≠ b) : closure (Ioo a b) = Icc a b :=
@@ -3727,12 +2470,6 @@ theorem closure_Ioo {a b : α} (hab : a ≠ b) : closure (Ioo a b) = Icc a b :=
     · rw [Icc_eq_empty_of_lt hab]; exact empty_subset _
 #align closure_Ioo closure_Ioo
 
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 /-- The closure of the interval `(a, b]` is the closed interval `[a, b]`. -/
 @[simp]
 theorem closure_Ioc {a b : α} (hab : a ≠ b) : closure (Ioc a b) = Icc a b :=
@@ -3743,12 +2480,6 @@ theorem closure_Ioc {a b : α} (hab : a ≠ b) : closure (Ioc a b) = Icc a b :=
     rw [closure_Ioo hab]
 #align closure_Ioc closure_Ioc
 
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 /-- The closure of the interval `[a, b)` is the closed interval `[a, b]`. -/
 @[simp]
 theorem closure_Ico {a b : α} (hab : a ≠ b) : closure (Ico a b) = Icc a b :=
@@ -3759,87 +2490,39 @@ theorem closure_Ico {a b : α} (hab : a ≠ b) : closure (Ico a b) = Icc a b :=
     rw [closure_Ioo hab]
 #align closure_Ico closure_Ico
 
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 @[simp]
 theorem interior_Ici' {a : α} (ha : (Iio a).Nonempty) : interior (Ici a) = Ioi a := by
   rw [← compl_Iio, interior_compl, closure_Iio' ha, compl_Iic]
 #align interior_Ici' interior_Ici'
 
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 theorem interior_Ici [NoMinOrder α] {a : α} : interior (Ici a) = Ioi a :=
   interior_Ici' nonempty_Iio
 #align interior_Ici interior_Ici
 
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 @[simp]
 theorem interior_Iic' {a : α} (ha : (Ioi a).Nonempty) : interior (Iic a) = Iio a :=
   @interior_Ici' αᵒᵈ _ _ _ _ _ ha
 #align interior_Iic' interior_Iic'
 
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-Case conversion may be inaccurate. Consider using '#align interior_Iic interior_Iicₓ'. -/
 theorem interior_Iic [NoMaxOrder α] {a : α} : interior (Iic a) = Iio a :=
   interior_Iic' nonempty_Ioi
 #align interior_Iic interior_Iic
 
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 @[simp]
 theorem interior_Icc [NoMinOrder α] [NoMaxOrder α] {a b : α} : interior (Icc a b) = Ioo a b := by
   rw [← Ici_inter_Iic, interior_inter, interior_Ici, interior_Iic, Ioi_inter_Iio]
 #align interior_Icc interior_Icc
 
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-Case conversion may be inaccurate. Consider using '#align interior_Ico interior_Icoₓ'. -/
 @[simp]
 theorem interior_Ico [NoMinOrder α] {a b : α} : interior (Ico a b) = Ioo a b := by
   rw [← Ici_inter_Iio, interior_inter, interior_Ici, interior_Iio, Ioi_inter_Iio]
 #align interior_Ico interior_Ico
 
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-Case conversion may be inaccurate. Consider using '#align interior_Ioc interior_Iocₓ'. -/
 @[simp]
 theorem interior_Ioc [NoMaxOrder α] {a b : α} : interior (Ioc a b) = Ioo a b := by
   rw [← Ioi_inter_Iic, interior_inter, interior_Ioi, interior_Iic, Ioi_inter_Iio]
 #align interior_Ioc interior_Ioc
 
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-Case conversion may be inaccurate. Consider using '#align closure_interior_Icc closure_interior_Iccₓ'. -/
 theorem closure_interior_Icc {a b : α} (h : a ≠ b) : closure (interior (Icc a b)) = Icc a b :=
   (closure_minimal interior_subset isClosed_Icc).antisymm <|
     calc
@@ -3849,12 +2532,6 @@ theorem closure_interior_Icc {a b : α} (h : a ≠ b) : closure (interior (Icc a
       
 #align closure_interior_Icc closure_interior_Icc
 
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-Case conversion may be inaccurate. Consider using '#align Ioc_subset_closure_interior Ioc_subset_closure_interiorₓ'. -/
 theorem Ioc_subset_closure_interior (a b : α) : Ioc a b ⊆ closure (interior (Ioc a b)) :=
   by
   rcases eq_or_ne a b with (rfl | h)
@@ -3868,295 +2545,127 @@ theorem Ioc_subset_closure_interior (a b : α) : Ioc a b ⊆ closure (interior (
       
 #align Ioc_subset_closure_interior Ioc_subset_closure_interior
 
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-Case conversion may be inaccurate. Consider using '#align Ico_subset_closure_interior Ico_subset_closure_interiorₓ'. -/
 theorem Ico_subset_closure_interior (a b : α) : Ico a b ⊆ closure (interior (Ico a b)) := by
   simpa only [dual_Ioc] using Ioc_subset_closure_interior (OrderDual.toDual b) (OrderDual.toDual a)
 #align Ico_subset_closure_interior Ico_subset_closure_interior
 
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 @[simp]
 theorem frontier_Ici' {a : α} (ha : (Iio a).Nonempty) : frontier (Ici a) = {a} := by
   simp [frontier, ha]
 #align frontier_Ici' frontier_Ici'
 
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 theorem frontier_Ici [NoMinOrder α] {a : α} : frontier (Ici a) = {a} :=
   frontier_Ici' nonempty_Iio
 #align frontier_Ici frontier_Ici
 
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 @[simp]
 theorem frontier_Iic' {a : α} (ha : (Ioi a).Nonempty) : frontier (Iic a) = {a} := by
   simp [frontier, ha]
 #align frontier_Iic' frontier_Iic'
 
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 theorem frontier_Iic [NoMaxOrder α] {a : α} : frontier (Iic a) = {a} :=
   frontier_Iic' nonempty_Ioi
 #align frontier_Iic frontier_Iic
 
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 @[simp]
 theorem frontier_Ioi' {a : α} (ha : (Ioi a).Nonempty) : frontier (Ioi a) = {a} := by
   simp [frontier, closure_Ioi' ha, Iic_diff_Iio, Icc_self]
 #align frontier_Ioi' frontier_Ioi'
 
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 theorem frontier_Ioi [NoMaxOrder α] {a : α} : frontier (Ioi a) = {a} :=
   frontier_Ioi' nonempty_Ioi
 #align frontier_Ioi frontier_Ioi
 
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 @[simp]
 theorem frontier_Iio' {a : α} (ha : (Iio a).Nonempty) : frontier (Iio a) = {a} := by
   simp [frontier, closure_Iio' ha, Iic_diff_Iio, Icc_self]
 #align frontier_Iio' frontier_Iio'
 
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 theorem frontier_Iio [NoMinOrder α] {a : α} : frontier (Iio a) = {a} :=
   frontier_Iio' nonempty_Iio
 #align frontier_Iio frontier_Iio
 
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 @[simp]
 theorem frontier_Icc [NoMinOrder α] [NoMaxOrder α] {a b : α} (h : a ≤ b) :
     frontier (Icc a b) = {a, b} := by simp [frontier, h, Icc_diff_Ioo_same]
 #align frontier_Icc frontier_Icc
 
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-Case conversion may be inaccurate. Consider using '#align frontier_Ioo frontier_Iooₓ'. -/
 @[simp]
 theorem frontier_Ioo {a b : α} (h : a < b) : frontier (Ioo a b) = {a, b} := by
   rw [frontier, closure_Ioo h.ne, interior_Ioo, Icc_diff_Ioo_same h.le]
 #align frontier_Ioo frontier_Ioo
 
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-Case conversion may be inaccurate. Consider using '#align frontier_Ico frontier_Icoₓ'. -/
 @[simp]
 theorem frontier_Ico [NoMinOrder α] {a b : α} (h : a < b) : frontier (Ico a b) = {a, b} := by
   rw [frontier, closure_Ico h.ne, interior_Ico, Icc_diff_Ioo_same h.le]
 #align frontier_Ico frontier_Ico
 
-/- warning: frontier_Ioc -> frontier_Ioc is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align frontier_Ioc frontier_Iocₓ'. -/
 @[simp]
 theorem frontier_Ioc [NoMaxOrder α] {a b : α} (h : a < b) : frontier (Ioc a b) = {a, b} := by
   rw [frontier, closure_Ioc h.ne, interior_Ioc, Icc_diff_Ioo_same h.le]
 #align frontier_Ioc frontier_Ioc
 
-/- warning: nhds_within_Ioi_ne_bot' -> nhdsWithin_Ioi_neBot' is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (Set.Nonempty.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (Set.Nonempty.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
-Case conversion may be inaccurate. Consider using '#align nhds_within_Ioi_ne_bot' nhdsWithin_Ioi_neBot'ₓ'. -/
 theorem nhdsWithin_Ioi_neBot' {a b : α} (H₁ : (Ioi a).Nonempty) (H₂ : a ≤ b) : NeBot (𝓝[Ioi a] b) :=
   mem_closure_iff_nhdsWithin_neBot.1 <| by rwa [closure_Ioi' H₁]
 #align nhds_within_Ioi_ne_bot' nhdsWithin_Ioi_neBot'
 
-/- warning: nhds_within_Ioi_ne_bot -> nhdsWithin_Ioi_neBot is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
-Case conversion may be inaccurate. Consider using '#align nhds_within_Ioi_ne_bot nhdsWithin_Ioi_neBotₓ'. -/
 theorem nhdsWithin_Ioi_neBot [NoMaxOrder α] {a b : α} (H : a ≤ b) : NeBot (𝓝[Ioi a] b) :=
   nhdsWithin_Ioi_neBot' nonempty_Ioi H
 #align nhds_within_Ioi_ne_bot nhdsWithin_Ioi_neBot
 
-/- warning: nhds_within_Ioi_self_ne_bot' -> nhdsWithin_Ioi_self_neBot' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α}, (Set.Nonempty.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α}, (Set.Nonempty.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
-Case conversion may be inaccurate. Consider using '#align nhds_within_Ioi_self_ne_bot' nhdsWithin_Ioi_self_neBot'ₓ'. -/
 theorem nhdsWithin_Ioi_self_neBot' {a : α} (H : (Ioi a).Nonempty) : NeBot (𝓝[>] a) :=
   nhdsWithin_Ioi_neBot' H (le_refl a)
 #align nhds_within_Ioi_self_ne_bot' nhdsWithin_Ioi_self_neBot'
 
-/- warning: nhds_within_Ioi_self_ne_bot -> nhdsWithin_Ioi_self_neBot is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α), Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α), Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))
-Case conversion may be inaccurate. Consider using '#align nhds_within_Ioi_self_ne_bot nhdsWithin_Ioi_self_neBotₓ'. -/
 @[instance]
 theorem nhdsWithin_Ioi_self_neBot [NoMaxOrder α] (a : α) : NeBot (𝓝[>] a) :=
   nhdsWithin_Ioi_neBot (le_refl a)
 #align nhds_within_Ioi_self_ne_bot nhdsWithin_Ioi_self_neBot
 
-/- warning: filter.eventually.exists_gt -> Filter.Eventually.exists_gt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {p : α -> Prop}, (Filter.Eventually.{u1} α (fun (x : α) => p x) (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) (fun (H : GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) => p b)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {p : α -> Prop}, (Filter.Eventually.{u1} α (fun (x : α) => p x) (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (b : α) => And (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b a) (p b)))
-Case conversion may be inaccurate. Consider using '#align filter.eventually.exists_gt Filter.Eventually.exists_gtₓ'. -/
 theorem Filter.Eventually.exists_gt [NoMaxOrder α] {a : α} {p : α → Prop} (h : ∀ᶠ x in 𝓝 a, p x) :
     ∃ b > a, p b := by
   simpa only [exists_prop, gt_iff_lt, and_comm'] using
     ((h.filter_mono (@nhdsWithin_le_nhds _ _ a (Ioi a))).And self_mem_nhdsWithin).exists
 #align filter.eventually.exists_gt Filter.Eventually.exists_gt
 
-/- warning: nhds_within_Iio_ne_bot' -> nhdsWithin_Iio_neBot' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {b : α} {c : α}, (Set.Nonempty.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b c) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) c)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {b : α} {c : α}, (Set.Nonempty.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b c) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) c)))
-Case conversion may be inaccurate. Consider using '#align nhds_within_Iio_ne_bot' nhdsWithin_Iio_neBot'ₓ'. -/
 theorem nhdsWithin_Iio_neBot' {b c : α} (H₁ : (Iio c).Nonempty) (H₂ : b ≤ c) : NeBot (𝓝[Iio c] b) :=
   mem_closure_iff_nhdsWithin_neBot.1 <| by rwa [closure_Iio' H₁]
 #align nhds_within_Iio_ne_bot' nhdsWithin_Iio_neBot'
 
-/- warning: nhds_within_Iio_ne_bot -> nhdsWithin_Iio_neBot is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)))
-Case conversion may be inaccurate. Consider using '#align nhds_within_Iio_ne_bot nhdsWithin_Iio_neBotₓ'. -/
 theorem nhdsWithin_Iio_neBot [NoMinOrder α] {a b : α} (H : a ≤ b) : NeBot (𝓝[Iio b] a) :=
   nhdsWithin_Iio_neBot' nonempty_Iio H
 #align nhds_within_Iio_ne_bot nhdsWithin_Iio_neBot
 
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {b : α}, (Set.Nonempty.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {b : α}, (Set.Nonempty.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)))
-Case conversion may be inaccurate. Consider using '#align nhds_within_Iio_self_ne_bot' nhdsWithin_Iio_self_neBot'ₓ'. -/
 theorem nhdsWithin_Iio_self_neBot' {b : α} (H : (Iio b).Nonempty) : NeBot (𝓝[<] b) :=
   nhdsWithin_Iio_neBot' H (le_refl b)
 #align nhds_within_Iio_self_ne_bot' nhdsWithin_Iio_self_neBot'
 
-/- warning: nhds_within_Iio_self_ne_bot -> nhdsWithin_Iio_self_neBot is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α), Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α), Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))
-Case conversion may be inaccurate. Consider using '#align nhds_within_Iio_self_ne_bot nhdsWithin_Iio_self_neBotₓ'. -/
 @[instance]
 theorem nhdsWithin_Iio_self_neBot [NoMinOrder α] (a : α) : NeBot (𝓝[<] a) :=
   nhdsWithin_Iio_neBot (le_refl a)
 #align nhds_within_Iio_self_ne_bot nhdsWithin_Iio_self_neBot
 
-/- warning: filter.eventually.exists_lt -> Filter.Eventually.exists_lt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {p : α -> Prop}, (Filter.Eventually.{u1} α (fun (x : α) => p x) (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) (fun (H : LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) => p b)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {p : α -> Prop}, (Filter.Eventually.{u1} α (fun (x : α) => p x) (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (b : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b a) (p b)))
-Case conversion may be inaccurate. Consider using '#align filter.eventually.exists_lt Filter.Eventually.exists_ltₓ'. -/
 theorem Filter.Eventually.exists_lt [NoMinOrder α] {a : α} {p : α → Prop} (h : ∀ᶠ x in 𝓝 a, p x) :
     ∃ b < a, p b :=
   @Filter.Eventually.exists_gt αᵒᵈ _ _ _ _ _ _ _ h
 #align filter.eventually.exists_lt Filter.Eventually.exists_lt
 
-/- warning: right_nhds_within_Ico_ne_bot -> right_nhdsWithin_Ico_neBot is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)))
-Case conversion may be inaccurate. Consider using '#align right_nhds_within_Ico_ne_bot right_nhdsWithin_Ico_neBotₓ'. -/
 theorem right_nhdsWithin_Ico_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ico a b] b) :=
   (isLUB_Ico H).nhdsWithin_neBot (nonempty_Ico.2 H)
 #align right_nhds_within_Ico_ne_bot right_nhdsWithin_Ico_neBot
 
-/- warning: left_nhds_within_Ioc_ne_bot -> left_nhdsWithin_Ioc_neBot is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)))
-Case conversion may be inaccurate. Consider using '#align left_nhds_within_Ioc_ne_bot left_nhdsWithin_Ioc_neBotₓ'. -/
 theorem left_nhdsWithin_Ioc_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ioc a b] a) :=
   (isGLB_Ioc H).nhdsWithin_neBot (nonempty_Ioc.2 H)
 #align left_nhds_within_Ioc_ne_bot left_nhdsWithin_Ioc_neBot
 
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-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)))
-Case conversion may be inaccurate. Consider using '#align left_nhds_within_Ioo_ne_bot left_nhdsWithin_Ioo_neBotₓ'. -/
 theorem left_nhdsWithin_Ioo_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ioo a b] a) :=
   (isGLB_Ioo H).nhdsWithin_neBot (nonempty_Ioo.2 H)
 #align left_nhds_within_Ioo_ne_bot left_nhdsWithin_Ioo_neBot
 
-/- warning: right_nhds_within_Ioo_ne_bot -> right_nhdsWithin_Ioo_neBot is a dubious translation:
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 theorem right_nhdsWithin_Ioo_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ioo a b] b) :=
   (isLUB_Ioo H).nhdsWithin_neBot (nonempty_Ioo.2 H)
 #align right_nhds_within_Ioo_ne_bot right_nhdsWithin_Ioo_neBot
 
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 theorem comap_coe_nhdsWithin_Iio_of_Ioo_subset (hb : s ⊆ Iio b)
     (hs : s.Nonempty → ∃ a < b, Ioo a b ⊆ s) : comap (coe : s → α) (𝓝[<] b) = atTop :=
   by
@@ -4176,24 +2685,12 @@ theorem comap_coe_nhdsWithin_Iio_of_Ioo_subset (hb : s ⊆ Iio b)
     exact ⟨Ioo x b, Ioo_mem_nhdsWithin_Iio (right_mem_Ioc.2 <| hb x.2), fun z hz => hx _ hz.1.le⟩
 #align comap_coe_nhds_within_Iio_of_Ioo_subset comap_coe_nhdsWithin_Iio_of_Ioo_subset
 
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 theorem comap_coe_nhdsWithin_Ioi_of_Ioo_subset (ha : s ⊆ Ioi a)
     (hs : s.Nonempty → ∃ b > a, Ioo a b ⊆ s) : comap (coe : s → α) (𝓝[>] a) = atBot :=
   comap_coe_nhdsWithin_Iio_of_Ioo_subset (show ofDual ⁻¹' s ⊆ Iio (toDual a) from ha) fun h => by
     simpa only [OrderDual.exists, dual_Ioo] using hs h
 #align comap_coe_nhds_within_Ioi_of_Ioo_subset comap_coe_nhdsWithin_Ioi_of_Ioo_subset
 
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 theorem map_coe_atTop_of_Ioo_subset (hb : s ⊆ Iio b) (hs : ∀ a' < b, ∃ a < b, Ioo a b ⊆ s) :
     map (coe : s → α) atTop = 𝓝[<] b :=
   by
@@ -4205,12 +2702,6 @@ theorem map_coe_atTop_of_Ioo_subset (hb : s ⊆ Iio b) (hs : ∀ a' < b, ∃ a <
     exact (mem_nhdsWithin_Iio_iff_exists_Ioo_subset' ha).2 (hs a ha)
 #align map_coe_at_top_of_Ioo_subset map_coe_atTop_of_Ioo_subset
 
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 theorem map_coe_atBot_of_Ioo_subset (ha : s ⊆ Ioi a) (hs : ∀ b' > a, ∃ b > a, Ioo a b ⊆ s) :
     map (coe : s → α) atBot = 𝓝[>] a :=
   by
@@ -4220,12 +2711,6 @@ theorem map_coe_atBot_of_Ioo_subset (ha : s ⊆ Ioi a) (hs : ∀ b' > a, ∃ b >
   simpa only [OrderDual.exists, dual_Ioo] using hs b' hb'
 #align map_coe_at_bot_of_Ioo_subset map_coe_atBot_of_Ioo_subset
 
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 /-- The `at_top` filter for an open interval `Ioo a b` comes from the left-neighbourhoods filter at
 the right endpoint in the ambient order. -/
 theorem comap_coe_Ioo_nhdsWithin_Iio (a b : α) : comap (coe : Ioo a b → α) (𝓝[<] b) = atTop :=
@@ -4233,12 +2718,6 @@ theorem comap_coe_Ioo_nhdsWithin_Iio (a b : α) : comap (coe : Ioo a b → α) (
     ⟨a, nonempty_Ioo.1 h, Subset.refl _⟩
 #align comap_coe_Ioo_nhds_within_Iio comap_coe_Ioo_nhdsWithin_Iio
 
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 /-- The `at_bot` filter for an open interval `Ioo a b` comes from the right-neighbourhoods filter at
 the left endpoint in the ambient order. -/
 theorem comap_coe_Ioo_nhdsWithin_Ioi (a b : α) : comap (coe : Ioo a b → α) (𝓝[>] a) = atBot :=
@@ -4246,65 +2725,29 @@ theorem comap_coe_Ioo_nhdsWithin_Ioi (a b : α) : comap (coe : Ioo a b → α) (
     ⟨b, nonempty_Ioo.1 h, Subset.refl _⟩
 #align comap_coe_Ioo_nhds_within_Ioi comap_coe_Ioo_nhdsWithin_Ioi
 
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 theorem comap_coe_Ioi_nhdsWithin_Ioi (a : α) : comap (coe : Ioi a → α) (𝓝[>] a) = atBot :=
   comap_coe_nhdsWithin_Ioi_of_Ioo_subset (Subset.refl _) fun ⟨x, hx⟩ => ⟨x, hx, Ioo_subset_Ioi_self⟩
 #align comap_coe_Ioi_nhds_within_Ioi comap_coe_Ioi_nhdsWithin_Ioi
 
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 theorem comap_coe_Iio_nhdsWithin_Iio (a : α) : comap (coe : Iio a → α) (𝓝[<] a) = atTop :=
   @comap_coe_Ioi_nhdsWithin_Ioi αᵒᵈ _ _ _ _ a
 #align comap_coe_Iio_nhds_within_Iio comap_coe_Iio_nhdsWithin_Iio
 
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 @[simp]
 theorem map_coe_Ioo_atTop {a b : α} (h : a < b) : map (coe : Ioo a b → α) atTop = 𝓝[<] b :=
   map_coe_atTop_of_Ioo_subset Ioo_subset_Iio_self fun _ _ => ⟨_, h, Subset.refl _⟩
 #align map_coe_Ioo_at_top map_coe_Ioo_atTop
 
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 @[simp]
 theorem map_coe_Ioo_atBot {a b : α} (h : a < b) : map (coe : Ioo a b → α) atBot = 𝓝[>] a :=
   map_coe_atBot_of_Ioo_subset Ioo_subset_Ioi_self fun _ _ => ⟨_, h, Subset.refl _⟩
 #align map_coe_Ioo_at_bot map_coe_Ioo_atBot
 
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 @[simp]
 theorem map_coe_Ioi_atBot (a : α) : map (coe : Ioi a → α) atBot = 𝓝[>] a :=
   map_coe_atBot_of_Ioo_subset (Subset.refl _) fun b hb => ⟨b, hb, Ioo_subset_Ioi_self⟩
 #align map_coe_Ioi_at_bot map_coe_Ioi_atBot
 
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 @[simp]
 theorem map_coe_Iio_atTop (a : α) : map (coe : Iio a → α) atTop = 𝓝[<] a :=
   @map_coe_Ioi_atBot αᵒᵈ _ _ _ _ _
@@ -4312,78 +2755,48 @@ theorem map_coe_Iio_atTop (a : α) : map (coe : Iio a → α) atTop = 𝓝[<] a
 
 variable {l : Filter β} {f : α → β}
 
-/- warning: tendsto_comp_coe_Ioo_at_top -> tendsto_comp_coe_Ioo_atTop is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tendsto_comp_coe_Ioo_at_top tendsto_comp_coe_Ioo_atTopₓ'. -/
 @[simp]
 theorem tendsto_comp_coe_Ioo_atTop (h : a < b) :
     Tendsto (fun x : Ioo a b => f x) atTop l ↔ Tendsto f (𝓝[<] b) l := by
   rw [← map_coe_Ioo_atTop h, tendsto_map'_iff]
 #align tendsto_comp_coe_Ioo_at_top tendsto_comp_coe_Ioo_atTop
 
-/- warning: tendsto_comp_coe_Ioo_at_bot -> tendsto_comp_coe_Ioo_atBot is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tendsto_comp_coe_Ioo_at_bot tendsto_comp_coe_Ioo_atBotₓ'. -/
 @[simp]
 theorem tendsto_comp_coe_Ioo_atBot (h : a < b) :
     Tendsto (fun x : Ioo a b => f x) atBot l ↔ Tendsto f (𝓝[>] a) l := by
   rw [← map_coe_Ioo_atBot h, tendsto_map'_iff]
 #align tendsto_comp_coe_Ioo_at_bot tendsto_comp_coe_Ioo_atBot
 
-/- warning: tendsto_comp_coe_Ioi_at_bot -> tendsto_comp_coe_Ioi_atBot is a dubious translation:
-<too large>
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 @[simp]
 theorem tendsto_comp_coe_Ioi_atBot :
     Tendsto (fun x : Ioi a => f x) atBot l ↔ Tendsto f (𝓝[>] a) l := by
   rw [← map_coe_Ioi_atBot, tendsto_map'_iff]
 #align tendsto_comp_coe_Ioi_at_bot tendsto_comp_coe_Ioi_atBot
 
-/- warning: tendsto_comp_coe_Iio_at_top -> tendsto_comp_coe_Iio_atTop is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tendsto_comp_coe_Iio_at_top tendsto_comp_coe_Iio_atTopₓ'. -/
 @[simp]
 theorem tendsto_comp_coe_Iio_atTop :
     Tendsto (fun x : Iio a => f x) atTop l ↔ Tendsto f (𝓝[<] a) l := by
   rw [← map_coe_Iio_atTop, tendsto_map'_iff]
 #align tendsto_comp_coe_Iio_at_top tendsto_comp_coe_Iio_atTop
 
-/- warning: tendsto_Ioo_at_top -> tendsto_Ioo_atTop is a dubious translation:
-<too large>
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 @[simp]
 theorem tendsto_Ioo_atTop {f : β → Ioo a b} :
     Tendsto f l atTop ↔ Tendsto (fun x => (f x : α)) l (𝓝[<] b) := by
   rw [← comap_coe_Ioo_nhdsWithin_Iio, tendsto_comap_iff]
 #align tendsto_Ioo_at_top tendsto_Ioo_atTop
 
-/- warning: tendsto_Ioo_at_bot -> tendsto_Ioo_atBot is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align tendsto_Ioo_at_bot tendsto_Ioo_atBotₓ'. -/
 @[simp]
 theorem tendsto_Ioo_atBot {f : β → Ioo a b} :
     Tendsto f l atBot ↔ Tendsto (fun x => (f x : α)) l (𝓝[>] a) := by
   rw [← comap_coe_Ioo_nhdsWithin_Ioi, tendsto_comap_iff]
 #align tendsto_Ioo_at_bot tendsto_Ioo_atBot
 
-/- warning: tendsto_Ioi_at_bot -> tendsto_Ioi_atBot is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align tendsto_Ioi_at_bot tendsto_Ioi_atBotₓ'. -/
 @[simp]
 theorem tendsto_Ioi_atBot {f : β → Ioi a} :
     Tendsto f l atBot ↔ Tendsto (fun x => (f x : α)) l (𝓝[>] a) := by
   rw [← comap_coe_Ioi_nhdsWithin_Ioi, tendsto_comap_iff]
 #align tendsto_Ioi_at_bot tendsto_Ioi_atBot
 
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-Case conversion may be inaccurate. Consider using '#align tendsto_Iio_at_top tendsto_Iio_atTopₓ'. -/
 @[simp]
 theorem tendsto_Iio_atTop {f : β → Iio a} :
     Tendsto f l atTop ↔ Tendsto (fun x => (f x : α)) l (𝓝[<] a) := by
@@ -4401,12 +2814,6 @@ instance (x : α) [Nontrivial α] : NeBot (𝓝[≠] x) :=
   obtain ⟨z, hz⟩ : ∃ z, a < z ∧ z < x := exists_between hy.1
   exact ⟨z, us ⟨hab ⟨hz.1, hz.2.trans hy.2⟩, hz.2.Ne⟩⟩
 
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-Case conversion may be inaccurate. Consider using '#align dense.exists_countable_dense_subset_no_bot_top Dense.exists_countable_dense_subset_no_bot_topₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 /-- Let `s` be a dense set in a nontrivial dense linear order `α`. If `s` is a
 separable space (e.g., if `α` has a second countable topology), then there exists a countable
@@ -4426,12 +2833,6 @@ theorem Dense.exists_countable_dense_subset_no_bot_top [Nontrivial α] {s : Set
 
 variable (α)
 
-/- warning: exists_countable_dense_no_bot_top -> exists_countable_dense_no_bot_top is a dubious translation:
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-  forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : TopologicalSpace.SeparableSpace.{u1} α _inst_1] [_inst_6 : Nontrivial.{u1} α], Exists.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => And (Set.Countable.{u1} α s) (And (Dense.{u1} α _inst_1 s) (And (forall (x : α), (IsBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))) (forall (x : α), (IsTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))))
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-  forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : TopologicalSpace.SeparableSpace.{u1} α _inst_1] [_inst_6 : Nontrivial.{u1} α], Exists.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => And (Set.Countable.{u1} α s) (And (Dense.{u1} α _inst_1 s) (And (forall (x : α), (IsBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s))) (forall (x : α), (IsTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s))))))
-Case conversion may be inaccurate. Consider using '#align exists_countable_dense_no_bot_top exists_countable_dense_no_bot_topₓ'. -/
 /-- If `α` is a nontrivial separable dense linear order, then there exists a
 countable dense set `s : set α` that contains neither top nor bottom elements of `α`.
 For a dense set containing both bot and top elements, see
@@ -4448,56 +2849,26 @@ section CompleteLinearOrder
 variable [CompleteLinearOrder α] [TopologicalSpace α] [OrderTopology α] [CompleteLinearOrder β]
   [TopologicalSpace β] [OrderClosedTopology β] [Nonempty γ]
 
-/- warning: Sup_mem_closure -> sSup_mem_closure is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))) s) (closure.{u1} α _inst_8 s))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_9)))) s) (closure.{u1} α _inst_8 s))
-Case conversion may be inaccurate. Consider using '#align Sup_mem_closure sSup_mem_closureₓ'. -/
 theorem sSup_mem_closure {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
     {s : Set α} (hs : s.Nonempty) : sSup s ∈ closure s :=
   (isLUB_sSup s).mem_closure hs
 #align Sup_mem_closure sSup_mem_closure
 
-/- warning: Inf_mem_closure -> sInf_mem_closure is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))) s) (closure.{u1} α _inst_8 s))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_9)))) s) (closure.{u1} α _inst_8 s))
-Case conversion may be inaccurate. Consider using '#align Inf_mem_closure sInf_mem_closureₓ'. -/
 theorem sInf_mem_closure {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
     {s : Set α} (hs : s.Nonempty) : sInf s ∈ closure s :=
   (isGLB_sInf s).mem_closure hs
 #align Inf_mem_closure sInf_mem_closure
 
-/- warning: is_closed.Sup_mem -> IsClosed.sSup_mem is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (IsClosed.{u1} α _inst_8 s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_9)))) s) s)
-Case conversion may be inaccurate. Consider using '#align is_closed.Sup_mem IsClosed.sSup_memₓ'. -/
 theorem IsClosed.sSup_mem {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α]
     [OrderTopology α] {s : Set α} (hs : s.Nonempty) (hc : IsClosed s) : sSup s ∈ s :=
   (isLUB_sSup s).mem_of_isClosed hs hc
 #align is_closed.Sup_mem IsClosed.sSup_mem
 
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-but is expected to have type
-  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (IsClosed.{u1} α _inst_8 s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_9)))) s) s)
-Case conversion may be inaccurate. Consider using '#align is_closed.Inf_mem IsClosed.sInf_memₓ'. -/
 theorem IsClosed.sInf_mem {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α]
     [OrderTopology α] {s : Set α} (hs : s.Nonempty) (hc : IsClosed s) : sInf s ∈ s :=
   (isGLB_sInf s).mem_of_isClosed hs hc
 #align is_closed.Inf_mem IsClosed.sInf_mem
 
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align monotone.map_Sup_of_continuous_at' Monotone.map_sSup_of_continuousAt'ₓ'. -/
 /-- A monotone function continuous at the supremum of a nonempty set sends this supremum to
 the supremum of the image of this set. -/
 theorem Monotone.map_sSup_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
@@ -4509,12 +2880,6 @@ theorem Monotone.map_sSup_of_continuousAt' {f : α → β} {s : Set α} (Cf : Co
         Cf.mono_left inf_le_left).sSup_eq.symm
 #align monotone.map_Sup_of_continuous_at' Monotone.map_sSup_of_continuousAt'
 
-/- warning: monotone.map_Sup_of_continuous_at -> Monotone.map_sSup_of_continuousAt is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) (Bot.bot.{u2} β (ConditionallyCompleteLinearOrderBot.toHasBot.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align monotone.map_Sup_of_continuous_at Monotone.map_sSup_of_continuousAtₓ'. -/
 /-- A monotone function `f` sending `bot` to `bot` and continuous at the supremum of a set sends
 this supremum to the supremum of the image of this set. -/
 theorem Monotone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
@@ -4525,12 +2890,6 @@ theorem Monotone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : Con
   · exact Mf.map_Sup_of_continuous_at' Cf h
 #align monotone.map_Sup_of_continuous_at Monotone.map_sSup_of_continuousAt
 
-/- warning: monotone.map_supr_of_continuous_at' -> Monotone.map_iSup_of_continuousAt' is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} [_inst_8 : Nonempty.{u3} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι (fun (i : ι) => g i))) (iSup.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (fun (i : ι) => f (g i))))
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-  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} [_inst_8 : Nonempty.{u1} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Monotone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι (fun (i : ι) => g i))) (iSup.{u3, u1} β (ConditionallyCompleteLattice.toSupSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (fun (i : ι) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align monotone.map_supr_of_continuous_at' Monotone.map_iSup_of_continuousAt'ₓ'. -/
 /-- A monotone function continuous at the indexed supremum over a nonempty `Sort` sends this indexed
 supremum to the indexed supremum of the composition. -/
 theorem Monotone.map_iSup_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
@@ -4538,12 +2897,6 @@ theorem Monotone.map_iSup_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α 
   rw [iSup, Mf.map_Sup_of_continuous_at' Cf (range_nonempty g), ← range_comp, iSup]
 #align monotone.map_supr_of_continuous_at' Monotone.map_iSup_of_continuousAt'
 
-/- warning: monotone.map_supr_of_continuous_at -> Monotone.map_iSup_of_continuousAt is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) (Bot.bot.{u2} β (ConditionallyCompleteLinearOrderBot.toHasBot.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι (fun (i : ι) => g i))) (iSup.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (fun (i : ι) => f (g i))))
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-Case conversion may be inaccurate. Consider using '#align monotone.map_supr_of_continuous_at Monotone.map_iSup_of_continuousAtₓ'. -/
 /-- If a monotone function sending `bot` to `bot` is continuous at the indexed supremum over
 a `Sort`, then it sends this indexed supremum to the indexed supremum of the composition. -/
 theorem Monotone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
@@ -4552,12 +2905,6 @@ theorem Monotone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι
   rw [iSup, Mf.map_Sup_of_continuous_at Cf fbot, ← range_comp, iSup]
 #align monotone.map_supr_of_continuous_at Monotone.map_iSup_of_continuousAt
 
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align monotone.map_Inf_of_continuous_at' Monotone.map_sInf_of_continuousAt'ₓ'. -/
 /-- A monotone function continuous at the infimum of a nonempty set sends this infimum to
 the infimum of the image of this set. -/
 theorem Monotone.map_sInf_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
@@ -4565,12 +2912,6 @@ theorem Monotone.map_sInf_of_continuousAt' {f : α → β} {s : Set α} (Cf : Co
   @Monotone.map_sSup_of_continuousAt' αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual hs
 #align monotone.map_Inf_of_continuous_at' Monotone.map_sInf_of_continuousAt'
 
-/- warning: monotone.map_Inf_of_continuous_at -> Monotone.map_sInf_of_continuousAt is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
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-Case conversion may be inaccurate. Consider using '#align monotone.map_Inf_of_continuous_at Monotone.map_sInf_of_continuousAtₓ'. -/
 /-- A monotone function `f` sending `top` to `top` and continuous at the infimum of a set sends
 this infimum to the infimum of the image of this set. -/
 theorem Monotone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
@@ -4578,12 +2919,6 @@ theorem Monotone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : Con
   @Monotone.map_sSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual ftop
 #align monotone.map_Inf_of_continuous_at Monotone.map_sInf_of_continuousAt
 
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} [_inst_8 : Nonempty.{u3} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι (fun (i : ι) => g i))) (iInf.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (fun (i : ι) => f (g i))))
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-Case conversion may be inaccurate. Consider using '#align monotone.map_infi_of_continuous_at' Monotone.map_iInf_of_continuousAt'ₓ'. -/
 /-- A monotone function continuous at the indexed infimum over a nonempty `Sort` sends this indexed
 infimum to the indexed infimum of the composition. -/
 theorem Monotone.map_iInf_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
@@ -4591,12 +2926,6 @@ theorem Monotone.map_iInf_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α 
   @Monotone.map_iSup_of_continuousAt' αᵒᵈ βᵒᵈ _ _ _ _ _ _ ι _ f g Cf Mf.dual
 #align monotone.map_infi_of_continuous_at' Monotone.map_iInf_of_continuousAt'
 
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) (iInf.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (Function.comp.{u3, succ u1, succ u2} ι α β f g)))
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-Case conversion may be inaccurate. Consider using '#align monotone.map_infi_of_continuous_at Monotone.map_iInf_of_continuousAtₓ'. -/
 /-- If a monotone function sending `top` to `top` is continuous at the indexed infimum over
 a `Sort`, then it sends this indexed infimum to the indexed infimum of the composition. -/
 theorem Monotone.map_iInf_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
@@ -4604,12 +2933,6 @@ theorem Monotone.map_iInf_of_continuousAt {ι : Sort _} {f : α → β} {g : ι
   @Monotone.map_iSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ ι f g Cf Mf.dual ftop
 #align monotone.map_infi_of_continuous_at Monotone.map_iInf_of_continuousAt
 
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-Case conversion may be inaccurate. Consider using '#align antitone.map_Sup_of_continuous_at' Antitone.map_sSup_of_continuousAt'ₓ'. -/
 /-- An antitone function continuous at the supremum of a nonempty set sends this supremum to
 the infimum of the image of this set. -/
 theorem Antitone.map_sSup_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
@@ -4618,12 +2941,6 @@ theorem Antitone.map_sSup_of_continuousAt' {f : α → β} {s : Set α} (Cf : Co
     hs
 #align antitone.map_Sup_of_continuous_at' Antitone.map_sSup_of_continuousAt'
 
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-Case conversion may be inaccurate. Consider using '#align antitone.map_Sup_of_continuous_at Antitone.map_sSup_of_continuousAtₓ'. -/
 /-- An antitone function `f` sending `bot` to `top` and continuous at the supremum of a set sends
 this supremum to the infimum of the image of this set. -/
 theorem Antitone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
@@ -4632,12 +2949,6 @@ theorem Antitone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : Con
     fbot
 #align antitone.map_Sup_of_continuous_at Antitone.map_sSup_of_continuousAt
 
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-Case conversion may be inaccurate. Consider using '#align antitone.map_supr_of_continuous_at' Antitone.map_iSup_of_continuousAt'ₓ'. -/
 /-- An antitone function continuous at the indexed supremum over a nonempty `Sort` sends this
 indexed supremum to the indexed infimum of the composition. -/
 theorem Antitone.map_iSup_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
@@ -4645,12 +2956,6 @@ theorem Antitone.map_iSup_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α 
   Monotone.map_iSup_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (iSup g) from Cf) Af
 #align antitone.map_supr_of_continuous_at' Antitone.map_iSup_of_continuousAt'
 
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-Case conversion may be inaccurate. Consider using '#align antitone.map_supr_of_continuous_at Antitone.map_iSup_of_continuousAtₓ'. -/
 /-- An antitone function sending `bot` to `top` is continuous at the indexed supremum over
 a `Sort`, then it sends this indexed supremum to the indexed supremum of the composition. -/
 theorem Antitone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
@@ -4660,12 +2965,6 @@ theorem Antitone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι
     fbot
 #align antitone.map_supr_of_continuous_at Antitone.map_iSup_of_continuousAt
 
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-Case conversion may be inaccurate. Consider using '#align antitone.map_Inf_of_continuous_at' Antitone.map_sInf_of_continuousAt'ₓ'. -/
 /-- An antitone function continuous at the infimum of a nonempty set sends this infimum to
 the supremum of the image of this set. -/
 theorem Antitone.map_sInf_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
@@ -4674,12 +2973,6 @@ theorem Antitone.map_sInf_of_continuousAt' {f : α → β} {s : Set α} (Cf : Co
     hs
 #align antitone.map_Inf_of_continuous_at' Antitone.map_sInf_of_continuousAt'
 
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-Case conversion may be inaccurate. Consider using '#align antitone.map_Inf_of_continuous_at Antitone.map_sInf_of_continuousAtₓ'. -/
 /-- An antitone function `f` sending `top` to `bot` and continuous at the infimum of a set sends
 this infimum to the supremum of the image of this set. -/
 theorem Antitone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
@@ -4688,12 +2981,6 @@ theorem Antitone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : Con
     ftop
 #align antitone.map_Inf_of_continuous_at Antitone.map_sInf_of_continuousAt
 
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} [_inst_8 : Nonempty.{u3} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι (fun (i : ι) => g i))) (iSup.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (fun (i : ι) => f (g i))))
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-  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} [_inst_8 : Nonempty.{u1} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Antitone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι (fun (i : ι) => g i))) (iSup.{u3, u1} β (ConditionallyCompleteLattice.toSupSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (fun (i : ι) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align antitone.map_infi_of_continuous_at' Antitone.map_iInf_of_continuousAt'ₓ'. -/
 /-- An antitone function continuous at the indexed infimum over a nonempty `Sort` sends this indexed
 infimum to the indexed supremum of the composition. -/
 theorem Antitone.map_iInf_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
@@ -4701,12 +2988,6 @@ theorem Antitone.map_iInf_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α 
   Monotone.map_iInf_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (iInf g) from Cf) Af
 #align antitone.map_infi_of_continuous_at' Antitone.map_iInf_of_continuousAt'
 
-/- warning: antitone.map_infi_of_continuous_at -> Antitone.map_iInf_of_continuousAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (Bot.bot.{u2} β (ConditionallyCompleteLinearOrderBot.toHasBot.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) (iSup.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (Function.comp.{u3, succ u1, succ u2} ι α β f g)))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Antitone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (Top.top.{u2} α (CompleteLattice.toTop.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (Bot.bot.{u3} β (ConditionallyCompleteLinearOrderBot.toBot.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) -> (Eq.{succ u3} β (f (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) (iSup.{u3, u1} β (ConditionallyCompleteLattice.toSupSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (Function.comp.{u1, succ u2, succ u3} ι α β f g)))
-Case conversion may be inaccurate. Consider using '#align antitone.map_infi_of_continuous_at Antitone.map_iInf_of_continuousAtₓ'. -/
 /-- If an antitone function sending `top` to `bot` is continuous at the indexed infimum over
 a `Sort`, then it sends this indexed infimum to the indexed supremum of the composition. -/
 theorem Antitone.map_iInf_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
@@ -4722,54 +3003,24 @@ section ConditionallyCompleteLinearOrder
 variable [ConditionallyCompleteLinearOrder α] [TopologicalSpace α] [OrderTopology α]
   [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderClosedTopology β] [Nonempty γ]
 
-/- warning: cSup_mem_closure -> csSup_mem_closure 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)))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (closure.{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)))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (closure.{u1} α _inst_2 s))
-Case conversion may be inaccurate. Consider using '#align cSup_mem_closure csSup_mem_closureₓ'. -/
 theorem csSup_mem_closure {s : Set α} (hs : s.Nonempty) (B : BddAbove s) : sSup s ∈ closure s :=
   (isLUB_csSup hs B).mem_closure hs
 #align cSup_mem_closure csSup_mem_closure
 
-/- warning: cInf_mem_closure -> csInf_mem_closure 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}, (Set.Nonempty.{u1} α 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) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (closure.{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)))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (closure.{u1} α _inst_2 s))
-Case conversion may be inaccurate. Consider using '#align cInf_mem_closure csInf_mem_closureₓ'. -/
 theorem csInf_mem_closure {s : Set α} (hs : s.Nonempty) (B : BddBelow s) : sInf s ∈ closure s :=
   (isGLB_csInf hs B).mem_closure hs
 #align cInf_mem_closure csInf_mem_closure
 
-/- warning: is_closed.cSup_mem -> IsClosed.csSup_mem 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}, (IsClosed.{u1} α _inst_2 s) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (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}, (IsClosed.{u1} α _inst_2 s) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (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_closed.cSup_mem IsClosed.csSup_memₓ'. -/
 theorem IsClosed.csSup_mem {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddAbove s) :
     sSup s ∈ s :=
   (isLUB_csSup hs B).mem_of_isClosed hs hc
 #align is_closed.cSup_mem IsClosed.csSup_mem
 
-/- warning: is_closed.cInf_mem -> IsClosed.csInf_mem 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}, (IsClosed.{u1} α _inst_2 s) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_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}, (IsClosed.{u1} α _inst_2 s) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
-Case conversion may be inaccurate. Consider using '#align is_closed.cInf_mem IsClosed.csInf_memₓ'. -/
 theorem IsClosed.csInf_mem {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddBelow s) :
     sInf s ∈ s :=
   (isGLB_csInf hs B).mem_of_isClosed hs hc
 #align is_closed.cInf_mem IsClosed.csInf_mem
 
-/- warning: monotone.map_cSup_of_continuous_at -> Monotone.map_csSup_of_continuousAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align monotone.map_cSup_of_continuous_at Monotone.map_csSup_of_continuousAtₓ'. -/
 /-- If a monotone function is continuous at the supremum of a nonempty bounded above set `s`,
 then it sends this supremum to the supremum of the image of `s`. -/
 theorem Monotone.map_csSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
@@ -4780,12 +3031,6 @@ theorem Monotone.map_csSup_of_continuousAt {f : α → β} {s : Set α} (Cf : Co
   exact Cf.mono_left inf_le_left
 #align monotone.map_cSup_of_continuous_at Monotone.map_csSup_of_continuousAt
 
-/- warning: monotone.map_csupr_of_continuous_at -> Monotone.map_ciSup_of_continuousAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (iSup.{u2, succ u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (iSup.{u2, succ u3} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align monotone.map_csupr_of_continuous_at Monotone.map_ciSup_of_continuousAtₓ'. -/
 /-- If a monotone function is continuous at the indexed supremum of a bounded function on
 a nonempty `Sort`, then it sends this supremum to the supremum of the composition. -/
 theorem Monotone.map_ciSup_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
@@ -4793,12 +3038,6 @@ theorem Monotone.map_ciSup_of_continuousAt {f : α → β} {g : γ → α} (Cf :
   rw [iSup, Mf.map_cSup_of_continuous_at Cf (range_nonempty _) H, ← range_comp, iSup]
 #align monotone.map_csupr_of_continuous_at Monotone.map_ciSup_of_continuousAt
 
-/- warning: monotone.map_cInf_of_continuous_at -> Monotone.map_csInf_of_continuousAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align monotone.map_cInf_of_continuous_at Monotone.map_csInf_of_continuousAtₓ'. -/
 /-- If a monotone function is continuous at the infimum of a nonempty bounded below set `s`,
 then it sends this infimum to the infimum of the image of `s`. -/
 theorem Monotone.map_csInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
@@ -4806,12 +3045,6 @@ theorem Monotone.map_csInf_of_continuousAt {f : α → β} {s : Set α} (Cf : Co
   @Monotone.map_csSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual Ne H
 #align monotone.map_cInf_of_continuous_at Monotone.map_csInf_of_continuousAt
 
-/- warning: monotone.map_cinfi_of_continuous_at -> Monotone.map_ciInf_of_continuousAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (iInf.{u2, succ u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (iInf.{u2, succ u3} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align monotone.map_cinfi_of_continuous_at Monotone.map_ciInf_of_continuousAtₓ'. -/
 /-- A continuous monotone function sends indexed infimum to indexed infimum in conditionally
 complete linear order, under a boundedness assumption. -/
 theorem Monotone.map_ciInf_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
@@ -4819,12 +3052,6 @@ theorem Monotone.map_ciInf_of_continuousAt {f : α → β} {g : γ → α} (Cf :
   @Monotone.map_ciSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ _ Cf Mf.dual H
 #align monotone.map_cinfi_of_continuous_at Monotone.map_ciInf_of_continuousAt
 
-/- warning: antitone.map_cSup_of_continuous_at -> Antitone.map_csSup_of_continuousAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align antitone.map_cSup_of_continuous_at Antitone.map_csSup_of_continuousAtₓ'. -/
 /-- If an antitone function is continuous at the supremum of a nonempty bounded above set `s`,
 then it sends this supremum to the infimum of the image of `s`. -/
 theorem Antitone.map_csSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
@@ -4833,12 +3060,6 @@ theorem Antitone.map_csSup_of_continuousAt {f : α → β} {s : Set α} (Cf : Co
     Ne H
 #align antitone.map_cSup_of_continuous_at Antitone.map_csSup_of_continuousAt
 
-/- warning: antitone.map_csupr_of_continuous_at -> Antitone.map_ciSup_of_continuousAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (iInf.{u2, succ u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (iInf.{u2, succ u3} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align antitone.map_csupr_of_continuous_at Antitone.map_ciSup_of_continuousAtₓ'. -/
 /-- If an antitone function is continuous at the indexed supremum of a bounded function on
 a nonempty `Sort`, then it sends this supremum to the infimum of the composition. -/
 theorem Antitone.map_ciSup_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
@@ -4847,12 +3068,6 @@ theorem Antitone.map_ciSup_of_continuousAt {f : α → β} {g : γ → α} (Cf :
     Af H
 #align antitone.map_csupr_of_continuous_at Antitone.map_ciSup_of_continuousAt
 
-/- warning: antitone.map_cInf_of_continuous_at -> Antitone.map_csInf_of_continuousAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align antitone.map_cInf_of_continuous_at Antitone.map_csInf_of_continuousAtₓ'. -/
 /-- If an antitone function is continuous at the infimum of a nonempty bounded below set `s`,
 then it sends this infimum to the supremum of the image of `s`. -/
 theorem Antitone.map_csInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
@@ -4861,12 +3076,6 @@ theorem Antitone.map_csInf_of_continuousAt {f : α → β} {s : Set α} (Cf : Co
     Ne H
 #align antitone.map_cInf_of_continuous_at Antitone.map_csInf_of_continuousAt
 
-/- warning: antitone.map_cinfi_of_continuous_at -> Antitone.map_ciInf_of_continuousAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (iSup.{u2, succ u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (iSup.{u2, succ u3} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align antitone.map_cinfi_of_continuous_at Antitone.map_ciInf_of_continuousAtₓ'. -/
 /-- A continuous antitone function sends indexed infimum to indexed supremum in conditionally
 complete linear order, under a boundedness assumption. -/
 theorem Antitone.map_ciInf_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
@@ -4875,12 +3084,6 @@ theorem Antitone.map_ciInf_of_continuousAt {f : α → β} {g : γ → α} (Cf :
     Af H
 #align antitone.map_cinfi_of_continuous_at Antitone.map_ciInf_of_continuousAt
 
-/- warning: monotone.tendsto_nhds_within_Iio -> Monotone.tendsto_nhdsWithin_Iio is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_8 : LinearOrder.{u1} α] [_inst_9 : TopologicalSpace.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_9 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8))))] [_inst_11 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_12 : TopologicalSpace.{u2} β] [_inst_13 : OrderTopology.{u2} β _inst_12 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11)))))] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11))))) f) -> (forall (x : α), Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_9 x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) x)) (nhds.{u2} β _inst_12 (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11)) (Set.image.{u1, u2} α β f (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) x)))))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_8 : LinearOrder.{u2} α] [_inst_9 : TopologicalSpace.{u2} α] [_inst_10 : OrderTopology.{u2} α _inst_9 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8)))))] [_inst_11 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_12 : TopologicalSpace.{u1} β] [_inst_13 : OrderTopology.{u1} β _inst_12 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11)))))] {f : α -> β}, (Monotone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11))))) f) -> (forall (x : α), Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_9 x (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) x)) (nhds.{u1} β _inst_12 (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11)) (Set.image.{u2, u1} α β f (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) x)))))
-Case conversion may be inaccurate. Consider using '#align monotone.tendsto_nhds_within_Iio Monotone.tendsto_nhdsWithin_Iioₓ'. -/
 /-- A monotone map has a limit to the left of any point `x`, equal to `Sup (f '' (Iio x))`. -/
 theorem Monotone.tendsto_nhdsWithin_Iio {α β : Type _} [LinearOrder α] [TopologicalSpace α]
     [OrderTopology α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderTopology β]
@@ -4898,12 +3101,6 @@ theorem Monotone.tendsto_nhdsWithin_Iio {α β : Type _} [LinearOrder α] [Topol
     exact le_csSup (Mf.map_bdd_above bddAbove_Iio) (mem_image_of_mem _ hy)
 #align monotone.tendsto_nhds_within_Iio Monotone.tendsto_nhdsWithin_Iio
 
-/- warning: monotone.tendsto_nhds_within_Ioi -> Monotone.tendsto_nhdsWithin_Ioi is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_8 : LinearOrder.{u1} α] [_inst_9 : TopologicalSpace.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_9 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8))))] [_inst_11 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_12 : TopologicalSpace.{u2} β] [_inst_13 : OrderTopology.{u2} β _inst_12 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11)))))] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11))))) f) -> (forall (x : α), Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_9 x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) x)) (nhds.{u2} β _inst_12 (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11)) (Set.image.{u1, u2} α β f (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) x)))))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_8 : LinearOrder.{u2} α] [_inst_9 : TopologicalSpace.{u2} α] [_inst_10 : OrderTopology.{u2} α _inst_9 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8)))))] [_inst_11 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_12 : TopologicalSpace.{u1} β] [_inst_13 : OrderTopology.{u1} β _inst_12 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11)))))] {f : α -> β}, (Monotone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11))))) f) -> (forall (x : α), Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_9 x (Set.Ioi.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) x)) (nhds.{u1} β _inst_12 (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11)) (Set.image.{u2, u1} α β f (Set.Ioi.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) x)))))
-Case conversion may be inaccurate. Consider using '#align monotone.tendsto_nhds_within_Ioi Monotone.tendsto_nhdsWithin_Ioiₓ'. -/
 /-- A monotone map has a limit to the right of any point `x`, equal to `Inf (f '' (Ioi x))`. -/
 theorem Monotone.tendsto_nhdsWithin_Ioi {α β : Type _} [LinearOrder α] [TopologicalSpace α]
     [OrderTopology α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderTopology β]
@@ -4919,22 +3116,10 @@ section LinearOrderedAddCommGroup
 
 variable [LinearOrder α] [Zero α] [TopologicalSpace α] [OrderTopology α]
 
-/- warning: eventually_nhds_within_pos_mem_Ioo -> eventually_nhdsWithin_pos_mem_Ioo is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Zero.{u1} α] [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : OrderTopology.{u1} α _inst_3 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))] {ε : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_2))) ε) -> (Filter.Eventually.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_2))) ε)) (nhdsWithin.{u1} α _inst_3 (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_2))) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_2))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Zero.{u1} α] [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : OrderTopology.{u1} α _inst_3 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))] {ε : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_2)) ε) -> (Filter.Eventually.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_2)) ε)) (nhdsWithin.{u1} α _inst_3 (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_2)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_2)))))
-Case conversion may be inaccurate. Consider using '#align eventually_nhds_within_pos_mem_Ioo eventually_nhdsWithin_pos_mem_Iooₓ'. -/
 theorem eventually_nhdsWithin_pos_mem_Ioo {ε : α} (h : 0 < ε) : ∀ᶠ x in 𝓝[>] 0, x ∈ Ioo 0 ε :=
   Ioo_mem_nhdsWithin_Ioi (left_mem_Ico.2 h)
 #align eventually_nhds_within_pos_mem_Ioo eventually_nhdsWithin_pos_mem_Ioo
 
-/- warning: eventually_nhds_within_pos_mem_Ioc -> eventually_nhdsWithin_pos_mem_Ioc is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Zero.{u1} α] [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : OrderTopology.{u1} α _inst_3 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))] {ε : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_2))) ε) -> (Filter.Eventually.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_2))) ε)) (nhdsWithin.{u1} α _inst_3 (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_2))) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_2))))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Zero.{u1} α] [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : OrderTopology.{u1} α _inst_3 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))] {ε : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_2)) ε) -> (Filter.Eventually.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_2)) ε)) (nhdsWithin.{u1} α _inst_3 (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_2)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_2)))))
-Case conversion may be inaccurate. Consider using '#align eventually_nhds_within_pos_mem_Ioc eventually_nhdsWithin_pos_mem_Iocₓ'. -/
 theorem eventually_nhdsWithin_pos_mem_Ioc {ε : α} (h : 0 < ε) : ∀ᶠ x in 𝓝[>] 0, x ∈ Ioc 0 ε :=
   Ioc_mem_nhdsWithin_Ioi (left_mem_Ico.2 h)
 #align eventually_nhds_within_pos_mem_Ioc eventually_nhdsWithin_pos_mem_Ioc

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

@@ -1022,8 +1022,7 @@ theorem continuous_if_le [TopologicalSpace γ] [∀ x, Decidable (f x ≤ g x)]
   by
   refine' continuous_if (fun a ha => hfg _ (frontier_le_subset_eq hf hg ha)) _ (hg'.mono _)
   · rwa [(isClosed_le hf hg).closure_eq]
-  · simp only [not_le]
-    exact closure_lt_subset_le hg hf
+  · simp only [not_le]; exact closure_lt_subset_le hg hf
 #align continuous_if_le continuous_if_le
 
 /- warning: continuous.if_le -> Continuous.if_le is a dubious translation:
@@ -1072,9 +1071,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align continuous.min Continuous.minₓ'. -/
 @[continuity]
 theorem Continuous.min (hf : Continuous f) (hg : Continuous g) :
-    Continuous fun b => min (f b) (g b) :=
-  by
-  simp only [min_def]
+    Continuous fun b => min (f b) (g b) := by simp only [min_def];
   exact hf.if_le hg hf hg fun x => id
 #align continuous.min Continuous.min
 
@@ -1141,10 +1138,8 @@ but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {f : β -> α} {l : Filter.{u2} β} {a : α}, (Filter.Tendsto.{u2, u1} β α f l (nhds.{u1} α _inst_1 a)) -> (Filter.Tendsto.{u2, u1} β α (fun (i : β) => Max.max.{u1} α (LinearOrder.toMax.{u1} α _inst_2) a (f i)) l (nhds.{u1} α _inst_1 a))
 Case conversion may be inaccurate. Consider using '#align filter.tendsto.max_right Filter.Tendsto.max_rightₓ'. -/
 theorem Filter.Tendsto.max_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
-    Tendsto (fun i => max a (f i)) l (𝓝 a) :=
-  by
-  convert((continuous_max.comp (@Continuous.Prod.mk α α _ _ a)).Tendsto a).comp h
-  simp
+    Tendsto (fun i => max a (f i)) l (𝓝 a) := by
+  convert((continuous_max.comp (@Continuous.Prod.mk α α _ _ a)).Tendsto a).comp h; simp
 #align filter.tendsto.max_right Filter.Tendsto.max_right
 
 /- warning: filter.tendsto.max_left -> Filter.Tendsto.max_left is a dubious translation:
@@ -1154,10 +1149,7 @@ but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {f : β -> α} {l : Filter.{u2} β} {a : α}, (Filter.Tendsto.{u2, u1} β α f l (nhds.{u1} α _inst_1 a)) -> (Filter.Tendsto.{u2, u1} β α (fun (i : β) => Max.max.{u1} α (LinearOrder.toMax.{u1} α _inst_2) (f i) a) l (nhds.{u1} α _inst_1 a))
 Case conversion may be inaccurate. Consider using '#align filter.tendsto.max_left Filter.Tendsto.max_leftₓ'. -/
 theorem Filter.Tendsto.max_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
-    Tendsto (fun i => max (f i) a) l (𝓝 a) :=
-  by
-  simp_rw [max_comm _ a]
-  exact h.max_right
+    Tendsto (fun i => max (f i) a) l (𝓝 a) := by simp_rw [max_comm _ a]; exact h.max_right
 #align filter.tendsto.max_left Filter.Tendsto.max_left
 
 /- warning: filter.tendsto_nhds_max_right -> Filter.tendsto_nhds_max_right is a dubious translation:
@@ -1180,9 +1172,7 @@ but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {f : β -> α} {l : Filter.{u2} β} {a : α}, (Filter.Tendsto.{u2, u1} β α f l (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) -> (Filter.Tendsto.{u2, u1} β α (fun (i : β) => Max.max.{u1} α (LinearOrder.toMax.{u1} α _inst_2) (f i) a) l (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
 Case conversion may be inaccurate. Consider using '#align filter.tendsto_nhds_max_left Filter.tendsto_nhds_max_leftₓ'. -/
 theorem Filter.tendsto_nhds_max_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝[>] a)) :
-    Tendsto (fun i => max (f i) a) l (𝓝[>] a) :=
-  by
-  simp_rw [max_comm _ a]
+    Tendsto (fun i => max (f i) a) l (𝓝[>] a) := by simp_rw [max_comm _ a];
   exact Filter.tendsto_nhds_max_right h
 #align filter.tendsto_nhds_max_left Filter.tendsto_nhds_max_left
 
@@ -2109,8 +2099,7 @@ theorem exists_Icc_mem_subset_of_mem_nhdsWithin_Ici {a : α} {s : Set α} (hs :
     ∃ (b : _)(_ : a ≤ b), Icc a b ∈ 𝓝[≥] a ∧ Icc a b ⊆ s :=
   by
   rcases(em (IsMax a)).imp_right not_is_max_iff.mp with (ha | ha)
-  · use a
-    simpa [ha.Ici_eq] using hs
+  · use a; simpa [ha.Ici_eq] using hs
   · rcases(nhdsWithin_Ici_basis' ha).mem_iff.mp hs with ⟨b, hab, hbs⟩
     rcases eq_empty_or_nonempty (Ioo a b) with (H | ⟨c, hac, hcb⟩)
     · have : Ico a b = Icc a a := by rw [← Icc_union_Ioo_eq_Ico le_rfl hab, H, union_empty]
@@ -2325,8 +2314,7 @@ theorem countable_of_isolated_right' [SecondCountableTopology α] :
       exact False.elim (lt_irrefl _ ((Hy _ _ x't.1 H).trans_lt h'))
   refine' this.countable_of_is_open (fun x hx => _) fun x hx => ⟨x, hz x hx, le_rfl⟩
   suffices H : Ioc (z x) x = Ioo (z x) (y x)
-  · rw [H]
-    exact isOpen_Ioo
+  · rw [H]; exact isOpen_Ioo
   exact subset.antisymm (Ioc_subset_Ioo_right (hy x hx.1)) fun u hu => ⟨hu.1, Hy _ _ hx.1 hu.2⟩
 #align countable_of_isolated_right countable_of_isolated_right'
 
@@ -2342,9 +2330,7 @@ theorem countable_of_isolated_left' [SecondCountableTopology α] :
     Set.Countable { x : α | ∃ y, y < x ∧ Ioo y x = ∅ } :=
   by
   convert@countable_of_isolated_right' αᵒᵈ _ _ _ _
-  have : ∀ x y : α, Ioo x y = { z | z < y ∧ x < z } :=
-    by
-    simp_rw [and_comm', Ioo]
+  have : ∀ x y : α, Ioo x y = { z | z < y ∧ x < z } := by simp_rw [and_comm', Ioo];
     simp only [eq_self_iff_true, forall₂_true_iff]
   simp_rw [this]
   rfl
@@ -3134,9 +3120,7 @@ Case conversion may be inaccurate. Consider using '#align filter.tendsto.at_top_
 /-- In a linearly ordered additive commutative group with the order topology, if `f` tends to
 `at_top` and `g` tends to `C` then `f + g` tends to `at_top`. -/
 theorem Filter.Tendsto.atTop_add {C : α} (hf : Tendsto f l atTop) (hg : Tendsto g l (𝓝 C)) :
-    Tendsto (fun x => f x + g x) l atTop :=
-  by
-  conv in _ + _ => rw [add_comm]
+    Tendsto (fun x => f x + g x) l atTop := by conv in _ + _ => rw [add_comm];
   exact hg.add_at_top hf
 #align filter.tendsto.at_top_add Filter.Tendsto.atTop_add
 
@@ -3149,9 +3133,7 @@ Case conversion may be inaccurate. Consider using '#align filter.tendsto.at_bot_
 /-- In a linearly ordered additive commutative group with the order topology, if `f` tends to
 `at_bot` and `g` tends to `C` then `f + g` tends to `at_bot`. -/
 theorem Filter.Tendsto.atBot_add {C : α} (hf : Tendsto f l atBot) (hg : Tendsto g l (𝓝 C)) :
-    Tendsto (fun x => f x + g x) l atBot :=
-  by
-  conv in _ + _ => rw [add_comm]
+    Tendsto (fun x => f x + g x) l atBot := by conv in _ + _ => rw [add_comm];
   exact hg.add_at_bot hf
 #align filter.tendsto.at_bot_add Filter.Tendsto.atBot_add
 
@@ -3497,10 +3479,7 @@ theorem IsLUB.exists_seq_strictMono_tendsto_of_not_mem {t : Set α} {x : α}
   · simp only [ge_iff_le, eventually_at_top]
     refine' ⟨n, fun p hp => _⟩
     have up : u p ∈ Icc (u n) x := ⟨S.monotone hp, (I p).le⟩
-    have : Icc (u n) x ⊆ s n := by
-      cases n
-      · exact (hf 0 l hl).1
-      · exact (hf n.succ (u n) (I n)).1
+    have : Icc (u n) x ⊆ s n := by cases n; · exact (hf 0 l hl).1; · exact (hf n.succ (u n) (I n)).1
     exact this up
   · cases n
     · exact (hf 0 l hl).2.2.2
@@ -3745,8 +3724,7 @@ theorem closure_Ioo {a b : α} (hab : a ≠ b) : closure (Ioo a b) = Icc a b :=
       have hab' : (Ioo a b).Nonempty := nonempty_Ioo.2 hab
       simp only [insert_subset, singleton_subset_iff]
       exact ⟨(isGLB_Ioo hab).mem_closure hab', (isLUB_Ioo hab).mem_closure hab'⟩
-    · rw [Icc_eq_empty_of_lt hab]
-      exact empty_subset _
+    · rw [Icc_eq_empty_of_lt hab]; exact empty_subset _
 #align closure_Ioo closure_Ioo
 
 /- warning: closure_Ioc -> closure_Ioc is a dubious translation:
@@ -4442,10 +4420,8 @@ theorem Dense.exists_countable_dense_subset_no_bot_top [Nontrivial α] {s : Set
   · exact (diff_subset _ _).trans hts
   · exact htc.mono (diff_subset _ _)
   · exact htd.diff_finite ((subsingleton_is_bot α).Finite.union (subsingleton_is_top α).Finite)
-  · intro x hx
-    simp [hx]
-  · intro x hx
-    simp [hx]
+  · intro x hx; simp [hx]
+  · intro x hx; simp [hx]
 #align dense.exists_countable_dense_subset_no_bot_top Dense.exists_countable_dense_subset_no_bot_top
 
 variable (α)

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

@@ -1013,10 +1013,7 @@ theorem frontier_lt_subset_eq (hf : Continuous f) (hg : Continuous g) :
 #align frontier_lt_subset_eq frontier_lt_subset_eq
 
 /- warning: continuous_if_le -> continuous_if_le is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {f : β -> α} {g : β -> α} [_inst_4 : TopologicalSpace.{u2} β] [_inst_5 : TopologicalSpace.{u3} γ] [_inst_6 : forall (x : β), Decidable (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f x) (g x))] {f' : β -> γ} {g' : β -> γ}, (Continuous.{u2, u1} β α _inst_4 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_4 _inst_1 g) -> (ContinuousOn.{u2, u3} β γ _inst_4 _inst_5 f' (setOf.{u2} β (fun (x : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f x) (g x)))) -> (ContinuousOn.{u2, u3} β γ _inst_4 _inst_5 g' (setOf.{u2} β (fun (x : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (g x) (f x)))) -> (forall (x : β), (Eq.{succ u1} α (f x) (g x)) -> (Eq.{succ u3} γ (f' x) (g' x))) -> (Continuous.{u2, u3} β γ _inst_4 _inst_5 (fun (x : β) => ite.{succ u3} γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f x) (g x)) (_inst_6 x) (f' x) (g' x)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {f : β -> α} {g : β -> α} [_inst_4 : TopologicalSpace.{u2} β] [_inst_5 : TopologicalSpace.{u3} γ] [_inst_6 : forall (x : β), Decidable (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f x) (g x))] {f' : β -> γ} {g' : β -> γ}, (Continuous.{u2, u1} β α _inst_4 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_4 _inst_1 g) -> (ContinuousOn.{u2, u3} β γ _inst_4 _inst_5 f' (setOf.{u2} β (fun (x : β) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f x) (g x)))) -> (ContinuousOn.{u2, u3} β γ _inst_4 _inst_5 g' (setOf.{u2} β (fun (x : β) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (g x) (f x)))) -> (forall (x : β), (Eq.{succ u1} α (f x) (g x)) -> (Eq.{succ u3} γ (f' x) (g' x))) -> (Continuous.{u2, u3} β γ _inst_4 _inst_5 (fun (x : β) => ite.{succ u3} γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f x) (g x)) (_inst_6 x) (f' x) (g' x)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align continuous_if_le continuous_if_leₓ'. -/
 theorem continuous_if_le [TopologicalSpace γ] [∀ x, Decidable (f x ≤ g x)] {f' g' : β → γ}
     (hf : Continuous f) (hg : Continuous g) (hf' : ContinuousOn f' { x | f x ≤ g x })
@@ -1030,10 +1027,7 @@ theorem continuous_if_le [TopologicalSpace γ] [∀ x, Decidable (f x ≤ g x)]
 #align continuous_if_le continuous_if_le
 
 /- warning: continuous.if_le -> Continuous.if_le is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {f : β -> α} {g : β -> α} [_inst_4 : TopologicalSpace.{u2} β] [_inst_5 : TopologicalSpace.{u3} γ] [_inst_6 : forall (x : β), Decidable (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f x) (g x))] {f' : β -> γ} {g' : β -> γ}, (Continuous.{u2, u3} β γ _inst_4 _inst_5 f') -> (Continuous.{u2, u3} β γ _inst_4 _inst_5 g') -> (Continuous.{u2, u1} β α _inst_4 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_4 _inst_1 g) -> (forall (x : β), (Eq.{succ u1} α (f x) (g x)) -> (Eq.{succ u3} γ (f' x) (g' x))) -> (Continuous.{u2, u3} β γ _inst_4 _inst_5 (fun (x : β) => ite.{succ u3} γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f x) (g x)) (_inst_6 x) (f' x) (g' x)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {f : β -> α} {g : β -> α} [_inst_4 : TopologicalSpace.{u2} β] [_inst_5 : TopologicalSpace.{u3} γ] [_inst_6 : forall (x : β), Decidable (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f x) (g x))] {f' : β -> γ} {g' : β -> γ}, (Continuous.{u2, u3} β γ _inst_4 _inst_5 f') -> (Continuous.{u2, u3} β γ _inst_4 _inst_5 g') -> (Continuous.{u2, u1} β α _inst_4 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_4 _inst_1 g) -> (forall (x : β), (Eq.{succ u1} α (f x) (g x)) -> (Eq.{succ u3} γ (f' x) (g' x))) -> (Continuous.{u2, u3} β γ _inst_4 _inst_5 (fun (x : β) => ite.{succ u3} γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f x) (g x)) (_inst_6 x) (f' x) (g' x)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align continuous.if_le Continuous.if_leₓ'. -/
 theorem Continuous.if_le [TopologicalSpace γ] [∀ x, Decidable (f x ≤ g x)] {f' g' : β → γ}
     (hf' : Continuous f') (hg' : Continuous g') (hf : Continuous f) (hg : Continuous g)
@@ -3645,10 +3639,7 @@ theorem exists_seq_strictAnti_tendsto_nhdsWithin [DenselyOrdered α] [NoMaxOrder
 #align exists_seq_strict_anti_tendsto_nhds_within exists_seq_strictAnti_tendsto_nhdsWithin
 
 /- warning: exists_seq_strict_anti_strict_mono_tendsto -> exists_seq_strictAnti_strictMono_tendsto is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] [_inst_7 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))))] [_inst_8 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_1] {x : α} {y : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))) x y) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => Exists.{succ u1} (Nat -> α) (fun (v : Nat -> α) => And (StrictAnti.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) u) (And (StrictMono.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) v) (And (forall (k : Nat), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (u k) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) x y)) (And (forall (l : Nat), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (v l) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) x y)) (And (forall (k : Nat) (l : Nat), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))) (u k) (v l)) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α _inst_1 x)) (Filter.Tendsto.{0, u1} Nat α v (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α _inst_1 y))))))))))
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+<too large>
 Case conversion may be inaccurate. Consider using '#align exists_seq_strict_anti_strict_mono_tendsto exists_seq_strictAnti_strictMono_tendstoₓ'. -/
 theorem exists_seq_strictAnti_strictMono_tendsto [DenselyOrdered α] [FirstCountableTopology α]
     {x y : α} (h : x < y) :
@@ -4344,10 +4335,7 @@ theorem map_coe_Iio_atTop (a : α) : map (coe : Iio a → α) atTop = 𝓝[<] a
 variable {l : Filter β} {f : α → β}
 
 /- warning: tendsto_comp_coe_Ioo_at_top -> tendsto_comp_coe_Ioo_atTop is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align tendsto_comp_coe_Ioo_at_top tendsto_comp_coe_Ioo_atTopₓ'. -/
 @[simp]
 theorem tendsto_comp_coe_Ioo_atTop (h : a < b) :
@@ -4356,10 +4344,7 @@ theorem tendsto_comp_coe_Ioo_atTop (h : a < b) :
 #align tendsto_comp_coe_Ioo_at_top tendsto_comp_coe_Ioo_atTop
 
 /- warning: tendsto_comp_coe_Ioo_at_bot -> tendsto_comp_coe_Ioo_atBot is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align tendsto_comp_coe_Ioo_at_bot tendsto_comp_coe_Ioo_atBotₓ'. -/
 @[simp]
 theorem tendsto_comp_coe_Ioo_atBot (h : a < b) :
@@ -4368,10 +4353,7 @@ theorem tendsto_comp_coe_Ioo_atBot (h : a < b) :
 #align tendsto_comp_coe_Ioo_at_bot tendsto_comp_coe_Ioo_atBot
 
 /- warning: tendsto_comp_coe_Ioi_at_bot -> tendsto_comp_coe_Ioi_atBot is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align tendsto_comp_coe_Ioi_at_bot tendsto_comp_coe_Ioi_atBotₓ'. -/
 @[simp]
 theorem tendsto_comp_coe_Ioi_atBot :
@@ -4380,10 +4362,7 @@ theorem tendsto_comp_coe_Ioi_atBot :
 #align tendsto_comp_coe_Ioi_at_bot tendsto_comp_coe_Ioi_atBot
 
 /- warning: tendsto_comp_coe_Iio_at_top -> tendsto_comp_coe_Iio_atTop is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align tendsto_comp_coe_Iio_at_top tendsto_comp_coe_Iio_atTopₓ'. -/
 @[simp]
 theorem tendsto_comp_coe_Iio_atTop :
@@ -4392,10 +4371,7 @@ theorem tendsto_comp_coe_Iio_atTop :
 #align tendsto_comp_coe_Iio_at_top tendsto_comp_coe_Iio_atTop
 
 /- warning: tendsto_Ioo_at_top -> tendsto_Ioo_atTop is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align tendsto_Ioo_at_top tendsto_Ioo_atTopₓ'. -/
 @[simp]
 theorem tendsto_Ioo_atTop {f : β → Ioo a b} :
@@ -4404,10 +4380,7 @@ theorem tendsto_Ioo_atTop {f : β → Ioo a b} :
 #align tendsto_Ioo_at_top tendsto_Ioo_atTop
 
 /- warning: tendsto_Ioo_at_bot -> tendsto_Ioo_atBot is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α} {l : Filter.{u2} β} {f : β -> (Set.Elem.{u1} α (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))}, Iff (Filter.Tendsto.{u2, u1} β (Set.Elem.{u1} α (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) f l (Filter.atBot.{u1} (Set.Elem.{u1} α (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))))) (Filter.Tendsto.{u2, u1} β α (fun (x : β) => Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (f x)) l (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align tendsto_Ioo_at_bot tendsto_Ioo_atBotₓ'. -/
 @[simp]
 theorem tendsto_Ioo_atBot {f : β → Ioo a b} :

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

@@ -138,7 +138,7 @@ end Subtype
 
 /- warning: is_closed_le_prod -> isClosed_le_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2], IsClosed.{u1} (Prod.{u1, u1} α α) (Prod.topologicalSpace.{u1, u1} α α _inst_1 _inst_1) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2], IsClosed.{u1} (Prod.{u1, u1} α α) (Prod.topologicalSpace.{u1, u1} α α _inst_1 _inst_1) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2], IsClosed.{u1} (Prod.{u1, u1} α α) (instTopologicalSpaceProd.{u1, u1} α α _inst_1 _inst_1) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)))
 Case conversion may be inaccurate. Consider using '#align is_closed_le_prod isClosed_le_prodₓ'. -/
@@ -146,18 +146,26 @@ theorem isClosed_le_prod : IsClosed { p : α × α | p.1 ≤ p.2 } :=
   t.isClosed_le'
 #align is_closed_le_prod isClosed_le_prod
 
-#print isClosed_le /-
+/- warning: is_closed_le -> isClosed_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {g : β -> α}, (Continuous.{u2, u1} β α _inst_3 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_3 _inst_1 g) -> (IsClosed.{u2} β _inst_3 (setOf.{u2} β (fun (b : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (f b) (g b))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {g : β -> α}, (Continuous.{u2, u1} β α _inst_3 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_3 _inst_1 g) -> (IsClosed.{u2} β _inst_3 (setOf.{u2} β (fun (b : β) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f b) (g b))))
+Case conversion may be inaccurate. Consider using '#align is_closed_le isClosed_leₓ'. -/
 theorem isClosed_le [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
     IsClosed { b | f b ≤ g b } :=
   continuous_iff_isClosed.mp (hf.prod_mk hg) _ isClosed_le_prod
 #align is_closed_le isClosed_le
--/
 
-#print isClosed_le' /-
+/- warning: is_closed_le' -> isClosed_le' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] (a : α), IsClosed.{u1} α _inst_1 (setOf.{u1} α (fun (b : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] (a : α), IsClosed.{u1} α _inst_1 (setOf.{u1} α (fun (b : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b a))
+Case conversion may be inaccurate. Consider using '#align is_closed_le' isClosed_le'ₓ'. -/
 theorem isClosed_le' (a : α) : IsClosed { b | b ≤ a } :=
   isClosed_le continuous_id continuous_const
 #align is_closed_le' isClosed_le'
--/
 
 #print isClosed_Iic /-
 theorem isClosed_Iic {a : α} : IsClosed (Iic a) :=
@@ -165,11 +173,15 @@ theorem isClosed_Iic {a : α} : IsClosed (Iic a) :=
 #align is_closed_Iic isClosed_Iic
 -/
 
-#print isClosed_ge' /-
+/- warning: is_closed_ge' -> isClosed_ge' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] (a : α), IsClosed.{u1} α _inst_1 (setOf.{u1} α (fun (b : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] (a : α), IsClosed.{u1} α _inst_1 (setOf.{u1} α (fun (b : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a b))
+Case conversion may be inaccurate. Consider using '#align is_closed_ge' isClosed_ge'ₓ'. -/
 theorem isClosed_ge' (a : α) : IsClosed { b | a ≤ b } :=
   isClosed_le continuous_const continuous_id
 #align is_closed_ge' isClosed_ge'
--/
 
 #print isClosed_Ici /-
 theorem isClosed_Ici {a : α} : IsClosed (Ici a) :=
@@ -207,98 +219,148 @@ theorem closure_Ici (a : α) : closure (Ici a) = Ici a :=
 #align closure_Ici closure_Ici
 -/
 
-#print le_of_tendsto_of_tendsto /-
+/- warning: le_of_tendsto_of_tendsto -> le_of_tendsto_of_tendsto is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {g : β -> α} {b : Filter.{u2} β} {a₁ : α} {a₂ : α} [_inst_3 : Filter.NeBot.{u2} β b], (Filter.Tendsto.{u2, u1} β α f b (nhds.{u1} α _inst_1 a₁)) -> (Filter.Tendsto.{u2, u1} β α g b (nhds.{u1} α _inst_1 a₂)) -> (Filter.EventuallyLE.{u2, u1} β α (Preorder.toHasLe.{u1} α _inst_2) b f g) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a₁ a₂)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {g : β -> α} {b : Filter.{u2} β} {a₁ : α} {a₂ : α} [_inst_3 : Filter.NeBot.{u2} β b], (Filter.Tendsto.{u2, u1} β α f b (nhds.{u1} α _inst_1 a₁)) -> (Filter.Tendsto.{u2, u1} β α g b (nhds.{u1} α _inst_1 a₂)) -> (Filter.EventuallyLE.{u2, u1} β α (Preorder.toLE.{u1} α _inst_2) b f g) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a₁ a₂)
+Case conversion may be inaccurate. Consider using '#align le_of_tendsto_of_tendsto le_of_tendsto_of_tendstoₓ'. -/
 theorem le_of_tendsto_of_tendsto {f g : β → α} {b : Filter β} {a₁ a₂ : α} [NeBot b]
     (hf : Tendsto f b (𝓝 a₁)) (hg : Tendsto g b (𝓝 a₂)) (h : f ≤ᶠ[b] g) : a₁ ≤ a₂ :=
   have : Tendsto (fun b => (f b, g b)) b (𝓝 (a₁, a₂)) := by
     rw [nhds_prod_eq] <;> exact hf.prod_mk hg
   show (a₁, a₂) ∈ { p : α × α | p.1 ≤ p.2 } from t.isClosed_le'.mem_of_tendsto this h
 #align le_of_tendsto_of_tendsto le_of_tendsto_of_tendsto
--/
 
+/- warning: tendsto_le_of_eventually_le -> tendsto_le_of_eventuallyLE is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {g : β -> α} {b : Filter.{u2} β} {a₁ : α} {a₂ : α} [_inst_3 : Filter.NeBot.{u2} β b], (Filter.Tendsto.{u2, u1} β α f b (nhds.{u1} α _inst_1 a₁)) -> (Filter.Tendsto.{u2, u1} β α g b (nhds.{u1} α _inst_1 a₂)) -> (Filter.EventuallyLE.{u2, u1} β α (Preorder.toHasLe.{u1} α _inst_2) b f g) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a₁ a₂)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {g : β -> α} {b : Filter.{u2} β} {a₁ : α} {a₂ : α} [_inst_3 : Filter.NeBot.{u2} β b], (Filter.Tendsto.{u2, u1} β α f b (nhds.{u1} α _inst_1 a₁)) -> (Filter.Tendsto.{u2, u1} β α g b (nhds.{u1} α _inst_1 a₂)) -> (Filter.EventuallyLE.{u2, u1} β α (Preorder.toLE.{u1} α _inst_2) b f g) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a₁ a₂)
+Case conversion may be inaccurate. Consider using '#align tendsto_le_of_eventually_le tendsto_le_of_eventuallyLEₓ'. -/
 alias le_of_tendsto_of_tendsto ← tendsto_le_of_eventuallyLE
 #align tendsto_le_of_eventually_le tendsto_le_of_eventuallyLE
 
-#print le_of_tendsto_of_tendsto' /-
+/- warning: le_of_tendsto_of_tendsto' -> le_of_tendsto_of_tendsto' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {g : β -> α} {b : Filter.{u2} β} {a₁ : α} {a₂ : α} [_inst_3 : Filter.NeBot.{u2} β b], (Filter.Tendsto.{u2, u1} β α f b (nhds.{u1} α _inst_1 a₁)) -> (Filter.Tendsto.{u2, u1} β α g b (nhds.{u1} α _inst_1 a₂)) -> (forall (x : β), LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (f x) (g x)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a₁ a₂)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {g : β -> α} {b : Filter.{u2} β} {a₁ : α} {a₂ : α} [_inst_3 : Filter.NeBot.{u2} β b], (Filter.Tendsto.{u2, u1} β α f b (nhds.{u1} α _inst_1 a₁)) -> (Filter.Tendsto.{u2, u1} β α g b (nhds.{u1} α _inst_1 a₂)) -> (forall (x : β), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f x) (g x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a₁ a₂)
+Case conversion may be inaccurate. Consider using '#align le_of_tendsto_of_tendsto' le_of_tendsto_of_tendsto'ₓ'. -/
 theorem le_of_tendsto_of_tendsto' {f g : β → α} {b : Filter β} {a₁ a₂ : α} [NeBot b]
     (hf : Tendsto f b (𝓝 a₁)) (hg : Tendsto g b (𝓝 a₂)) (h : ∀ x, f x ≤ g x) : a₁ ≤ a₂ :=
   le_of_tendsto_of_tendsto hf hg (eventually_of_forall h)
 #align le_of_tendsto_of_tendsto' le_of_tendsto_of_tendsto'
--/
 
-#print le_of_tendsto /-
+/- warning: le_of_tendsto -> le_of_tendsto is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {a : α} {b : α} {x : Filter.{u2} β} [_inst_3 : Filter.NeBot.{u2} β x], (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) -> (Filter.Eventually.{u2} β (fun (c : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (f c) b) x) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a b)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {a : α} {b : α} {x : Filter.{u2} β} [_inst_3 : Filter.NeBot.{u2} β x], (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) -> (Filter.Eventually.{u2} β (fun (c : β) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f c) b) x) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a b)
+Case conversion may be inaccurate. Consider using '#align le_of_tendsto le_of_tendstoₓ'. -/
 theorem le_of_tendsto {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
     (h : ∀ᶠ c in x, f c ≤ b) : a ≤ b :=
   le_of_tendsto_of_tendsto limUnder tendsto_const_nhds h
 #align le_of_tendsto le_of_tendsto
--/
 
-#print le_of_tendsto' /-
+/- warning: le_of_tendsto' -> le_of_tendsto' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {a : α} {b : α} {x : Filter.{u2} β} [_inst_3 : Filter.NeBot.{u2} β x], (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) -> (forall (c : β), LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (f c) b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a b)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {a : α} {b : α} {x : Filter.{u2} β} [_inst_3 : Filter.NeBot.{u2} β x], (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) -> (forall (c : β), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f c) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a b)
+Case conversion may be inaccurate. Consider using '#align le_of_tendsto' le_of_tendsto'ₓ'. -/
 theorem le_of_tendsto' {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
     (h : ∀ c, f c ≤ b) : a ≤ b :=
   le_of_tendsto limUnder (eventually_of_forall h)
 #align le_of_tendsto' le_of_tendsto'
--/
 
-#print ge_of_tendsto /-
+/- warning: ge_of_tendsto -> ge_of_tendsto is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {a : α} {b : α} {x : Filter.{u2} β} [_inst_3 : Filter.NeBot.{u2} β x], (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) -> (Filter.Eventually.{u2} β (fun (c : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b (f c)) x) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b a)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {a : α} {b : α} {x : Filter.{u2} β} [_inst_3 : Filter.NeBot.{u2} β x], (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) -> (Filter.Eventually.{u2} β (fun (c : β) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (f c)) x) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b a)
+Case conversion may be inaccurate. Consider using '#align ge_of_tendsto ge_of_tendstoₓ'. -/
 theorem ge_of_tendsto {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
     (h : ∀ᶠ c in x, b ≤ f c) : b ≤ a :=
   le_of_tendsto_of_tendsto tendsto_const_nhds limUnder h
 #align ge_of_tendsto ge_of_tendsto
--/
 
-#print ge_of_tendsto' /-
+/- warning: ge_of_tendsto' -> ge_of_tendsto' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {a : α} {b : α} {x : Filter.{u2} β} [_inst_3 : Filter.NeBot.{u2} β x], (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) -> (forall (c : β), LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b (f c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) b a)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {a : α} {b : α} {x : Filter.{u2} β} [_inst_3 : Filter.NeBot.{u2} β x], (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) -> (forall (c : β), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b (f c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) b a)
+Case conversion may be inaccurate. Consider using '#align ge_of_tendsto' ge_of_tendsto'ₓ'. -/
 theorem ge_of_tendsto' {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
     (h : ∀ c, b ≤ f c) : b ≤ a :=
   ge_of_tendsto limUnder (eventually_of_forall h)
 #align ge_of_tendsto' ge_of_tendsto'
--/
 
-#print closure_le_eq /-
+/- warning: closure_le_eq -> closure_le_eq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {g : β -> α}, (Continuous.{u2, u1} β α _inst_3 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_3 _inst_1 g) -> (Eq.{succ u2} (Set.{u2} β) (closure.{u2} β _inst_3 (setOf.{u2} β (fun (b : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (f b) (g b)))) (setOf.{u2} β (fun (b : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (f b) (g b))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {g : β -> α}, (Continuous.{u2, u1} β α _inst_3 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_3 _inst_1 g) -> (Eq.{succ u2} (Set.{u2} β) (closure.{u2} β _inst_3 (setOf.{u2} β (fun (b : β) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f b) (g b)))) (setOf.{u2} β (fun (b : β) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f b) (g b))))
+Case conversion may be inaccurate. Consider using '#align closure_le_eq closure_le_eqₓ'. -/
 @[simp]
 theorem closure_le_eq [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
     closure { b | f b ≤ g b } = { b | f b ≤ g b } :=
   (isClosed_le hf hg).closure_eq
 #align closure_le_eq closure_le_eq
--/
 
-#print closure_lt_subset_le /-
+/- warning: closure_lt_subset_le -> closure_lt_subset_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {g : β -> α}, (Continuous.{u2, u1} β α _inst_3 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_3 _inst_1 g) -> (HasSubset.Subset.{u2} (Set.{u2} β) (Set.hasSubset.{u2} β) (closure.{u2} β _inst_3 (setOf.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (f b) (g b)))) (setOf.{u2} β (fun (b : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (f b) (g b))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {g : β -> α}, (Continuous.{u2, u1} β α _inst_3 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_3 _inst_1 g) -> (HasSubset.Subset.{u2} (Set.{u2} β) (Set.instHasSubsetSet.{u2} β) (closure.{u2} β _inst_3 (setOf.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (f b) (g b)))) (setOf.{u2} β (fun (b : β) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f b) (g b))))
+Case conversion may be inaccurate. Consider using '#align closure_lt_subset_le closure_lt_subset_leₓ'. -/
 theorem closure_lt_subset_le [TopologicalSpace β] {f g : β → α} (hf : Continuous f)
     (hg : Continuous g) : closure { b | f b < g b } ⊆ { b | f b ≤ g b } :=
   (closure_minimal fun x => le_of_lt) <| isClosed_le hf hg
 #align closure_lt_subset_le closure_lt_subset_le
--/
 
-#print ContinuousWithinAt.closure_le /-
+/- warning: continuous_within_at.closure_le -> ContinuousWithinAt.closure_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} {x : β}, (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (closure.{u2} β _inst_3 s)) -> (ContinuousWithinAt.{u2, u1} β α _inst_3 _inst_1 f s x) -> (ContinuousWithinAt.{u2, u1} β α _inst_3 _inst_1 g s x) -> (forall (y : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) y s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (f y) (g y))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (f x) (g x))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β} {x : β}, (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (closure.{u2} β _inst_3 s)) -> (ContinuousWithinAt.{u2, u1} β α _inst_3 _inst_1 f s x) -> (ContinuousWithinAt.{u2, u1} β α _inst_3 _inst_1 g s x) -> (forall (y : β), (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) y s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f y) (g y))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f x) (g x))
+Case conversion may be inaccurate. Consider using '#align continuous_within_at.closure_le ContinuousWithinAt.closure_leₓ'. -/
 theorem ContinuousWithinAt.closure_le [TopologicalSpace β] {f g : β → α} {s : Set β} {x : β}
     (hx : x ∈ closure s) (hf : ContinuousWithinAt f s x) (hg : ContinuousWithinAt g s x)
     (h : ∀ y ∈ s, f y ≤ g y) : f x ≤ g x :=
   show (f x, g x) ∈ { p : α × α | p.1 ≤ p.2 } from
     OrderClosedTopology.isClosed_le'.closure_subset ((hf.Prod hg).mem_closure hx h)
 #align continuous_within_at.closure_le ContinuousWithinAt.closure_le
--/
 
-#print IsClosed.isClosed_le /-
+/- warning: is_closed.is_closed_le -> IsClosed.isClosed_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β}, (IsClosed.{u2} β _inst_3 s) -> (ContinuousOn.{u2, u1} β α _inst_3 _inst_1 f s) -> (ContinuousOn.{u2, u1} β α _inst_3 _inst_1 g s) -> (IsClosed.{u2} β _inst_3 (Sep.sep.{u2, u2} β (Set.{u2} β) (Set.hasSep.{u2} β) (fun (x : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (f x) (g x)) s))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β}, (IsClosed.{u2} β _inst_3 s) -> (ContinuousOn.{u2, u1} β α _inst_3 _inst_1 f s) -> (ContinuousOn.{u2, u1} β α _inst_3 _inst_1 g s) -> (IsClosed.{u2} β _inst_3 (setOf.{u2} β (fun (x : β) => And (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f x) (g x)))))
+Case conversion may be inaccurate. Consider using '#align is_closed.is_closed_le IsClosed.isClosed_leₓ'. -/
 /-- If `s` is a closed set and two functions `f` and `g` are continuous on `s`,
 then the set `{x ∈ s | f x ≤ g x}` is a closed set. -/
 theorem IsClosed.isClosed_le [TopologicalSpace β] {f g : β → α} {s : Set β} (hs : IsClosed s)
     (hf : ContinuousOn f s) (hg : ContinuousOn g s) : IsClosed ({ x ∈ s | f x ≤ g x }) :=
   (hf.Prod hg).preimage_closed_of_closed hs OrderClosedTopology.isClosed_le'
 #align is_closed.is_closed_le IsClosed.isClosed_le
--/
 
-#print le_on_closure /-
+/- warning: le_on_closure -> le_on_closure is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β}, (forall (x : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (f x) (g x))) -> (ContinuousOn.{u2, u1} β α _inst_3 _inst_1 f (closure.{u2} β _inst_3 s)) -> (ContinuousOn.{u2, u1} β α _inst_3 _inst_1 g (closure.{u2} β _inst_3 s)) -> (forall {{x : β}}, (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x (closure.{u2} β _inst_3 s)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (f x) (g x)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {g : β -> α} {s : Set.{u2} β}, (forall (x : β), (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f x) (g x))) -> (ContinuousOn.{u2, u1} β α _inst_3 _inst_1 f (closure.{u2} β _inst_3 s)) -> (ContinuousOn.{u2, u1} β α _inst_3 _inst_1 g (closure.{u2} β _inst_3 s)) -> (forall {{x : β}}, (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x (closure.{u2} β _inst_3 s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f x) (g x)))
+Case conversion may be inaccurate. Consider using '#align le_on_closure le_on_closureₓ'. -/
 theorem le_on_closure [TopologicalSpace β] {f g : β → α} {s : Set β} (h : ∀ x ∈ s, f x ≤ g x)
     (hf : ContinuousOn f (closure s)) (hg : ContinuousOn g (closure s)) ⦃x⦄ (hx : x ∈ closure s) :
     f x ≤ g x :=
   have : s ⊆ { y ∈ closure s | f y ≤ g y } := fun y hy => ⟨subset_closure hy, h y hy⟩
   (closure_minimal this (isClosed_closure.isClosed_le hf hg) hx).2
 #align le_on_closure le_on_closure
--/
 
 /- warning: is_closed.epigraph -> IsClosed.epigraph is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {s : Set.{u2} β}, (IsClosed.{u2} β _inst_3 s) -> (ContinuousOn.{u2, u1} β α _inst_3 _inst_1 f s) -> (IsClosed.{max u2 u1} (Prod.{u2, u1} β α) (Prod.topologicalSpace.{u2, u1} β α _inst_3 _inst_1) (setOf.{max u2 u1} (Prod.{u2, u1} β α) (fun (p : Prod.{u2, u1} β α) => And (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) (Prod.fst.{u2, u1} β α p) s) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f (Prod.fst.{u2, u1} β α p)) (Prod.snd.{u2, u1} β α p)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {s : Set.{u2} β}, (IsClosed.{u2} β _inst_3 s) -> (ContinuousOn.{u2, u1} β α _inst_3 _inst_1 f s) -> (IsClosed.{max u2 u1} (Prod.{u2, u1} β α) (Prod.topologicalSpace.{u2, u1} β α _inst_3 _inst_1) (setOf.{max u2 u1} (Prod.{u2, u1} β α) (fun (p : Prod.{u2, u1} β α) => And (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) (Prod.fst.{u2, u1} β α p) s) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (f (Prod.fst.{u2, u1} β α p)) (Prod.snd.{u2, u1} β α p)))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {s : Set.{u2} β}, (IsClosed.{u2} β _inst_3 s) -> (ContinuousOn.{u2, u1} β α _inst_3 _inst_1 f s) -> (IsClosed.{max u1 u2} (Prod.{u2, u1} β α) (instTopologicalSpaceProd.{u2, u1} β α _inst_3 _inst_1) (setOf.{max u1 u2} (Prod.{u2, u1} β α) (fun (p : Prod.{u2, u1} β α) => And (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) (Prod.fst.{u2, u1} β α p) s) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f (Prod.fst.{u2, u1} β α p)) (Prod.snd.{u2, u1} β α p)))))
 Case conversion may be inaccurate. Consider using '#align is_closed.epigraph IsClosed.epigraphₓ'. -/
@@ -309,7 +371,7 @@ theorem IsClosed.epigraph [TopologicalSpace β] {f : β → α} {s : Set β} (hs
 
 /- warning: is_closed.hypograph -> IsClosed.hypograph is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {s : Set.{u2} β}, (IsClosed.{u2} β _inst_3 s) -> (ContinuousOn.{u2, u1} β α _inst_3 _inst_1 f s) -> (IsClosed.{max u2 u1} (Prod.{u2, u1} β α) (Prod.topologicalSpace.{u2, u1} β α _inst_3 _inst_1) (setOf.{max u2 u1} (Prod.{u2, u1} β α) (fun (p : Prod.{u2, u1} β α) => And (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) (Prod.fst.{u2, u1} β α p) s) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (Prod.snd.{u2, u1} β α p) (f (Prod.fst.{u2, u1} β α p))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {s : Set.{u2} β}, (IsClosed.{u2} β _inst_3 s) -> (ContinuousOn.{u2, u1} β α _inst_3 _inst_1 f s) -> (IsClosed.{max u2 u1} (Prod.{u2, u1} β α) (Prod.topologicalSpace.{u2, u1} β α _inst_3 _inst_1) (setOf.{max u2 u1} (Prod.{u2, u1} β α) (fun (p : Prod.{u2, u1} β α) => And (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) (Prod.fst.{u2, u1} β α p) s) (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (Prod.snd.{u2, u1} β α p) (f (Prod.fst.{u2, u1} β α p))))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_3 : TopologicalSpace.{u2} β] {f : β -> α} {s : Set.{u2} β}, (IsClosed.{u2} β _inst_3 s) -> (ContinuousOn.{u2, u1} β α _inst_3 _inst_1 f s) -> (IsClosed.{max u1 u2} (Prod.{u2, u1} β α) (instTopologicalSpaceProd.{u2, u1} β α _inst_3 _inst_1) (setOf.{max u1 u2} (Prod.{u2, u1} β α) (fun (p : Prod.{u2, u1} β α) => And (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) (Prod.fst.{u2, u1} β α p) s) (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (Prod.snd.{u2, u1} β α p) (f (Prod.fst.{u2, u1} β α p))))))
 Case conversion may be inaccurate. Consider using '#align is_closed.hypograph IsClosed.hypographₓ'. -/
@@ -320,11 +382,15 @@ theorem IsClosed.hypograph [TopologicalSpace β] {f : β → α} {s : Set β} (h
 
 omit t
 
-#print nhdsWithin_Ici_neBot /-
+/- warning: nhds_within_Ici_ne_bot -> nhdsWithin_Ici_neBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ici.{u1} α _inst_2 a)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ici.{u1} α _inst_2 a)))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Ici_ne_bot nhdsWithin_Ici_neBotₓ'. -/
 theorem nhdsWithin_Ici_neBot {a b : α} (H₂ : a ≤ b) : NeBot (𝓝[Ici a] b) :=
   nhdsWithin_neBot_of_mem H₂
 #align nhds_within_Ici_ne_bot nhdsWithin_Ici_neBot
--/
 
 #print nhdsWithin_Ici_self_neBot /-
 @[instance]
@@ -333,11 +399,15 @@ theorem nhdsWithin_Ici_self_neBot (a : α) : NeBot (𝓝[≥] a) :=
 #align nhds_within_Ici_self_ne_bot nhdsWithin_Ici_self_neBot
 -/
 
-#print nhdsWithin_Iic_neBot /-
+/- warning: nhds_within_Iic_ne_bot -> nhdsWithin_Iic_neBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 b)))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Iic_ne_bot nhdsWithin_Iic_neBotₓ'. -/
 theorem nhdsWithin_Iic_neBot {a b : α} (H : a ≤ b) : NeBot (𝓝[Iic b] a) :=
   nhdsWithin_neBot_of_mem H
 #align nhds_within_Iic_ne_bot nhdsWithin_Iic_neBot
--/
 
 #print nhdsWithin_Iic_self_neBot /-
 @[instance]
@@ -371,7 +441,7 @@ variable [TopologicalSpace α] [LinearOrder α] [OrderClosedTopology α]
 
 /- warning: is_open_lt_prod -> isOpen_lt_prod is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))], IsOpen.{u1} (Prod.{u1, u1} α α) (Prod.topologicalSpace.{u1, u1} α α _inst_1 _inst_1) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))], IsOpen.{u1} (Prod.{u1, u1} α α) (Prod.topologicalSpace.{u1, u1} α α _inst_1 _inst_1) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))], IsOpen.{u1} (Prod.{u1, u1} α α) (instTopologicalSpaceProd.{u1, u1} α α _inst_1 _inst_1) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)))
 Case conversion may be inaccurate. Consider using '#align is_open_lt_prod isOpen_lt_prodₓ'. -/
@@ -381,12 +451,16 @@ theorem isOpen_lt_prod : IsOpen { p : α × α | p.1 < p.2 } :=
   exact isClosed_le continuous_snd continuous_fst
 #align is_open_lt_prod isOpen_lt_prod
 
-#print isOpen_lt /-
+/- warning: is_open_lt -> isOpen_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : TopologicalSpace.{u2} β] {f : β -> α} {g : β -> α}, (Continuous.{u2, u1} β α _inst_4 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_4 _inst_1 g) -> (IsOpen.{u2} β _inst_4 (setOf.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f b) (g b))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : TopologicalSpace.{u2} β] {f : β -> α} {g : β -> α}, (Continuous.{u2, u1} β α _inst_4 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_4 _inst_1 g) -> (IsOpen.{u2} β _inst_4 (setOf.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f b) (g b))))
+Case conversion may be inaccurate. Consider using '#align is_open_lt isOpen_ltₓ'. -/
 theorem isOpen_lt [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
     IsOpen { b | f b < g b } := by
   simp [lt_iff_not_ge, -not_le] <;> exact (isClosed_le hg hf).isOpen_compl
 #align is_open_lt isOpen_lt
--/
 
 variable {a b : α}
 
@@ -435,81 +509,129 @@ theorem Ioo_subset_closure_interior : Ioo a b ⊆ closure (interior (Ioo a b)) :
 #align Ioo_subset_closure_interior Ioo_subset_closure_interior
 -/
 
-#print Iio_mem_nhds /-
+/- warning: Iio_mem_nhds -> Iio_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b) (nhds.{u1} α _inst_1 a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b) (nhds.{u1} α _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align Iio_mem_nhds Iio_mem_nhdsₓ'. -/
 theorem Iio_mem_nhds {a b : α} (h : a < b) : Iio b ∈ 𝓝 a :=
   IsOpen.mem_nhds isOpen_Iio h
 #align Iio_mem_nhds Iio_mem_nhds
--/
 
-#print Ioi_mem_nhds /-
+/- warning: Ioi_mem_nhds -> Ioi_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a) (nhds.{u1} α _inst_1 b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a) (nhds.{u1} α _inst_1 b))
+Case conversion may be inaccurate. Consider using '#align Ioi_mem_nhds Ioi_mem_nhdsₓ'. -/
 theorem Ioi_mem_nhds {a b : α} (h : a < b) : Ioi a ∈ 𝓝 b :=
   IsOpen.mem_nhds isOpen_Ioi h
 #align Ioi_mem_nhds Ioi_mem_nhds
--/
 
-#print Iic_mem_nhds /-
+/- warning: Iic_mem_nhds -> Iic_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b) (nhds.{u1} α _inst_1 a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b) (nhds.{u1} α _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align Iic_mem_nhds Iic_mem_nhdsₓ'. -/
 theorem Iic_mem_nhds {a b : α} (h : a < b) : Iic b ∈ 𝓝 a :=
   mem_of_superset (Iio_mem_nhds h) Iio_subset_Iic_self
 #align Iic_mem_nhds Iic_mem_nhds
--/
 
-#print Ici_mem_nhds /-
+/- warning: Ici_mem_nhds -> Ici_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a) (nhds.{u1} α _inst_1 b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a) (nhds.{u1} α _inst_1 b))
+Case conversion may be inaccurate. Consider using '#align Ici_mem_nhds Ici_mem_nhdsₓ'. -/
 theorem Ici_mem_nhds {a b : α} (h : a < b) : Ici a ∈ 𝓝 b :=
   mem_of_superset (Ioi_mem_nhds h) Ioi_subset_Ici_self
 #align Ici_mem_nhds Ici_mem_nhds
--/
 
-#print Ioo_mem_nhds /-
+/- warning: Ioo_mem_nhds -> Ioo_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α} {x : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a x) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x b) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) (nhds.{u1} α _inst_1 x))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α} {x : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a x) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x b) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) (nhds.{u1} α _inst_1 x))
+Case conversion may be inaccurate. Consider using '#align Ioo_mem_nhds Ioo_mem_nhdsₓ'. -/
 theorem Ioo_mem_nhds {a b x : α} (ha : a < x) (hb : x < b) : Ioo a b ∈ 𝓝 x :=
   IsOpen.mem_nhds isOpen_Ioo ⟨ha, hb⟩
 #align Ioo_mem_nhds Ioo_mem_nhds
--/
 
-#print Ioc_mem_nhds /-
+/- warning: Ioc_mem_nhds -> Ioc_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α} {x : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a x) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x b) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) (nhds.{u1} α _inst_1 x))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α} {x : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a x) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x b) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) (nhds.{u1} α _inst_1 x))
+Case conversion may be inaccurate. Consider using '#align Ioc_mem_nhds Ioc_mem_nhdsₓ'. -/
 theorem Ioc_mem_nhds {a b x : α} (ha : a < x) (hb : x < b) : Ioc a b ∈ 𝓝 x :=
   mem_of_superset (Ioo_mem_nhds ha hb) Ioo_subset_Ioc_self
 #align Ioc_mem_nhds Ioc_mem_nhds
--/
 
-#print Ico_mem_nhds /-
+/- warning: Ico_mem_nhds -> Ico_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α} {x : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a x) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x b) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) (nhds.{u1} α _inst_1 x))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α} {x : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a x) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x b) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) (nhds.{u1} α _inst_1 x))
+Case conversion may be inaccurate. Consider using '#align Ico_mem_nhds Ico_mem_nhdsₓ'. -/
 theorem Ico_mem_nhds {a b x : α} (ha : a < x) (hb : x < b) : Ico a b ∈ 𝓝 x :=
   mem_of_superset (Ioo_mem_nhds ha hb) Ioo_subset_Ico_self
 #align Ico_mem_nhds Ico_mem_nhds
--/
 
-#print Icc_mem_nhds /-
+/- warning: Icc_mem_nhds -> Icc_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α} {x : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a x) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x b) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) (nhds.{u1} α _inst_1 x))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α} {x : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a x) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x b) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) (nhds.{u1} α _inst_1 x))
+Case conversion may be inaccurate. Consider using '#align Icc_mem_nhds Icc_mem_nhdsₓ'. -/
 theorem Icc_mem_nhds {a b x : α} (ha : a < x) (hb : x < b) : Icc a b ∈ 𝓝 x :=
   mem_of_superset (Ioo_mem_nhds ha hb) Ioo_subset_Icc_self
 #align Icc_mem_nhds Icc_mem_nhds
--/
 
-#print eventually_lt_of_tendsto_lt /-
+/- warning: eventually_lt_of_tendsto_lt -> eventually_lt_of_tendsto_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {l : Filter.{u2} γ} {f : γ -> α} {u : α} {v : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) v u) -> (Filter.Tendsto.{u2, u1} γ α f l (nhds.{u1} α _inst_1 v)) -> (Filter.Eventually.{u2} γ (fun (a : γ) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f a) u) l)
+but is expected to have type
+  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {l : Filter.{u2} γ} {f : γ -> α} {u : α} {v : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) v u) -> (Filter.Tendsto.{u2, u1} γ α f l (nhds.{u1} α _inst_1 v)) -> (Filter.Eventually.{u2} γ (fun (a : γ) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f a) u) l)
+Case conversion may be inaccurate. Consider using '#align eventually_lt_of_tendsto_lt eventually_lt_of_tendsto_ltₓ'. -/
 theorem eventually_lt_of_tendsto_lt {l : Filter γ} {f : γ → α} {u v : α} (hv : v < u)
     (h : Filter.Tendsto f l (𝓝 v)) : ∀ᶠ a in l, f a < u :=
   tendsto_nhds.1 h (· < u) isOpen_Iio hv
 #align eventually_lt_of_tendsto_lt eventually_lt_of_tendsto_lt
--/
 
-#print eventually_gt_of_tendsto_gt /-
+/- warning: eventually_gt_of_tendsto_gt -> eventually_gt_of_tendsto_gt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {l : Filter.{u2} γ} {f : γ -> α} {u : α} {v : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) u v) -> (Filter.Tendsto.{u2, u1} γ α f l (nhds.{u1} α _inst_1 v)) -> (Filter.Eventually.{u2} γ (fun (a : γ) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) u (f a)) l)
+but is expected to have type
+  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {l : Filter.{u2} γ} {f : γ -> α} {u : α} {v : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) u v) -> (Filter.Tendsto.{u2, u1} γ α f l (nhds.{u1} α _inst_1 v)) -> (Filter.Eventually.{u2} γ (fun (a : γ) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) u (f a)) l)
+Case conversion may be inaccurate. Consider using '#align eventually_gt_of_tendsto_gt eventually_gt_of_tendsto_gtₓ'. -/
 theorem eventually_gt_of_tendsto_gt {l : Filter γ} {f : γ → α} {u v : α} (hv : u < v)
     (h : Filter.Tendsto f l (𝓝 v)) : ∀ᶠ a in l, u < f a :=
   tendsto_nhds.1 h (· > u) isOpen_Ioi hv
 #align eventually_gt_of_tendsto_gt eventually_gt_of_tendsto_gt
--/
 
-#print eventually_le_of_tendsto_lt /-
+/- warning: eventually_le_of_tendsto_lt -> eventually_le_of_tendsto_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {l : Filter.{u2} γ} {f : γ -> α} {u : α} {v : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) v u) -> (Filter.Tendsto.{u2, u1} γ α f l (nhds.{u1} α _inst_1 v)) -> (Filter.Eventually.{u2} γ (fun (a : γ) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f a) u) l)
+but is expected to have type
+  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {l : Filter.{u2} γ} {f : γ -> α} {u : α} {v : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) v u) -> (Filter.Tendsto.{u2, u1} γ α f l (nhds.{u1} α _inst_1 v)) -> (Filter.Eventually.{u2} γ (fun (a : γ) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f a) u) l)
+Case conversion may be inaccurate. Consider using '#align eventually_le_of_tendsto_lt eventually_le_of_tendsto_ltₓ'. -/
 theorem eventually_le_of_tendsto_lt {l : Filter γ} {f : γ → α} {u v : α} (hv : v < u)
     (h : Tendsto f l (𝓝 v)) : ∀ᶠ a in l, f a ≤ u :=
   (eventually_lt_of_tendsto_lt hv h).mono fun v => le_of_lt
 #align eventually_le_of_tendsto_lt eventually_le_of_tendsto_lt
--/
 
-#print eventually_ge_of_tendsto_gt /-
+/- warning: eventually_ge_of_tendsto_gt -> eventually_ge_of_tendsto_gt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {l : Filter.{u2} γ} {f : γ -> α} {u : α} {v : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) u v) -> (Filter.Tendsto.{u2, u1} γ α f l (nhds.{u1} α _inst_1 v)) -> (Filter.Eventually.{u2} γ (fun (a : γ) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) u (f a)) l)
+but is expected to have type
+  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {l : Filter.{u2} γ} {f : γ -> α} {u : α} {v : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) u v) -> (Filter.Tendsto.{u2, u1} γ α f l (nhds.{u1} α _inst_1 v)) -> (Filter.Eventually.{u2} γ (fun (a : γ) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) u (f a)) l)
+Case conversion may be inaccurate. Consider using '#align eventually_ge_of_tendsto_gt eventually_ge_of_tendsto_gtₓ'. -/
 theorem eventually_ge_of_tendsto_gt {l : Filter γ} {f : γ → α} {u v : α} (hv : u < v)
     (h : Tendsto f l (𝓝 v)) : ∀ᶠ a in l, u ≤ f a :=
   (eventually_gt_of_tendsto_gt hv h).mono fun v => le_of_lt
 #align eventually_ge_of_tendsto_gt eventually_ge_of_tendsto_gt
--/
 
 variable [TopologicalSpace γ]
 
@@ -553,37 +675,53 @@ theorem Icc_mem_nhdsWithin_Ioi {a b c : α} (H : b ∈ Ico a c) : Icc a c ∈ 
 #align Icc_mem_nhds_within_Ioi Icc_mem_nhdsWithin_Ioi
 -/
 
-#print nhdsWithin_Ioc_eq_nhdsWithin_Ioi /-
+/- warning: nhds_within_Ioc_eq_nhds_within_Ioi -> nhdsWithin_Ioc_eq_nhdsWithin_Ioi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Ioc_eq_nhds_within_Ioi nhdsWithin_Ioc_eq_nhdsWithin_Ioiₓ'. -/
 @[simp]
 theorem nhdsWithin_Ioc_eq_nhdsWithin_Ioi {a b : α} (h : a < b) : 𝓝[Ioc a b] a = 𝓝[>] a :=
   le_antisymm (nhdsWithin_mono _ Ioc_subset_Ioi_self) <|
     nhdsWithin_le_of_mem <| Ioc_mem_nhdsWithin_Ioi <| left_mem_Ico.2 h
 #align nhds_within_Ioc_eq_nhds_within_Ioi nhdsWithin_Ioc_eq_nhdsWithin_Ioi
--/
 
-#print nhdsWithin_Ioo_eq_nhdsWithin_Ioi /-
+/- warning: nhds_within_Ioo_eq_nhds_within_Ioi -> nhdsWithin_Ioo_eq_nhdsWithin_Ioi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Ioo_eq_nhds_within_Ioi nhdsWithin_Ioo_eq_nhdsWithin_Ioiₓ'. -/
 @[simp]
 theorem nhdsWithin_Ioo_eq_nhdsWithin_Ioi {a b : α} (h : a < b) : 𝓝[Ioo a b] a = 𝓝[>] a :=
   le_antisymm (nhdsWithin_mono _ Ioo_subset_Ioi_self) <|
     nhdsWithin_le_of_mem <| Ioo_mem_nhdsWithin_Ioi <| left_mem_Ico.2 h
 #align nhds_within_Ioo_eq_nhds_within_Ioi nhdsWithin_Ioo_eq_nhdsWithin_Ioi
--/
 
-#print continuousWithinAt_Ioc_iff_Ioi /-
+/- warning: continuous_within_at_Ioc_iff_Ioi -> continuousWithinAt_Ioc_iff_Ioi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] {a : α} {b : α} {f : α -> β}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Iff (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) a) (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a) a))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_5 : TopologicalSpace.{u2} β] {a : α} {b : α} {f : α -> β}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Iff (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) a) (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a) a))
+Case conversion may be inaccurate. Consider using '#align continuous_within_at_Ioc_iff_Ioi continuousWithinAt_Ioc_iff_Ioiₓ'. -/
 @[simp]
 theorem continuousWithinAt_Ioc_iff_Ioi [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Ioc a b) a ↔ ContinuousWithinAt f (Ioi a) a := by
   simp only [ContinuousWithinAt, nhdsWithin_Ioc_eq_nhdsWithin_Ioi h]
 #align continuous_within_at_Ioc_iff_Ioi continuousWithinAt_Ioc_iff_Ioi
--/
 
-#print continuousWithinAt_Ioo_iff_Ioi /-
+/- warning: continuous_within_at_Ioo_iff_Ioi -> continuousWithinAt_Ioo_iff_Ioi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] {a : α} {b : α} {f : α -> β}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Iff (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) a) (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a) a))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_5 : TopologicalSpace.{u2} β] {a : α} {b : α} {f : α -> β}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Iff (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) a) (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a) a))
+Case conversion may be inaccurate. Consider using '#align continuous_within_at_Ioo_iff_Ioi continuousWithinAt_Ioo_iff_Ioiₓ'. -/
 @[simp]
 theorem continuousWithinAt_Ioo_iff_Ioi [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Ioo a b) a ↔ ContinuousWithinAt f (Ioi a) a := by
   simp only [ContinuousWithinAt, nhdsWithin_Ioo_eq_nhdsWithin_Ioi h]
 #align continuous_within_at_Ioo_iff_Ioi continuousWithinAt_Ioo_iff_Ioi
--/
 
 /-!
 #### Left neighborhoods, point excluded
@@ -615,35 +753,51 @@ theorem Icc_mem_nhdsWithin_Iio {a b c : α} (H : b ∈ Ioc a c) : Icc a c ∈ 
 #align Icc_mem_nhds_within_Iio Icc_mem_nhdsWithin_Iio
 -/
 
-#print nhdsWithin_Ico_eq_nhdsWithin_Iio /-
+/- warning: nhds_within_Ico_eq_nhds_within_Iio -> nhdsWithin_Ico_eq_nhdsWithin_Iio is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 b (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 b (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Ico_eq_nhds_within_Iio nhdsWithin_Ico_eq_nhdsWithin_Iioₓ'. -/
 @[simp]
 theorem nhdsWithin_Ico_eq_nhdsWithin_Iio {a b : α} (h : a < b) : 𝓝[Ico a b] b = 𝓝[<] b := by
   simpa only [dual_Ioc] using nhdsWithin_Ioc_eq_nhdsWithin_Ioi h.dual
 #align nhds_within_Ico_eq_nhds_within_Iio nhdsWithin_Ico_eq_nhdsWithin_Iio
--/
 
-#print nhdsWithin_Ioo_eq_nhdsWithin_Iio /-
+/- warning: nhds_within_Ioo_eq_nhds_within_Iio -> nhdsWithin_Ioo_eq_nhdsWithin_Iio is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 b (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 b (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Ioo_eq_nhds_within_Iio nhdsWithin_Ioo_eq_nhdsWithin_Iioₓ'. -/
 @[simp]
 theorem nhdsWithin_Ioo_eq_nhdsWithin_Iio {a b : α} (h : a < b) : 𝓝[Ioo a b] b = 𝓝[<] b := by
   simpa only [dual_Ioo] using nhdsWithin_Ioo_eq_nhdsWithin_Ioi h.dual
 #align nhds_within_Ioo_eq_nhds_within_Iio nhdsWithin_Ioo_eq_nhdsWithin_Iio
--/
 
-#print continuousWithinAt_Ico_iff_Iio /-
+/- warning: continuous_within_at_Ico_iff_Iio -> continuousWithinAt_Ico_iff_Iio is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : TopologicalSpace.{u2} γ] {a : α} {b : α} {f : α -> γ}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Iff (ContinuousWithinAt.{u1, u2} α γ _inst_1 _inst_4 f (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) b) (ContinuousWithinAt.{u1, u2} α γ _inst_1 _inst_4 f (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b) b))
+but is expected to have type
+  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : TopologicalSpace.{u2} γ] {a : α} {b : α} {f : α -> γ}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Iff (ContinuousWithinAt.{u1, u2} α γ _inst_1 _inst_4 f (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) b) (ContinuousWithinAt.{u1, u2} α γ _inst_1 _inst_4 f (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b) b))
+Case conversion may be inaccurate. Consider using '#align continuous_within_at_Ico_iff_Iio continuousWithinAt_Ico_iff_Iioₓ'. -/
 @[simp]
 theorem continuousWithinAt_Ico_iff_Iio {a b : α} {f : α → γ} (h : a < b) :
     ContinuousWithinAt f (Ico a b) b ↔ ContinuousWithinAt f (Iio b) b := by
   simp only [ContinuousWithinAt, nhdsWithin_Ico_eq_nhdsWithin_Iio h]
 #align continuous_within_at_Ico_iff_Iio continuousWithinAt_Ico_iff_Iio
--/
 
-#print continuousWithinAt_Ioo_iff_Iio /-
+/- warning: continuous_within_at_Ioo_iff_Iio -> continuousWithinAt_Ioo_iff_Iio is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : TopologicalSpace.{u2} γ] {a : α} {b : α} {f : α -> γ}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Iff (ContinuousWithinAt.{u1, u2} α γ _inst_1 _inst_4 f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) b) (ContinuousWithinAt.{u1, u2} α γ _inst_1 _inst_4 f (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b) b))
+but is expected to have type
+  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : TopologicalSpace.{u2} γ] {a : α} {b : α} {f : α -> γ}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Iff (ContinuousWithinAt.{u1, u2} α γ _inst_1 _inst_4 f (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) b) (ContinuousWithinAt.{u1, u2} α γ _inst_1 _inst_4 f (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b) b))
+Case conversion may be inaccurate. Consider using '#align continuous_within_at_Ioo_iff_Iio continuousWithinAt_Ioo_iff_Iioₓ'. -/
 @[simp]
 theorem continuousWithinAt_Ioo_iff_Iio {a b : α} {f : α → γ} (h : a < b) :
     ContinuousWithinAt f (Ioo a b) b ↔ ContinuousWithinAt f (Iio b) b := by
   simp only [ContinuousWithinAt, nhdsWithin_Ioo_eq_nhdsWithin_Iio h]
 #align continuous_within_at_Ioo_iff_Iio continuousWithinAt_Ioo_iff_Iio
--/
 
 /-!
 #### Right neighborhoods, point included
@@ -675,37 +829,53 @@ theorem Icc_mem_nhdsWithin_Ici {a b c : α} (H : b ∈ Ico a c) : Icc a c ∈ 
 #align Icc_mem_nhds_within_Ici Icc_mem_nhdsWithin_Ici
 -/
 
-#print nhdsWithin_Icc_eq_nhdsWithin_Ici /-
+/- warning: nhds_within_Icc_eq_nhds_within_Ici -> nhdsWithin_Icc_eq_nhdsWithin_Ici is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Icc_eq_nhds_within_Ici nhdsWithin_Icc_eq_nhdsWithin_Iciₓ'. -/
 @[simp]
 theorem nhdsWithin_Icc_eq_nhdsWithin_Ici {a b : α} (h : a < b) : 𝓝[Icc a b] a = 𝓝[≥] a :=
   le_antisymm (nhdsWithin_mono _ Icc_subset_Ici_self) <|
     nhdsWithin_le_of_mem <| Icc_mem_nhdsWithin_Ici <| left_mem_Ico.2 h
 #align nhds_within_Icc_eq_nhds_within_Ici nhdsWithin_Icc_eq_nhdsWithin_Ici
--/
 
-#print nhdsWithin_Ico_eq_nhdsWithin_Ici /-
+/- warning: nhds_within_Ico_eq_nhds_within_Ici -> nhdsWithin_Ico_eq_nhdsWithin_Ici is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Ico_eq_nhds_within_Ici nhdsWithin_Ico_eq_nhdsWithin_Iciₓ'. -/
 @[simp]
 theorem nhdsWithin_Ico_eq_nhdsWithin_Ici {a b : α} (h : a < b) : 𝓝[Ico a b] a = 𝓝[≥] a :=
   le_antisymm (nhdsWithin_mono _ fun x => And.left) <|
     nhdsWithin_le_of_mem <| Ico_mem_nhdsWithin_Ici <| left_mem_Ico.2 h
 #align nhds_within_Ico_eq_nhds_within_Ici nhdsWithin_Ico_eq_nhdsWithin_Ici
--/
 
-#print continuousWithinAt_Icc_iff_Ici /-
+/- warning: continuous_within_at_Icc_iff_Ici -> continuousWithinAt_Icc_iff_Ici is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] {a : α} {b : α} {f : α -> β}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Iff (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) a) (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a) a))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_5 : TopologicalSpace.{u2} β] {a : α} {b : α} {f : α -> β}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Iff (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) a) (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a) a))
+Case conversion may be inaccurate. Consider using '#align continuous_within_at_Icc_iff_Ici continuousWithinAt_Icc_iff_Iciₓ'. -/
 @[simp]
 theorem continuousWithinAt_Icc_iff_Ici [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Icc a b) a ↔ ContinuousWithinAt f (Ici a) a := by
   simp only [ContinuousWithinAt, nhdsWithin_Icc_eq_nhdsWithin_Ici h]
 #align continuous_within_at_Icc_iff_Ici continuousWithinAt_Icc_iff_Ici
--/
 
-#print continuousWithinAt_Ico_iff_Ici /-
+/- warning: continuous_within_at_Ico_iff_Ici -> continuousWithinAt_Ico_iff_Ici is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] {a : α} {b : α} {f : α -> β}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Iff (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) a) (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a) a))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_5 : TopologicalSpace.{u2} β] {a : α} {b : α} {f : α -> β}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Iff (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) a) (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a) a))
+Case conversion may be inaccurate. Consider using '#align continuous_within_at_Ico_iff_Ici continuousWithinAt_Ico_iff_Iciₓ'. -/
 @[simp]
 theorem continuousWithinAt_Ico_iff_Ici [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Ico a b) a ↔ ContinuousWithinAt f (Ici a) a := by
   simp only [ContinuousWithinAt, nhdsWithin_Ico_eq_nhdsWithin_Ici h]
 #align continuous_within_at_Ico_iff_Ici continuousWithinAt_Ico_iff_Ici
--/
 
 /-!
 #### Left neighborhoods, point included
@@ -737,35 +907,51 @@ theorem Icc_mem_nhdsWithin_Iic {a b c : α} (H : b ∈ Ioc a c) : Icc a c ∈ 
 #align Icc_mem_nhds_within_Iic Icc_mem_nhdsWithin_Iic
 -/
 
-#print nhdsWithin_Icc_eq_nhdsWithin_Iic /-
+/- warning: nhds_within_Icc_eq_nhds_within_Iic -> nhdsWithin_Icc_eq_nhdsWithin_Iic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 b (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (nhdsWithin.{u1} α _inst_1 b (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 b (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (nhdsWithin.{u1} α _inst_1 b (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Icc_eq_nhds_within_Iic nhdsWithin_Icc_eq_nhdsWithin_Iicₓ'. -/
 @[simp]
 theorem nhdsWithin_Icc_eq_nhdsWithin_Iic {a b : α} (h : a < b) : 𝓝[Icc a b] b = 𝓝[≤] b := by
   simpa only [dual_Icc] using nhdsWithin_Icc_eq_nhdsWithin_Ici h.dual
 #align nhds_within_Icc_eq_nhds_within_Iic nhdsWithin_Icc_eq_nhdsWithin_Iic
--/
 
-#print nhdsWithin_Ioc_eq_nhdsWithin_Iic /-
+/- warning: nhds_within_Ioc_eq_nhds_within_Iic -> nhdsWithin_Ioc_eq_nhdsWithin_Iic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 b (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (nhdsWithin.{u1} α _inst_1 b (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 b (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (nhdsWithin.{u1} α _inst_1 b (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Ioc_eq_nhds_within_Iic nhdsWithin_Ioc_eq_nhdsWithin_Iicₓ'. -/
 @[simp]
 theorem nhdsWithin_Ioc_eq_nhdsWithin_Iic {a b : α} (h : a < b) : 𝓝[Ioc a b] b = 𝓝[≤] b := by
   simpa only [dual_Ico] using nhdsWithin_Ico_eq_nhdsWithin_Ici h.dual
 #align nhds_within_Ioc_eq_nhds_within_Iic nhdsWithin_Ioc_eq_nhdsWithin_Iic
--/
 
-#print continuousWithinAt_Icc_iff_Iic /-
+/- warning: continuous_within_at_Icc_iff_Iic -> continuousWithinAt_Icc_iff_Iic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] {a : α} {b : α} {f : α -> β}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Iff (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) b) (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b) b))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_5 : TopologicalSpace.{u2} β] {a : α} {b : α} {f : α -> β}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Iff (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) b) (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b) b))
+Case conversion may be inaccurate. Consider using '#align continuous_within_at_Icc_iff_Iic continuousWithinAt_Icc_iff_Iicₓ'. -/
 @[simp]
 theorem continuousWithinAt_Icc_iff_Iic [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Icc a b) b ↔ ContinuousWithinAt f (Iic b) b := by
   simp only [ContinuousWithinAt, nhdsWithin_Icc_eq_nhdsWithin_Iic h]
 #align continuous_within_at_Icc_iff_Iic continuousWithinAt_Icc_iff_Iic
--/
 
-#print continuousWithinAt_Ioc_iff_Iic /-
+/- warning: continuous_within_at_Ioc_iff_Iic -> continuousWithinAt_Ioc_iff_Iic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : TopologicalSpace.{u2} β] {a : α} {b : α} {f : α -> β}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Iff (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) b) (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b) b))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_5 : TopologicalSpace.{u2} β] {a : α} {b : α} {f : α -> β}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Iff (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) b) (ContinuousWithinAt.{u1, u2} α β _inst_1 _inst_5 f (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b) b))
+Case conversion may be inaccurate. Consider using '#align continuous_within_at_Ioc_iff_Iic continuousWithinAt_Ioc_iff_Iicₓ'. -/
 @[simp]
 theorem continuousWithinAt_Ioc_iff_Iic [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
     ContinuousWithinAt f (Ioc a b) b ↔ ContinuousWithinAt f (Iic b) b := by
   simp only [ContinuousWithinAt, nhdsWithin_Ioc_eq_nhdsWithin_Iic h]
 #align continuous_within_at_Ioc_iff_Iic continuousWithinAt_Ioc_iff_Iic
--/
 
 end LinearOrder
 
@@ -777,14 +963,23 @@ section
 
 variable [TopologicalSpace β]
 
-#print lt_subset_interior_le /-
+/- warning: lt_subset_interior_le -> lt_subset_interior_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {f : β -> α} {g : β -> α} [_inst_4 : TopologicalSpace.{u2} β], (Continuous.{u2, u1} β α _inst_4 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_4 _inst_1 g) -> (HasSubset.Subset.{u2} (Set.{u2} β) (Set.hasSubset.{u2} β) (setOf.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f b) (g b))) (interior.{u2} β _inst_4 (setOf.{u2} β (fun (b : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f b) (g b)))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {f : β -> α} {g : β -> α} [_inst_4 : TopologicalSpace.{u2} β], (Continuous.{u2, u1} β α _inst_4 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_4 _inst_1 g) -> (HasSubset.Subset.{u2} (Set.{u2} β) (Set.instHasSubsetSet.{u2} β) (setOf.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f b) (g b))) (interior.{u2} β _inst_4 (setOf.{u2} β (fun (b : β) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f b) (g b)))))
+Case conversion may be inaccurate. Consider using '#align lt_subset_interior_le lt_subset_interior_leₓ'. -/
 theorem lt_subset_interior_le (hf : Continuous f) (hg : Continuous g) :
     { b | f b < g b } ⊆ interior { b | f b ≤ g b } :=
   (interior_maximal fun p => le_of_lt) <| isOpen_lt hf hg
 #align lt_subset_interior_le lt_subset_interior_le
--/
 
-#print frontier_le_subset_eq /-
+/- warning: frontier_le_subset_eq -> frontier_le_subset_eq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {f : β -> α} {g : β -> α} [_inst_4 : TopologicalSpace.{u2} β], (Continuous.{u2, u1} β α _inst_4 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_4 _inst_1 g) -> (HasSubset.Subset.{u2} (Set.{u2} β) (Set.hasSubset.{u2} β) (frontier.{u2} β _inst_4 (setOf.{u2} β (fun (b : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f b) (g b)))) (setOf.{u2} β (fun (b : β) => Eq.{succ u1} α (f b) (g b))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {f : β -> α} {g : β -> α} [_inst_4 : TopologicalSpace.{u2} β], (Continuous.{u2, u1} β α _inst_4 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_4 _inst_1 g) -> (HasSubset.Subset.{u2} (Set.{u2} β) (Set.instHasSubsetSet.{u2} β) (frontier.{u2} β _inst_4 (setOf.{u2} β (fun (b : β) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f b) (g b)))) (setOf.{u2} β (fun (b : β) => Eq.{succ u1} α (f b) (g b))))
+Case conversion may be inaccurate. Consider using '#align frontier_le_subset_eq frontier_le_subset_eqₓ'. -/
 theorem frontier_le_subset_eq (hf : Continuous f) (hg : Continuous g) :
     frontier { b | f b ≤ g b } ⊆ { b | f b = g b } :=
   by
@@ -793,7 +988,6 @@ theorem frontier_le_subset_eq (hf : Continuous f) (hg : Continuous g) :
   refine' le_antisymm hb₁ (closure_lt_subset_le hg hf _)
   convert hb₂ using 2; simp only [not_le.symm]; rfl
 #align frontier_le_subset_eq frontier_le_subset_eq
--/
 
 #print frontier_Iic_subset /-
 theorem frontier_Iic_subset (a : α) : frontier (Iic a) ⊆ {a} :=
@@ -807,14 +1001,23 @@ theorem frontier_Ici_subset (a : α) : frontier (Ici a) ⊆ {a} :=
 #align frontier_Ici_subset frontier_Ici_subset
 -/
 
-#print frontier_lt_subset_eq /-
+/- warning: frontier_lt_subset_eq -> frontier_lt_subset_eq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {f : β -> α} {g : β -> α} [_inst_4 : TopologicalSpace.{u2} β], (Continuous.{u2, u1} β α _inst_4 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_4 _inst_1 g) -> (HasSubset.Subset.{u2} (Set.{u2} β) (Set.hasSubset.{u2} β) (frontier.{u2} β _inst_4 (setOf.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f b) (g b)))) (setOf.{u2} β (fun (b : β) => Eq.{succ u1} α (f b) (g b))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {f : β -> α} {g : β -> α} [_inst_4 : TopologicalSpace.{u2} β], (Continuous.{u2, u1} β α _inst_4 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_4 _inst_1 g) -> (HasSubset.Subset.{u2} (Set.{u2} β) (Set.instHasSubsetSet.{u2} β) (frontier.{u2} β _inst_4 (setOf.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f b) (g b)))) (setOf.{u2} β (fun (b : β) => Eq.{succ u1} α (f b) (g b))))
+Case conversion may be inaccurate. Consider using '#align frontier_lt_subset_eq frontier_lt_subset_eqₓ'. -/
 theorem frontier_lt_subset_eq (hf : Continuous f) (hg : Continuous g) :
     frontier { b | f b < g b } ⊆ { b | f b = g b } := by
   rw [← frontier_compl] <;> convert frontier_le_subset_eq hg hf <;> simp [ext_iff, eq_comm]
 #align frontier_lt_subset_eq frontier_lt_subset_eq
--/
 
-#print continuous_if_le /-
+/- warning: continuous_if_le -> continuous_if_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {f : β -> α} {g : β -> α} [_inst_4 : TopologicalSpace.{u2} β] [_inst_5 : TopologicalSpace.{u3} γ] [_inst_6 : forall (x : β), Decidable (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f x) (g x))] {f' : β -> γ} {g' : β -> γ}, (Continuous.{u2, u1} β α _inst_4 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_4 _inst_1 g) -> (ContinuousOn.{u2, u3} β γ _inst_4 _inst_5 f' (setOf.{u2} β (fun (x : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f x) (g x)))) -> (ContinuousOn.{u2, u3} β γ _inst_4 _inst_5 g' (setOf.{u2} β (fun (x : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (g x) (f x)))) -> (forall (x : β), (Eq.{succ u1} α (f x) (g x)) -> (Eq.{succ u3} γ (f' x) (g' x))) -> (Continuous.{u2, u3} β γ _inst_4 _inst_5 (fun (x : β) => ite.{succ u3} γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f x) (g x)) (_inst_6 x) (f' x) (g' x)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {f : β -> α} {g : β -> α} [_inst_4 : TopologicalSpace.{u2} β] [_inst_5 : TopologicalSpace.{u3} γ] [_inst_6 : forall (x : β), Decidable (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f x) (g x))] {f' : β -> γ} {g' : β -> γ}, (Continuous.{u2, u1} β α _inst_4 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_4 _inst_1 g) -> (ContinuousOn.{u2, u3} β γ _inst_4 _inst_5 f' (setOf.{u2} β (fun (x : β) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f x) (g x)))) -> (ContinuousOn.{u2, u3} β γ _inst_4 _inst_5 g' (setOf.{u2} β (fun (x : β) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (g x) (f x)))) -> (forall (x : β), (Eq.{succ u1} α (f x) (g x)) -> (Eq.{succ u3} γ (f' x) (g' x))) -> (Continuous.{u2, u3} β γ _inst_4 _inst_5 (fun (x : β) => ite.{succ u3} γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f x) (g x)) (_inst_6 x) (f' x) (g' x)))
+Case conversion may be inaccurate. Consider using '#align continuous_if_le continuous_if_leₓ'. -/
 theorem continuous_if_le [TopologicalSpace γ] [∀ x, Decidable (f x ≤ g x)] {f' g' : β → γ}
     (hf : Continuous f) (hg : Continuous g) (hf' : ContinuousOn f' { x | f x ≤ g x })
     (hg' : ContinuousOn g' { x | g x ≤ f x }) (hfg : ∀ x, f x = g x → f' x = g' x) :
@@ -825,17 +1028,25 @@ theorem continuous_if_le [TopologicalSpace γ] [∀ x, Decidable (f x ≤ g x)]
   · simp only [not_le]
     exact closure_lt_subset_le hg hf
 #align continuous_if_le continuous_if_le
--/
 
-#print Continuous.if_le /-
+/- warning: continuous.if_le -> Continuous.if_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {f : β -> α} {g : β -> α} [_inst_4 : TopologicalSpace.{u2} β] [_inst_5 : TopologicalSpace.{u3} γ] [_inst_6 : forall (x : β), Decidable (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f x) (g x))] {f' : β -> γ} {g' : β -> γ}, (Continuous.{u2, u3} β γ _inst_4 _inst_5 f') -> (Continuous.{u2, u3} β γ _inst_4 _inst_5 g') -> (Continuous.{u2, u1} β α _inst_4 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_4 _inst_1 g) -> (forall (x : β), (Eq.{succ u1} α (f x) (g x)) -> (Eq.{succ u3} γ (f' x) (g' x))) -> (Continuous.{u2, u3} β γ _inst_4 _inst_5 (fun (x : β) => ite.{succ u3} γ (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f x) (g x)) (_inst_6 x) (f' x) (g' x)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {f : β -> α} {g : β -> α} [_inst_4 : TopologicalSpace.{u2} β] [_inst_5 : TopologicalSpace.{u3} γ] [_inst_6 : forall (x : β), Decidable (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f x) (g x))] {f' : β -> γ} {g' : β -> γ}, (Continuous.{u2, u3} β γ _inst_4 _inst_5 f') -> (Continuous.{u2, u3} β γ _inst_4 _inst_5 g') -> (Continuous.{u2, u1} β α _inst_4 _inst_1 f) -> (Continuous.{u2, u1} β α _inst_4 _inst_1 g) -> (forall (x : β), (Eq.{succ u1} α (f x) (g x)) -> (Eq.{succ u3} γ (f' x) (g' x))) -> (Continuous.{u2, u3} β γ _inst_4 _inst_5 (fun (x : β) => ite.{succ u3} γ (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f x) (g x)) (_inst_6 x) (f' x) (g' x)))
+Case conversion may be inaccurate. Consider using '#align continuous.if_le Continuous.if_leₓ'. -/
 theorem Continuous.if_le [TopologicalSpace γ] [∀ x, Decidable (f x ≤ g x)] {f' g' : β → γ}
     (hf' : Continuous f') (hg' : Continuous g') (hf : Continuous f) (hg : Continuous g)
     (hfg : ∀ x, f x = g x → f' x = g' x) : Continuous fun x => if f x ≤ g x then f' x else g' x :=
   continuous_if_le hf hg hf'.ContinuousOn hg'.ContinuousOn hfg
 #align continuous.if_le Continuous.if_le
--/
 
-#print Filter.Tendsto.eventually_lt /-
+/- warning: tendsto.eventually_lt -> Filter.Tendsto.eventually_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {l : Filter.{u2} γ} {f : γ -> α} {g : γ -> α} {y : α} {z : α}, (Filter.Tendsto.{u2, u1} γ α f l (nhds.{u1} α _inst_1 y)) -> (Filter.Tendsto.{u2, u1} γ α g l (nhds.{u1} α _inst_1 z)) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) y z) -> (Filter.Eventually.{u2} γ (fun (x : γ) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f x) (g x)) l)
+but is expected to have type
+  forall {α : Type.{u1}} {γ : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {l : Filter.{u2} γ} {f : γ -> α} {g : γ -> α} {y : α} {z : α}, (Filter.Tendsto.{u2, u1} γ α f l (nhds.{u1} α _inst_1 y)) -> (Filter.Tendsto.{u2, u1} γ α g l (nhds.{u1} α _inst_1 z)) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) y z) -> (Filter.Eventually.{u2} γ (fun (x : γ) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f x) (g x)) l)
+Case conversion may be inaccurate. Consider using '#align tendsto.eventually_lt Filter.Tendsto.eventually_ltₓ'. -/
 theorem Filter.Tendsto.eventually_lt {l : Filter γ} {f g : γ → α} {y z : α} (hf : Tendsto f l (𝓝 y))
     (hg : Tendsto g l (𝓝 z)) (hyz : y < z) : ∀ᶠ x in l, f x < g x :=
   by
@@ -847,14 +1058,17 @@ theorem Filter.Tendsto.eventually_lt {l : Filter γ} {f g : γ → α} {y z : α
     filter_upwards [hf (Iio_mem_nhds hyw), hg (Ioi_mem_nhds hwz)]
     exact fun x => lt_trans
 #align tendsto.eventually_lt Filter.Tendsto.eventually_lt
--/
 
-#print ContinuousAt.eventually_lt /-
+/- warning: continuous_at.eventually_lt -> ContinuousAt.eventually_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {f : β -> α} {g : β -> α} [_inst_4 : TopologicalSpace.{u2} β] {x₀ : β}, (ContinuousAt.{u2, u1} β α _inst_4 _inst_1 f x₀) -> (ContinuousAt.{u2, u1} β α _inst_4 _inst_1 g x₀) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f x₀) (g x₀)) -> (Filter.Eventually.{u2} β (fun (x : β) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (f x) (g x)) (nhds.{u2} β _inst_4 x₀))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {f : β -> α} {g : β -> α} [_inst_4 : TopologicalSpace.{u2} β] {x₀ : β}, (ContinuousAt.{u2, u1} β α _inst_4 _inst_1 f x₀) -> (ContinuousAt.{u2, u1} β α _inst_4 _inst_1 g x₀) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f x₀) (g x₀)) -> (Filter.Eventually.{u2} β (fun (x : β) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (f x) (g x)) (nhds.{u2} β _inst_4 x₀))
+Case conversion may be inaccurate. Consider using '#align continuous_at.eventually_lt ContinuousAt.eventually_ltₓ'. -/
 theorem ContinuousAt.eventually_lt {x₀ : β} (hf : ContinuousAt f x₀) (hg : ContinuousAt g x₀)
     (hfg : f x₀ < g x₀) : ∀ᶠ x in 𝓝 x₀, f x < g x :=
   Filter.Tendsto.eventually_lt hf hg hfg
 #align continuous_at.eventually_lt ContinuousAt.eventually_lt
--/
 
 /- warning: continuous.min -> Continuous.min is a dubious translation:
 lean 3 declaration is
@@ -1024,7 +1238,7 @@ theorem Filter.tendsto_nhds_min_left {l : Filter β} {a : α} (h : Tendsto f l (
 
 /- warning: dense.exists_lt -> Dense.exists_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) y x)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) y x)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) y x)))
 Case conversion may be inaccurate. Consider using '#align dense.exists_lt Dense.exists_ltₓ'. -/
@@ -1034,7 +1248,7 @@ theorem Dense.exists_lt [NoMinOrder α] {s : Set α} (hs : Dense s) (x : α) : 
 
 /- warning: dense.exists_gt -> Dense.exists_gt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x y)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x y)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x y)))
 Case conversion may be inaccurate. Consider using '#align dense.exists_gt Dense.exists_gtₓ'. -/
@@ -1044,7 +1258,7 @@ theorem Dense.exists_gt [NoMaxOrder α] {s : Set α} (hs : Dense s) (x : α) : 
 
 /- warning: dense.exists_le -> Dense.exists_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) y x)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) y x)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) y x)))
 Case conversion may be inaccurate. Consider using '#align dense.exists_le Dense.exists_leₓ'. -/
@@ -1054,7 +1268,7 @@ theorem Dense.exists_le [NoMinOrder α] {s : Set α} (hs : Dense s) (x : α) : 
 
 /- warning: dense.exists_ge -> Dense.exists_ge is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x y)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x y)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x y)))
 Case conversion may be inaccurate. Consider using '#align dense.exists_ge Dense.exists_geₓ'. -/
@@ -1064,7 +1278,7 @@ theorem Dense.exists_ge [NoMaxOrder α] {s : Set α} (hs : Dense s) (x : α) : 
 
 /- warning: dense.exists_le' -> Dense.exists_le' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), (IsBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s)) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) y x)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), (IsBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s)) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) y x)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), (IsBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) y x)))
 Case conversion may be inaccurate. Consider using '#align dense.exists_le' Dense.exists_le'ₓ'. -/
@@ -1079,7 +1293,7 @@ theorem Dense.exists_le' {s : Set α} (hs : Dense s) (hbot : ∀ x, IsBot x →
 
 /- warning: dense.exists_ge' -> Dense.exists_ge' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), (IsTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s)) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x y)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), (IsTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s)) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x y)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall (x : α), (IsTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)) -> (forall (x : α), Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x y)))
 Case conversion may be inaccurate. Consider using '#align dense.exists_ge' Dense.exists_ge'ₓ'. -/
@@ -1090,7 +1304,7 @@ theorem Dense.exists_ge' {s : Set α} (hs : Dense s) (htop : ∀ x, IsTop x →
 
 /- warning: dense.exists_between -> Dense.exists_between is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall {x : α} {y : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x y) -> (Exists.{succ u1} α (fun (z : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) z s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) z s) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) z (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) x y)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall {x : α} {y : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x y) -> (Exists.{succ u1} α (fun (z : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) z s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) z s) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) z (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) x y)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {s : Set.{u1} α}, (Dense.{u1} α _inst_1 s) -> (forall {x : α} {y : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x y) -> (Exists.{succ u1} α (fun (z : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) z s) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) z (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) x y)))))
 Case conversion may be inaccurate. Consider using '#align dense.exists_between Dense.exists_betweenₓ'. -/
@@ -1226,41 +1440,65 @@ theorem isOpen_iff_generate_intervals {s : Set α} :
 #align is_open_iff_generate_intervals isOpen_iff_generate_intervals
 -/
 
-#print isOpen_lt' /-
+/- warning: is_open_lt' -> isOpen_lt' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), IsOpen.{u1} α _inst_1 (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), IsOpen.{u1} α _inst_1 (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b))
+Case conversion may be inaccurate. Consider using '#align is_open_lt' isOpen_lt'ₓ'. -/
 theorem isOpen_lt' (a : α) : IsOpen { b : α | a < b } := by
   rw [@isOpen_iff_generate_intervals α _ _ t] <;> exact generate_open.basic _ ⟨a, Or.inl rfl⟩
 #align is_open_lt' isOpen_lt'
--/
 
-#print isOpen_gt' /-
+/- warning: is_open_gt' -> isOpen_gt' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), IsOpen.{u1} α _inst_1 (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) b a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), IsOpen.{u1} α _inst_1 (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) b a))
+Case conversion may be inaccurate. Consider using '#align is_open_gt' isOpen_gt'ₓ'. -/
 theorem isOpen_gt' (a : α) : IsOpen { b : α | b < a } := by
   rw [@isOpen_iff_generate_intervals α _ _ t] <;> exact generate_open.basic _ ⟨a, Or.inr rfl⟩
 #align is_open_gt' isOpen_gt'
--/
 
-#print lt_mem_nhds /-
+/- warning: lt_mem_nhds -> lt_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a x) (nhds.{u1} α _inst_1 b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a x) (nhds.{u1} α _inst_1 b))
+Case conversion may be inaccurate. Consider using '#align lt_mem_nhds lt_mem_nhdsₓ'. -/
 theorem lt_mem_nhds {a b : α} (h : a < b) : ∀ᶠ x in 𝓝 b, a < x :=
   IsOpen.mem_nhds (isOpen_lt' _) h
 #align lt_mem_nhds lt_mem_nhds
--/
 
-#print le_mem_nhds /-
+/- warning: le_mem_nhds -> le_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a x) (nhds.{u1} α _inst_1 b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a x) (nhds.{u1} α _inst_1 b))
+Case conversion may be inaccurate. Consider using '#align le_mem_nhds le_mem_nhdsₓ'. -/
 theorem le_mem_nhds {a b : α} (h : a < b) : ∀ᶠ x in 𝓝 b, a ≤ x :=
   (𝓝 b).sets_of_superset (lt_mem_nhds h) fun b hb => le_of_lt hb
 #align le_mem_nhds le_mem_nhds
--/
 
-#print gt_mem_nhds /-
+/- warning: gt_mem_nhds -> gt_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) x b) (nhds.{u1} α _inst_1 a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) x b) (nhds.{u1} α _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align gt_mem_nhds gt_mem_nhdsₓ'. -/
 theorem gt_mem_nhds {a b : α} (h : a < b) : ∀ᶠ x in 𝓝 a, x < b :=
   IsOpen.mem_nhds (isOpen_gt' _) h
 #align gt_mem_nhds gt_mem_nhds
--/
 
-#print ge_mem_nhds /-
+/- warning: ge_mem_nhds -> ge_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) x b) (nhds.{u1} α _inst_1 a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) x b) (nhds.{u1} α _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align ge_mem_nhds ge_mem_nhdsₓ'. -/
 theorem ge_mem_nhds {a b : α} (h : a < b) : ∀ᶠ x in 𝓝 a, x ≤ b :=
   (𝓝 a).sets_of_superset (gt_mem_nhds h) fun b hb => le_of_lt hb
 #align ge_mem_nhds ge_mem_nhds
--/
 
 /- warning: nhds_eq_order -> nhds_eq_order is a dubious translation:
 lean 3 declaration is
@@ -1282,12 +1520,16 @@ theorem nhds_eq_order (a : α) : 𝓝 a = (⨅ b ∈ Iio a, 𝓟 (Ioi b)) ⊓ 
             | _, h, Or.inr rfl => inf_le_of_right_le <| iInf_le_of_le b <| iInf_le _ h)
 #align nhds_eq_order nhds_eq_order
 
-#print tendsto_order /-
+/- warning: tendsto_order -> tendsto_order is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {a : α} {x : Filter.{u2} β}, Iff (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) (And (forall (a' : α), (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a' a) -> (Filter.Eventually.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a' (f b)) x)) (forall (a' : α), (GT.gt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a' a) -> (Filter.Eventually.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (f b) a') x)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {a : α} {x : Filter.{u2} β}, Iff (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) (And (forall (a' : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a' a) -> (Filter.Eventually.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a' (f b)) x)) (forall (a' : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α _inst_2) a' a) -> (Filter.Eventually.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (f b) a') x)))
+Case conversion may be inaccurate. Consider using '#align tendsto_order tendsto_orderₓ'. -/
 theorem tendsto_order {f : β → α} {a : α} {x : Filter β} :
     Tendsto f x (𝓝 a) ↔ (∀ a' < a, ∀ᶠ b in x, a' < f b) ∧ ∀ a' > a, ∀ᶠ b in x, f b < a' := by
   simp [nhds_eq_order a, tendsto_inf, tendsto_infi, tendsto_principal]
 #align tendsto_order tendsto_order
--/
 
 #print tendstoIccClassNhds /-
 instance tendstoIccClassNhds (a : α) : TendstoIxxClass Icc (𝓝 a) (𝓝 a) :=
@@ -1319,7 +1561,12 @@ instance tendstoIooClassNhds (a : α) : TendstoIxxClass Ioo (𝓝 a) (𝓝 a) :=
 #align tendsto_Ioo_class_nhds tendstoIooClassNhds
 -/
 
-#print tendsto_of_tendsto_of_tendsto_of_le_of_le' /-
+/- warning: tendsto_of_tendsto_of_tendsto_of_le_of_le' -> tendsto_of_tendsto_of_tendsto_of_le_of_le' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {g : β -> α} {h : β -> α} {b : Filter.{u2} β} {a : α}, (Filter.Tendsto.{u2, u1} β α g b (nhds.{u1} α _inst_1 a)) -> (Filter.Tendsto.{u2, u1} β α h b (nhds.{u1} α _inst_1 a)) -> (Filter.Eventually.{u2} β (fun (b : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (g b) (f b)) b) -> (Filter.Eventually.{u2} β (fun (b : β) => LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (f b) (h b)) b) -> (Filter.Tendsto.{u2, u1} β α f b (nhds.{u1} α _inst_1 a))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {g : β -> α} {h : β -> α} {b : Filter.{u2} β} {a : α}, (Filter.Tendsto.{u2, u1} β α g b (nhds.{u1} α _inst_1 a)) -> (Filter.Tendsto.{u2, u1} β α h b (nhds.{u1} α _inst_1 a)) -> (Filter.Eventually.{u2} β (fun (b : β) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (g b) (f b)) b) -> (Filter.Eventually.{u2} β (fun (b : β) => LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f b) (h b)) b) -> (Filter.Tendsto.{u2, u1} β α f b (nhds.{u1} α _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_of_tendsto_of_tendsto_of_le_of_le'ₓ'. -/
 /-- **Squeeze theorem** (also known as **sandwich theorem**). This version assumes that inequalities
 hold eventually for the filter. -/
 theorem tendsto_of_tendsto_of_tendsto_of_le_of_le' {f g h : β → α} {b : Filter β} {a : α}
@@ -1327,9 +1574,13 @@ theorem tendsto_of_tendsto_of_tendsto_of_le_of_le' {f g h : β → α} {b : Filt
     (hfh : ∀ᶠ b in b, f b ≤ h b) : Tendsto f b (𝓝 a) :=
   (hg.Icc hh).of_smallSets <| hgf.And hfh
 #align tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_of_tendsto_of_tendsto_of_le_of_le'
--/
 
-#print tendsto_of_tendsto_of_tendsto_of_le_of_le /-
+/- warning: tendsto_of_tendsto_of_tendsto_of_le_of_le -> tendsto_of_tendsto_of_tendsto_of_le_of_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {g : β -> α} {h : β -> α} {b : Filter.{u2} β} {a : α}, (Filter.Tendsto.{u2, u1} β α g b (nhds.{u1} α _inst_1 a)) -> (Filter.Tendsto.{u2, u1} β α h b (nhds.{u1} α _inst_1 a)) -> (LE.le.{max u2 u1} (β -> α) (Pi.hasLe.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => Preorder.toHasLe.{u1} α _inst_2)) g f) -> (LE.le.{max u2 u1} (β -> α) (Pi.hasLe.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => Preorder.toHasLe.{u1} α _inst_2)) f h) -> (Filter.Tendsto.{u2, u1} β α f b (nhds.{u1} α _inst_1 a))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {g : β -> α} {h : β -> α} {b : Filter.{u2} β} {a : α}, (Filter.Tendsto.{u2, u1} β α g b (nhds.{u1} α _inst_1 a)) -> (Filter.Tendsto.{u2, u1} β α h b (nhds.{u1} α _inst_1 a)) -> (LE.le.{max u1 u2} (β -> α) (Pi.hasLe.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => Preorder.toLE.{u1} α _inst_2)) g f) -> (LE.le.{max u1 u2} (β -> α) (Pi.hasLe.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => Preorder.toLE.{u1} α _inst_2)) f h) -> (Filter.Tendsto.{u2, u1} β α f b (nhds.{u1} α _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align tendsto_of_tendsto_of_tendsto_of_le_of_le tendsto_of_tendsto_of_tendsto_of_le_of_leₓ'. -/
 /-- **Squeeze theorem** (also known as **sandwich theorem**). This version assumes that inequalities
 hold everywhere. -/
 theorem tendsto_of_tendsto_of_tendsto_of_le_of_le {f g h : β → α} {b : Filter β} {a : α}
@@ -1338,11 +1589,10 @@ theorem tendsto_of_tendsto_of_tendsto_of_le_of_le {f g h : β → α} {b : Filte
   tendsto_of_tendsto_of_tendsto_of_le_of_le' hg hh (eventually_of_forall hgf)
     (eventually_of_forall hfh)
 #align tendsto_of_tendsto_of_tendsto_of_le_of_le tendsto_of_tendsto_of_tendsto_of_le_of_le
--/
 
 /- warning: nhds_order_unbounded -> nhds_order_unbounded is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u)) -> (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a)) -> (Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (u : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Ioo.{u1} α _inst_2 l u)))))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a u)) -> (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) l a)) -> (Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) l a) (fun (h₂ : LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) l a) => iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (u : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a u) (fun (h₂ : LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Ioo.{u1} α _inst_2 l u)))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u)) -> (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a)) -> (Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (u : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Ioo.{u1} α _inst_2 l u)))))))
 Case conversion may be inaccurate. Consider using '#align nhds_order_unbounded nhds_order_unboundedₓ'. -/
@@ -1355,7 +1605,12 @@ theorem nhds_order_unbounded {a : α} (hu : ∃ u, a < u) (hl : ∃ l, l < a) :
   rfl
 #align nhds_order_unbounded nhds_order_unbounded
 
-#print tendsto_order_unbounded /-
+/- warning: tendsto_order_unbounded -> tendsto_order_unbounded is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {a : α} {x : Filter.{u2} β}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a u)) -> (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) l a)) -> (forall (l : α) (u : α), (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) l a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a u) -> (Filter.Eventually.{u2} β (fun (b : β) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) l (f b)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (f b) u)) x)) -> (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {f : β -> α} {a : α} {x : Filter.{u2} β}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u)) -> (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a)) -> (forall (l : α) (u : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) -> (Filter.Eventually.{u2} β (fun (b : β) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l (f b)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (f b) u)) x)) -> (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align tendsto_order_unbounded tendsto_order_unboundedₓ'. -/
 theorem tendsto_order_unbounded {f : β → α} {a : α} {x : Filter β} (hu : ∃ u, a < u)
     (hl : ∃ l, l < a) (h : ∀ l u, l < a → a < u → ∀ᶠ b in x, l < f b ∧ f b < u) :
     Tendsto f x (𝓝 a) := by
@@ -1365,7 +1620,6 @@ theorem tendsto_order_unbounded {f : β → α} {a : α} {x : Filter β} (hu : 
         tendsto_infi.2 fun hl =>
           tendsto_infi.2 fun u => tendsto_infi.2 fun hu => tendsto_principal.2 <| h l u hl hu
 #align tendsto_order_unbounded tendsto_order_unbounded
--/
 
 end Preorder
 
@@ -1394,7 +1648,7 @@ instance tendstoIccClassNhdsPi {ι : Type _} {α : ι → Type _} [∀ i, Preord
 
 /- warning: induced_order_topology' -> induced_orderTopology' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [ta : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTopology.{u2} β ta _inst_2] (f : α -> β), (forall {x : α} {y : α}, Iff (LT.lt.{u2} β (Preorder.toLT.{u2} β _inst_2) (f x) (f y)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) x y)) -> (forall {a : α} {x : β}, (LT.lt.{u2} β (Preorder.toLT.{u2} β _inst_2) x (f a)) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) b a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) b a) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x (f b))))) -> (forall {a : α} {x : β}, (LT.lt.{u2} β (Preorder.toLT.{u2} β _inst_2) (f a) x) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (GT.gt.{u1} α (Preorder.toLT.{u1} α _inst_1) b a) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α _inst_1) b a) => LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (f b) x)))) -> (OrderTopology.{u1} α (TopologicalSpace.induced.{u1, u2} α β f ta) _inst_1)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [ta : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTopology.{u2} β ta _inst_2] (f : α -> β), (forall {x : α} {y : α}, Iff (LT.lt.{u2} β (Preorder.toHasLt.{u2} β _inst_2) (f x) (f y)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_1) x y)) -> (forall {a : α} {x : β}, (LT.lt.{u2} β (Preorder.toHasLt.{u2} β _inst_2) x (f a)) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_1) b a) (fun (H : LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_1) b a) => LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) x (f b))))) -> (forall {a : α} {x : β}, (LT.lt.{u2} β (Preorder.toHasLt.{u2} β _inst_2) (f a) x) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (GT.gt.{u1} α (Preorder.toHasLt.{u1} α _inst_1) b a) (fun (H : GT.gt.{u1} α (Preorder.toHasLt.{u1} α _inst_1) b a) => LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (f b) x)))) -> (OrderTopology.{u1} α (TopologicalSpace.induced.{u1, u2} α β f ta) _inst_1)
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [ta : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTopology.{u2} β ta _inst_2] (f : α -> β), (forall {x : α} {y : α}, Iff (LT.lt.{u2} β (Preorder.toLT.{u2} β _inst_2) (f x) (f y)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) x y)) -> (forall {a : α} {x : β}, (LT.lt.{u2} β (Preorder.toLT.{u2} β _inst_2) x (f a)) -> (Exists.{succ u1} α (fun (b : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) b a) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) x (f b))))) -> (forall {a : α} {x : β}, (LT.lt.{u2} β (Preorder.toLT.{u2} β _inst_2) (f a) x) -> (Exists.{succ u1} α (fun (b : α) => And (GT.gt.{u1} α (Preorder.toLT.{u1} α _inst_1) b a) (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (f b) x)))) -> (OrderTopology.{u1} α (TopologicalSpace.induced.{u1, u2} α β f ta) _inst_1)
 Case conversion may be inaccurate. Consider using '#align induced_order_topology' induced_orderTopology'ₓ'. -/
@@ -1433,7 +1687,12 @@ theorem induced_orderTopology' {α : Type u} {β : Type v} [Preorder α] [ta : T
       exact fun c hc => lt_of_lt_of_le (hf.2 hc) xb
 #align induced_order_topology' induced_orderTopology'
 
-#print induced_orderTopology /-
+/- warning: induced_order_topology -> induced_orderTopology is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [ta : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTopology.{u2} β ta _inst_2] (f : α -> β), (forall {x : α} {y : α}, Iff (LT.lt.{u2} β (Preorder.toHasLt.{u2} β _inst_2) (f x) (f y)) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_1) x y)) -> (forall {x : β} {y : β}, (LT.lt.{u2} β (Preorder.toHasLt.{u2} β _inst_2) x y) -> (Exists.{succ u1} α (fun (a : α) => And (LT.lt.{u2} β (Preorder.toHasLt.{u2} β _inst_2) x (f a)) (LT.lt.{u2} β (Preorder.toHasLt.{u2} β _inst_2) (f a) y)))) -> (OrderTopology.{u1} α (TopologicalSpace.induced.{u1, u2} α β f ta) _inst_1)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [ta : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTopology.{u2} β ta _inst_2] (f : α -> β), (forall {x : α} {y : α}, Iff (LT.lt.{u2} β (Preorder.toLT.{u2} β _inst_2) (f x) (f y)) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_1) x y)) -> (forall {x : β} {y : β}, (LT.lt.{u2} β (Preorder.toLT.{u2} β _inst_2) x y) -> (Exists.{succ u1} α (fun (a : α) => And (LT.lt.{u2} β (Preorder.toLT.{u2} β _inst_2) x (f a)) (LT.lt.{u2} β (Preorder.toLT.{u2} β _inst_2) (f a) y)))) -> (OrderTopology.{u1} α (TopologicalSpace.induced.{u1, u2} α β f ta) _inst_1)
+Case conversion may be inaccurate. Consider using '#align induced_order_topology induced_orderTopologyₓ'. -/
 theorem induced_orderTopology {α : Type u} {β : Type v} [Preorder α] [ta : TopologicalSpace β]
     [Preorder β] [OrderTopology β] (f : α → β) (hf : ∀ {x y}, f x < f y ↔ x < y)
     (H : ∀ {x y}, x < y → ∃ a, x < f a ∧ f a < y) : @OrderTopology _ (induced f ta) _ :=
@@ -1445,7 +1704,6 @@ theorem induced_orderTopology {α : Type u} {β : Type v} [Preorder α] [ta : To
     let ⟨b, ab, bx⟩ := H ax
     ⟨b, hf.1 ab, le_of_lt bx⟩
 #align induced_order_topology induced_orderTopology
--/
 
 #print orderTopology_of_ordConnected /-
 /-- On an `ord_connected` subset of a linear order, the order topology for the restriction of the
@@ -1498,7 +1756,7 @@ instance orderTopology_of_ordConnected {α : Type u} [ta : TopologicalSpace α]
 
 /- warning: nhds_within_Ici_eq'' -> nhdsWithin_Ici_eq'' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (u : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 u)))) (Filter.principal.{u1} α (Set.Ici.{u1} α _inst_2 a)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (u : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 u)))) (Filter.principal.{u1} α (Set.Ici.{u1} α _inst_2 a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (u : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 u)))) (Filter.principal.{u1} α (Set.Ici.{u1} α _inst_2 a)))
 Case conversion may be inaccurate. Consider using '#align nhds_within_Ici_eq'' nhdsWithin_Ici_eq''ₓ'. -/
@@ -1512,7 +1770,7 @@ theorem nhdsWithin_Ici_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology 
 
 /- warning: nhds_within_Iic_eq'' -> nhdsWithin_Iic_eq'' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l)))) (Filter.principal.{u1} α (Set.Iic.{u1} α _inst_2 a)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l)))) (Filter.principal.{u1} α (Set.Iic.{u1} α _inst_2 a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l)))) (Filter.principal.{u1} α (Set.Iic.{u1} α _inst_2 a)))
 Case conversion may be inaccurate. Consider using '#align nhds_within_Iic_eq'' nhdsWithin_Iic_eq''ₓ'. -/
@@ -1523,7 +1781,7 @@ theorem nhdsWithin_Iic_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology 
 
 /- warning: nhds_within_Ici_eq' -> nhdsWithin_Ici_eq' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u)) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (u : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Ico.{u1} α _inst_2 a u)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a u)) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (u : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Ico.{u1} α _inst_2 a u)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u)) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (u : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Ico.{u1} α _inst_2 a u)))))
 Case conversion may be inaccurate. Consider using '#align nhds_within_Ici_eq' nhdsWithin_Ici_eq'ₓ'. -/
@@ -1534,7 +1792,7 @@ theorem nhdsWithin_Ici_eq' [TopologicalSpace α] [Preorder α] [OrderTopology α
 
 /- warning: nhds_within_Iic_eq' -> nhdsWithin_Iic_eq' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a)) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioc.{u1} α _inst_2 l a)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) l a)) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioc.{u1} α _inst_2 l a)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a)) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioc.{u1} α _inst_2 l a)))))
 Case conversion may be inaccurate. Consider using '#align nhds_within_Iic_eq' nhdsWithin_Iic_eq'ₓ'. -/
@@ -1543,7 +1801,12 @@ theorem nhdsWithin_Iic_eq' [TopologicalSpace α] [Preorder α] [OrderTopology α
   simp only [nhdsWithin_Iic_eq'', biInf_inf ha, inf_principal, Ioi_inter_Iic]
 #align nhds_within_Iic_eq' nhdsWithin_Iic_eq'
 
-#print nhdsWithin_Ici_basis' /-
+/- warning: nhds_within_Ici_basis' -> nhdsWithin_Ici_basis' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u)) -> (Filter.HasBasis.{u1, succ u1} α α (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (u : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u) (fun (u : α) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a u)) -> (Filter.HasBasis.{u1, succ u1} α α (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a u) (fun (u : α) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Ici_basis' nhdsWithin_Ici_basis'ₓ'. -/
 theorem nhdsWithin_Ici_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopology α] {a : α}
     (ha : ∃ u, a < u) : (𝓝[≥] a).HasBasis (fun u => a < u) fun u => Ico a u :=
   (nhdsWithin_Ici_eq' ha).symm ▸
@@ -1553,34 +1816,45 @@ theorem nhdsWithin_Ici_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopol
           Ico_subset_Ico_right (min_le_right _ _)⟩)
       ha
 #align nhds_within_Ici_basis' nhdsWithin_Ici_basis'
--/
 
-#print nhdsWithin_Iic_basis' /-
+/- warning: nhds_within_Iic_basis' -> nhdsWithin_Iic_basis' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α}, (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a)) -> (Filter.HasBasis.{u1, succ u1} α α (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (l : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a) (fun (l : α) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α}, (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l a)) -> (Filter.HasBasis.{u1, succ u1} α α (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l a) (fun (l : α) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Iic_basis' nhdsWithin_Iic_basis'ₓ'. -/
 theorem nhdsWithin_Iic_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopology α] {a : α}
     (ha : ∃ l, l < a) : (𝓝[≤] a).HasBasis (fun l => l < a) fun l => Ioc l a :=
   by
   convert@nhdsWithin_Ici_basis' αᵒᵈ _ _ _ (to_dual a) ha
   exact funext fun x => (@dual_Ico _ _ _ _).symm
 #align nhds_within_Iic_basis' nhdsWithin_Iic_basis'
--/
 
-#print nhdsWithin_Ici_basis /-
+/- warning: nhds_within_Ici_basis -> nhdsWithin_Ici_basis is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α), Filter.HasBasis.{u1, succ u1} α α (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (u : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u) (fun (u : α) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α), Filter.HasBasis.{u1, succ u1} α α (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a u) (fun (u : α) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u)
+Case conversion may be inaccurate. Consider using '#align nhds_within_Ici_basis nhdsWithin_Ici_basisₓ'. -/
 theorem nhdsWithin_Ici_basis [TopologicalSpace α] [LinearOrder α] [OrderTopology α] [NoMaxOrder α]
     (a : α) : (𝓝[≥] a).HasBasis (fun u => a < u) fun u => Ico a u :=
   nhdsWithin_Ici_basis' (exists_gt a)
 #align nhds_within_Ici_basis nhdsWithin_Ici_basis
--/
 
-#print nhdsWithin_Iic_basis /-
+/- warning: nhds_within_Iic_basis -> nhdsWithin_Iic_basis is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α), Filter.HasBasis.{u1, succ u1} α α (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (l : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a) (fun (l : α) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α), Filter.HasBasis.{u1, succ u1} α α (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l a) (fun (l : α) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a)
+Case conversion may be inaccurate. Consider using '#align nhds_within_Iic_basis nhdsWithin_Iic_basisₓ'. -/
 theorem nhdsWithin_Iic_basis [TopologicalSpace α] [LinearOrder α] [OrderTopology α] [NoMinOrder α]
     (a : α) : (𝓝[≤] a).HasBasis (fun l => l < a) fun l => Ioc l a :=
   nhdsWithin_Iic_basis' (exists_lt a)
 #align nhds_within_Iic_basis nhdsWithin_Iic_basis
--/
 
 /- warning: nhds_top_order -> nhds_top_order is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_2)] [_inst_4 : OrderTopology.{u1} α _inst_1 _inst_2], Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α _inst_2)] [_inst_4 : OrderTopology.{u1} α _inst_1 _inst_2], Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_2) _inst_3))) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) l (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_2) _inst_3))) (fun (h₂ : LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) l (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α _inst_2) _inst_3))) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_2)] [_inst_4 : OrderTopology.{u1} α _inst_1 _inst_2], Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l))))
 Case conversion may be inaccurate. Consider using '#align nhds_top_order nhds_top_orderₓ'. -/
@@ -1590,7 +1864,7 @@ theorem nhds_top_order [TopologicalSpace α] [Preorder α] [OrderTop α] [OrderT
 
 /- warning: nhds_bot_order -> nhds_bot_order is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_2)] [_inst_4 : OrderTopology.{u1} α _inst_1 _inst_2], Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3)) l) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3)) l) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 l))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α _inst_2)] [_inst_4 : OrderTopology.{u1} α _inst_1 _inst_2], Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_2) _inst_3))) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_2) _inst_3)) l) (fun (h₂ : LT.lt.{u1} α (Preorder.toHasLt.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α _inst_2) _inst_3)) l) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 l))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_2)] [_inst_4 : OrderTopology.{u1} α _inst_1 _inst_2], Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3)) l) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3)) l) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 l))))
 Case conversion may be inaccurate. Consider using '#align nhds_bot_order nhds_bot_orderₓ'. -/
@@ -1600,7 +1874,7 @@ theorem nhds_bot_order [TopologicalSpace α] [Preorder α] [OrderBot α] [OrderT
 
 /- warning: nhds_top_basis -> nhds_top_basis is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : Nontrivial.{u1} α], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3))) (fun (a : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3))) (fun (a : α) => Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : Nontrivial.{u1} α], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3))) (fun (a : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3))) (fun (a : α) => Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_5 : Nontrivial.{u1} α], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) _inst_3))) (fun (a : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) _inst_3))) (fun (a : α) => Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)
 Case conversion may be inaccurate. Consider using '#align nhds_top_basis nhds_top_basisₓ'. -/
@@ -1613,7 +1887,7 @@ theorem nhds_top_basis [TopologicalSpace α] [LinearOrder α] [OrderTop α] [Ord
 
 /- warning: nhds_bot_basis -> nhds_bot_basis is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : Nontrivial.{u1} α], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3))) (fun (a : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3)) a) (fun (a : α) => Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : Nontrivial.{u1} α], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3))) (fun (a : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3)) a) (fun (a : α) => Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_5 : Nontrivial.{u1} α], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) _inst_3))) (fun (a : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) _inst_3)) a) (fun (a : α) => Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)
 Case conversion may be inaccurate. Consider using '#align nhds_bot_basis nhds_bot_basisₓ'. -/
@@ -1624,7 +1898,7 @@ theorem nhds_bot_basis [TopologicalSpace α] [LinearOrder α] [OrderBot α] [Ord
 
 /- warning: nhds_top_basis_Ici -> nhds_top_basis_Ici is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : Nontrivial.{u1} α] [_inst_6 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3))) (fun (a : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3))) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : Nontrivial.{u1} α] [_inst_6 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3))) (fun (a : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3))) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_5 : Nontrivial.{u1} α] [_inst_6 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) _inst_3))) (fun (a : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) _inst_3))) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align nhds_top_basis_Ici nhds_top_basis_Iciₓ'. -/
@@ -1639,7 +1913,7 @@ theorem nhds_top_basis_Ici [TopologicalSpace α] [LinearOrder α] [OrderTop α]
 
 /- warning: nhds_bot_basis_Iic -> nhds_bot_basis_Iic is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : Nontrivial.{u1} α] [_inst_6 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3))) (fun (a : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3)) a) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_5 : Nontrivial.{u1} α] [_inst_6 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3))) (fun (a : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) _inst_3)) a) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_4 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_5 : Nontrivial.{u1} α] [_inst_6 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) _inst_3))) (fun (a : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) _inst_3)) a) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align nhds_bot_basis_Iic nhds_bot_basis_Iicₓ'. -/
@@ -1650,7 +1924,7 @@ theorem nhds_bot_basis_Iic [TopologicalSpace α] [LinearOrder α] [OrderBot α]
 
 /- warning: tendsto_nhds_top_mono -> tendsto_nhds_top_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β _inst_2) l f g) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)))) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toHasLe.{u2} β _inst_2) l f g) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β _inst_2) l f g) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))))
 Case conversion may be inaccurate. Consider using '#align tendsto_nhds_top_mono tendsto_nhds_top_monoₓ'. -/
@@ -1664,7 +1938,7 @@ theorem tendsto_nhds_top_mono [TopologicalSpace β] [Preorder β] [OrderTop β]
 
 /- warning: tendsto_nhds_bot_mono -> tendsto_nhds_bot_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β _inst_2) l g f) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)))) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toHasLe.{u2} β _inst_2) l g f) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β _inst_2) l g f) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))))
 Case conversion may be inaccurate. Consider using '#align tendsto_nhds_bot_mono tendsto_nhds_bot_monoₓ'. -/
@@ -1675,7 +1949,7 @@ theorem tendsto_nhds_bot_mono [TopologicalSpace β] [Preorder β] [OrderBot β]
 
 /- warning: tendsto_nhds_top_mono' -> tendsto_nhds_top_mono' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))) -> (LE.le.{max u1 u2} (α -> β) (Pi.hasLe.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Preorder.toLE.{u2} β _inst_2)) f g) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)))) -> (LE.le.{max u1 u2} (α -> β) (Pi.hasLe.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Preorder.toHasLe.{u2} β _inst_2)) f g) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))) -> (LE.le.{max u1 u2} (α -> β) (Pi.hasLe.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Preorder.toLE.{u2} β _inst_2)) f g) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))))
 Case conversion may be inaccurate. Consider using '#align tendsto_nhds_top_mono' tendsto_nhds_top_mono'ₓ'. -/
@@ -1686,7 +1960,7 @@ theorem tendsto_nhds_top_mono' [TopologicalSpace β] [Preorder β] [OrderTop β]
 
 /- warning: tendsto_nhds_bot_mono' -> tendsto_nhds_bot_mono' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))) -> (LE.le.{max u1 u2} (α -> β) (Pi.hasLe.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Preorder.toLE.{u2} β _inst_2)) g f) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3)))) -> (LE.le.{max u1 u2} (α -> β) (Pi.hasLe.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Preorder.toHasLe.{u2} β _inst_2)) g f) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toHasLe.{u2} β _inst_2) _inst_3))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))) -> (LE.le.{max u1 u2} (α -> β) (Pi.hasLe.{u1, u2} α (fun (ᾰ : α) => β) (fun (i : α) => Preorder.toLE.{u2} β _inst_2)) g f) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))))
 Case conversion may be inaccurate. Consider using '#align tendsto_nhds_bot_mono' tendsto_nhds_bot_mono'ₓ'. -/
@@ -1703,29 +1977,45 @@ section OrderClosedTopology
 
 variable [OrderClosedTopology α] {a b : α}
 
-#print eventually_le_nhds /-
+/- warning: eventually_le_nhds -> eventually_le_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x b) (nhds.{u1} α _inst_1 a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x b) (nhds.{u1} α _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align eventually_le_nhds eventually_le_nhdsₓ'. -/
 theorem eventually_le_nhds (hab : a < b) : ∀ᶠ x in 𝓝 a, x ≤ b :=
   eventually_iff.mpr (mem_nhds_iff.mpr ⟨Iio b, Iio_subset_Iic_self, isOpen_Iio, hab⟩)
 #align eventually_le_nhds eventually_le_nhds
--/
 
-#print eventually_lt_nhds /-
+/- warning: eventually_lt_nhds -> eventually_lt_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x b) (nhds.{u1} α _inst_1 a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x b) (nhds.{u1} α _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align eventually_lt_nhds eventually_lt_nhdsₓ'. -/
 theorem eventually_lt_nhds (hab : a < b) : ∀ᶠ x in 𝓝 a, x < b :=
   eventually_iff.mpr (mem_nhds_iff.mpr ⟨Iio b, rfl.Subset, isOpen_Iio, hab⟩)
 #align eventually_lt_nhds eventually_lt_nhds
--/
 
-#print eventually_ge_nhds /-
+/- warning: eventually_ge_nhds -> eventually_ge_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) -> (Filter.Eventually.{u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b x) (nhds.{u1} α _inst_1 a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b a) -> (Filter.Eventually.{u1} α (fun (x : α) => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b x) (nhds.{u1} α _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align eventually_ge_nhds eventually_ge_nhdsₓ'. -/
 theorem eventually_ge_nhds (hab : b < a) : ∀ᶠ x in 𝓝 a, b ≤ x :=
   eventually_iff.mpr (mem_nhds_iff.mpr ⟨Ioi b, Ioi_subset_Ici_self, isOpen_Ioi, hab⟩)
 #align eventually_ge_nhds eventually_ge_nhds
--/
 
-#print eventually_gt_nhds /-
+/- warning: eventually_gt_nhds -> eventually_gt_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b x) (nhds.{u1} α _inst_1 a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b a) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b x) (nhds.{u1} α _inst_1 a))
+Case conversion may be inaccurate. Consider using '#align eventually_gt_nhds eventually_gt_nhdsₓ'. -/
 theorem eventually_gt_nhds (hab : b < a) : ∀ᶠ x in 𝓝 a, b < x :=
   eventually_iff.mpr (mem_nhds_iff.mpr ⟨Ioi b, rfl.Subset, isOpen_Ioi, hab⟩)
 #align eventually_gt_nhds eventually_gt_nhds
--/
 
 end OrderClosedTopology
 
@@ -1733,7 +2023,12 @@ section OrderTopology
 
 variable [OrderTopology α]
 
-#print order_separated /-
+/- warning: order_separated -> order_separated is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a₁ : α} {a₂ : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a₁ a₂) -> (Exists.{succ u1} (Set.{u1} α) (fun (u : Set.{u1} α) => Exists.{succ u1} (Set.{u1} α) (fun (v : Set.{u1} α) => And (IsOpen.{u1} α _inst_1 u) (And (IsOpen.{u1} α _inst_1 v) (And (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a₁ u) (And (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a₂ v) (forall (b₁ : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b₁ u) -> (forall (b₂ : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b₂ v) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b₁ b₂)))))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a₁ : α} {a₂ : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a₁ a₂) -> (Exists.{succ u1} (Set.{u1} α) (fun (u : Set.{u1} α) => Exists.{succ u1} (Set.{u1} α) (fun (v : Set.{u1} α) => And (IsOpen.{u1} α _inst_1 u) (And (IsOpen.{u1} α _inst_1 v) (And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a₁ u) (And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a₂ v) (forall (b₁ : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b₁ u) -> (forall (b₂ : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b₂ v) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b₁ b₂)))))))))
+Case conversion may be inaccurate. Consider using '#align order_separated order_separatedₓ'. -/
 theorem order_separated {a₁ a₂ : α} (h : a₁ < a₂) :
     ∃ u v : Set α, IsOpen u ∧ IsOpen v ∧ a₁ ∈ u ∧ a₂ ∈ v ∧ ∀ b₁ ∈ u, ∀ b₂ ∈ v, b₁ < b₂ :=
   match dense_or_discrete a₁ a₂ with
@@ -1748,7 +2043,6 @@ theorem order_separated {a₁ a₂ : α} (h : a₁ < a₂) :
         _ ≤ b₂ := h₁ _ hb₂
         ⟩
 #align order_separated order_separated
--/
 
 #print OrderTopology.to_orderClosedTopology /-
 -- see Note [lower instance priority]
@@ -1764,7 +2058,7 @@ instance (priority := 100) OrderTopology.to_orderClosedTopology : OrderClosedTop
 
 /- warning: exists_Ioc_subset_of_mem_nhds -> exists_Ioc_subset_of_mem_nhds is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a)) -> (Exists.{succ u1} α (fun (l : α) => Exists.{0} (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a)) -> (Exists.{succ u1} α (fun (l : α) => Exists.{0} (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a) (fun (H : LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l a)) -> (Exists.{succ u1} α (fun (l : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l a) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s)))
 Case conversion may be inaccurate. Consider using '#align exists_Ioc_subset_of_mem_nhds exists_Ioc_subset_of_mem_nhdsₓ'. -/
@@ -1775,7 +2069,7 @@ theorem exists_Ioc_subset_of_mem_nhds {a : α} {s : Set α} (hs : s ∈ 𝓝 a)
 
 /- warning: exists_Ioc_subset_of_mem_nhds' -> exists_Ioc_subset_of_mem_nhds' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (forall {l : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a) -> (Exists.{succ u1} α (fun (l' : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l' (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l' (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l' a) s))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (forall {l : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a) -> (Exists.{succ u1} α (fun (l' : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l' (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l' (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l' a) s))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (forall {l : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l a) -> (Exists.{succ u1} α (fun (l' : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l' (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l' a) s))))
 Case conversion may be inaccurate. Consider using '#align exists_Ioc_subset_of_mem_nhds' exists_Ioc_subset_of_mem_nhds'ₓ'. -/
@@ -1788,7 +2082,7 @@ theorem exists_Ioc_subset_of_mem_nhds' {a : α} {s : Set α} (hs : s ∈ 𝓝 a)
 
 /- warning: exists_Ico_subset_of_mem_nhds' -> exists_Ico_subset_of_mem_nhds' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (forall {u : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u) -> (Exists.{succ u1} α (fun (u' : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u' (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u' (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u') s))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (forall {u : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u) -> (Exists.{succ u1} α (fun (u' : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u' (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u' (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u') s))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (forall {u : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a u) -> (Exists.{succ u1} α (fun (u' : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) u' (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u') s))))
 Case conversion may be inaccurate. Consider using '#align exists_Ico_subset_of_mem_nhds' exists_Ico_subset_of_mem_nhds'ₓ'. -/
@@ -1800,7 +2094,7 @@ theorem exists_Ico_subset_of_mem_nhds' {a : α} {s : Set α} (hs : s ∈ 𝓝 a)
 
 /- warning: exists_Ico_subset_of_mem_nhds -> exists_Ico_subset_of_mem_nhds is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u)) -> (Exists.{succ u1} α (fun (u : α) => Exists.{0} (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u) (fun (_x : LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u)) -> (Exists.{succ u1} α (fun (u : α) => Exists.{0} (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u) (fun (_x : LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a u)) -> (Exists.{succ u1} α (fun (u : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a u) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u) s)))
 Case conversion may be inaccurate. Consider using '#align exists_Ico_subset_of_mem_nhds exists_Ico_subset_of_mem_nhdsₓ'. -/
@@ -1813,7 +2107,7 @@ theorem exists_Ico_subset_of_mem_nhds {a : α} {s : Set α} (hs : s ∈ 𝓝 a)
 
 /- warning: exists_Icc_mem_subset_of_mem_nhds_within_Ici -> exists_Icc_mem_subset_of_mem_nhdsWithin_Ici is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) (fun (_x : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) => And (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) a b) s))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) (fun (_x : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) => And (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) a b) s))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) -> (Exists.{succ u1} α (fun (b : α) => And (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) (And (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) s))))
 Case conversion may be inaccurate. Consider using '#align exists_Icc_mem_subset_of_mem_nhds_within_Ici exists_Icc_mem_subset_of_mem_nhdsWithin_Iciₓ'. -/
@@ -1833,7 +2127,7 @@ theorem exists_Icc_mem_subset_of_mem_nhdsWithin_Ici {a : α} {s : Set α} (hs :
 
 /- warning: exists_Icc_mem_subset_of_mem_nhds_within_Iic -> exists_Icc_mem_subset_of_mem_nhdsWithin_Iic is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) (fun (H : LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) => And (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b a) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) b a) s))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) (fun (H : LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) => And (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b a) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) b a) s))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) -> (Exists.{succ u1} α (fun (b : α) => And (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b a) (And (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b a) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b a) s))))
 Case conversion may be inaccurate. Consider using '#align exists_Icc_mem_subset_of_mem_nhds_within_Iic exists_Icc_mem_subset_of_mem_nhdsWithin_Iicₓ'. -/
@@ -1857,7 +2151,12 @@ theorem exists_Icc_mem_subset_of_mem_nhds {a : α} {s : Set α} (hs : s ∈ 𝓝
 #align exists_Icc_mem_subset_of_mem_nhds exists_Icc_mem_subset_of_mem_nhds
 -/
 
-#print IsOpen.exists_Ioo_subset /-
+/- warning: is_open.exists_Ioo_subset -> IsOpen.exists_Ioo_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : Nontrivial.{u1} α] {s : Set.{u1} α}, (IsOpen.{u1} α _inst_1 s) -> (Set.Nonempty.{u1} α s) -> (Exists.{succ u1} α (fun (a : α) => Exists.{succ u1} α (fun (b : α) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) a b) s))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : Nontrivial.{u1} α] {s : Set.{u1} α}, (IsOpen.{u1} α _inst_1 s) -> (Set.Nonempty.{u1} α s) -> (Exists.{succ u1} α (fun (a : α) => Exists.{succ u1} α (fun (b : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) s))))
+Case conversion may be inaccurate. Consider using '#align is_open.exists_Ioo_subset IsOpen.exists_Ioo_subsetₓ'. -/
 theorem IsOpen.exists_Ioo_subset [Nontrivial α] {s : Set α} (hs : IsOpen s) (h : s.Nonempty) :
     ∃ a b, a < b ∧ Ioo a b ⊆ s :=
   by
@@ -1872,11 +2171,10 @@ theorem IsOpen.exists_Ioo_subset [Nontrivial α] {s : Set α} (hs : IsOpen s) (h
       exists_Ioc_subset_of_mem_nhds (hs.mem_nhds hx) ⟨y, H⟩
     exact ⟨l, x, lx, Ioo_subset_Ioc_self.trans hl⟩
 #align is_open.exists_Ioo_subset IsOpen.exists_Ioo_subset
--/
 
 /- warning: dense_of_exists_between -> dense_of_exists_between is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : Nontrivial.{u1} α] {s : Set.{u1} α}, (forall {{a : α}} {{b : α}}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Exists.{succ u1} α (fun (c : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a c) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) c b))))) -> (Dense.{u1} α _inst_1 s)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : Nontrivial.{u1} α] {s : Set.{u1} α}, (forall {{a : α}} {{b : α}}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Exists.{succ u1} α (fun (c : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a c) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) c b))))) -> (Dense.{u1} α _inst_1 s)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : Nontrivial.{u1} α] {s : Set.{u1} α}, (forall {{a : α}} {{b : α}}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Exists.{succ u1} α (fun (c : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c s) (And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a c) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) c b))))) -> (Dense.{u1} α _inst_1 s)
 Case conversion may be inaccurate. Consider using '#align dense_of_exists_between dense_of_exists_betweenₓ'. -/
@@ -1891,7 +2189,7 @@ theorem dense_of_exists_between [Nontrivial α] {s : Set α}
 
 /- warning: dense_iff_exists_between -> dense_iff_exists_between is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : Nontrivial.{u1} α] {s : Set.{u1} α}, Iff (Dense.{u1} α _inst_1 s) (forall (a : α) (b : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Exists.{succ u1} α (fun (c : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a c) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) c b)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : Nontrivial.{u1} α] {s : Set.{u1} α}, Iff (Dense.{u1} α _inst_1 s) (forall (a : α) (b : α), (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Exists.{succ u1} α (fun (c : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a c) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) c b)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : Nontrivial.{u1} α] {s : Set.{u1} α}, Iff (Dense.{u1} α _inst_1 s) (forall (a : α) (b : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Exists.{succ u1} α (fun (c : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c s) (And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a c) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) c b)))))
 Case conversion may be inaccurate. Consider using '#align dense_iff_exists_between dense_iff_exists_betweenₓ'. -/
@@ -1903,7 +2201,12 @@ theorem dense_iff_exists_between [DenselyOrdered α] [Nontrivial α] {s : Set α
   ⟨fun h a b hab => h.exists_between hab, dense_of_exists_between⟩
 #align dense_iff_exists_between dense_iff_exists_between
 
-#print mem_nhds_iff_exists_Ioo_subset' /-
+/- warning: mem_nhds_iff_exists_Ioo_subset' -> mem_nhds_iff_exists_Ioo_subset' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {s : Set.{u1} α}, (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a)) -> (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u)) -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α _inst_1 a)) (Exists.{succ u1} α (fun (l : α) => Exists.{succ u1} α (fun (u : α) => And (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l u)) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) l u) s)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l a)) -> (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a u)) -> (Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhds.{u1} α _inst_1 a)) (Exists.{succ u1} α (fun (l : α) => Exists.{succ u1} α (fun (u : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l u)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l u) s)))))
+Case conversion may be inaccurate. Consider using '#align mem_nhds_iff_exists_Ioo_subset' mem_nhds_iff_exists_Ioo_subset'ₓ'. -/
 /-- A set is a neighborhood of `a` if and only if it contains an interval `(l, u)` containing `a`,
 provided `a` is neither a bottom element nor a top element. -/
 theorem mem_nhds_iff_exists_Ioo_subset' {a : α} {s : Set α} (hl : ∃ l, l < a) (hu : ∃ u, a < u) :
@@ -1917,39 +2220,59 @@ theorem mem_nhds_iff_exists_Ioo_subset' {a : α} {s : Set α} (hl : ∃ l, l < a
   · rintro ⟨l, u, ha, h⟩
     apply mem_of_superset (Ioo_mem_nhds ha.1 ha.2) h
 #align mem_nhds_iff_exists_Ioo_subset' mem_nhds_iff_exists_Ioo_subset'
--/
 
-#print mem_nhds_iff_exists_Ioo_subset /-
+/- warning: mem_nhds_iff_exists_Ioo_subset -> mem_nhds_iff_exists_Ioo_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α _inst_1 a)) (Exists.{succ u1} α (fun (l : α) => Exists.{succ u1} α (fun (u : α) => And (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l u)) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) l u) s))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhds.{u1} α _inst_1 a)) (Exists.{succ u1} α (fun (l : α) => Exists.{succ u1} α (fun (u : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l u)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l u) s))))
+Case conversion may be inaccurate. Consider using '#align mem_nhds_iff_exists_Ioo_subset mem_nhds_iff_exists_Ioo_subsetₓ'. -/
 /-- A set is a neighborhood of `a` if and only if it contains an interval `(l, u)` containing `a`.
 -/
 theorem mem_nhds_iff_exists_Ioo_subset [NoMaxOrder α] [NoMinOrder α] {a : α} {s : Set α} :
     s ∈ 𝓝 a ↔ ∃ l u, a ∈ Ioo l u ∧ Ioo l u ⊆ s :=
   mem_nhds_iff_exists_Ioo_subset' (exists_lt a) (exists_gt a)
 #align mem_nhds_iff_exists_Ioo_subset mem_nhds_iff_exists_Ioo_subset
--/
 
-#print nhds_basis_Ioo' /-
+/- warning: nhds_basis_Ioo' -> nhds_basis_Ioo' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α}, (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a)) -> (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u)) -> (Filter.HasBasis.{u1, succ u1} α (Prod.{u1, u1} α α) (nhds.{u1} α _inst_1 a) (fun (b : Prod.{u1, u1} α α) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (Prod.fst.{u1, u1} α α b) a) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a (Prod.snd.{u1, u1} α α b))) (fun (b : Prod.{u1, u1} α α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (Prod.fst.{u1, u1} α α b) (Prod.snd.{u1, u1} α α b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α}, (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l a)) -> (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a u)) -> (Filter.HasBasis.{u1, succ u1} α (Prod.{u1, u1} α α) (nhds.{u1} α _inst_1 a) (fun (b : Prod.{u1, u1} α α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (Prod.fst.{u1, u1} α α b) a) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a (Prod.snd.{u1, u1} α α b))) (fun (b : Prod.{u1, u1} α α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (Prod.fst.{u1, u1} α α b) (Prod.snd.{u1, u1} α α b)))
+Case conversion may be inaccurate. Consider using '#align nhds_basis_Ioo' nhds_basis_Ioo'ₓ'. -/
 theorem nhds_basis_Ioo' {a : α} (hl : ∃ l, l < a) (hu : ∃ u, a < u) :
     (𝓝 a).HasBasis (fun b : α × α => b.1 < a ∧ a < b.2) fun b => Ioo b.1 b.2 :=
   ⟨fun s => (mem_nhds_iff_exists_Ioo_subset' hl hu).trans <| by simp⟩
 #align nhds_basis_Ioo' nhds_basis_Ioo'
--/
 
-#print nhds_basis_Ioo /-
+/- warning: nhds_basis_Ioo -> nhds_basis_Ioo is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α), Filter.HasBasis.{u1, succ u1} α (Prod.{u1, u1} α α) (nhds.{u1} α _inst_1 a) (fun (b : Prod.{u1, u1} α α) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (Prod.fst.{u1, u1} α α b) a) (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a (Prod.snd.{u1, u1} α α b))) (fun (b : Prod.{u1, u1} α α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (Prod.fst.{u1, u1} α α b) (Prod.snd.{u1, u1} α α b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α), Filter.HasBasis.{u1, succ u1} α (Prod.{u1, u1} α α) (nhds.{u1} α _inst_1 a) (fun (b : Prod.{u1, u1} α α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) (Prod.fst.{u1, u1} α α b) a) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a (Prod.snd.{u1, u1} α α b))) (fun (b : Prod.{u1, u1} α α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (Prod.fst.{u1, u1} α α b) (Prod.snd.{u1, u1} α α b))
+Case conversion may be inaccurate. Consider using '#align nhds_basis_Ioo nhds_basis_Iooₓ'. -/
 theorem nhds_basis_Ioo [NoMaxOrder α] [NoMinOrder α] (a : α) :
     (𝓝 a).HasBasis (fun b : α × α => b.1 < a ∧ a < b.2) fun b => Ioo b.1 b.2 :=
   nhds_basis_Ioo' (exists_lt a) (exists_gt a)
 #align nhds_basis_Ioo nhds_basis_Ioo
--/
 
-#print Filter.Eventually.exists_Ioo_subset /-
+/- warning: filter.eventually.exists_Ioo_subset -> Filter.Eventually.exists_Ioo_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {p : α -> Prop}, (Filter.Eventually.{u1} α (fun (x : α) => p x) (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (l : α) => Exists.{succ u1} α (fun (u : α) => And (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l u)) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) l u) (setOf.{u1} α (fun (x : α) => p x))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {p : α -> Prop}, (Filter.Eventually.{u1} α (fun (x : α) => p x) (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (l : α) => Exists.{succ u1} α (fun (u : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l u)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l u) (setOf.{u1} α (fun (x : α) => p x))))))
+Case conversion may be inaccurate. Consider using '#align filter.eventually.exists_Ioo_subset Filter.Eventually.exists_Ioo_subsetₓ'. -/
 theorem Filter.Eventually.exists_Ioo_subset [NoMaxOrder α] [NoMinOrder α] {a : α} {p : α → Prop}
     (hp : ∀ᶠ x in 𝓝 a, p x) : ∃ l u, a ∈ Ioo l u ∧ Ioo l u ⊆ { x | p x } :=
   mem_nhds_iff_exists_Ioo_subset.1 hp
 #align filter.eventually.exists_Ioo_subset Filter.Eventually.exists_Ioo_subset
--/
 
-#print countable_of_isolated_right' /-
+/- warning: countable_of_isolated_right -> countable_of_isolated_right' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : TopologicalSpace.SecondCountableTopology.{u1} α _inst_1], Set.Countable.{u1} α (setOf.{u1} α (fun (x : α) => Exists.{succ u1} α (fun (y : α) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x y) (Eq.{succ u1} (Set.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) x y) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : TopologicalSpace.SecondCountableTopology.{u1} α _inst_1], Set.Countable.{u1} α (setOf.{u1} α (fun (x : α) => Exists.{succ u1} α (fun (y : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x y) (Eq.{succ u1} (Set.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) x y) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))))))
+Case conversion may be inaccurate. Consider using '#align countable_of_isolated_right countable_of_isolated_right'ₓ'. -/
 /-- The set of points which are isolated on the right is countable when the space is
 second-countable. -/
 theorem countable_of_isolated_right' [SecondCountableTopology α] :
@@ -2012,9 +2335,13 @@ theorem countable_of_isolated_right' [SecondCountableTopology α] :
     exact isOpen_Ioo
   exact subset.antisymm (Ioc_subset_Ioo_right (hy x hx.1)) fun u hu => ⟨hu.1, Hy _ _ hx.1 hu.2⟩
 #align countable_of_isolated_right countable_of_isolated_right'
--/
 
-#print countable_of_isolated_left' /-
+/- warning: countable_of_isolated_left -> countable_of_isolated_left' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : TopologicalSpace.SecondCountableTopology.{u1} α _inst_1], Set.Countable.{u1} α (setOf.{u1} α (fun (x : α) => Exists.{succ u1} α (fun (y : α) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) y x) (Eq.{succ u1} (Set.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) y x) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : TopologicalSpace.SecondCountableTopology.{u1} α _inst_1], Set.Countable.{u1} α (setOf.{u1} α (fun (x : α) => Exists.{succ u1} α (fun (y : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) y x) (Eq.{succ u1} (Set.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) y x) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))))))
+Case conversion may be inaccurate. Consider using '#align countable_of_isolated_left countable_of_isolated_left'ₓ'. -/
 /-- The set of points which are isolated on the left is countable when the space is
 second-countable. -/
 theorem countable_of_isolated_left' [SecondCountableTopology α] :
@@ -2028,11 +2355,10 @@ theorem countable_of_isolated_left' [SecondCountableTopology α] :
   simp_rw [this]
   rfl
 #align countable_of_isolated_left countable_of_isolated_left'
--/
 
 /- warning: set.pairwise_disjoint.countable_of_Ioo -> Set.PairwiseDisjoint.countable_of_Ioo is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : TopologicalSpace.SecondCountableTopology.{u1} α _inst_1] {y : α -> α} {s : Set.{u1} α}, (Set.PairwiseDisjoint.{u1, u1} (Set.{u1} α) α (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s (fun (x : α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) x (y x))) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x (y x))) -> (Set.Countable.{u1} α s)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : TopologicalSpace.SecondCountableTopology.{u1} α _inst_1] {y : α -> α} {s : Set.{u1} α}, (Set.PairwiseDisjoint.{u1, u1} (Set.{u1} α) α (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) s (fun (x : α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) x (y x))) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x (y x))) -> (Set.Countable.{u1} α s)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : TopologicalSpace.SecondCountableTopology.{u1} α _inst_1] {y : α -> α} {s : Set.{u1} α}, (Set.PairwiseDisjoint.{u1, u1} (Set.{u1} α) α (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) s (fun (x : α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) x (y x))) -> (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x (y x))) -> (Set.Countable.{u1} α s)
 Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint.countable_of_Ioo Set.PairwiseDisjoint.countable_of_Iooₓ'. -/
@@ -2070,15 +2396,19 @@ e.g., `ι → ℝ`.
 variable {ι : Type _} {π : ι → Type _} [Finite ι] [∀ i, LinearOrder (π i)]
   [∀ i, TopologicalSpace (π i)] [∀ i, OrderTopology (π i)] {a b x : ∀ i, π i} {a' b' x' : ι → α}
 
-#print pi_Iic_mem_nhds /-
+/- warning: pi_Iic_mem_nhds -> pi_Iic_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {π : ι -> Type.{u2}} [_inst_4 : Finite.{succ u1} ι] [_inst_5 : forall (i : ι), LinearOrder.{u2} (π i)] [_inst_6 : forall (i : ι), TopologicalSpace.{u2} (π i)] [_inst_7 : forall (i : ι), OrderTopology.{u2} (π i) (_inst_6 i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))] {a : forall (i : ι), π i} {x : forall (i : ι), π i}, (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toHasLt.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) (x i) (a i)) -> (Membership.Mem.{max u1 u2, max u1 u2} (Set.{max u1 u2} (forall (i : ι), π i)) (Filter.{max u1 u2} (forall (i : ι), π i)) (Filter.hasMem.{max u1 u2} (forall (i : ι), π i)) (Set.Iic.{max u1 u2} (forall (i : ι), π i) (Pi.preorder.{u1, u2} ι (fun (i : ι) => π i) (fun (i : ι) => PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) a) (nhds.{max u1 u2} (forall (i : ι), π i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => π i) (fun (a : ι) => _inst_6 a)) x))
+but is expected to have type
+  forall {ι : Type.{u1}} {π : ι -> Type.{u2}} [_inst_4 : Finite.{succ u1} ι] [_inst_5 : forall (i : ι), LinearOrder.{u2} (π i)] [_inst_6 : forall (i : ι), TopologicalSpace.{u2} (π i)] [_inst_7 : forall (i : ι), OrderTopology.{u2} (π i) (_inst_6 i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))] {a : forall (i : ι), π i} {x : forall (i : ι), π i}, (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toLT.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) (x i) (a i)) -> (Membership.mem.{max u1 u2, max u1 u2} (Set.{max u1 u2} (forall (i : ι), π i)) (Filter.{max u1 u2} (forall (i : ι), π i)) (instMembershipSetFilter.{max u1 u2} (forall (i : ι), π i)) (Set.Iic.{max u1 u2} (forall (i : ι), π i) (Pi.preorder.{u1, u2} ι (fun (i : ι) => π i) (fun (i : ι) => PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) a) (nhds.{max u1 u2} (forall (i : ι), π i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => π i) (fun (a : ι) => _inst_6 a)) x))
+Case conversion may be inaccurate. Consider using '#align pi_Iic_mem_nhds pi_Iic_mem_nhdsₓ'. -/
 theorem pi_Iic_mem_nhds (ha : ∀ i, x i < a i) : Iic a ∈ 𝓝 x :=
   pi_univ_Iic a ▸ set_pi_mem_nhds (Set.toFinite _) fun i _ => Iic_mem_nhds (ha _)
 #align pi_Iic_mem_nhds pi_Iic_mem_nhds
--/
 
 /- warning: pi_Iic_mem_nhds' -> pi_Iic_mem_nhds' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {ι : Type.{u2}} [_inst_4 : Finite.{succ u2} ι] {a' : ι -> α} {x' : ι -> α}, (forall (i : ι), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (x' i) (a' i)) -> (Membership.Mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (Filter.hasMem.{max u2 u1} (ι -> α)) (Set.Iic.{max u2 u1} (ι -> α) (Pi.preorder.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {ι : Type.{u2}} [_inst_4 : Finite.{succ u2} ι] {a' : ι -> α} {x' : ι -> α}, (forall (i : ι), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (x' i) (a' i)) -> (Membership.Mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (Filter.hasMem.{max u2 u1} (ι -> α)) (Set.Iic.{max u2 u1} (ι -> α) (Pi.preorder.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {ι : Type.{u1}} [_inst_4 : Finite.{succ u1} ι] {a' : ι -> α} {x' : ι -> α}, (forall (i : ι), LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (x' i) (a' i)) -> (Membership.mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (instMembershipSetFilter.{max u2 u1} (ι -> α)) (Set.Iic.{max u2 u1} (ι -> α) (Pi.preorder.{u1, u2} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) a') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u1, u2} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
 Case conversion may be inaccurate. Consider using '#align pi_Iic_mem_nhds' pi_Iic_mem_nhds'ₓ'. -/
@@ -2086,15 +2416,19 @@ theorem pi_Iic_mem_nhds' (ha : ∀ i, x' i < a' i) : Iic a' ∈ 𝓝 x' :=
   pi_Iic_mem_nhds ha
 #align pi_Iic_mem_nhds' pi_Iic_mem_nhds'
 
-#print pi_Ici_mem_nhds /-
+/- warning: pi_Ici_mem_nhds -> pi_Ici_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {π : ι -> Type.{u2}} [_inst_4 : Finite.{succ u1} ι] [_inst_5 : forall (i : ι), LinearOrder.{u2} (π i)] [_inst_6 : forall (i : ι), TopologicalSpace.{u2} (π i)] [_inst_7 : forall (i : ι), OrderTopology.{u2} (π i) (_inst_6 i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))] {a : forall (i : ι), π i} {x : forall (i : ι), π i}, (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toHasLt.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) (a i) (x i)) -> (Membership.Mem.{max u1 u2, max u1 u2} (Set.{max u1 u2} (forall (i : ι), π i)) (Filter.{max u1 u2} (forall (i : ι), π i)) (Filter.hasMem.{max u1 u2} (forall (i : ι), π i)) (Set.Ici.{max u1 u2} (forall (i : ι), π i) (Pi.preorder.{u1, u2} ι (fun (i : ι) => π i) (fun (i : ι) => PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) a) (nhds.{max u1 u2} (forall (i : ι), π i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => π i) (fun (a : ι) => _inst_6 a)) x))
+but is expected to have type
+  forall {ι : Type.{u1}} {π : ι -> Type.{u2}} [_inst_4 : Finite.{succ u1} ι] [_inst_5 : forall (i : ι), LinearOrder.{u2} (π i)] [_inst_6 : forall (i : ι), TopologicalSpace.{u2} (π i)] [_inst_7 : forall (i : ι), OrderTopology.{u2} (π i) (_inst_6 i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))] {a : forall (i : ι), π i} {x : forall (i : ι), π i}, (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toLT.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) (a i) (x i)) -> (Membership.mem.{max u1 u2, max u1 u2} (Set.{max u1 u2} (forall (i : ι), π i)) (Filter.{max u1 u2} (forall (i : ι), π i)) (instMembershipSetFilter.{max u1 u2} (forall (i : ι), π i)) (Set.Ici.{max u1 u2} (forall (i : ι), π i) (Pi.preorder.{u1, u2} ι (fun (i : ι) => π i) (fun (i : ι) => PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) a) (nhds.{max u1 u2} (forall (i : ι), π i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => π i) (fun (a : ι) => _inst_6 a)) x))
+Case conversion may be inaccurate. Consider using '#align pi_Ici_mem_nhds pi_Ici_mem_nhdsₓ'. -/
 theorem pi_Ici_mem_nhds (ha : ∀ i, a i < x i) : Ici a ∈ 𝓝 x :=
   pi_univ_Ici a ▸ set_pi_mem_nhds (Set.toFinite _) fun i _ => Ici_mem_nhds (ha _)
 #align pi_Ici_mem_nhds pi_Ici_mem_nhds
--/
 
 /- warning: pi_Ici_mem_nhds' -> pi_Ici_mem_nhds' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {ι : Type.{u2}} [_inst_4 : Finite.{succ u2} ι] {a' : ι -> α} {x' : ι -> α}, (forall (i : ι), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (a' i) (x' i)) -> (Membership.Mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (Filter.hasMem.{max u2 u1} (ι -> α)) (Set.Ici.{max u2 u1} (ι -> α) (Pi.preorder.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {ι : Type.{u2}} [_inst_4 : Finite.{succ u2} ι] {a' : ι -> α} {x' : ι -> α}, (forall (i : ι), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (a' i) (x' i)) -> (Membership.Mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (Filter.hasMem.{max u2 u1} (ι -> α)) (Set.Ici.{max u2 u1} (ι -> α) (Pi.preorder.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {ι : Type.{u1}} [_inst_4 : Finite.{succ u1} ι] {a' : ι -> α} {x' : ι -> α}, (forall (i : ι), LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (a' i) (x' i)) -> (Membership.mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (instMembershipSetFilter.{max u2 u1} (ι -> α)) (Set.Ici.{max u2 u1} (ι -> α) (Pi.preorder.{u1, u2} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) a') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u1, u2} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
 Case conversion may be inaccurate. Consider using '#align pi_Ici_mem_nhds' pi_Ici_mem_nhds'ₓ'. -/
@@ -2102,15 +2436,19 @@ theorem pi_Ici_mem_nhds' (ha : ∀ i, a' i < x' i) : Ici a' ∈ 𝓝 x' :=
   pi_Ici_mem_nhds ha
 #align pi_Ici_mem_nhds' pi_Ici_mem_nhds'
 
-#print pi_Icc_mem_nhds /-
+/- warning: pi_Icc_mem_nhds -> pi_Icc_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {π : ι -> Type.{u2}} [_inst_4 : Finite.{succ u1} ι] [_inst_5 : forall (i : ι), LinearOrder.{u2} (π i)] [_inst_6 : forall (i : ι), TopologicalSpace.{u2} (π i)] [_inst_7 : forall (i : ι), OrderTopology.{u2} (π i) (_inst_6 i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))] {a : forall (i : ι), π i} {b : forall (i : ι), π i} {x : forall (i : ι), π i}, (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toHasLt.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) (a i) (x i)) -> (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toHasLt.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) (x i) (b i)) -> (Membership.Mem.{max u1 u2, max u1 u2} (Set.{max u1 u2} (forall (i : ι), π i)) (Filter.{max u1 u2} (forall (i : ι), π i)) (Filter.hasMem.{max u1 u2} (forall (i : ι), π i)) (Set.Icc.{max u1 u2} (forall (i : ι), π i) (Pi.preorder.{u1, u2} ι (fun (i : ι) => π i) (fun (i : ι) => PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) a b) (nhds.{max u1 u2} (forall (i : ι), π i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => π i) (fun (a : ι) => _inst_6 a)) x))
+but is expected to have type
+  forall {ι : Type.{u1}} {π : ι -> Type.{u2}} [_inst_4 : Finite.{succ u1} ι] [_inst_5 : forall (i : ι), LinearOrder.{u2} (π i)] [_inst_6 : forall (i : ι), TopologicalSpace.{u2} (π i)] [_inst_7 : forall (i : ι), OrderTopology.{u2} (π i) (_inst_6 i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))] {a : forall (i : ι), π i} {b : forall (i : ι), π i} {x : forall (i : ι), π i}, (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toLT.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) (a i) (x i)) -> (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toLT.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) (x i) (b i)) -> (Membership.mem.{max u1 u2, max u1 u2} (Set.{max u1 u2} (forall (i : ι), π i)) (Filter.{max u1 u2} (forall (i : ι), π i)) (instMembershipSetFilter.{max u1 u2} (forall (i : ι), π i)) (Set.Icc.{max u1 u2} (forall (i : ι), π i) (Pi.preorder.{u1, u2} ι (fun (i : ι) => π i) (fun (i : ι) => PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) a b) (nhds.{max u1 u2} (forall (i : ι), π i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => π i) (fun (a : ι) => _inst_6 a)) x))
+Case conversion may be inaccurate. Consider using '#align pi_Icc_mem_nhds pi_Icc_mem_nhdsₓ'. -/
 theorem pi_Icc_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Icc a b ∈ 𝓝 x :=
   pi_univ_Icc a b ▸ set_pi_mem_nhds finite_univ fun i _ => Icc_mem_nhds (ha _) (hb _)
 #align pi_Icc_mem_nhds pi_Icc_mem_nhds
--/
 
 /- warning: pi_Icc_mem_nhds' -> pi_Icc_mem_nhds' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {ι : Type.{u2}} [_inst_4 : Finite.{succ u2} ι] {a' : ι -> α} {b' : ι -> α} {x' : ι -> α}, (forall (i : ι), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (a' i) (x' i)) -> (forall (i : ι), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (x' i) (b' i)) -> (Membership.Mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (Filter.hasMem.{max u2 u1} (ι -> α)) (Set.Icc.{max u2 u1} (ι -> α) (Pi.preorder.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a' b') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {ι : Type.{u2}} [_inst_4 : Finite.{succ u2} ι] {a' : ι -> α} {b' : ι -> α} {x' : ι -> α}, (forall (i : ι), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (a' i) (x' i)) -> (forall (i : ι), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (x' i) (b' i)) -> (Membership.Mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (Filter.hasMem.{max u2 u1} (ι -> α)) (Set.Icc.{max u2 u1} (ι -> α) (Pi.preorder.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a' b') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {ι : Type.{u1}} [_inst_4 : Finite.{succ u1} ι] {a' : ι -> α} {b' : ι -> α} {x' : ι -> α}, (forall (i : ι), LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (a' i) (x' i)) -> (forall (i : ι), LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (x' i) (b' i)) -> (Membership.mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (instMembershipSetFilter.{max u2 u1} (ι -> α)) (Set.Icc.{max u2 u1} (ι -> α) (Pi.preorder.{u1, u2} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) a' b') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u1, u2} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
 Case conversion may be inaccurate. Consider using '#align pi_Icc_mem_nhds' pi_Icc_mem_nhds'ₓ'. -/
@@ -2120,17 +2458,21 @@ theorem pi_Icc_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : I
 
 variable [Nonempty ι]
 
-#print pi_Iio_mem_nhds /-
+/- warning: pi_Iio_mem_nhds -> pi_Iio_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {π : ι -> Type.{u2}} [_inst_4 : Finite.{succ u1} ι] [_inst_5 : forall (i : ι), LinearOrder.{u2} (π i)] [_inst_6 : forall (i : ι), TopologicalSpace.{u2} (π i)] [_inst_7 : forall (i : ι), OrderTopology.{u2} (π i) (_inst_6 i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))] {a : forall (i : ι), π i} {x : forall (i : ι), π i} [_inst_8 : Nonempty.{succ u1} ι], (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toHasLt.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) (x i) (a i)) -> (Membership.Mem.{max u1 u2, max u1 u2} (Set.{max u1 u2} (forall (i : ι), π i)) (Filter.{max u1 u2} (forall (i : ι), π i)) (Filter.hasMem.{max u1 u2} (forall (i : ι), π i)) (Set.Iio.{max u1 u2} (forall (i : ι), π i) (Pi.preorder.{u1, u2} ι (fun (i : ι) => π i) (fun (i : ι) => PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) a) (nhds.{max u1 u2} (forall (i : ι), π i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => π i) (fun (a : ι) => _inst_6 a)) x))
+but is expected to have type
+  forall {ι : Type.{u1}} {π : ι -> Type.{u2}} [_inst_4 : Finite.{succ u1} ι] [_inst_5 : forall (i : ι), LinearOrder.{u2} (π i)] [_inst_6 : forall (i : ι), TopologicalSpace.{u2} (π i)] [_inst_7 : forall (i : ι), OrderTopology.{u2} (π i) (_inst_6 i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))] {a : forall (i : ι), π i} {x : forall (i : ι), π i} [_inst_8 : Nonempty.{succ u1} ι], (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toLT.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) (x i) (a i)) -> (Membership.mem.{max u1 u2, max u1 u2} (Set.{max u1 u2} (forall (i : ι), π i)) (Filter.{max u1 u2} (forall (i : ι), π i)) (instMembershipSetFilter.{max u1 u2} (forall (i : ι), π i)) (Set.Iio.{max u1 u2} (forall (i : ι), π i) (Pi.preorder.{u1, u2} ι (fun (i : ι) => π i) (fun (i : ι) => PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) a) (nhds.{max u1 u2} (forall (i : ι), π i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => π i) (fun (a : ι) => _inst_6 a)) x))
+Case conversion may be inaccurate. Consider using '#align pi_Iio_mem_nhds pi_Iio_mem_nhdsₓ'. -/
 theorem pi_Iio_mem_nhds (ha : ∀ i, x i < a i) : Iio a ∈ 𝓝 x :=
   by
   refine' mem_of_superset (set_pi_mem_nhds (Set.toFinite _) fun i _ => _) (pi_univ_Iio_subset a)
   exact Iio_mem_nhds (ha i)
 #align pi_Iio_mem_nhds pi_Iio_mem_nhds
--/
 
 /- warning: pi_Iio_mem_nhds' -> pi_Iio_mem_nhds' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {ι : Type.{u2}} [_inst_4 : Finite.{succ u2} ι] {a' : ι -> α} {x' : ι -> α} [_inst_8 : Nonempty.{succ u2} ι], (forall (i : ι), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (x' i) (a' i)) -> (Membership.Mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (Filter.hasMem.{max u2 u1} (ι -> α)) (Set.Iio.{max u2 u1} (ι -> α) (Pi.preorder.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {ι : Type.{u2}} [_inst_4 : Finite.{succ u2} ι] {a' : ι -> α} {x' : ι -> α} [_inst_8 : Nonempty.{succ u2} ι], (forall (i : ι), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (x' i) (a' i)) -> (Membership.Mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (Filter.hasMem.{max u2 u1} (ι -> α)) (Set.Iio.{max u2 u1} (ι -> α) (Pi.preorder.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {ι : Type.{u1}} [_inst_4 : Finite.{succ u1} ι] {a' : ι -> α} {x' : ι -> α} [_inst_8 : Nonempty.{succ u1} ι], (forall (i : ι), LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (x' i) (a' i)) -> (Membership.mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (instMembershipSetFilter.{max u2 u1} (ι -> α)) (Set.Iio.{max u2 u1} (ι -> α) (Pi.preorder.{u1, u2} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) a') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u1, u2} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
 Case conversion may be inaccurate. Consider using '#align pi_Iio_mem_nhds' pi_Iio_mem_nhds'ₓ'. -/
@@ -2138,15 +2480,19 @@ theorem pi_Iio_mem_nhds' (ha : ∀ i, x' i < a' i) : Iio a' ∈ 𝓝 x' :=
   pi_Iio_mem_nhds ha
 #align pi_Iio_mem_nhds' pi_Iio_mem_nhds'
 
-#print pi_Ioi_mem_nhds /-
+/- warning: pi_Ioi_mem_nhds -> pi_Ioi_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {π : ι -> Type.{u2}} [_inst_4 : Finite.{succ u1} ι] [_inst_5 : forall (i : ι), LinearOrder.{u2} (π i)] [_inst_6 : forall (i : ι), TopologicalSpace.{u2} (π i)] [_inst_7 : forall (i : ι), OrderTopology.{u2} (π i) (_inst_6 i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))] {a : forall (i : ι), π i} {x : forall (i : ι), π i} [_inst_8 : Nonempty.{succ u1} ι], (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toHasLt.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) (a i) (x i)) -> (Membership.Mem.{max u1 u2, max u1 u2} (Set.{max u1 u2} (forall (i : ι), π i)) (Filter.{max u1 u2} (forall (i : ι), π i)) (Filter.hasMem.{max u1 u2} (forall (i : ι), π i)) (Set.Ioi.{max u1 u2} (forall (i : ι), π i) (Pi.preorder.{u1, u2} ι (fun (i : ι) => π i) (fun (i : ι) => PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) a) (nhds.{max u1 u2} (forall (i : ι), π i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => π i) (fun (a : ι) => _inst_6 a)) x))
+but is expected to have type
+  forall {ι : Type.{u1}} {π : ι -> Type.{u2}} [_inst_4 : Finite.{succ u1} ι] [_inst_5 : forall (i : ι), LinearOrder.{u2} (π i)] [_inst_6 : forall (i : ι), TopologicalSpace.{u2} (π i)] [_inst_7 : forall (i : ι), OrderTopology.{u2} (π i) (_inst_6 i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))] {a : forall (i : ι), π i} {x : forall (i : ι), π i} [_inst_8 : Nonempty.{succ u1} ι], (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toLT.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) (a i) (x i)) -> (Membership.mem.{max u1 u2, max u1 u2} (Set.{max u1 u2} (forall (i : ι), π i)) (Filter.{max u1 u2} (forall (i : ι), π i)) (instMembershipSetFilter.{max u1 u2} (forall (i : ι), π i)) (Set.Ioi.{max u1 u2} (forall (i : ι), π i) (Pi.preorder.{u1, u2} ι (fun (i : ι) => π i) (fun (i : ι) => PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) a) (nhds.{max u1 u2} (forall (i : ι), π i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => π i) (fun (a : ι) => _inst_6 a)) x))
+Case conversion may be inaccurate. Consider using '#align pi_Ioi_mem_nhds pi_Ioi_mem_nhdsₓ'. -/
 theorem pi_Ioi_mem_nhds (ha : ∀ i, a i < x i) : Ioi a ∈ 𝓝 x :=
   @pi_Iio_mem_nhds ι (fun i => (π i)ᵒᵈ) _ _ _ _ _ _ _ ha
 #align pi_Ioi_mem_nhds pi_Ioi_mem_nhds
--/
 
 /- warning: pi_Ioi_mem_nhds' -> pi_Ioi_mem_nhds' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {ι : Type.{u2}} [_inst_4 : Finite.{succ u2} ι] {a' : ι -> α} {x' : ι -> α} [_inst_8 : Nonempty.{succ u2} ι], (forall (i : ι), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (a' i) (x' i)) -> (Membership.Mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (Filter.hasMem.{max u2 u1} (ι -> α)) (Set.Ioi.{max u2 u1} (ι -> α) (Pi.preorder.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {ι : Type.{u2}} [_inst_4 : Finite.{succ u2} ι] {a' : ι -> α} {x' : ι -> α} [_inst_8 : Nonempty.{succ u2} ι], (forall (i : ι), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (a' i) (x' i)) -> (Membership.Mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (Filter.hasMem.{max u2 u1} (ι -> α)) (Set.Ioi.{max u2 u1} (ι -> α) (Pi.preorder.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {ι : Type.{u1}} [_inst_4 : Finite.{succ u1} ι] {a' : ι -> α} {x' : ι -> α} [_inst_8 : Nonempty.{succ u1} ι], (forall (i : ι), LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (a' i) (x' i)) -> (Membership.mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (instMembershipSetFilter.{max u2 u1} (ι -> α)) (Set.Ioi.{max u2 u1} (ι -> α) (Pi.preorder.{u1, u2} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) a') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u1, u2} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
 Case conversion may be inaccurate. Consider using '#align pi_Ioi_mem_nhds' pi_Ioi_mem_nhds'ₓ'. -/
@@ -2154,17 +2500,21 @@ theorem pi_Ioi_mem_nhds' (ha : ∀ i, a' i < x' i) : Ioi a' ∈ 𝓝 x' :=
   pi_Ioi_mem_nhds ha
 #align pi_Ioi_mem_nhds' pi_Ioi_mem_nhds'
 
-#print pi_Ioc_mem_nhds /-
+/- warning: pi_Ioc_mem_nhds -> pi_Ioc_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {π : ι -> Type.{u2}} [_inst_4 : Finite.{succ u1} ι] [_inst_5 : forall (i : ι), LinearOrder.{u2} (π i)] [_inst_6 : forall (i : ι), TopologicalSpace.{u2} (π i)] [_inst_7 : forall (i : ι), OrderTopology.{u2} (π i) (_inst_6 i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))] {a : forall (i : ι), π i} {b : forall (i : ι), π i} {x : forall (i : ι), π i} [_inst_8 : Nonempty.{succ u1} ι], (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toHasLt.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) (a i) (x i)) -> (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toHasLt.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) (x i) (b i)) -> (Membership.Mem.{max u1 u2, max u1 u2} (Set.{max u1 u2} (forall (i : ι), π i)) (Filter.{max u1 u2} (forall (i : ι), π i)) (Filter.hasMem.{max u1 u2} (forall (i : ι), π i)) (Set.Ioc.{max u1 u2} (forall (i : ι), π i) (Pi.preorder.{u1, u2} ι (fun (i : ι) => π i) (fun (i : ι) => PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) a b) (nhds.{max u1 u2} (forall (i : ι), π i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => π i) (fun (a : ι) => _inst_6 a)) x))
+but is expected to have type
+  forall {ι : Type.{u1}} {π : ι -> Type.{u2}} [_inst_4 : Finite.{succ u1} ι] [_inst_5 : forall (i : ι), LinearOrder.{u2} (π i)] [_inst_6 : forall (i : ι), TopologicalSpace.{u2} (π i)] [_inst_7 : forall (i : ι), OrderTopology.{u2} (π i) (_inst_6 i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))] {a : forall (i : ι), π i} {b : forall (i : ι), π i} {x : forall (i : ι), π i} [_inst_8 : Nonempty.{succ u1} ι], (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toLT.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) (a i) (x i)) -> (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toLT.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) (x i) (b i)) -> (Membership.mem.{max u1 u2, max u1 u2} (Set.{max u1 u2} (forall (i : ι), π i)) (Filter.{max u1 u2} (forall (i : ι), π i)) (instMembershipSetFilter.{max u1 u2} (forall (i : ι), π i)) (Set.Ioc.{max u1 u2} (forall (i : ι), π i) (Pi.preorder.{u1, u2} ι (fun (i : ι) => π i) (fun (i : ι) => PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) a b) (nhds.{max u1 u2} (forall (i : ι), π i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => π i) (fun (a : ι) => _inst_6 a)) x))
+Case conversion may be inaccurate. Consider using '#align pi_Ioc_mem_nhds pi_Ioc_mem_nhdsₓ'. -/
 theorem pi_Ioc_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Ioc a b ∈ 𝓝 x :=
   by
   refine' mem_of_superset (set_pi_mem_nhds (Set.toFinite _) fun i _ => _) (pi_univ_Ioc_subset a b)
   exact Ioc_mem_nhds (ha i) (hb i)
 #align pi_Ioc_mem_nhds pi_Ioc_mem_nhds
--/
 
 /- warning: pi_Ioc_mem_nhds' -> pi_Ioc_mem_nhds' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {ι : Type.{u2}} [_inst_4 : Finite.{succ u2} ι] {a' : ι -> α} {b' : ι -> α} {x' : ι -> α} [_inst_8 : Nonempty.{succ u2} ι], (forall (i : ι), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (a' i) (x' i)) -> (forall (i : ι), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (x' i) (b' i)) -> (Membership.Mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (Filter.hasMem.{max u2 u1} (ι -> α)) (Set.Ioc.{max u2 u1} (ι -> α) (Pi.preorder.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a' b') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {ι : Type.{u2}} [_inst_4 : Finite.{succ u2} ι] {a' : ι -> α} {b' : ι -> α} {x' : ι -> α} [_inst_8 : Nonempty.{succ u2} ι], (forall (i : ι), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (a' i) (x' i)) -> (forall (i : ι), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (x' i) (b' i)) -> (Membership.Mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (Filter.hasMem.{max u2 u1} (ι -> α)) (Set.Ioc.{max u2 u1} (ι -> α) (Pi.preorder.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a' b') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {ι : Type.{u1}} [_inst_4 : Finite.{succ u1} ι] {a' : ι -> α} {b' : ι -> α} {x' : ι -> α} [_inst_8 : Nonempty.{succ u1} ι], (forall (i : ι), LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (a' i) (x' i)) -> (forall (i : ι), LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (x' i) (b' i)) -> (Membership.mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (instMembershipSetFilter.{max u2 u1} (ι -> α)) (Set.Ioc.{max u2 u1} (ι -> α) (Pi.preorder.{u1, u2} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) a' b') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u1, u2} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
 Case conversion may be inaccurate. Consider using '#align pi_Ioc_mem_nhds' pi_Ioc_mem_nhds'ₓ'. -/
@@ -2172,17 +2522,21 @@ theorem pi_Ioc_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : I
   pi_Ioc_mem_nhds ha hb
 #align pi_Ioc_mem_nhds' pi_Ioc_mem_nhds'
 
-#print pi_Ico_mem_nhds /-
+/- warning: pi_Ico_mem_nhds -> pi_Ico_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {π : ι -> Type.{u2}} [_inst_4 : Finite.{succ u1} ι] [_inst_5 : forall (i : ι), LinearOrder.{u2} (π i)] [_inst_6 : forall (i : ι), TopologicalSpace.{u2} (π i)] [_inst_7 : forall (i : ι), OrderTopology.{u2} (π i) (_inst_6 i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))] {a : forall (i : ι), π i} {b : forall (i : ι), π i} {x : forall (i : ι), π i} [_inst_8 : Nonempty.{succ u1} ι], (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toHasLt.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) (a i) (x i)) -> (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toHasLt.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) (x i) (b i)) -> (Membership.Mem.{max u1 u2, max u1 u2} (Set.{max u1 u2} (forall (i : ι), π i)) (Filter.{max u1 u2} (forall (i : ι), π i)) (Filter.hasMem.{max u1 u2} (forall (i : ι), π i)) (Set.Ico.{max u1 u2} (forall (i : ι), π i) (Pi.preorder.{u1, u2} ι (fun (i : ι) => π i) (fun (i : ι) => PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) a b) (nhds.{max u1 u2} (forall (i : ι), π i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => π i) (fun (a : ι) => _inst_6 a)) x))
+but is expected to have type
+  forall {ι : Type.{u1}} {π : ι -> Type.{u2}} [_inst_4 : Finite.{succ u1} ι] [_inst_5 : forall (i : ι), LinearOrder.{u2} (π i)] [_inst_6 : forall (i : ι), TopologicalSpace.{u2} (π i)] [_inst_7 : forall (i : ι), OrderTopology.{u2} (π i) (_inst_6 i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))] {a : forall (i : ι), π i} {b : forall (i : ι), π i} {x : forall (i : ι), π i} [_inst_8 : Nonempty.{succ u1} ι], (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toLT.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) (a i) (x i)) -> (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toLT.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) (x i) (b i)) -> (Membership.mem.{max u1 u2, max u1 u2} (Set.{max u1 u2} (forall (i : ι), π i)) (Filter.{max u1 u2} (forall (i : ι), π i)) (instMembershipSetFilter.{max u1 u2} (forall (i : ι), π i)) (Set.Ico.{max u1 u2} (forall (i : ι), π i) (Pi.preorder.{u1, u2} ι (fun (i : ι) => π i) (fun (i : ι) => PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) a b) (nhds.{max u1 u2} (forall (i : ι), π i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => π i) (fun (a : ι) => _inst_6 a)) x))
+Case conversion may be inaccurate. Consider using '#align pi_Ico_mem_nhds pi_Ico_mem_nhdsₓ'. -/
 theorem pi_Ico_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Ico a b ∈ 𝓝 x :=
   by
   refine' mem_of_superset (set_pi_mem_nhds (Set.toFinite _) fun i _ => _) (pi_univ_Ico_subset a b)
   exact Ico_mem_nhds (ha i) (hb i)
 #align pi_Ico_mem_nhds pi_Ico_mem_nhds
--/
 
 /- warning: pi_Ico_mem_nhds' -> pi_Ico_mem_nhds' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {ι : Type.{u2}} [_inst_4 : Finite.{succ u2} ι] {a' : ι -> α} {b' : ι -> α} {x' : ι -> α} [_inst_8 : Nonempty.{succ u2} ι], (forall (i : ι), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (a' i) (x' i)) -> (forall (i : ι), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (x' i) (b' i)) -> (Membership.Mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (Filter.hasMem.{max u2 u1} (ι -> α)) (Set.Ico.{max u2 u1} (ι -> α) (Pi.preorder.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a' b') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {ι : Type.{u2}} [_inst_4 : Finite.{succ u2} ι] {a' : ι -> α} {b' : ι -> α} {x' : ι -> α} [_inst_8 : Nonempty.{succ u2} ι], (forall (i : ι), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (a' i) (x' i)) -> (forall (i : ι), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (x' i) (b' i)) -> (Membership.Mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (Filter.hasMem.{max u2 u1} (ι -> α)) (Set.Ico.{max u2 u1} (ι -> α) (Pi.preorder.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a' b') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {ι : Type.{u1}} [_inst_4 : Finite.{succ u1} ι] {a' : ι -> α} {b' : ι -> α} {x' : ι -> α} [_inst_8 : Nonempty.{succ u1} ι], (forall (i : ι), LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (a' i) (x' i)) -> (forall (i : ι), LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (x' i) (b' i)) -> (Membership.mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (instMembershipSetFilter.{max u2 u1} (ι -> α)) (Set.Ico.{max u2 u1} (ι -> α) (Pi.preorder.{u1, u2} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) a' b') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u1, u2} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
 Case conversion may be inaccurate. Consider using '#align pi_Ico_mem_nhds' pi_Ico_mem_nhds'ₓ'. -/
@@ -2190,17 +2544,21 @@ theorem pi_Ico_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : I
   pi_Ico_mem_nhds ha hb
 #align pi_Ico_mem_nhds' pi_Ico_mem_nhds'
 
-#print pi_Ioo_mem_nhds /-
+/- warning: pi_Ioo_mem_nhds -> pi_Ioo_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {π : ι -> Type.{u2}} [_inst_4 : Finite.{succ u1} ι] [_inst_5 : forall (i : ι), LinearOrder.{u2} (π i)] [_inst_6 : forall (i : ι), TopologicalSpace.{u2} (π i)] [_inst_7 : forall (i : ι), OrderTopology.{u2} (π i) (_inst_6 i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))] {a : forall (i : ι), π i} {b : forall (i : ι), π i} {x : forall (i : ι), π i} [_inst_8 : Nonempty.{succ u1} ι], (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toHasLt.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) (a i) (x i)) -> (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toHasLt.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) (x i) (b i)) -> (Membership.Mem.{max u1 u2, max u1 u2} (Set.{max u1 u2} (forall (i : ι), π i)) (Filter.{max u1 u2} (forall (i : ι), π i)) (Filter.hasMem.{max u1 u2} (forall (i : ι), π i)) (Set.Ioo.{max u1 u2} (forall (i : ι), π i) (Pi.preorder.{u1, u2} ι (fun (i : ι) => π i) (fun (i : ι) => PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (LinearOrder.toLattice.{u2} (π i) (_inst_5 i)))))) a b) (nhds.{max u1 u2} (forall (i : ι), π i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => π i) (fun (a : ι) => _inst_6 a)) x))
+but is expected to have type
+  forall {ι : Type.{u1}} {π : ι -> Type.{u2}} [_inst_4 : Finite.{succ u1} ι] [_inst_5 : forall (i : ι), LinearOrder.{u2} (π i)] [_inst_6 : forall (i : ι), TopologicalSpace.{u2} (π i)] [_inst_7 : forall (i : ι), OrderTopology.{u2} (π i) (_inst_6 i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))] {a : forall (i : ι), π i} {b : forall (i : ι), π i} {x : forall (i : ι), π i} [_inst_8 : Nonempty.{succ u1} ι], (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toLT.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) (a i) (x i)) -> (forall (i : ι), LT.lt.{u2} (π i) (Preorder.toLT.{u2} (π i) (PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) (x i) (b i)) -> (Membership.mem.{max u1 u2, max u1 u2} (Set.{max u1 u2} (forall (i : ι), π i)) (Filter.{max u1 u2} (forall (i : ι), π i)) (instMembershipSetFilter.{max u1 u2} (forall (i : ι), π i)) (Set.Ioo.{max u1 u2} (forall (i : ι), π i) (Pi.preorder.{u1, u2} ι (fun (i : ι) => π i) (fun (i : ι) => PartialOrder.toPreorder.{u2} (π i) (SemilatticeInf.toPartialOrder.{u2} (π i) (Lattice.toSemilatticeInf.{u2} (π i) (DistribLattice.toLattice.{u2} (π i) (instDistribLattice.{u2} (π i) (_inst_5 i))))))) a b) (nhds.{max u1 u2} (forall (i : ι), π i) (Pi.topologicalSpace.{u1, u2} ι (fun (i : ι) => π i) (fun (a : ι) => _inst_6 a)) x))
+Case conversion may be inaccurate. Consider using '#align pi_Ioo_mem_nhds pi_Ioo_mem_nhdsₓ'. -/
 theorem pi_Ioo_mem_nhds (ha : ∀ i, a i < x i) (hb : ∀ i, x i < b i) : Ioo a b ∈ 𝓝 x :=
   by
   refine' mem_of_superset (set_pi_mem_nhds (Set.toFinite _) fun i _ => _) (pi_univ_Ioo_subset a b)
   exact Ioo_mem_nhds (ha i) (hb i)
 #align pi_Ioo_mem_nhds pi_Ioo_mem_nhds
--/
 
 /- warning: pi_Ioo_mem_nhds' -> pi_Ioo_mem_nhds' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {ι : Type.{u2}} [_inst_4 : Finite.{succ u2} ι] {a' : ι -> α} {b' : ι -> α} {x' : ι -> α} [_inst_8 : Nonempty.{succ u2} ι], (forall (i : ι), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (a' i) (x' i)) -> (forall (i : ι), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (x' i) (b' i)) -> (Membership.Mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (Filter.hasMem.{max u2 u1} (ι -> α)) (Set.Ioo.{max u2 u1} (ι -> α) (Pi.preorder.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a' b') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {ι : Type.{u2}} [_inst_4 : Finite.{succ u2} ι] {a' : ι -> α} {b' : ι -> α} {x' : ι -> α} [_inst_8 : Nonempty.{succ u2} ι], (forall (i : ι), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (a' i) (x' i)) -> (forall (i : ι), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) (x' i) (b' i)) -> (Membership.Mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (Filter.hasMem.{max u2 u1} (ι -> α)) (Set.Ioo.{max u2 u1} (ι -> α) (Pi.preorder.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a' b') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u2, u1} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : LinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))] {ι : Type.{u1}} [_inst_4 : Finite.{succ u1} ι] {a' : ι -> α} {b' : ι -> α} {x' : ι -> α} [_inst_8 : Nonempty.{succ u1} ι], (forall (i : ι), LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (a' i) (x' i)) -> (forall (i : ι), LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) (x' i) (b' i)) -> (Membership.mem.{max u2 u1, max u2 u1} (Set.{max u2 u1} (ι -> α)) (Filter.{max u2 u1} (ι -> α)) (instMembershipSetFilter.{max u2 u1} (ι -> α)) (Set.Ioo.{max u2 u1} (ι -> α) (Pi.preorder.{u1, u2} ι (fun (ᾰ : ι) => α) (fun (i : ι) => PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_2)))))) a' b') (nhds.{max u2 u1} (ι -> α) (Pi.topologicalSpace.{u1, u2} ι (fun (ᾰ : ι) => α) (fun (a : ι) => _inst_1)) x'))
 Case conversion may be inaccurate. Consider using '#align pi_Ioo_mem_nhds' pi_Ioo_mem_nhds'ₓ'. -/
@@ -2212,7 +2570,7 @@ end Pi
 
 /- warning: disjoint_nhds_at_top -> disjoint_nhds_atTop is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (x : α), Disjoint.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α) (BoundedOrder.toOrderBot.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (CompleteLattice.toBoundedOrder.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (nhds.{u1} α _inst_1 x) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (x : α), Disjoint.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α) (BoundedOrder.toOrderBot.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (CompleteLattice.toBoundedOrder.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (nhds.{u1} α _inst_1 x) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (x : α), Disjoint.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α) (BoundedOrder.toOrderBot.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (CompleteLattice.toBoundedOrder.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (nhds.{u1} α _inst_1 x) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align disjoint_nhds_at_top disjoint_nhds_atTopₓ'. -/
@@ -2225,7 +2583,7 @@ theorem disjoint_nhds_atTop [NoMaxOrder α] (x : α) : Disjoint (𝓝 x) atTop :
 
 /- warning: inf_nhds_at_top -> inf_nhds_atTop is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (x : α), Eq.{succ u1} (Filter.{u1} α) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (nhds.{u1} α _inst_1 x) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (x : α), Eq.{succ u1} (Filter.{u1} α) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (nhds.{u1} α _inst_1 x) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (x : α), Eq.{succ u1} (Filter.{u1} α) (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) (nhds.{u1} α _inst_1 x) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))
 Case conversion may be inaccurate. Consider using '#align inf_nhds_at_top inf_nhds_atTopₓ'. -/
@@ -2236,7 +2594,7 @@ theorem inf_nhds_atTop [NoMaxOrder α] (x : α) : 𝓝 x ⊓ atTop = ⊥ :=
 
 /- warning: disjoint_nhds_at_bot -> disjoint_nhds_atBot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (x : α), Disjoint.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α) (BoundedOrder.toOrderBot.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (CompleteLattice.toBoundedOrder.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (nhds.{u1} α _inst_1 x) (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (x : α), Disjoint.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α) (BoundedOrder.toOrderBot.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (CompleteLattice.toBoundedOrder.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (nhds.{u1} α _inst_1 x) (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (x : α), Disjoint.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α) (BoundedOrder.toOrderBot.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (CompleteLattice.toBoundedOrder.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (nhds.{u1} α _inst_1 x) (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align disjoint_nhds_at_bot disjoint_nhds_atBotₓ'. -/
@@ -2246,7 +2604,7 @@ theorem disjoint_nhds_atBot [NoMinOrder α] (x : α) : Disjoint (𝓝 x) atBot :
 
 /- warning: inf_nhds_at_bot -> inf_nhds_atBot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (x : α), Eq.{succ u1} (Filter.{u1} α) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (nhds.{u1} α _inst_1 x) (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (x : α), Eq.{succ u1} (Filter.{u1} α) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (nhds.{u1} α _inst_1 x) (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (x : α), Eq.{succ u1} (Filter.{u1} α) (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) (nhds.{u1} α _inst_1 x) (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))
 Case conversion may be inaccurate. Consider using '#align inf_nhds_at_bot inf_nhds_atBotₓ'. -/
@@ -2255,33 +2613,49 @@ theorem inf_nhds_atBot [NoMinOrder α] (x : α) : 𝓝 x ⊓ atBot = ⊥ :=
   @inf_nhds_atTop αᵒᵈ _ _ _ _ x
 #align inf_nhds_at_bot inf_nhds_atBot
 
-#print not_tendsto_nhds_of_tendsto_atTop /-
+/- warning: not_tendsto_nhds_of_tendsto_at_top -> not_tendsto_nhds_of_tendsto_atTop is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {F : Filter.{u2} β} [_inst_5 : Filter.NeBot.{u2} β F] {f : β -> α}, (Filter.Tendsto.{u2, u1} β α f F (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))) -> (forall (x : α), Not (Filter.Tendsto.{u2, u1} β α f F (nhds.{u1} α _inst_1 x)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {F : Filter.{u2} β} [_inst_5 : Filter.NeBot.{u2} β F] {f : β -> α}, (Filter.Tendsto.{u2, u1} β α f F (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))) -> (forall (x : α), Not (Filter.Tendsto.{u2, u1} β α f F (nhds.{u1} α _inst_1 x)))
+Case conversion may be inaccurate. Consider using '#align not_tendsto_nhds_of_tendsto_at_top not_tendsto_nhds_of_tendsto_atTopₓ'. -/
 theorem not_tendsto_nhds_of_tendsto_atTop [NoMaxOrder α] {F : Filter β} [NeBot F] {f : β → α}
     (hf : Tendsto f F atTop) (x : α) : ¬Tendsto f F (𝓝 x) :=
   hf.not_tendsto (disjoint_nhds_atTop x).symm
 #align not_tendsto_nhds_of_tendsto_at_top not_tendsto_nhds_of_tendsto_atTop
--/
 
-#print not_tendsto_atTop_of_tendsto_nhds /-
+/- warning: not_tendsto_at_top_of_tendsto_nhds -> not_tendsto_atTop_of_tendsto_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {F : Filter.{u2} β} [_inst_5 : Filter.NeBot.{u2} β F] {f : β -> α} {x : α}, (Filter.Tendsto.{u2, u1} β α f F (nhds.{u1} α _inst_1 x)) -> (Not (Filter.Tendsto.{u2, u1} β α f F (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {F : Filter.{u2} β} [_inst_5 : Filter.NeBot.{u2} β F] {f : β -> α} {x : α}, (Filter.Tendsto.{u2, u1} β α f F (nhds.{u1} α _inst_1 x)) -> (Not (Filter.Tendsto.{u2, u1} β α f F (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))))
+Case conversion may be inaccurate. Consider using '#align not_tendsto_at_top_of_tendsto_nhds not_tendsto_atTop_of_tendsto_nhdsₓ'. -/
 theorem not_tendsto_atTop_of_tendsto_nhds [NoMaxOrder α] {F : Filter β} [NeBot F] {f : β → α}
     {x : α} (hf : Tendsto f F (𝓝 x)) : ¬Tendsto f F atTop :=
   hf.not_tendsto (disjoint_nhds_atTop x)
 #align not_tendsto_at_top_of_tendsto_nhds not_tendsto_atTop_of_tendsto_nhds
--/
 
-#print not_tendsto_nhds_of_tendsto_atBot /-
+/- warning: not_tendsto_nhds_of_tendsto_at_bot -> not_tendsto_nhds_of_tendsto_atBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {F : Filter.{u2} β} [_inst_5 : Filter.NeBot.{u2} β F] {f : β -> α}, (Filter.Tendsto.{u2, u1} β α f F (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))) -> (forall (x : α), Not (Filter.Tendsto.{u2, u1} β α f F (nhds.{u1} α _inst_1 x)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {F : Filter.{u2} β} [_inst_5 : Filter.NeBot.{u2} β F] {f : β -> α}, (Filter.Tendsto.{u2, u1} β α f F (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))) -> (forall (x : α), Not (Filter.Tendsto.{u2, u1} β α f F (nhds.{u1} α _inst_1 x)))
+Case conversion may be inaccurate. Consider using '#align not_tendsto_nhds_of_tendsto_at_bot not_tendsto_nhds_of_tendsto_atBotₓ'. -/
 theorem not_tendsto_nhds_of_tendsto_atBot [NoMinOrder α] {F : Filter β} [NeBot F] {f : β → α}
     (hf : Tendsto f F atBot) (x : α) : ¬Tendsto f F (𝓝 x) :=
   hf.not_tendsto (disjoint_nhds_atBot x).symm
 #align not_tendsto_nhds_of_tendsto_at_bot not_tendsto_nhds_of_tendsto_atBot
--/
 
-#print not_tendsto_atBot_of_tendsto_nhds /-
+/- warning: not_tendsto_at_bot_of_tendsto_nhds -> not_tendsto_atBot_of_tendsto_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {F : Filter.{u2} β} [_inst_5 : Filter.NeBot.{u2} β F] {f : β -> α} {x : α}, (Filter.Tendsto.{u2, u1} β α f F (nhds.{u1} α _inst_1 x)) -> (Not (Filter.Tendsto.{u2, u1} β α f F (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {F : Filter.{u2} β} [_inst_5 : Filter.NeBot.{u2} β F] {f : β -> α} {x : α}, (Filter.Tendsto.{u2, u1} β α f F (nhds.{u1} α _inst_1 x)) -> (Not (Filter.Tendsto.{u2, u1} β α f F (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))))
+Case conversion may be inaccurate. Consider using '#align not_tendsto_at_bot_of_tendsto_nhds not_tendsto_atBot_of_tendsto_nhdsₓ'. -/
 theorem not_tendsto_atBot_of_tendsto_nhds [NoMinOrder α] {F : Filter β} [NeBot F] {f : β → α}
     {x : α} (hf : Tendsto f F (𝓝 x)) : ¬Tendsto f F atBot :=
   hf.not_tendsto (disjoint_nhds_atBot x)
 #align not_tendsto_at_bot_of_tendsto_nhds not_tendsto_atBot_of_tendsto_nhds
--/
 
 /-!
 ### Neighborhoods to the left and to the right on an `order_topology`
@@ -2293,7 +2667,7 @@ intervals to the right or to the left of `a`. We give now these characterization
 
 /- warning: tfae_mem_nhds_within_Ioi -> TFAE_mem_nhdsWithin_Ioi is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (forall (s : Set.{u1} α), List.TFAE (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s))) (List.nil.{0} Prop)))))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (forall (s : Set.{u1} α), List.TFAE (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s))) (List.nil.{0} Prop)))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (forall (s : Set.{u1} α), List.TFAE (List.cons.{0} Prop (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (List.cons.{0} Prop (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (List.cons.{0} Prop (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (u : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u) s))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (u : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u) s))) (List.nil.{0} Prop)))))))
 Case conversion may be inaccurate. Consider using '#align tfae_mem_nhds_within_Ioi TFAE_mem_nhdsWithin_Ioiₓ'. -/
@@ -2335,7 +2709,7 @@ theorem TFAE_mem_nhdsWithin_Ioi {a b : α} (hab : a < b) (s : Set α) :
 
 /- warning: mem_nhds_within_Ioi_iff_exists_mem_Ioc_Ioo_subset -> mem_nhdsWithin_Ioi_iff_exists_mem_Ioc_Ioo_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {u' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u') -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u')) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u')) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {u' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u') -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u')) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u')) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {u' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a u') -> (Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (u : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u')) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u) s))))
 Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Ioi_iff_exists_mem_Ioc_Ioo_subset mem_nhdsWithin_Ioi_iff_exists_mem_Ioc_Ioo_subsetₓ'. -/
@@ -2346,7 +2720,7 @@ theorem mem_nhdsWithin_Ioi_iff_exists_mem_Ioc_Ioo_subset {a u' : α} {s : Set α
 
 /- warning: mem_nhds_within_Ioi_iff_exists_Ioo_subset' -> mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {u' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u') -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {u' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u') -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {u' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a u') -> (Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (u : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u) s))))
 Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Ioi_iff_exists_Ioo_subset' mem_nhdsWithin_Ioi_iff_exists_Ioo_subset'ₓ'. -/
@@ -2359,7 +2733,7 @@ theorem mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' {a u' : α} {s : Set α} (hu'
 
 /- warning: mem_nhds_within_Ioi_iff_exists_Ioo_subset -> mem_nhdsWithin_Ioi_iff_exists_Ioo_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (u : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u) s)))
 Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Ioi_iff_exists_Ioo_subset mem_nhdsWithin_Ioi_iff_exists_Ioo_subsetₓ'. -/
@@ -2373,7 +2747,7 @@ theorem mem_nhdsWithin_Ioi_iff_exists_Ioo_subset [NoMaxOrder α] {a : α} {s : S
 
 /- warning: mem_nhds_within_Ioi_iff_exists_Ioc_subset -> mem_nhdsWithin_Ioi_iff_exists_Ioc_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (u : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u) s)))
 Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Ioi_iff_exists_Ioc_subset mem_nhdsWithin_Ioi_iff_exists_Ioc_subsetₓ'. -/
@@ -2393,7 +2767,7 @@ theorem mem_nhdsWithin_Ioi_iff_exists_Ioc_subset [NoMaxOrder α] [DenselyOrdered
 
 /- warning: tfae_mem_nhds_within_Iio -> TFAE_mem_nhdsWithin_Iio is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (forall (s : Set.{u1} α), List.TFAE (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) l b) s))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) l b) s))) (List.nil.{0} Prop)))))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (forall (s : Set.{u1} α), List.TFAE (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) l b) s))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) l b) s))) (List.nil.{0} Prop)))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (forall (s : Set.{u1} α), List.TFAE (List.cons.{0} Prop (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b))) (List.cons.{0} Prop (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (List.cons.{0} Prop (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l b) s))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l b) s))) (List.nil.{0} Prop)))))))
 Case conversion may be inaccurate. Consider using '#align tfae_mem_nhds_within_Iio TFAE_mem_nhdsWithin_Iioₓ'. -/
@@ -2420,7 +2794,7 @@ theorem TFAE_mem_nhdsWithin_Iio {a b : α} (h : a < b) (s : Set α) :
 
 /- warning: mem_nhds_within_Iio_iff_exists_mem_Ico_Ioo_subset -> mem_nhdsWithin_Iio_iff_exists_mem_Ico_Ioo_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l' a) -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l' a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l' a)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l' a) -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l' a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l' a)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l' a) -> (Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l' a)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s))))
 Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Iio_iff_exists_mem_Ico_Ioo_subset mem_nhdsWithin_Iio_iff_exists_mem_Ico_Ioo_subsetₓ'. -/
@@ -2431,7 +2805,7 @@ theorem mem_nhdsWithin_Iio_iff_exists_mem_Ico_Ioo_subset {a l' : α} {s : Set α
 
 /- warning: mem_nhds_within_Iio_iff_exists_Ioo_subset' -> mem_nhdsWithin_Iio_iff_exists_Ioo_subset' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l' a) -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l' a) -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l' a) -> (Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s))))
 Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Iio_iff_exists_Ioo_subset' mem_nhdsWithin_Iio_iff_exists_Ioo_subset'ₓ'. -/
@@ -2444,7 +2818,7 @@ theorem mem_nhdsWithin_Iio_iff_exists_Ioo_subset' {a l' : α} {s : Set α} (hl'
 
 /- warning: mem_nhds_within_Iio_iff_exists_Ioo_subset -> mem_nhdsWithin_Iio_iff_exists_Ioo_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s)))
 Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Iio_iff_exists_Ioo_subset mem_nhdsWithin_Iio_iff_exists_Ioo_subsetₓ'. -/
@@ -2458,7 +2832,7 @@ theorem mem_nhdsWithin_Iio_iff_exists_Ioo_subset [NoMinOrder α] {a : α} {s : S
 
 /- warning: mem_nhds_within_Iio_iff_exists_Ico_subset -> mem_nhdsWithin_Iio_iff_exists_Ico_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s)))
 Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Iio_iff_exists_Ico_subset mem_nhdsWithin_Iio_iff_exists_Ico_subsetₓ'. -/
@@ -2473,7 +2847,7 @@ theorem mem_nhdsWithin_Iio_iff_exists_Ico_subset [NoMinOrder α] [DenselyOrdered
 
 /- warning: tfae_mem_nhds_within_Ici -> TFAE_mem_nhdsWithin_Ici is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (forall (s : Set.{u1} α), List.TFAE (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s))) (List.nil.{0} Prop)))))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (forall (s : Set.{u1} α), List.TFAE (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s))) (List.nil.{0} Prop)))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (forall (s : Set.{u1} α), List.TFAE (List.cons.{0} Prop (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (List.cons.{0} Prop (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (List.cons.{0} Prop (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (u : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u) s))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (u : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u) s))) (List.nil.{0} Prop)))))))
 Case conversion may be inaccurate. Consider using '#align tfae_mem_nhds_within_Ici TFAE_mem_nhdsWithin_Iciₓ'. -/
@@ -2510,7 +2884,7 @@ theorem TFAE_mem_nhdsWithin_Ici {a b : α} (hab : a < b) (s : Set α) :
 
 /- warning: mem_nhds_within_Ici_iff_exists_mem_Ioc_Ico_subset -> mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {u' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u') -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u')) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u')) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {u' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u') -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u')) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u')) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {u' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a u') -> (Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (u : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) u (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u')) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u) s))))
 Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Ici_iff_exists_mem_Ioc_Ico_subset mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subsetₓ'. -/
@@ -2521,7 +2895,7 @@ theorem mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subset {a u' : α} {s : Set α
 
 /- warning: mem_nhds_within_Ici_iff_exists_Ico_subset' -> mem_nhdsWithin_Ici_iff_exists_Ico_subset' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {u' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u') -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {u' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u') -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {u' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a u') -> (Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (u : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u) s))))
 Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Ici_iff_exists_Ico_subset' mem_nhdsWithin_Ici_iff_exists_Ico_subset'ₓ'. -/
@@ -2534,7 +2908,7 @@ theorem mem_nhdsWithin_Ici_iff_exists_Ico_subset' {a u' : α} {s : Set α} (hu'
 
 /- warning: mem_nhds_within_Ici_iff_exists_Ico_subset -> mem_nhdsWithin_Ici_iff_exists_Ico_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (u : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) u (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u) s)))
 Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Ici_iff_exists_Ico_subset mem_nhdsWithin_Ici_iff_exists_Ico_subsetₓ'. -/
@@ -2546,14 +2920,23 @@ theorem mem_nhdsWithin_Ici_iff_exists_Ico_subset [NoMaxOrder α] {a : α} {s : S
   mem_nhdsWithin_Ici_iff_exists_Ico_subset' hu'
 #align mem_nhds_within_Ici_iff_exists_Ico_subset mem_nhdsWithin_Ici_iff_exists_Ico_subset
 
-#print nhdsWithin_Ici_basis_Ico /-
+/- warning: nhds_within_Ici_basis_Ico -> nhdsWithin_Ici_basis_Ico is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α), Filter.HasBasis.{u1, succ u1} α α (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (u : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α), Filter.HasBasis.{u1, succ u1} α α (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a u) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)
+Case conversion may be inaccurate. Consider using '#align nhds_within_Ici_basis_Ico nhdsWithin_Ici_basis_Icoₓ'. -/
 theorem nhdsWithin_Ici_basis_Ico [NoMaxOrder α] (a : α) :
     (𝓝[≥] a).HasBasis (fun u => a < u) (Ico a) :=
   ⟨fun s => mem_nhdsWithin_Ici_iff_exists_Ico_subset⟩
 #align nhds_within_Ici_basis_Ico nhdsWithin_Ici_basis_Ico
--/
 
-#print mem_nhdsWithin_Ici_iff_exists_Icc_subset /-
+/- warning: mem_nhds_within_Ici_iff_exists_Icc_subset -> mem_nhdsWithin_Ici_iff_exists_Icc_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (u : α) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a u) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) a u) s)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (u : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a u) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a u) s)))
+Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Ici_iff_exists_Icc_subset mem_nhdsWithin_Ici_iff_exists_Icc_subsetₓ'. -/
 /-- A set is a neighborhood of `a` within `[a, +∞)` if and only if it contains an interval `[a, u]`
 with `a < u`. -/
 theorem mem_nhdsWithin_Ici_iff_exists_Icc_subset [NoMaxOrder α] [DenselyOrdered α] {a : α}
@@ -2567,11 +2950,10 @@ theorem mem_nhdsWithin_Ici_iff_exists_Icc_subset [NoMaxOrder α] [DenselyOrdered
   · rintro ⟨u, au, as⟩
     exact ⟨u, au, subset.trans Ico_subset_Icc_self as⟩
 #align mem_nhds_within_Ici_iff_exists_Icc_subset mem_nhdsWithin_Ici_iff_exists_Icc_subset
--/
 
 /- warning: tfae_mem_nhds_within_Iic -> TFAE_mem_nhdsWithin_Iic is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (forall (s : Set.{u1} α), List.TFAE (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l b) s))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l b) s))) (List.nil.{0} Prop)))))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (forall (s : Set.{u1} α), List.TFAE (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l b) s))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l b) s))) (List.nil.{0} Prop)))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (forall (s : Set.{u1} α), List.TFAE (List.cons.{0} Prop (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b))) (List.cons.{0} Prop (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (List.cons.{0} Prop (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 b (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l b) s))) (List.cons.{0} Prop (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l b) s))) (List.nil.{0} Prop)))))))
 Case conversion may be inaccurate. Consider using '#align tfae_mem_nhds_within_Iic TFAE_mem_nhdsWithin_Iicₓ'. -/
@@ -2598,7 +2980,7 @@ theorem TFAE_mem_nhdsWithin_Iic {a b : α} (h : a < b) (s : Set α) :
 
 /- warning: mem_nhds_within_Iic_iff_exists_mem_Ico_Ioc_subset -> mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l' a) -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l' a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l' a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l' a) -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l' a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l' a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l' a) -> (Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l' a)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s))))
 Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Iic_iff_exists_mem_Ico_Ioc_subset mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subsetₓ'. -/
@@ -2609,7 +2991,7 @@ theorem mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subset {a l' : α} {s : Set α
 
 /- warning: mem_nhds_within_Iic_iff_exists_Ioc_subset' -> mem_nhdsWithin_Iic_iff_exists_Ioc_subset' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l' a) -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l' a) -> (Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] {a : α} {l' : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l' a) -> (Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s))))
 Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Iic_iff_exists_Ioc_subset' mem_nhdsWithin_Iic_iff_exists_Ioc_subset'ₓ'. -/
@@ -2622,7 +3004,7 @@ theorem mem_nhdsWithin_Iic_iff_exists_Ioc_subset' {a l' : α} {s : Set α} (hl'
 
 /- warning: mem_nhds_within_Iic_iff_exists_Ioc_subset -> mem_nhdsWithin_Iic_iff_exists_Ioc_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (l : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) l (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s)))
 Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Iic_iff_exists_Ioc_subset mem_nhdsWithin_Iic_iff_exists_Ioc_subsetₓ'. -/
@@ -2634,7 +3016,12 @@ theorem mem_nhdsWithin_Iic_iff_exists_Ioc_subset [NoMinOrder α] {a : α} {s : S
   mem_nhdsWithin_Iic_iff_exists_Ioc_subset' hl'
 #align mem_nhds_within_Iic_iff_exists_Ioc_subset mem_nhdsWithin_Iic_iff_exists_Ioc_subset
 
-#print mem_nhdsWithin_Iic_iff_exists_Icc_subset /-
+/- warning: mem_nhds_within_Iic_iff_exists_Icc_subset -> mem_nhdsWithin_Iic_iff_exists_Icc_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Exists.{succ u1} α (fun (l : α) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) l a) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) l a) s)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Exists.{succ u1} α (fun (l : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) l a) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) l a) s)))
+Case conversion may be inaccurate. Consider using '#align mem_nhds_within_Iic_iff_exists_Icc_subset mem_nhdsWithin_Iic_iff_exists_Icc_subsetₓ'. -/
 /-- A set is a neighborhood of `a` within `(-∞, a]` if and only if it contains an interval `[l, a]`
 with `l < a`. -/
 theorem mem_nhdsWithin_Iic_iff_exists_Icc_subset [NoMinOrder α] [DenselyOrdered α] {a : α}
@@ -2644,7 +3031,6 @@ theorem mem_nhdsWithin_Iic_iff_exists_Icc_subset [NoMinOrder α] [DenselyOrdered
   simp_rw [show ∀ u : αᵒᵈ, @Icc αᵒᵈ _ a u = @Icc α _ u a from fun u => dual_Icc]
   rfl
 #align mem_nhds_within_Iic_iff_exists_Icc_subset mem_nhdsWithin_Iic_iff_exists_Icc_subset
--/
 
 end OrderTopology
 
@@ -2658,7 +3044,7 @@ variable {l : Filter β} {f g : β → α}
 
 /- warning: nhds_eq_infi_abs_sub -> nhds_eq_iInf_abs_sub is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (r : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) a b)) r)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (r : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) (fun (H : GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) a b)) r)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (r : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) a b)) r)))))
 Case conversion may be inaccurate. Consider using '#align nhds_eq_infi_abs_sub nhds_eq_iInf_abs_subₓ'. -/
@@ -2680,7 +3066,7 @@ theorem nhds_eq_iInf_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| <
 
 /- warning: order_topology_of_nhds_abs -> orderTopology_of_nhds_abs is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} α] [_inst_5 : LinearOrderedAddCommGroup.{u1} α], (forall (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_4 a) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (r : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_5))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))) a b)) r)))))) -> (OrderTopology.{u1} α _inst_4 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))
+  forall {α : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} α] [_inst_5 : LinearOrderedAddCommGroup.{u1} α], (forall (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_4 a) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (r : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))))))))) (fun (H : GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_5))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))) a b)) r)))))) -> (OrderTopology.{u1} α _inst_4 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} α] [_inst_5 : LinearOrderedAddCommGroup.{u1} α], (forall (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_4 a) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (r : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_5)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))) a b)) r)))))) -> (OrderTopology.{u1} α _inst_4 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))
 Case conversion may be inaccurate. Consider using '#align order_topology_of_nhds_abs orderTopology_of_nhds_absₓ'. -/
@@ -2695,7 +3081,7 @@ theorem orderTopology_of_nhds_abs {α : Type _} [TopologicalSpace α] [LinearOrd
 
 /- warning: linear_ordered_add_comm_group.tendsto_nhds -> LinearOrderedAddCommGroup.tendsto_nhds is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] {f : β -> α} {x : Filter.{u2} β} {a : α}, Iff (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) (forall (ε : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) ε (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) -> (Filter.Eventually.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) (f b) a)) ε) x))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] {f : β -> α} {x : Filter.{u2} β} {a : α}, Iff (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) (forall (ε : α), (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) ε (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) -> (Filter.Eventually.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) (f b) a)) ε) x))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] {f : β -> α} {x : Filter.{u2} β} {a : α}, Iff (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) (forall (ε : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) ε (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) -> (Filter.Eventually.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) (f b) a)) ε) x))
 Case conversion may be inaccurate. Consider using '#align linear_ordered_add_comm_group.tendsto_nhds LinearOrderedAddCommGroup.tendsto_nhdsₓ'. -/
@@ -2706,7 +3092,7 @@ theorem LinearOrderedAddCommGroup.tendsto_nhds {x : Filter β} {a : α} :
 
 /- warning: eventually_abs_sub_lt -> eventually_abs_sub_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α) {ε : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) ε) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) x a)) ε) (nhds.{u1} α _inst_1 a))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α) {ε : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) ε) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) x a)) ε) (nhds.{u1} α _inst_1 a))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α) {ε : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))) ε) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) x a)) ε) (nhds.{u1} α _inst_1 a))
 Case conversion may be inaccurate. Consider using '#align eventually_abs_sub_lt eventually_abs_sub_ltₓ'. -/
@@ -2777,7 +3163,7 @@ theorem Filter.Tendsto.atBot_add {C : α} (hf : Tendsto f l atBot) (hg : Tendsto
 
 /- warning: nhds_basis_Ioo_pos -> nhds_basis_Ioo_pos is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] (a : α), Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 a) (fun (ε : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) ε) (fun (ε : α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) a ε) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))) a ε))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] (a : α), Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 a) (fun (ε : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) ε) (fun (ε : α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) a ε) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))) a ε))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] (_inst_5 : α), Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 _inst_5) (fun (ε : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))) ε) (fun (ε : α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) _inst_5 ε) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))) _inst_5 ε))
 Case conversion may be inaccurate. Consider using '#align nhds_basis_Ioo_pos nhds_basis_Ioo_posₓ'. -/
@@ -2798,7 +3184,7 @@ theorem nhds_basis_Ioo_pos [NoMinOrder α] [NoMaxOrder α] (a : α) :
 
 /- warning: nhds_basis_abs_sub_lt -> nhds_basis_abs_sub_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] (a : α), Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 a) (fun (ε : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) ε) (fun (ε : α) => setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) b a)) ε))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] (a : α), Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 a) (fun (ε : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) ε) (fun (ε : α) => setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) b a)) ε))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] (_inst_5 : α), Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 _inst_5) (fun (ε : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))) ε) (fun (ε : α) => setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) b _inst_5)) ε))
 Case conversion may be inaccurate. Consider using '#align nhds_basis_abs_sub_lt nhds_basis_abs_sub_ltₓ'. -/
@@ -2815,7 +3201,7 @@ variable (α)
 
 /- warning: nhds_basis_zero_abs_sub_lt -> nhds_basis_zero_abs_sub_lt is a dubious translation:
 lean 3 declaration is
-  forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) (fun (ε : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) ε) (fun (ε : α) => setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) b) ε))
+  forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) (fun (ε : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) ε) (fun (ε : α) => setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) b) ε))
 but is expected to have type
   forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) (fun (ε : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))) ε) (fun (ε : α) => setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) b) ε))
 Case conversion may be inaccurate. Consider using '#align nhds_basis_zero_abs_sub_lt nhds_basis_zero_abs_sub_ltₓ'. -/
@@ -2828,7 +3214,7 @@ variable {α}
 
 /- warning: nhds_basis_Ioo_pos_of_pos -> nhds_basis_Ioo_pos_of_pos is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) a) -> (Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 a) (fun (ε : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) ε) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) ε a)) (fun (ε : α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) a ε) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))) a ε)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] {a : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) a) -> (Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 a) (fun (ε : α) => And (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) ε) (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) ε a)) (fun (ε : α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) a ε) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))) a ε)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] {_inst_5 : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))) _inst_5) -> (Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 _inst_5) (fun (ε : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))) ε) (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) ε _inst_5)) (fun (ε : α) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) _inst_5 ε) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))) _inst_5 ε)))
 Case conversion may be inaccurate. Consider using '#align nhds_basis_Ioo_pos_of_pos nhds_basis_Ioo_pos_of_posₓ'. -/
@@ -3080,7 +3466,12 @@ alias IsGLB.mem_of_isClosed ← IsClosed.isGLB_mem
 -/
 
 
-#print IsLUB.exists_seq_strictMono_tendsto_of_not_mem /-
+/- warning: is_lub.exists_seq_strict_mono_tendsto_of_not_mem -> IsLUB.exists_seq_strictMono_tendsto_of_not_mem is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] {t : Set.{u1} α} {x : α} [_inst_7 : Filter.IsCountablyGenerated.{u1} α (nhds.{u1} α _inst_1 x)], (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) t x) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t)) -> (Set.Nonempty.{u1} α t) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictMono.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) u) (And (forall (n : Nat), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))) (u n) x) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α _inst_1 x)) (forall (n : Nat), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (u n) t)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))] {t : Set.{u1} α} {x : α} [_inst_7 : Filter.IsCountablyGenerated.{u1} α (nhds.{u1} α _inst_1 x)], (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) t x) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t)) -> (Set.Nonempty.{u1} α t) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictMono.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) u) (And (forall (n : Nat), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))) (u n) x) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α _inst_1 x)) (forall (n : Nat), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (u n) t)))))
+Case conversion may be inaccurate. Consider using '#align is_lub.exists_seq_strict_mono_tendsto_of_not_mem IsLUB.exists_seq_strictMono_tendsto_of_not_memₓ'. -/
 theorem IsLUB.exists_seq_strictMono_tendsto_of_not_mem {t : Set α} {x : α}
     [IsCountablyGenerated (𝓝 x)] (htx : IsLUB t x) (not_mem : x ∉ t) (ht : t.Nonempty) :
     ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n < x) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t :=
@@ -3121,9 +3512,13 @@ theorem IsLUB.exists_seq_strictMono_tendsto_of_not_mem {t : Set α} {x : α}
     · exact (hf 0 l hl).2.2.2
     · exact (hf n.succ _ (I n)).2.2.2
 #align is_lub.exists_seq_strict_mono_tendsto_of_not_mem IsLUB.exists_seq_strictMono_tendsto_of_not_mem
--/
 
-#print IsLUB.exists_seq_monotone_tendsto /-
+/- warning: is_lub.exists_seq_monotone_tendsto -> IsLUB.exists_seq_monotone_tendsto is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] {t : Set.{u1} α} {x : α} [_inst_7 : Filter.IsCountablyGenerated.{u1} α (nhds.{u1} α _inst_1 x)], (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) t x) -> (Set.Nonempty.{u1} α t) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (Monotone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) u) (And (forall (n : Nat), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))) (u n) x) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α _inst_1 x)) (forall (n : Nat), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (u n) t)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))] {t : Set.{u1} α} {x : α} [_inst_7 : Filter.IsCountablyGenerated.{u1} α (nhds.{u1} α _inst_1 x)], (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) t x) -> (Set.Nonempty.{u1} α t) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (Monotone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) u) (And (forall (n : Nat), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))) (u n) x) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α _inst_1 x)) (forall (n : Nat), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (u n) t)))))
+Case conversion may be inaccurate. Consider using '#align is_lub.exists_seq_monotone_tendsto IsLUB.exists_seq_monotone_tendstoₓ'. -/
 theorem IsLUB.exists_seq_monotone_tendsto {t : Set α} {x : α} [IsCountablyGenerated (𝓝 x)]
     (htx : IsLUB t x) (ht : t.Nonempty) :
     ∃ u : ℕ → α, Monotone u ∧ (∀ n, u n ≤ x) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t :=
@@ -3133,9 +3528,13 @@ theorem IsLUB.exists_seq_monotone_tendsto {t : Set α} {x : α} [IsCountablyGene
   · rcases htx.exists_seq_strict_mono_tendsto_of_not_mem h ht with ⟨u, hu⟩
     exact ⟨u, hu.1.Monotone, fun n => (hu.2.1 n).le, hu.2.2⟩
 #align is_lub.exists_seq_monotone_tendsto IsLUB.exists_seq_monotone_tendsto
--/
 
-#print exists_seq_strictMono_tendsto' /-
+/- warning: exists_seq_strict_mono_tendsto' -> exists_seq_strictMono_tendsto' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_7 : LinearOrder.{u1} α] [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_7)))))] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_7))))] [_inst_11 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_8] {x : α} {y : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_7))))) y x) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictMono.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_7)))) u) (And (forall (n : Nat), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (u n) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_7)))) y x)) (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α _inst_8 x)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_7 : LinearOrder.{u1} α] [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_7))))))] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_7)))))] [_inst_11 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_8] {x : α} {y : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_7)))))) y x) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictMono.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_7))))) u) (And (forall (n : Nat), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (u n) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_7))))) y x)) (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α _inst_8 x)))))
+Case conversion may be inaccurate. Consider using '#align exists_seq_strict_mono_tendsto' exists_seq_strictMono_tendsto'ₓ'. -/
 theorem exists_seq_strictMono_tendsto' {α : Type _} [LinearOrder α] [TopologicalSpace α]
     [DenselyOrdered α] [OrderTopology α] [FirstCountableTopology α] {x y : α} (hy : y < x) :
     ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n ∈ Ioo y x) ∧ Tendsto u atTop (𝓝 x) :=
@@ -3145,9 +3544,13 @@ theorem exists_seq_strictMono_tendsto' {α : Type _} [LinearOrder α] [Topologic
   rcases(isLUB_Ioo hy).exists_seq_strictMono_tendsto_of_not_mem hx ht with ⟨u, hu⟩
   exact ⟨u, hu.1, hu.2.2.symm⟩
 #align exists_seq_strict_mono_tendsto' exists_seq_strictMono_tendsto'
--/
 
-#print exists_seq_strictMono_tendsto /-
+/- warning: exists_seq_strict_mono_tendsto -> exists_seq_strictMono_tendsto is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] [_inst_7 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))))] [_inst_8 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))))] [_inst_9 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_1] (x : α), Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictMono.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) u) (And (forall (n : Nat), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))) (u n) x) (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α _inst_1 x))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))] [_inst_7 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))))] [_inst_8 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))))] [_inst_9 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_1] (x : α), Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictMono.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) u) (And (forall (n : Nat), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))) (u n) x) (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α _inst_1 x))))
+Case conversion may be inaccurate. Consider using '#align exists_seq_strict_mono_tendsto exists_seq_strictMono_tendstoₓ'. -/
 theorem exists_seq_strictMono_tendsto [DenselyOrdered α] [NoMinOrder α] [FirstCountableTopology α]
     (x : α) : ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n < x) ∧ Tendsto u atTop (𝓝 x) :=
   by
@@ -3155,16 +3558,19 @@ theorem exists_seq_strictMono_tendsto [DenselyOrdered α] [NoMinOrder α] [First
   rcases exists_seq_strictMono_tendsto' hy with ⟨u, hu_mono, hu_mem, hux⟩
   exact ⟨u, hu_mono, fun n => (hu_mem n).2, hux⟩
 #align exists_seq_strict_mono_tendsto exists_seq_strictMono_tendsto
--/
 
-#print exists_seq_strictMono_tendsto_nhdsWithin /-
+/- warning: exists_seq_strict_mono_tendsto_nhds_within -> exists_seq_strictMono_tendsto_nhdsWithin is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] [_inst_7 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))))] [_inst_8 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))))] [_inst_9 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_1] (x : α), Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictMono.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) u) (And (forall (n : Nat), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))) (u n) x) (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhdsWithin.{u1} α _inst_1 x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) x)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))] [_inst_7 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))))] [_inst_8 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))))] [_inst_9 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_1] (x : α), Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictMono.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) u) (And (forall (n : Nat), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))) (u n) x) (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhdsWithin.{u1} α _inst_1 x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) x)))))
+Case conversion may be inaccurate. Consider using '#align exists_seq_strict_mono_tendsto_nhds_within exists_seq_strictMono_tendsto_nhdsWithinₓ'. -/
 theorem exists_seq_strictMono_tendsto_nhdsWithin [DenselyOrdered α] [NoMinOrder α]
     [FirstCountableTopology α] (x : α) :
     ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n < x) ∧ Tendsto u atTop (𝓝[<] x) :=
   let ⟨u, hu, hx, h⟩ := exists_seq_strictMono_tendsto x
   ⟨u, hu, hx, tendsto_nhdsWithin_mono_right (range_subset_iff.2 hx) <| tendsto_nhdsWithin_range.2 h⟩
 #align exists_seq_strict_mono_tendsto_nhds_within exists_seq_strictMono_tendsto_nhdsWithin
--/
 
 /- warning: exists_seq_tendsto_Sup -> exists_seq_tendsto_sSup is a dubious translation:
 lean 3 declaration is
@@ -3180,45 +3586,70 @@ theorem exists_seq_tendsto_sSup {α : Type _} [ConditionallyCompleteLinearOrder
   exact ⟨u, hu.1, hu.2.2⟩
 #align exists_seq_tendsto_Sup exists_seq_tendsto_sSup
 
-#print IsGLB.exists_seq_strictAnti_tendsto_of_not_mem /-
+/- warning: is_glb.exists_seq_strict_anti_tendsto_of_not_mem -> IsGLB.exists_seq_strictAnti_tendsto_of_not_mem is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] {t : Set.{u1} α} {x : α} [_inst_7 : Filter.IsCountablyGenerated.{u1} α (nhds.{u1} α _inst_1 x)], (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) t x) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t)) -> (Set.Nonempty.{u1} α t) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictAnti.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) u) (And (forall (n : Nat), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))) x (u n)) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α _inst_1 x)) (forall (n : Nat), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (u n) t)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))] {t : Set.{u1} α} {x : α} [_inst_7 : Filter.IsCountablyGenerated.{u1} α (nhds.{u1} α _inst_1 x)], (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) t x) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t)) -> (Set.Nonempty.{u1} α t) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictAnti.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) u) (And (forall (n : Nat), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))) x (u n)) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α _inst_1 x)) (forall (n : Nat), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (u n) t)))))
+Case conversion may be inaccurate. Consider using '#align is_glb.exists_seq_strict_anti_tendsto_of_not_mem IsGLB.exists_seq_strictAnti_tendsto_of_not_memₓ'. -/
 theorem IsGLB.exists_seq_strictAnti_tendsto_of_not_mem {t : Set α} {x : α}
     [IsCountablyGenerated (𝓝 x)] (htx : IsGLB t x) (not_mem : x ∉ t) (ht : t.Nonempty) :
     ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, x < u n) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t :=
   @IsLUB.exists_seq_strictMono_tendsto_of_not_mem αᵒᵈ _ _ _ t x _ htx not_mem ht
 #align is_glb.exists_seq_strict_anti_tendsto_of_not_mem IsGLB.exists_seq_strictAnti_tendsto_of_not_mem
--/
 
-#print IsGLB.exists_seq_antitone_tendsto /-
+/- warning: is_glb.exists_seq_antitone_tendsto -> IsGLB.exists_seq_antitone_tendsto is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] {t : Set.{u1} α} {x : α} [_inst_7 : Filter.IsCountablyGenerated.{u1} α (nhds.{u1} α _inst_1 x)], (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) t x) -> (Set.Nonempty.{u1} α t) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (Antitone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) u) (And (forall (n : Nat), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))) x (u n)) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α _inst_1 x)) (forall (n : Nat), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (u n) t)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))] {t : Set.{u1} α} {x : α} [_inst_7 : Filter.IsCountablyGenerated.{u1} α (nhds.{u1} α _inst_1 x)], (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) t x) -> (Set.Nonempty.{u1} α t) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (Antitone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) u) (And (forall (n : Nat), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))) x (u n)) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α _inst_1 x)) (forall (n : Nat), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (u n) t)))))
+Case conversion may be inaccurate. Consider using '#align is_glb.exists_seq_antitone_tendsto IsGLB.exists_seq_antitone_tendstoₓ'. -/
 theorem IsGLB.exists_seq_antitone_tendsto {t : Set α} {x : α} [IsCountablyGenerated (𝓝 x)]
     (htx : IsGLB t x) (ht : t.Nonempty) :
     ∃ u : ℕ → α, Antitone u ∧ (∀ n, x ≤ u n) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t :=
   @IsLUB.exists_seq_monotone_tendsto αᵒᵈ _ _ _ t x _ htx ht
 #align is_glb.exists_seq_antitone_tendsto IsGLB.exists_seq_antitone_tendsto
--/
 
-#print exists_seq_strictAnti_tendsto' /-
+/- warning: exists_seq_strict_anti_tendsto' -> exists_seq_strictAnti_tendsto' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] [_inst_7 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))))] [_inst_8 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_1] {x : α} {y : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))) x y) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictAnti.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) u) (And (forall (n : Nat), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (u n) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) x y)) (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α _inst_1 x)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))] [_inst_7 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))))] [_inst_8 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_1] {x : α} {y : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))) x y) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictAnti.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) u) (And (forall (n : Nat), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (u n) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) x y)) (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α _inst_1 x)))))
+Case conversion may be inaccurate. Consider using '#align exists_seq_strict_anti_tendsto' exists_seq_strictAnti_tendsto'ₓ'. -/
 theorem exists_seq_strictAnti_tendsto' [DenselyOrdered α] [FirstCountableTopology α] {x y : α}
     (hy : x < y) : ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, u n ∈ Ioo x y) ∧ Tendsto u atTop (𝓝 x) := by
   simpa only [dual_Ioo] using exists_seq_strictMono_tendsto' (OrderDual.toDual_lt_toDual.2 hy)
 #align exists_seq_strict_anti_tendsto' exists_seq_strictAnti_tendsto'
--/
 
-#print exists_seq_strictAnti_tendsto /-
+/- warning: exists_seq_strict_anti_tendsto -> exists_seq_strictAnti_tendsto is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] [_inst_7 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))))] [_inst_8 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))))] [_inst_9 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_1] (x : α), Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictAnti.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) u) (And (forall (n : Nat), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))) x (u n)) (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α _inst_1 x))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))] [_inst_7 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))))] [_inst_8 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))))] [_inst_9 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_1] (x : α), Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictAnti.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) u) (And (forall (n : Nat), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))) x (u n)) (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α _inst_1 x))))
+Case conversion may be inaccurate. Consider using '#align exists_seq_strict_anti_tendsto exists_seq_strictAnti_tendstoₓ'. -/
 theorem exists_seq_strictAnti_tendsto [DenselyOrdered α] [NoMaxOrder α] [FirstCountableTopology α]
     (x : α) : ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, x < u n) ∧ Tendsto u atTop (𝓝 x) :=
   @exists_seq_strictMono_tendsto αᵒᵈ _ _ _ _ _ _ x
 #align exists_seq_strict_anti_tendsto exists_seq_strictAnti_tendsto
--/
 
-#print exists_seq_strictAnti_tendsto_nhdsWithin /-
+/- warning: exists_seq_strict_anti_tendsto_nhds_within -> exists_seq_strictAnti_tendsto_nhdsWithin is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] [_inst_7 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))))] [_inst_8 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))))] [_inst_9 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_1] (x : α), Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictAnti.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) u) (And (forall (n : Nat), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))) x (u n)) (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhdsWithin.{u1} α _inst_1 x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) x)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))] [_inst_7 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))))] [_inst_8 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))))] [_inst_9 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_1] (x : α), Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (StrictAnti.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) u) (And (forall (n : Nat), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))) x (u n)) (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhdsWithin.{u1} α _inst_1 x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) x)))))
+Case conversion may be inaccurate. Consider using '#align exists_seq_strict_anti_tendsto_nhds_within exists_seq_strictAnti_tendsto_nhdsWithinₓ'. -/
 theorem exists_seq_strictAnti_tendsto_nhdsWithin [DenselyOrdered α] [NoMaxOrder α]
     [FirstCountableTopology α] (x : α) :
     ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, x < u n) ∧ Tendsto u atTop (𝓝[>] x) :=
   @exists_seq_strictMono_tendsto_nhdsWithin αᵒᵈ _ _ _ _ _ _ _
 #align exists_seq_strict_anti_tendsto_nhds_within exists_seq_strictAnti_tendsto_nhdsWithin
--/
 
-#print exists_seq_strictAnti_strictMono_tendsto /-
+/- warning: exists_seq_strict_anti_strict_mono_tendsto -> exists_seq_strictAnti_strictMono_tendsto is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] [_inst_7 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))))] [_inst_8 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_1] {x : α} {y : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))) x y) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => Exists.{succ u1} (Nat -> α) (fun (v : Nat -> α) => And (StrictAnti.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) u) (And (StrictMono.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) v) (And (forall (k : Nat), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (u k) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) x y)) (And (forall (l : Nat), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (v l) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) x y)) (And (forall (k : Nat) (l : Nat), LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))) (u k) (v l)) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α _inst_1 x)) (Filter.Tendsto.{0, u1} Nat α v (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α _inst_1 y))))))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))] [_inst_7 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))))] [_inst_8 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_1] {x : α} {y : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))) x y) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => Exists.{succ u1} (Nat -> α) (fun (v : Nat -> α) => And (StrictAnti.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) u) (And (StrictMono.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) v) (And (forall (k : Nat), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (u k) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) x y)) (And (forall (l : Nat), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (v l) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) x y)) (And (forall (k : Nat) (l : Nat), LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))) (u k) (v l)) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α _inst_1 x)) (Filter.Tendsto.{0, u1} Nat α v (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α _inst_1 y))))))))))
+Case conversion may be inaccurate. Consider using '#align exists_seq_strict_anti_strict_mono_tendsto exists_seq_strictAnti_strictMono_tendstoₓ'. -/
 theorem exists_seq_strictAnti_strictMono_tendsto [DenselyOrdered α] [FirstCountableTopology α]
     {x y : α} (h : x < y) :
     ∃ u v : ℕ → α,
@@ -3234,7 +3665,6 @@ theorem exists_seq_strictAnti_strictMono_tendsto [DenselyOrdered α] [FirstCount
     ⟨u, v, hu_anti, hv_mono, hu_mem, fun l => ⟨(hu_mem 0).1.trans (hv_mem l).1, (hv_mem l).2⟩,
       fun k l => (hu_anti.antitone (zero_le k)).trans_lt (hv_mem l).1, hux, hvy⟩
 #align exists_seq_strict_anti_strict_mono_tendsto exists_seq_strictAnti_strictMono_tendsto
--/
 
 /- warning: exists_seq_tendsto_Inf -> exists_seq_tendsto_sInf is a dubious translation:
 lean 3 declaration is
@@ -3255,7 +3685,12 @@ section DenselyOrdered
 variable [TopologicalSpace α] [LinearOrder α] [OrderTopology α] [DenselyOrdered α] {a b : α}
   {s : Set α}
 
-#print closure_Ioi' /-
+/- warning: closure_Ioi' -> closure_Ioi' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α}, (Set.Nonempty.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) -> (Eq.{succ u1} (Set.{u1} α) (closure.{u1} α _inst_1 (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α}, (Set.Nonempty.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) -> (Eq.{succ u1} (Set.{u1} α) (closure.{u1} α _inst_1 (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))
+Case conversion may be inaccurate. Consider using '#align closure_Ioi' closure_Ioi'ₓ'. -/
 /-- The closure of the interval `(a, +∞)` is the closed interval `[a, +∞)`, unless `a` is a top
 element. -/
 theorem closure_Ioi' {a : α} (h : (Ioi a).Nonempty) : closure (Ioi a) = Ici a :=
@@ -3265,33 +3700,49 @@ theorem closure_Ioi' {a : α} (h : (Ioi a).Nonempty) : closure (Ioi a) = Ici a :
   · rw [← diff_subset_closure_iff, Ici_diff_Ioi_same, singleton_subset_iff]
     exact is_glb_Ioi.mem_closure h
 #align closure_Ioi' closure_Ioi'
--/
 
-#print closure_Ioi /-
+/- warning: closure_Ioi -> closure_Ioi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α) [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))], Eq.{succ u1} (Set.{u1} α) (closure.{u1} α _inst_1 (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α) [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))], Eq.{succ u1} (Set.{u1} α) (closure.{u1} α _inst_1 (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)
+Case conversion may be inaccurate. Consider using '#align closure_Ioi closure_Ioiₓ'. -/
 /-- The closure of the interval `(a, +∞)` is the closed interval `[a, +∞)`. -/
 @[simp]
 theorem closure_Ioi (a : α) [NoMaxOrder α] : closure (Ioi a) = Ici a :=
   closure_Ioi' nonempty_Ioi
 #align closure_Ioi closure_Ioi
--/
 
-#print closure_Iio' /-
+/- warning: closure_Iio' -> closure_Iio' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α}, (Set.Nonempty.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) -> (Eq.{succ u1} (Set.{u1} α) (closure.{u1} α _inst_1 (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α}, (Set.Nonempty.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) -> (Eq.{succ u1} (Set.{u1} α) (closure.{u1} α _inst_1 (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))
+Case conversion may be inaccurate. Consider using '#align closure_Iio' closure_Iio'ₓ'. -/
 /-- The closure of the interval `(-∞, a)` is the closed interval `(-∞, a]`, unless `a` is a bottom
 element. -/
 theorem closure_Iio' (h : (Iio a).Nonempty) : closure (Iio a) = Iic a :=
   @closure_Ioi' αᵒᵈ _ _ _ _ _ h
 #align closure_Iio' closure_Iio'
--/
 
-#print closure_Iio /-
+/- warning: closure_Iio -> closure_Iio is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α) [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))], Eq.{succ u1} (Set.{u1} α) (closure.{u1} α _inst_1 (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α) [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))], Eq.{succ u1} (Set.{u1} α) (closure.{u1} α _inst_1 (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)
+Case conversion may be inaccurate. Consider using '#align closure_Iio closure_Iioₓ'. -/
 /-- The closure of the interval `(-∞, a)` is the interval `(-∞, a]`. -/
 @[simp]
 theorem closure_Iio (a : α) [NoMinOrder α] : closure (Iio a) = Iic a :=
   closure_Iio' nonempty_Iio
 #align closure_Iio closure_Iio
--/
 
-#print closure_Ioo /-
+/- warning: closure_Ioo -> closure_Ioo is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (Ne.{succ u1} α a b) -> (Eq.{succ u1} (Set.{u1} α) (closure.{u1} α _inst_1 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (Ne.{succ u1} α a b) -> (Eq.{succ u1} (Set.{u1} α) (closure.{u1} α _inst_1 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))
+Case conversion may be inaccurate. Consider using '#align closure_Ioo closure_Iooₓ'. -/
 /-- The closure of the open interval `(a, b)` is the closed interval `[a, b]`. -/
 @[simp]
 theorem closure_Ioo {a b : α} (hab : a ≠ b) : closure (Ioo a b) = Icc a b :=
@@ -3306,9 +3757,13 @@ theorem closure_Ioo {a b : α} (hab : a ≠ b) : closure (Ioo a b) = Icc a b :=
     · rw [Icc_eq_empty_of_lt hab]
       exact empty_subset _
 #align closure_Ioo closure_Ioo
--/
 
-#print closure_Ioc /-
+/- warning: closure_Ioc -> closure_Ioc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (Ne.{succ u1} α a b) -> (Eq.{succ u1} (Set.{u1} α) (closure.{u1} α _inst_1 (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (Ne.{succ u1} α a b) -> (Eq.{succ u1} (Set.{u1} α) (closure.{u1} α _inst_1 (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))
+Case conversion may be inaccurate. Consider using '#align closure_Ioc closure_Iocₓ'. -/
 /-- The closure of the interval `(a, b]` is the closed interval `[a, b]`. -/
 @[simp]
 theorem closure_Ioc {a b : α} (hab : a ≠ b) : closure (Ioc a b) = Icc a b :=
@@ -3318,9 +3773,13 @@ theorem closure_Ioc {a b : α} (hab : a ≠ b) : closure (Ioc a b) = Icc a b :=
   · apply subset.trans _ (closure_mono Ioo_subset_Ioc_self)
     rw [closure_Ioo hab]
 #align closure_Ioc closure_Ioc
--/
 
-#print closure_Ico /-
+/- warning: closure_Ico -> closure_Ico is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (Ne.{succ u1} α a b) -> (Eq.{succ u1} (Set.{u1} α) (closure.{u1} α _inst_1 (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (Ne.{succ u1} α a b) -> (Eq.{succ u1} (Set.{u1} α) (closure.{u1} α _inst_1 (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))
+Case conversion may be inaccurate. Consider using '#align closure_Ico closure_Icoₓ'. -/
 /-- The closure of the interval `[a, b)` is the closed interval `[a, b]`. -/
 @[simp]
 theorem closure_Ico {a b : α} (hab : a ≠ b) : closure (Ico a b) = Icc a b :=
@@ -3330,56 +3789,88 @@ theorem closure_Ico {a b : α} (hab : a ≠ b) : closure (Ico a b) = Icc a b :=
   · apply subset.trans _ (closure_mono Ioo_subset_Ico_self)
     rw [closure_Ioo hab]
 #align closure_Ico closure_Ico
--/
 
-#print interior_Ici' /-
+/- warning: interior_Ici' -> interior_Ici' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α}, (Set.Nonempty.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) -> (Eq.{succ u1} (Set.{u1} α) (interior.{u1} α _inst_1 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α}, (Set.Nonempty.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) -> (Eq.{succ u1} (Set.{u1} α) (interior.{u1} α _inst_1 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))
+Case conversion may be inaccurate. Consider using '#align interior_Ici' interior_Ici'ₓ'. -/
 @[simp]
 theorem interior_Ici' {a : α} (ha : (Iio a).Nonempty) : interior (Ici a) = Ioi a := by
   rw [← compl_Iio, interior_compl, closure_Iio' ha, compl_Iic]
 #align interior_Ici' interior_Ici'
--/
 
-#print interior_Ici /-
+/- warning: interior_Ici -> interior_Ici is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α}, Eq.{succ u1} (Set.{u1} α) (interior.{u1} α _inst_1 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α}, Eq.{succ u1} (Set.{u1} α) (interior.{u1} α _inst_1 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)
+Case conversion may be inaccurate. Consider using '#align interior_Ici interior_Iciₓ'. -/
 theorem interior_Ici [NoMinOrder α] {a : α} : interior (Ici a) = Ioi a :=
   interior_Ici' nonempty_Iio
 #align interior_Ici interior_Ici
--/
 
-#print interior_Iic' /-
+/- warning: interior_Iic' -> interior_Iic' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α}, (Set.Nonempty.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) -> (Eq.{succ u1} (Set.{u1} α) (interior.{u1} α _inst_1 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α}, (Set.Nonempty.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) -> (Eq.{succ u1} (Set.{u1} α) (interior.{u1} α _inst_1 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))
+Case conversion may be inaccurate. Consider using '#align interior_Iic' interior_Iic'ₓ'. -/
 @[simp]
 theorem interior_Iic' {a : α} (ha : (Ioi a).Nonempty) : interior (Iic a) = Iio a :=
   @interior_Ici' αᵒᵈ _ _ _ _ _ ha
 #align interior_Iic' interior_Iic'
--/
 
-#print interior_Iic /-
+/- warning: interior_Iic -> interior_Iic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α}, Eq.{succ u1} (Set.{u1} α) (interior.{u1} α _inst_1 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α}, Eq.{succ u1} (Set.{u1} α) (interior.{u1} α _inst_1 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)
+Case conversion may be inaccurate. Consider using '#align interior_Iic interior_Iicₓ'. -/
 theorem interior_Iic [NoMaxOrder α] {a : α} : interior (Iic a) = Iio a :=
   interior_Iic' nonempty_Ioi
 #align interior_Iic interior_Iic
--/
 
-#print interior_Icc /-
+/- warning: interior_Icc -> interior_Icc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_6 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, Eq.{succ u1} (Set.{u1} α) (interior.{u1} α _inst_1 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_6 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, Eq.{succ u1} (Set.{u1} α) (interior.{u1} α _inst_1 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)
+Case conversion may be inaccurate. Consider using '#align interior_Icc interior_Iccₓ'. -/
 @[simp]
 theorem interior_Icc [NoMinOrder α] [NoMaxOrder α] {a b : α} : interior (Icc a b) = Ioo a b := by
   rw [← Ici_inter_Iic, interior_inter, interior_Ici, interior_Iic, Ioi_inter_Iio]
 #align interior_Icc interior_Icc
--/
 
-#print interior_Ico /-
+/- warning: interior_Ico -> interior_Ico is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, Eq.{succ u1} (Set.{u1} α) (interior.{u1} α _inst_1 (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, Eq.{succ u1} (Set.{u1} α) (interior.{u1} α _inst_1 (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)
+Case conversion may be inaccurate. Consider using '#align interior_Ico interior_Icoₓ'. -/
 @[simp]
 theorem interior_Ico [NoMinOrder α] {a b : α} : interior (Ico a b) = Ioo a b := by
   rw [← Ici_inter_Iio, interior_inter, interior_Ici, interior_Iio, Ioi_inter_Iio]
 #align interior_Ico interior_Ico
--/
 
-#print interior_Ioc /-
+/- warning: interior_Ioc -> interior_Ioc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, Eq.{succ u1} (Set.{u1} α) (interior.{u1} α _inst_1 (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, Eq.{succ u1} (Set.{u1} α) (interior.{u1} α _inst_1 (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)
+Case conversion may be inaccurate. Consider using '#align interior_Ioc interior_Iocₓ'. -/
 @[simp]
 theorem interior_Ioc [NoMaxOrder α] {a b : α} : interior (Ioc a b) = Ioo a b := by
   rw [← Ioi_inter_Iic, interior_inter, interior_Ioi, interior_Iic, Ioi_inter_Iio]
 #align interior_Ioc interior_Ioc
--/
 
-#print closure_interior_Icc /-
+/- warning: closure_interior_Icc -> closure_interior_Icc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (Ne.{succ u1} α a b) -> (Eq.{succ u1} (Set.{u1} α) (closure.{u1} α _inst_1 (interior.{u1} α _inst_1 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (Ne.{succ u1} α a b) -> (Eq.{succ u1} (Set.{u1} α) (closure.{u1} α _inst_1 (interior.{u1} α _inst_1 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))
+Case conversion may be inaccurate. Consider using '#align closure_interior_Icc closure_interior_Iccₓ'. -/
 theorem closure_interior_Icc {a b : α} (h : a ≠ b) : closure (interior (Icc a b)) = Icc a b :=
   (closure_minimal interior_subset isClosed_Icc).antisymm <|
     calc
@@ -3388,9 +3879,13 @@ theorem closure_interior_Icc {a b : α} (h : a ≠ b) : closure (interior (Icc a
         closure_mono (interior_maximal Ioo_subset_Icc_self isOpen_Ioo)
       
 #align closure_interior_Icc closure_interior_Icc
--/
 
-#print Ioc_subset_closure_interior /-
+/- warning: Ioc_subset_closure_interior -> Ioc_subset_closure_interior is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α) (b : α), HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) (closure.{u1} α _inst_1 (interior.{u1} α _inst_1 (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α) (b : α), HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) (closure.{u1} α _inst_1 (interior.{u1} α _inst_1 (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)))
+Case conversion may be inaccurate. Consider using '#align Ioc_subset_closure_interior Ioc_subset_closure_interiorₓ'. -/
 theorem Ioc_subset_closure_interior (a b : α) : Ioc a b ⊆ closure (interior (Ioc a b)) :=
   by
   rcases eq_or_ne a b with (rfl | h)
@@ -3403,122 +3898,189 @@ theorem Ioc_subset_closure_interior (a b : α) : Ioc a b ⊆ closure (interior (
         closure_mono (interior_maximal Ioo_subset_Ioc_self isOpen_Ioo)
       
 #align Ioc_subset_closure_interior Ioc_subset_closure_interior
--/
 
-#print Ico_subset_closure_interior /-
+/- warning: Ico_subset_closure_interior -> Ico_subset_closure_interior is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α) (b : α), HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b) (closure.{u1} α _inst_1 (interior.{u1} α _inst_1 (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α) (b : α), HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) (closure.{u1} α _inst_1 (interior.{u1} α _inst_1 (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)))
+Case conversion may be inaccurate. Consider using '#align Ico_subset_closure_interior Ico_subset_closure_interiorₓ'. -/
 theorem Ico_subset_closure_interior (a b : α) : Ico a b ⊆ closure (interior (Ico a b)) := by
   simpa only [dual_Ioc] using Ioc_subset_closure_interior (OrderDual.toDual b) (OrderDual.toDual a)
 #align Ico_subset_closure_interior Ico_subset_closure_interior
--/
 
-#print frontier_Ici' /-
+/- warning: frontier_Ici' -> frontier_Ici' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α}, (Set.Nonempty.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α}, (Set.Nonempty.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a))
+Case conversion may be inaccurate. Consider using '#align frontier_Ici' frontier_Ici'ₓ'. -/
 @[simp]
 theorem frontier_Ici' {a : α} (ha : (Iio a).Nonempty) : frontier (Ici a) = {a} := by
   simp [frontier, ha]
 #align frontier_Ici' frontier_Ici'
--/
 
-#print frontier_Ici /-
+/- warning: frontier_Ici -> frontier_Ici is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α}, Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α}, Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)
+Case conversion may be inaccurate. Consider using '#align frontier_Ici frontier_Iciₓ'. -/
 theorem frontier_Ici [NoMinOrder α] {a : α} : frontier (Ici a) = {a} :=
   frontier_Ici' nonempty_Iio
 #align frontier_Ici frontier_Ici
--/
 
-#print frontier_Iic' /-
+/- warning: frontier_Iic' -> frontier_Iic' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α}, (Set.Nonempty.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α}, (Set.Nonempty.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a))
+Case conversion may be inaccurate. Consider using '#align frontier_Iic' frontier_Iic'ₓ'. -/
 @[simp]
 theorem frontier_Iic' {a : α} (ha : (Ioi a).Nonempty) : frontier (Iic a) = {a} := by
   simp [frontier, ha]
 #align frontier_Iic' frontier_Iic'
--/
 
-#print frontier_Iic /-
+/- warning: frontier_Iic -> frontier_Iic is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α}, Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α}, Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)
+Case conversion may be inaccurate. Consider using '#align frontier_Iic frontier_Iicₓ'. -/
 theorem frontier_Iic [NoMaxOrder α] {a : α} : frontier (Iic a) = {a} :=
   frontier_Iic' nonempty_Ioi
 #align frontier_Iic frontier_Iic
--/
 
-#print frontier_Ioi' /-
+/- warning: frontier_Ioi' -> frontier_Ioi' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α}, (Set.Nonempty.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α}, (Set.Nonempty.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a))
+Case conversion may be inaccurate. Consider using '#align frontier_Ioi' frontier_Ioi'ₓ'. -/
 @[simp]
 theorem frontier_Ioi' {a : α} (ha : (Ioi a).Nonempty) : frontier (Ioi a) = {a} := by
   simp [frontier, closure_Ioi' ha, Iic_diff_Iio, Icc_self]
 #align frontier_Ioi' frontier_Ioi'
--/
 
-#print frontier_Ioi /-
+/- warning: frontier_Ioi -> frontier_Ioi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α}, Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α}, Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)
+Case conversion may be inaccurate. Consider using '#align frontier_Ioi frontier_Ioiₓ'. -/
 theorem frontier_Ioi [NoMaxOrder α] {a : α} : frontier (Ioi a) = {a} :=
   frontier_Ioi' nonempty_Ioi
 #align frontier_Ioi frontier_Ioi
--/
 
-#print frontier_Iio' /-
+/- warning: frontier_Iio' -> frontier_Iio' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α}, (Set.Nonempty.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α}, (Set.Nonempty.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a))
+Case conversion may be inaccurate. Consider using '#align frontier_Iio' frontier_Iio'ₓ'. -/
 @[simp]
 theorem frontier_Iio' {a : α} (ha : (Iio a).Nonempty) : frontier (Iio a) = {a} := by
   simp [frontier, closure_Iio' ha, Iic_diff_Iio, Icc_self]
 #align frontier_Iio' frontier_Iio'
--/
 
-#print frontier_Iio /-
+/- warning: frontier_Iio -> frontier_Iio is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α}, Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α}, Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)
+Case conversion may be inaccurate. Consider using '#align frontier_Iio frontier_Iioₓ'. -/
 theorem frontier_Iio [NoMinOrder α] {a : α} : frontier (Iio a) = {a} :=
   frontier_Iio' nonempty_Iio
 #align frontier_Iio frontier_Iio
--/
 
-#print frontier_Icc /-
+/- warning: frontier_Icc -> frontier_Icc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_6 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_6 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b)))
+Case conversion may be inaccurate. Consider using '#align frontier_Icc frontier_Iccₓ'. -/
 @[simp]
 theorem frontier_Icc [NoMinOrder α] [NoMaxOrder α] {a b : α} (h : a ≤ b) :
     frontier (Icc a b) = {a, b} := by simp [frontier, h, Icc_diff_Ioo_same]
 #align frontier_Icc frontier_Icc
--/
 
-#print frontier_Ioo /-
+/- warning: frontier_Ioo -> frontier_Ioo is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b)))
+Case conversion may be inaccurate. Consider using '#align frontier_Ioo frontier_Iooₓ'. -/
 @[simp]
 theorem frontier_Ioo {a b : α} (h : a < b) : frontier (Ioo a b) = {a, b} := by
   rw [frontier, closure_Ioo h.ne, interior_Ioo, Icc_diff_Ioo_same h.le]
 #align frontier_Ioo frontier_Ioo
--/
 
-#print frontier_Ico /-
+/- warning: frontier_Ico -> frontier_Ico is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b)))
+Case conversion may be inaccurate. Consider using '#align frontier_Ico frontier_Icoₓ'. -/
 @[simp]
 theorem frontier_Ico [NoMinOrder α] {a b : α} (h : a < b) : frontier (Ico a b) = {a, b} := by
   rw [frontier, closure_Ico h.ne, interior_Ico, Icc_diff_Ioo_same h.le]
 #align frontier_Ico frontier_Ico
--/
 
-#print frontier_Ioc /-
+/- warning: frontier_Ioc -> frontier_Ioc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b)))
+Case conversion may be inaccurate. Consider using '#align frontier_Ioc frontier_Iocₓ'. -/
 @[simp]
 theorem frontier_Ioc [NoMaxOrder α] {a b : α} (h : a < b) : frontier (Ioc a b) = {a, b} := by
   rw [frontier, closure_Ioc h.ne, interior_Ioc, Icc_diff_Ioo_same h.le]
 #align frontier_Ioc frontier_Ioc
--/
 
-#print nhdsWithin_Ioi_neBot' /-
+/- warning: nhds_within_Ioi_ne_bot' -> nhdsWithin_Ioi_neBot' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (Set.Nonempty.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (Set.Nonempty.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Ioi_ne_bot' nhdsWithin_Ioi_neBot'ₓ'. -/
 theorem nhdsWithin_Ioi_neBot' {a b : α} (H₁ : (Ioi a).Nonempty) (H₂ : a ≤ b) : NeBot (𝓝[Ioi a] b) :=
   mem_closure_iff_nhdsWithin_neBot.1 <| by rwa [closure_Ioi' H₁]
 #align nhds_within_Ioi_ne_bot' nhdsWithin_Ioi_neBot'
--/
 
-#print nhdsWithin_Ioi_neBot /-
+/- warning: nhds_within_Ioi_ne_bot -> nhdsWithin_Ioi_neBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Ioi_ne_bot nhdsWithin_Ioi_neBotₓ'. -/
 theorem nhdsWithin_Ioi_neBot [NoMaxOrder α] {a b : α} (H : a ≤ b) : NeBot (𝓝[Ioi a] b) :=
   nhdsWithin_Ioi_neBot' nonempty_Ioi H
 #align nhds_within_Ioi_ne_bot nhdsWithin_Ioi_neBot
--/
 
-#print nhdsWithin_Ioi_self_neBot' /-
+/- warning: nhds_within_Ioi_self_ne_bot' -> nhdsWithin_Ioi_self_neBot' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α}, (Set.Nonempty.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α}, (Set.Nonempty.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Ioi_self_ne_bot' nhdsWithin_Ioi_self_neBot'ₓ'. -/
 theorem nhdsWithin_Ioi_self_neBot' {a : α} (H : (Ioi a).Nonempty) : NeBot (𝓝[>] a) :=
   nhdsWithin_Ioi_neBot' H (le_refl a)
 #align nhds_within_Ioi_self_ne_bot' nhdsWithin_Ioi_self_neBot'
--/
 
-#print nhdsWithin_Ioi_self_neBot /-
+/- warning: nhds_within_Ioi_self_ne_bot -> nhdsWithin_Ioi_self_neBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α), Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α), Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Ioi_self_ne_bot nhdsWithin_Ioi_self_neBotₓ'. -/
 @[instance]
 theorem nhdsWithin_Ioi_self_neBot [NoMaxOrder α] (a : α) : NeBot (𝓝[>] a) :=
   nhdsWithin_Ioi_neBot (le_refl a)
 #align nhds_within_Ioi_self_ne_bot nhdsWithin_Ioi_self_neBot
--/
 
 /- warning: filter.eventually.exists_gt -> Filter.Eventually.exists_gt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {p : α -> Prop}, (Filter.Eventually.{u1} α (fun (x : α) => p x) (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) => p b)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {p : α -> Prop}, (Filter.Eventually.{u1} α (fun (x : α) => p x) (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) (fun (H : GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) => p b)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {p : α -> Prop}, (Filter.Eventually.{u1} α (fun (x : α) => p x) (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (b : α) => And (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b a) (p b)))
 Case conversion may be inaccurate. Consider using '#align filter.eventually.exists_gt Filter.Eventually.exists_gtₓ'. -/
@@ -3528,34 +4090,50 @@ theorem Filter.Eventually.exists_gt [NoMaxOrder α] {a : α} {p : α → Prop} (
     ((h.filter_mono (@nhdsWithin_le_nhds _ _ a (Ioi a))).And self_mem_nhdsWithin).exists
 #align filter.eventually.exists_gt Filter.Eventually.exists_gt
 
-#print nhdsWithin_Iio_neBot' /-
+/- warning: nhds_within_Iio_ne_bot' -> nhdsWithin_Iio_neBot' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {b : α} {c : α}, (Set.Nonempty.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b c) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) c)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {b : α} {c : α}, (Set.Nonempty.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b c) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) c)))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Iio_ne_bot' nhdsWithin_Iio_neBot'ₓ'. -/
 theorem nhdsWithin_Iio_neBot' {b c : α} (H₁ : (Iio c).Nonempty) (H₂ : b ≤ c) : NeBot (𝓝[Iio c] b) :=
   mem_closure_iff_nhdsWithin_neBot.1 <| by rwa [closure_Iio' H₁]
 #align nhds_within_Iio_ne_bot' nhdsWithin_Iio_neBot'
--/
 
-#print nhdsWithin_Iio_neBot /-
+/- warning: nhds_within_Iio_ne_bot -> nhdsWithin_Iio_neBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Iio_ne_bot nhdsWithin_Iio_neBotₓ'. -/
 theorem nhdsWithin_Iio_neBot [NoMinOrder α] {a b : α} (H : a ≤ b) : NeBot (𝓝[Iio b] a) :=
   nhdsWithin_Iio_neBot' nonempty_Iio H
 #align nhds_within_Iio_ne_bot nhdsWithin_Iio_neBot
--/
 
-#print nhdsWithin_Iio_self_neBot' /-
+/- warning: nhds_within_Iio_self_ne_bot' -> nhdsWithin_Iio_self_neBot' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {b : α}, (Set.Nonempty.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {b : α}, (Set.Nonempty.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Iio_self_ne_bot' nhdsWithin_Iio_self_neBot'ₓ'. -/
 theorem nhdsWithin_Iio_self_neBot' {b : α} (H : (Iio b).Nonempty) : NeBot (𝓝[<] b) :=
   nhdsWithin_Iio_neBot' H (le_refl b)
 #align nhds_within_Iio_self_ne_bot' nhdsWithin_Iio_self_neBot'
--/
 
-#print nhdsWithin_Iio_self_neBot /-
+/- warning: nhds_within_Iio_self_ne_bot -> nhdsWithin_Iio_self_neBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α), Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α), Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))
+Case conversion may be inaccurate. Consider using '#align nhds_within_Iio_self_ne_bot nhdsWithin_Iio_self_neBotₓ'. -/
 @[instance]
 theorem nhdsWithin_Iio_self_neBot [NoMinOrder α] (a : α) : NeBot (𝓝[<] a) :=
   nhdsWithin_Iio_neBot (le_refl a)
 #align nhds_within_Iio_self_ne_bot nhdsWithin_Iio_self_neBot
--/
 
 /- warning: filter.eventually.exists_lt -> Filter.Eventually.exists_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {p : α -> Prop}, (Filter.Eventually.{u1} α (fun (x : α) => p x) (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) => p b)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {p : α -> Prop}, (Filter.Eventually.{u1} α (fun (x : α) => p x) (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) (fun (H : LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) => p b)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {p : α -> Prop}, (Filter.Eventually.{u1} α (fun (x : α) => p x) (nhds.{u1} α _inst_1 a)) -> (Exists.{succ u1} α (fun (b : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b a) (p b)))
 Case conversion may be inaccurate. Consider using '#align filter.eventually.exists_lt Filter.Eventually.exists_ltₓ'. -/
@@ -3564,33 +4142,49 @@ theorem Filter.Eventually.exists_lt [NoMinOrder α] {a : α} {p : α → Prop} (
   @Filter.Eventually.exists_gt αᵒᵈ _ _ _ _ _ _ _ h
 #align filter.eventually.exists_lt Filter.Eventually.exists_lt
 
-#print right_nhdsWithin_Ico_neBot /-
+/- warning: right_nhds_within_Ico_ne_bot -> right_nhdsWithin_Ico_neBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)))
+Case conversion may be inaccurate. Consider using '#align right_nhds_within_Ico_ne_bot right_nhdsWithin_Ico_neBotₓ'. -/
 theorem right_nhdsWithin_Ico_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ico a b] b) :=
   (isLUB_Ico H).nhdsWithin_neBot (nonempty_Ico.2 H)
 #align right_nhds_within_Ico_ne_bot right_nhdsWithin_Ico_neBot
--/
 
-#print left_nhdsWithin_Ioc_neBot /-
+/- warning: left_nhds_within_Ioc_ne_bot -> left_nhdsWithin_Ioc_neBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)))
+Case conversion may be inaccurate. Consider using '#align left_nhds_within_Ioc_ne_bot left_nhdsWithin_Ioc_neBotₓ'. -/
 theorem left_nhdsWithin_Ioc_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ioc a b] a) :=
   (isGLB_Ioc H).nhdsWithin_neBot (nonempty_Ioc.2 H)
 #align left_nhds_within_Ioc_ne_bot left_nhdsWithin_Ioc_neBot
--/
 
-#print left_nhdsWithin_Ioo_neBot /-
+/- warning: left_nhds_within_Ioo_ne_bot -> left_nhdsWithin_Ioo_neBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)))
+Case conversion may be inaccurate. Consider using '#align left_nhds_within_Ioo_ne_bot left_nhdsWithin_Ioo_neBotₓ'. -/
 theorem left_nhdsWithin_Ioo_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ioo a b] a) :=
   (isGLB_Ioo H).nhdsWithin_neBot (nonempty_Ioo.2 H)
 #align left_nhds_within_Ioo_ne_bot left_nhdsWithin_Ioo_neBot
--/
 
-#print right_nhdsWithin_Ioo_neBot /-
+/- warning: right_nhds_within_Ioo_ne_bot -> right_nhdsWithin_Ioo_neBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Filter.NeBot.{u1} α (nhdsWithin.{u1} α _inst_1 b (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)))
+Case conversion may be inaccurate. Consider using '#align right_nhds_within_Ioo_ne_bot right_nhdsWithin_Ioo_neBotₓ'. -/
 theorem right_nhdsWithin_Ioo_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ioo a b] b) :=
   (isLUB_Ioo H).nhdsWithin_neBot (nonempty_Ioo.2 H)
 #align right_nhds_within_Ioo_ne_bot right_nhdsWithin_Ioo_neBot
--/
 
 /- warning: comap_coe_nhds_within_Iio_of_Ioo_subset -> comap_coe_nhdsWithin_Iio_of_Ioo_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {b : α} {s : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) -> ((Set.Nonempty.{u1} α s) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a b) s)))) -> (Eq.{succ u1} (Filter.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (Filter.comap.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α ((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)))))) (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b))) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {b : α} {s : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) -> ((Set.Nonempty.{u1} α s) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) (fun (H : LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a b) s)))) -> (Eq.{succ u1} (Filter.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (Filter.comap.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α ((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)))))) (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b))) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {b : α} {s : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)) -> ((Set.Nonempty.{u1} α s) -> (Exists.{succ u1} α (fun (a : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) s)))) -> (Eq.{succ u1} (Filter.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s))) (Filter.comap.{u1, u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)) α (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)) (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b))) (Filter.atTop.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s))))
 Case conversion may be inaccurate. Consider using '#align comap_coe_nhds_within_Iio_of_Ioo_subset comap_coe_nhdsWithin_Iio_of_Ioo_subsetₓ'. -/
@@ -3615,7 +4209,7 @@ theorem comap_coe_nhdsWithin_Iio_of_Ioo_subset (hb : s ⊆ Iio b)
 
 /- warning: comap_coe_nhds_within_Ioi_of_Ioo_subset -> comap_coe_nhdsWithin_Ioi_of_Ioo_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) -> ((Set.Nonempty.{u1} α s) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a b) s)))) -> (Eq.{succ u1} (Filter.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (Filter.comap.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α ((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)))))) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) -> ((Set.Nonempty.{u1} α s) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) (fun (H : GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a b) s)))) -> (Eq.{succ u1} (Filter.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (Filter.comap.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α ((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)))))) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {s : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) -> ((Set.Nonempty.{u1} α s) -> (Exists.{succ u1} α (fun (b : α) => And (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b a) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) s)))) -> (Eq.{succ u1} (Filter.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s))) (Filter.comap.{u1, u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)) α (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Filter.atBot.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s))))
 Case conversion may be inaccurate. Consider using '#align comap_coe_nhds_within_Ioi_of_Ioo_subset comap_coe_nhdsWithin_Ioi_of_Ioo_subsetₓ'. -/
@@ -3627,7 +4221,7 @@ theorem comap_coe_nhdsWithin_Ioi_of_Ioo_subset (ha : s ⊆ Ioi a)
 
 /- warning: map_coe_at_top_of_Ioo_subset -> map_coe_atTop_of_Ioo_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {b : α} {s : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) -> (forall (a' : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a' b) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a b) s)))) -> (Eq.{succ u1} (Filter.{u1} α) (Filter.map.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α ((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)))))) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s)))) (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {b : α} {s : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) -> (forall (a' : α), (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a' b) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) (fun (H : LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a b) s)))) -> (Eq.{succ u1} (Filter.{u1} α) (Filter.map.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α ((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)))))) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s)))) (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {b : α} {s : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)) -> (forall (a' : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a' b) -> (Exists.{succ u1} α (fun (a : α) => And (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) s)))) -> (Eq.{succ u1} (Filter.{u1} α) (Filter.map.{u1, u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)) α (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)) (Filter.atTop.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)))) (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)))
 Case conversion may be inaccurate. Consider using '#align map_coe_at_top_of_Ioo_subset map_coe_atTop_of_Ioo_subsetₓ'. -/
@@ -3644,7 +4238,7 @@ theorem map_coe_atTop_of_Ioo_subset (hb : s ⊆ Iio b) (hs : ∀ a' < b, ∃ a <
 
 /- warning: map_coe_at_bot_of_Ioo_subset -> map_coe_atBot_of_Ioo_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) -> (forall (b' : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b' a) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a b) s)))) -> (Eq.{succ u1} (Filter.{u1} α) (Filter.map.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α ((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)))))) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s)))) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {s : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) -> (forall (b' : α), (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b' a) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) (fun (H : GT.gt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) b a) => 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 (LinearOrder.toLattice.{u1} α _inst_2)))) a b) s)))) -> (Eq.{succ u1} (Filter.{u1} α) (Filter.map.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α ((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)))))) (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 (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s)))) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {s : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) -> (forall (b' : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b' a) -> (Exists.{succ u1} α (fun (b : α) => And (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) b a) (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 (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b) s)))) -> (Eq.{succ u1} (Filter.{u1} α) (Filter.map.{u1, u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)) α (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)) (Filter.atBot.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s)))) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
 Case conversion may be inaccurate. Consider using '#align map_coe_at_bot_of_Ioo_subset map_coe_atBot_of_Ioo_subsetₓ'. -/
@@ -3657,129 +4251,193 @@ theorem map_coe_atBot_of_Ioo_subset (ha : s ⊆ Ioi a) (hs : ∀ b' > a, ∃ b >
   simpa only [OrderDual.exists, dual_Ioo] using hs b' hb'
 #align map_coe_at_bot_of_Ioo_subset map_coe_atBot_of_Ioo_subset
 
-#print comap_coe_Ioo_nhdsWithin_Iio /-
+/- warning: comap_coe_Ioo_nhds_within_Iio -> comap_coe_Ioo_nhdsWithin_Iio is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α) (b : α), Eq.{succ u1} (Filter.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (Filter.comap.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α ((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) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))))))) (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b))) (Filter.atTop.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α) (b : α), Eq.{succ u1} (Filter.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)))) (Filter.comap.{u1, u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) α (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b))) (Filter.atTop.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))))
+Case conversion may be inaccurate. Consider using '#align comap_coe_Ioo_nhds_within_Iio comap_coe_Ioo_nhdsWithin_Iioₓ'. -/
 /-- The `at_top` filter for an open interval `Ioo a b` comes from the left-neighbourhoods filter at
 the right endpoint in the ambient order. -/
 theorem comap_coe_Ioo_nhdsWithin_Iio (a b : α) : comap (coe : Ioo a b → α) (𝓝[<] b) = atTop :=
   comap_coe_nhdsWithin_Iio_of_Ioo_subset Ioo_subset_Iio_self fun h =>
     ⟨a, nonempty_Ioo.1 h, Subset.refl _⟩
 #align comap_coe_Ioo_nhds_within_Iio comap_coe_Ioo_nhdsWithin_Iio
--/
 
-#print comap_coe_Ioo_nhdsWithin_Ioi /-
+/- warning: comap_coe_Ioo_nhds_within_Ioi -> comap_coe_Ioo_nhdsWithin_Ioi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α) (b : α), Eq.{succ u1} (Filter.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))) (Filter.comap.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α ((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) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))))))) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Filter.atBot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α) (b : α), Eq.{succ u1} (Filter.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)))) (Filter.comap.{u1, u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) α (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Filter.atBot.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))))
+Case conversion may be inaccurate. Consider using '#align comap_coe_Ioo_nhds_within_Ioi comap_coe_Ioo_nhdsWithin_Ioiₓ'. -/
 /-- The `at_bot` filter for an open interval `Ioo a b` comes from the right-neighbourhoods filter at
 the left endpoint in the ambient order. -/
 theorem comap_coe_Ioo_nhdsWithin_Ioi (a b : α) : comap (coe : Ioo a b → α) (𝓝[>] a) = atBot :=
   comap_coe_nhdsWithin_Ioi_of_Ioo_subset Ioo_subset_Ioi_self fun h =>
     ⟨b, nonempty_Ioo.1 h, Subset.refl _⟩
 #align comap_coe_Ioo_nhds_within_Ioi comap_coe_Ioo_nhdsWithin_Ioi
--/
 
-#print comap_coe_Ioi_nhdsWithin_Ioi /-
+/- warning: comap_coe_Ioi_nhds_within_Ioi -> comap_coe_Ioi_nhdsWithin_Ioi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α), Eq.{succ u1} (Filter.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Filter.comap.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α ((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) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))))))) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Filter.atBot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α), Eq.{succ u1} (Filter.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))) (Filter.comap.{u1, u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) α (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Filter.atBot.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))))
+Case conversion may be inaccurate. Consider using '#align comap_coe_Ioi_nhds_within_Ioi comap_coe_Ioi_nhdsWithin_Ioiₓ'. -/
 theorem comap_coe_Ioi_nhdsWithin_Ioi (a : α) : comap (coe : Ioi a → α) (𝓝[>] a) = atBot :=
   comap_coe_nhdsWithin_Ioi_of_Ioo_subset (Subset.refl _) fun ⟨x, hx⟩ => ⟨x, hx, Ioo_subset_Ioi_self⟩
 #align comap_coe_Ioi_nhds_within_Ioi comap_coe_Ioi_nhdsWithin_Ioi
--/
 
-#print comap_coe_Iio_nhdsWithin_Iio /-
+/- warning: comap_coe_Iio_nhds_within_Iio -> comap_coe_Iio_nhdsWithin_Iio is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α), Eq.{succ u1} (Filter.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Filter.comap.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α ((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) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))))))) (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))) (Filter.atTop.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α), Eq.{succ u1} (Filter.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))) (Filter.comap.{u1, u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) α (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Filter.atTop.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))))
+Case conversion may be inaccurate. Consider using '#align comap_coe_Iio_nhds_within_Iio comap_coe_Iio_nhdsWithin_Iioₓ'. -/
 theorem comap_coe_Iio_nhdsWithin_Iio (a : α) : comap (coe : Iio a → α) (𝓝[<] a) = atTop :=
   @comap_coe_Ioi_nhdsWithin_Ioi αᵒᵈ _ _ _ _ a
 #align comap_coe_Iio_nhds_within_Iio comap_coe_Iio_nhdsWithin_Iio
--/
 
-#print map_coe_Ioo_atTop /-
+/- warning: map_coe_Ioo_at_top -> map_coe_Ioo_atTop is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (Filter.map.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α ((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) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))))))) (Filter.atTop.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))))) (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (Filter.map.{u1, u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) α (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (Filter.atTop.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))))) (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)))
+Case conversion may be inaccurate. Consider using '#align map_coe_Ioo_at_top map_coe_Ioo_atTopₓ'. -/
 @[simp]
 theorem map_coe_Ioo_atTop {a b : α} (h : a < b) : map (coe : Ioo a b → α) atTop = 𝓝[<] b :=
   map_coe_atTop_of_Ioo_subset Ioo_subset_Iio_self fun _ _ => ⟨_, h, Subset.refl _⟩
 #align map_coe_Ioo_at_top map_coe_Ioo_atTop
--/
 
-#print map_coe_Ioo_atBot /-
+/- warning: map_coe_Ioo_at_bot -> map_coe_Ioo_atBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (Filter.map.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α ((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) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))))))) (Filter.atBot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))))) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Filter.{u1} α) (Filter.map.{u1, u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) α (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (Filter.atBot.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))))) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
+Case conversion may be inaccurate. Consider using '#align map_coe_Ioo_at_bot map_coe_Ioo_atBotₓ'. -/
 @[simp]
 theorem map_coe_Ioo_atBot {a b : α} (h : a < b) : map (coe : Ioo a b → α) atBot = 𝓝[>] a :=
   map_coe_atBot_of_Ioo_subset Ioo_subset_Ioi_self fun _ _ => ⟨_, h, Subset.refl _⟩
 #align map_coe_Ioo_at_bot map_coe_Ioo_atBot
--/
 
-#print map_coe_Ioi_atBot /-
+/- warning: map_coe_Ioi_at_bot -> map_coe_Ioi_atBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α), Eq.{succ u1} (Filter.{u1} α) (Filter.map.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α ((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) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))))))) (Filter.atBot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))))) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α), Eq.{succ u1} (Filter.{u1} α) (Filter.map.{u1, u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) α (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Filter.atBot.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))))) (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))
+Case conversion may be inaccurate. Consider using '#align map_coe_Ioi_at_bot map_coe_Ioi_atBotₓ'. -/
 @[simp]
 theorem map_coe_Ioi_atBot (a : α) : map (coe : Ioi a → α) atBot = 𝓝[>] a :=
   map_coe_atBot_of_Ioo_subset (Subset.refl _) fun b hb => ⟨b, hb, Ioo_subset_Ioi_self⟩
 #align map_coe_Ioi_at_bot map_coe_Ioi_atBot
--/
 
-#print map_coe_Iio_atTop /-
+/- warning: map_coe_Iio_at_top -> map_coe_Iio_atTop is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (a : α), Eq.{succ u1} (Filter.{u1} α) (Filter.map.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α ((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) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))))))) (Filter.atTop.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))))) (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (a : α), Eq.{succ u1} (Filter.{u1} α) (Filter.map.{u1, u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) α (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Filter.atTop.{u1} (Subtype.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))))) (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))
+Case conversion may be inaccurate. Consider using '#align map_coe_Iio_at_top map_coe_Iio_atTopₓ'. -/
 @[simp]
 theorem map_coe_Iio_atTop (a : α) : map (coe : Iio a → α) atTop = 𝓝[<] a :=
   @map_coe_Ioi_atBot αᵒᵈ _ _ _ _ _
 #align map_coe_Iio_at_top map_coe_Iio_atTop
--/
 
 variable {l : Filter β} {f : α → β}
 
-#print tendsto_comp_coe_Ioo_atTop /-
+/- warning: tendsto_comp_coe_Ioo_at_top -> tendsto_comp_coe_Ioo_atTop is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α} {l : Filter.{u2} β} {f : α -> β}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Iff (Filter.Tendsto.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) β (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) => 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) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)))))) x)) (Filter.atTop.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)))) l) (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)) l))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α} {l : Filter.{u2} β} {f : α -> β}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Iff (Filter.Tendsto.{u1, u2} (Set.Elem.{u1} α (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) β (fun (x : Set.Elem.{u1} α (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) => f (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) x)) (Filter.atTop.{u1} (Set.Elem.{u1} α (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)))) l) (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)) l))
+Case conversion may be inaccurate. Consider using '#align tendsto_comp_coe_Ioo_at_top tendsto_comp_coe_Ioo_atTopₓ'. -/
 @[simp]
 theorem tendsto_comp_coe_Ioo_atTop (h : a < b) :
     Tendsto (fun x : Ioo a b => f x) atTop l ↔ Tendsto f (𝓝[<] b) l := by
   rw [← map_coe_Ioo_atTop h, tendsto_map'_iff]
 #align tendsto_comp_coe_Ioo_at_top tendsto_comp_coe_Ioo_atTop
--/
 
-#print tendsto_comp_coe_Ioo_atBot /-
+/- warning: tendsto_comp_coe_Ioo_at_bot -> tendsto_comp_coe_Ioo_atBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α} {l : Filter.{u2} β} {f : α -> β}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Iff (Filter.Tendsto.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) β (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) => 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) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)))))) x)) (Filter.atBot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)))) l) (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) l))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α} {l : Filter.{u2} β} {f : α -> β}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Iff (Filter.Tendsto.{u1, u2} (Set.Elem.{u1} α (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) β (fun (x : Set.Elem.{u1} α (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) => f (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) x)) (Filter.atBot.{u1} (Set.Elem.{u1} α (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)))) l) (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) l))
+Case conversion may be inaccurate. Consider using '#align tendsto_comp_coe_Ioo_at_bot tendsto_comp_coe_Ioo_atBotₓ'. -/
 @[simp]
 theorem tendsto_comp_coe_Ioo_atBot (h : a < b) :
     Tendsto (fun x : Ioo a b => f x) atBot l ↔ Tendsto f (𝓝[>] a) l := by
   rw [← map_coe_Ioo_atBot h, tendsto_map'_iff]
 #align tendsto_comp_coe_Ioo_at_bot tendsto_comp_coe_Ioo_atBot
--/
 
-#print tendsto_comp_coe_Ioi_atBot /-
+/- warning: tendsto_comp_coe_Ioi_at_bot -> tendsto_comp_coe_Ioi_atBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {l : Filter.{u2} β} {f : α -> β}, Iff (Filter.Tendsto.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) β (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => 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) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))))) x)) (Filter.atBot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))) l) (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) l)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {l : Filter.{u2} β} {f : α -> β}, Iff (Filter.Tendsto.{u1, u2} (Set.Elem.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) β (fun (x : Set.Elem.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) => f (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) x)) (Filter.atBot.{u1} (Set.Elem.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))) l) (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) l)
+Case conversion may be inaccurate. Consider using '#align tendsto_comp_coe_Ioi_at_bot tendsto_comp_coe_Ioi_atBotₓ'. -/
 @[simp]
 theorem tendsto_comp_coe_Ioi_atBot :
     Tendsto (fun x : Ioi a => f x) atBot l ↔ Tendsto f (𝓝[>] a) l := by
   rw [← map_coe_Ioi_atBot, tendsto_map'_iff]
 #align tendsto_comp_coe_Ioi_at_bot tendsto_comp_coe_Ioi_atBot
--/
 
-#print tendsto_comp_coe_Iio_atTop /-
+/- warning: tendsto_comp_coe_Iio_at_top -> tendsto_comp_coe_Iio_atTop is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {l : Filter.{u2} β} {f : α -> β}, Iff (Filter.Tendsto.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) β (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) => 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) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))))) x)) (Filter.atTop.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))) l) (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) l)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {l : Filter.{u2} β} {f : α -> β}, Iff (Filter.Tendsto.{u1, u2} (Set.Elem.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) β (fun (x : Set.Elem.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) => f (Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) x)) (Filter.atTop.{u1} (Set.Elem.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))) l) (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) l)
+Case conversion may be inaccurate. Consider using '#align tendsto_comp_coe_Iio_at_top tendsto_comp_coe_Iio_atTopₓ'. -/
 @[simp]
 theorem tendsto_comp_coe_Iio_atTop :
     Tendsto (fun x : Iio a => f x) atTop l ↔ Tendsto f (𝓝[<] a) l := by
   rw [← map_coe_Iio_atTop, tendsto_map'_iff]
 #align tendsto_comp_coe_Iio_at_top tendsto_comp_coe_Iio_atTop
--/
 
-#print tendsto_Ioo_atTop /-
+/- warning: tendsto_Ioo_at_top -> tendsto_Ioo_atTop is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α} {l : Filter.{u2} β} {f : β -> (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))}, Iff (Filter.Tendsto.{u2, u1} β (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) f l (Filter.atTop.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))))) (Filter.Tendsto.{u2, u1} β α (fun (x : β) => (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) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)))))) (f x)) l (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) b)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α} {l : Filter.{u2} β} {f : β -> (Set.Elem.{u1} α (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))}, Iff (Filter.Tendsto.{u2, u1} β (Set.Elem.{u1} α (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) f l (Filter.atTop.{u1} (Set.Elem.{u1} α (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))))) (Filter.Tendsto.{u2, u1} β α (fun (x : β) => Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (f x)) l (nhdsWithin.{u1} α _inst_1 b (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) b)))
+Case conversion may be inaccurate. Consider using '#align tendsto_Ioo_at_top tendsto_Ioo_atTopₓ'. -/
 @[simp]
 theorem tendsto_Ioo_atTop {f : β → Ioo a b} :
     Tendsto f l atTop ↔ Tendsto (fun x => (f x : α)) l (𝓝[<] b) := by
   rw [← comap_coe_Ioo_nhdsWithin_Iio, tendsto_comap_iff]
 #align tendsto_Ioo_at_top tendsto_Ioo_atTop
--/
 
-#print tendsto_Ioo_atBot /-
+/- warning: tendsto_Ioo_at_bot -> tendsto_Ioo_atBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α} {l : Filter.{u2} β} {f : β -> (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))}, Iff (Filter.Tendsto.{u2, u1} β (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) f l (Filter.atBot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b))))) (Filter.Tendsto.{u2, u1} β α (fun (x : β) => (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) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)))))) (f x)) l (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α} {l : Filter.{u2} β} {f : β -> (Set.Elem.{u1} α (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))}, Iff (Filter.Tendsto.{u2, u1} β (Set.Elem.{u1} α (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) f l (Filter.atBot.{u1} (Set.Elem.{u1} α (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b))))) (Filter.Tendsto.{u2, u1} β α (fun (x : β) => Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (f x)) l (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
+Case conversion may be inaccurate. Consider using '#align tendsto_Ioo_at_bot tendsto_Ioo_atBotₓ'. -/
 @[simp]
 theorem tendsto_Ioo_atBot {f : β → Ioo a b} :
     Tendsto f l atBot ↔ Tendsto (fun x => (f x : α)) l (𝓝[>] a) := by
   rw [← comap_coe_Ioo_nhdsWithin_Ioi, tendsto_comap_iff]
 #align tendsto_Ioo_at_bot tendsto_Ioo_atBot
--/
 
-#print tendsto_Ioi_atBot /-
+/- warning: tendsto_Ioi_at_bot -> tendsto_Ioi_atBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {l : Filter.{u2} β} {f : β -> (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))}, Iff (Filter.Tendsto.{u2, u1} β (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) f l (Filter.atBot.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))))) (Filter.Tendsto.{u2, u1} β α (fun (x : β) => (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) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))))) (f x)) l (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {l : Filter.{u2} β} {f : β -> (Set.Elem.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))}, Iff (Filter.Tendsto.{u2, u1} β (Set.Elem.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) f l (Filter.atBot.{u1} (Set.Elem.{u1} α (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))))) (Filter.Tendsto.{u2, u1} β α (fun (x : β) => Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (f x)) l (nhdsWithin.{u1} α _inst_1 a (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
+Case conversion may be inaccurate. Consider using '#align tendsto_Ioi_at_bot tendsto_Ioi_atBotₓ'. -/
 @[simp]
 theorem tendsto_Ioi_atBot {f : β → Ioi a} :
     Tendsto f l atBot ↔ Tendsto (fun x => (f x : α)) l (𝓝[>] a) := by
   rw [← comap_coe_Ioi_nhdsWithin_Ioi, tendsto_comap_iff]
 #align tendsto_Ioi_at_bot tendsto_Ioi_atBot
--/
 
-#print tendsto_Iio_atTop /-
+/- warning: tendsto_Iio_at_top -> tendsto_Iio_atTop is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {l : Filter.{u2} β} {f : β -> (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))}, Iff (Filter.Tendsto.{u2, u1} β (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) f l (Filter.atTop.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a))))) (Filter.Tendsto.{u2, u1} β α (fun (x : β) => (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) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))))) (f x)) l (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {l : Filter.{u2} β} {f : β -> (Set.Elem.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))}, Iff (Filter.Tendsto.{u2, u1} β (Set.Elem.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) f l (Filter.atTop.{u1} (Set.Elem.{u1} α (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (Subtype.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a))))) (Filter.Tendsto.{u2, u1} β α (fun (x : β) => Subtype.val.{succ u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)) (f x)) l (nhdsWithin.{u1} α _inst_1 a (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a)))
+Case conversion may be inaccurate. Consider using '#align tendsto_Iio_at_top tendsto_Iio_atTopₓ'. -/
 @[simp]
 theorem tendsto_Iio_atTop {f : β → Iio a} :
     Tendsto f l atTop ↔ Tendsto (fun x => (f x : α)) l (𝓝[<] a) := by
   rw [← comap_coe_Iio_nhdsWithin_Iio, tendsto_comap_iff]
 #align tendsto_Iio_at_top tendsto_Iio_atTop
--/
 
 instance (x : α) [Nontrivial α] : NeBot (𝓝[≠] x) :=
   by
@@ -3794,7 +4452,7 @@ instance (x : α) [Nontrivial α] : NeBot (𝓝[≠] x) :=
 
 /- warning: dense.exists_countable_dense_subset_no_bot_top -> Dense.exists_countable_dense_subset_no_bot_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : Nontrivial.{u1} α] {s : Set.{u1} α} [_inst_6 : TopologicalSpace.SeparableSpace.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.topologicalSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1)], (Dense.{u1} α _inst_1 s) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) (fun (H : HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) => And (Set.Countable.{u1} α t) (And (Dense.{u1} α _inst_1 t) (And (forall (x : α), (IsBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t))) (forall (x : α), (IsTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t))))))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : Nontrivial.{u1} α] {s : Set.{u1} α} [_inst_6 : TopologicalSpace.SeparableSpace.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (Subtype.topologicalSpace.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) _inst_1)], (Dense.{u1} α _inst_1 s) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) (fun (H : HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) => And (Set.Countable.{u1} α t) (And (Dense.{u1} α _inst_1 t) (And (forall (x : α), (IsBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t))) (forall (x : α), (IsTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t))))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : Nontrivial.{u1} α] {s : Set.{u1} α} [_inst_6 : TopologicalSpace.SeparableSpace.{u1} (Set.Elem.{u1} α s) (instTopologicalSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1)], (Dense.{u1} α _inst_1 s) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) (And (Set.Countable.{u1} α t) (And (Dense.{u1} α _inst_1 t) (And (forall (x : α), (IsBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t))) (forall (x : α), (IsTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t))))))))
 Case conversion may be inaccurate. Consider using '#align dense.exists_countable_dense_subset_no_bot_top Dense.exists_countable_dense_subset_no_bot_topₓ'. -/
@@ -3819,7 +4477,12 @@ theorem Dense.exists_countable_dense_subset_no_bot_top [Nontrivial α] {s : Set
 
 variable (α)
 
-#print exists_countable_dense_no_bot_top /-
+/- warning: exists_countable_dense_no_bot_top -> exists_countable_dense_no_bot_top is a dubious translation:
+lean 3 declaration is
+  forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : TopologicalSpace.SeparableSpace.{u1} α _inst_1] [_inst_6 : Nontrivial.{u1} α], Exists.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => And (Set.Countable.{u1} α s) (And (Dense.{u1} α _inst_1 s) (And (forall (x : α), (IsBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))) (forall (x : α), (IsTop.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) x) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))))
+but is expected to have type
+  forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : TopologicalSpace.SeparableSpace.{u1} α _inst_1] [_inst_6 : Nontrivial.{u1} α], Exists.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => And (Set.Countable.{u1} α s) (And (Dense.{u1} α _inst_1 s) (And (forall (x : α), (IsBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s))) (forall (x : α), (IsTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s))))))
+Case conversion may be inaccurate. Consider using '#align exists_countable_dense_no_bot_top exists_countable_dense_no_bot_topₓ'. -/
 /-- If `α` is a nontrivial separable dense linear order, then there exists a
 countable dense set `s : set α` that contains neither top nor bottom elements of `α`.
 For a dense set containing both bot and top elements, see
@@ -3828,7 +4491,6 @@ theorem exists_countable_dense_no_bot_top [SeparableSpace α] [Nontrivial α] :
     ∃ s : Set α, s.Countable ∧ Dense s ∧ (∀ x, IsBot x → x ∉ s) ∧ ∀ x, IsTop x → x ∉ s := by
   simpa using dense_univ.exists_countable_dense_subset_no_bot_top
 #align exists_countable_dense_no_bot_top exists_countable_dense_no_bot_top
--/
 
 end DenselyOrdered
 
@@ -4308,17 +4970,25 @@ section LinearOrderedAddCommGroup
 
 variable [LinearOrder α] [Zero α] [TopologicalSpace α] [OrderTopology α]
 
-#print eventually_nhdsWithin_pos_mem_Ioo /-
+/- warning: eventually_nhds_within_pos_mem_Ioo -> eventually_nhdsWithin_pos_mem_Ioo is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Zero.{u1} α] [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : OrderTopology.{u1} α _inst_3 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))] {ε : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_2))) ε) -> (Filter.Eventually.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_2))) ε)) (nhdsWithin.{u1} α _inst_3 (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_2))) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_2))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Zero.{u1} α] [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : OrderTopology.{u1} α _inst_3 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))] {ε : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_2)) ε) -> (Filter.Eventually.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_2)) ε)) (nhdsWithin.{u1} α _inst_3 (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_2)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_2)))))
+Case conversion may be inaccurate. Consider using '#align eventually_nhds_within_pos_mem_Ioo eventually_nhdsWithin_pos_mem_Iooₓ'. -/
 theorem eventually_nhdsWithin_pos_mem_Ioo {ε : α} (h : 0 < ε) : ∀ᶠ x in 𝓝[>] 0, x ∈ Ioo 0 ε :=
   Ioo_mem_nhdsWithin_Ioi (left_mem_Ico.2 h)
 #align eventually_nhds_within_pos_mem_Ioo eventually_nhdsWithin_pos_mem_Ioo
--/
 
-#print eventually_nhdsWithin_pos_mem_Ioc /-
+/- warning: eventually_nhds_within_pos_mem_Ioc -> eventually_nhdsWithin_pos_mem_Ioc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Zero.{u1} α] [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : OrderTopology.{u1} α _inst_3 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))] {ε : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_2))) ε) -> (Filter.Eventually.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_2))) ε)) (nhdsWithin.{u1} α _inst_3 (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_2))) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α _inst_2))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Zero.{u1} α] [_inst_3 : TopologicalSpace.{u1} α] [_inst_4 : OrderTopology.{u1} α _inst_3 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))] {ε : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_2)) ε) -> (Filter.Eventually.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_2)) ε)) (nhdsWithin.{u1} α _inst_3 (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_2)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α _inst_2)))))
+Case conversion may be inaccurate. Consider using '#align eventually_nhds_within_pos_mem_Ioc eventually_nhdsWithin_pos_mem_Iocₓ'. -/
 theorem eventually_nhdsWithin_pos_mem_Ioc {ε : α} (h : 0 < ε) : ∀ᶠ x in 𝓝[>] 0, x ∈ Ioc 0 ε :=
   Ioc_mem_nhdsWithin_Ioi (left_mem_Ico.2 h)
 #align eventually_nhds_within_pos_mem_Ioc eventually_nhdsWithin_pos_mem_Ioc
--/
 
 end LinearOrderedAddCommGroup
 

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

@@ -1174,7 +1174,7 @@ instance {ι : Type _} {α : ι → Type _} [∀ i, Preorder (α i)] [∀ i, Top
   constructor
   simp only [Pi.le_def, set_of_forall]
   exact
-    isClosed_interᵢ fun i =>
+    isClosed_iInter fun i =>
       isClosed_le ((continuous_apply i).comp continuous_fst)
         ((continuous_apply i).comp continuous_snd)
 
@@ -1264,22 +1264,22 @@ theorem ge_mem_nhds {a b : α} (h : a < b) : ∀ᶠ x in 𝓝 a, x ≤ b :=
 
 /- warning: nhds_eq_order -> nhds_eq_order is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (b : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Iio.{u1} α _inst_2 a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Iio.{u1} α _inst_2 a)) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 b)))) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (b : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Ioi.{u1} α _inst_2 a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Ioi.{u1} α _inst_2 a)) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 b)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (b : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Iio.{u1} α _inst_2 a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Iio.{u1} α _inst_2 a)) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 b)))) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (b : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Ioi.{u1} α _inst_2 a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Ioi.{u1} α _inst_2 a)) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 b)))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (b : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Iio.{u1} α _inst_2 a)) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Iio.{u1} α _inst_2 a)) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 b)))) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (b : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Ioi.{u1} α _inst_2 a)) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Ioi.{u1} α _inst_2 a)) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 b)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (b : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Iio.{u1} α _inst_2 a)) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Iio.{u1} α _inst_2 a)) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 b)))) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (b : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Ioi.{u1} α _inst_2 a)) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Ioi.{u1} α _inst_2 a)) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 b)))))
 Case conversion may be inaccurate. Consider using '#align nhds_eq_order nhds_eq_orderₓ'. -/
 theorem nhds_eq_order (a : α) : 𝓝 a = (⨅ b ∈ Iio a, 𝓟 (Ioi b)) ⊓ ⨅ b ∈ Ioi a, 𝓟 (Iio b) := by
   rw [t.topology_eq_generate_intervals, nhds_generate_from] <;>
     exact
       le_antisymm
         (le_inf
-          (le_infᵢ₂ fun b hb => infᵢ_le_of_le { c : α | b < c } <| infᵢ_le _ ⟨hb, b, Or.inl rfl⟩)
-          (le_infᵢ₂ fun b hb => infᵢ_le_of_le { c : α | c < b } <| infᵢ_le _ ⟨hb, b, Or.inr rfl⟩))
-        (le_infᵢ fun s =>
-          le_infᵢ fun ⟨ha, b, hs⟩ =>
+          (le_iInf₂ fun b hb => iInf_le_of_le { c : α | b < c } <| iInf_le _ ⟨hb, b, Or.inl rfl⟩)
+          (le_iInf₂ fun b hb => iInf_le_of_le { c : α | c < b } <| iInf_le _ ⟨hb, b, Or.inr rfl⟩))
+        (le_iInf fun s =>
+          le_iInf fun ⟨ha, b, hs⟩ =>
             match s, ha, hs with
-            | _, h, Or.inl rfl => inf_le_of_left_le <| infᵢ_le_of_le b <| infᵢ_le _ h
-            | _, h, Or.inr rfl => inf_le_of_right_le <| infᵢ_le_of_le b <| infᵢ_le _ h)
+            | _, h, Or.inl rfl => inf_le_of_left_le <| iInf_le_of_le b <| iInf_le _ h
+            | _, h, Or.inr rfl => inf_le_of_right_le <| iInf_le_of_le b <| iInf_le _ h)
 #align nhds_eq_order nhds_eq_order
 
 #print tendsto_order /-
@@ -1292,7 +1292,7 @@ theorem tendsto_order {f : β → α} {a : α} {x : Filter β} :
 #print tendstoIccClassNhds /-
 instance tendstoIccClassNhds (a : α) : TendstoIxxClass Icc (𝓝 a) (𝓝 a) :=
   by
-  simp only [nhds_eq_order, infᵢ_subtype']
+  simp only [nhds_eq_order, iInf_subtype']
   refine'
     ((has_basis_infi_principal_finite _).inf (has_basis_infi_principal_finite _)).TendstoIxxClass
       fun s hs => _
@@ -1342,16 +1342,16 @@ theorem tendsto_of_tendsto_of_tendsto_of_le_of_le {f g h : β → α} {b : Filte
 
 /- warning: nhds_order_unbounded -> nhds_order_unbounded is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u)) -> (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a)) -> (Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (u : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Ioo.{u1} α _inst_2 l u)))))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u)) -> (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a)) -> (Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (u : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Ioo.{u1} α _inst_2 l u)))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u)) -> (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a)) -> (Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (u : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Ioo.{u1} α _inst_2 l u)))))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u)) -> (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a)) -> (Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (u : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Ioo.{u1} α _inst_2 l u)))))))
 Case conversion may be inaccurate. Consider using '#align nhds_order_unbounded nhds_order_unboundedₓ'. -/
 theorem nhds_order_unbounded {a : α} (hu : ∃ u, a < u) (hl : ∃ l, l < a) :
     𝓝 a = ⨅ (l) (h₂ : l < a) (u) (h₂ : a < u), 𝓟 (Ioo l u) :=
   by
   have : ∃ u, u ∈ Ioi a := hu
   have : ∃ l, l ∈ Iio a := hl
-  simp only [nhds_eq_order, inf_binfᵢ, binfᵢ_inf, *, inf_principal, Ioi_inter_Iio]
+  simp only [nhds_eq_order, inf_biInf, biInf_inf, *, inf_principal, Ioi_inter_Iio]
   rfl
 #align nhds_order_unbounded nhds_order_unbounded
 
@@ -1407,7 +1407,7 @@ theorem induced_orderTopology' {α : Type u} {β : Type v} [Preorder α] [ta : T
   refine' ⟨eq_of_nhds_eq_nhds fun a => _⟩
   rw [nhds_induced, nhds_generate_from, nhds_eq_order (f a)]
   apply le_antisymm
-  · refine' le_infᵢ fun s => le_infᵢ fun hs => le_principal_iff.2 _
+  · refine' le_iInf fun s => le_iInf fun hs => le_principal_iff.2 _
     rcases hs with ⟨ab, b, rfl | rfl⟩
     ·
       exact
@@ -1424,7 +1424,7 @@ theorem induced_orderTopology' {α : Type u} {β : Type v} [Preorder α] [ta : T
               mem_infi_of_mem _ <| mem_infi_of_mem (hf.2 ab) <| mem_principal_self _,
             fun x => hf.1⟩
   · rw [← map_le_iff_le_comap]
-    refine' le_inf _ _ <;> refine' le_infᵢ fun x => le_infᵢ fun h => le_principal_iff.2 _ <;> simp
+    refine' le_inf _ _ <;> refine' le_iInf fun x => le_iInf fun h => le_principal_iff.2 _ <;> simp
     · rcases H₁ h with ⟨b, ab, xb⟩
       refine' mem_infi_of_mem _ (mem_infi_of_mem ⟨ab, b, Or.inl rfl⟩ (mem_principal.2 _))
       exact fun c hc => lt_of_le_of_lt xb (hf.2 hc)
@@ -1457,7 +1457,7 @@ instance orderTopology_of_ordConnected {α : Type u} [ta : TopologicalSpace α]
   refine' ⟨eq_of_nhds_eq_nhds fun a => _⟩
   rw [nhds_induced, nhds_generate_from, nhds_eq_order (a : α)]
   apply le_antisymm
-  · refine' le_infᵢ fun s => le_infᵢ fun hs => le_principal_iff.2 _
+  · refine' le_iInf fun s => le_iInf fun hs => le_principal_iff.2 _
     rcases hs with ⟨ab, b, rfl | rfl⟩
     · refine' ⟨Ioi b, _, fun _ => id⟩
       refine' mem_inf_of_left (mem_infi_of_mem b _)
@@ -1467,7 +1467,7 @@ instance orderTopology_of_ordConnected {α : Type u} [ta : TopologicalSpace α]
       exact mem_infi_of_mem ab (mem_principal_self (Iio b))
   · rw [← map_le_iff_le_comap]
     refine' le_inf _ _
-    · refine' le_infᵢ fun x => le_infᵢ fun h => le_principal_iff.2 _
+    · refine' le_iInf fun x => le_iInf fun h => le_principal_iff.2 _
       by_cases hx : x ∈ t
       · refine' mem_infi_of_mem (Ioi ⟨x, hx⟩) (mem_infi_of_mem ⟨h, ⟨⟨x, hx⟩, Or.inl rfl⟩⟩ _)
         exact fun _ => id
@@ -1480,7 +1480,7 @@ instance orderTopology_of_ordConnected {α : Type u} [ta : TopologicalSpace α]
       contrapose!
       -- here we use the `ord_connected` hypothesis
       exact fun hx => ht.out y.2 a.2 ⟨le_of_not_gt hx, le_of_lt h⟩
-    · refine' le_infᵢ fun x => le_infᵢ fun h => le_principal_iff.2 _
+    · refine' le_iInf fun x => le_iInf fun h => le_principal_iff.2 _
       by_cases hx : x ∈ t
       · refine' mem_infi_of_mem (Iio ⟨x, hx⟩) (mem_infi_of_mem ⟨h, ⟨⟨x, hx⟩, Or.inr rfl⟩⟩ _)
         exact fun _ => id
@@ -1498,23 +1498,23 @@ instance orderTopology_of_ordConnected {α : Type u} [ta : TopologicalSpace α]
 
 /- warning: nhds_within_Ici_eq'' -> nhdsWithin_Ici_eq'' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (u : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 u)))) (Filter.principal.{u1} α (Set.Ici.{u1} α _inst_2 a)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (u : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 u)))) (Filter.principal.{u1} α (Set.Ici.{u1} α _inst_2 a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (u : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 u)))) (Filter.principal.{u1} α (Set.Ici.{u1} α _inst_2 a)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (u : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 u)))) (Filter.principal.{u1} α (Set.Ici.{u1} α _inst_2 a)))
 Case conversion may be inaccurate. Consider using '#align nhds_within_Ici_eq'' nhdsWithin_Ici_eq''ₓ'. -/
 theorem nhdsWithin_Ici_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology α] (a : α) :
     𝓝[≥] a = (⨅ (u) (hu : a < u), 𝓟 (Iio u)) ⊓ 𝓟 (Ici a) :=
   by
   rw [nhdsWithin, nhds_eq_order]
   refine' le_antisymm (inf_le_inf_right _ inf_le_right) (le_inf (le_inf _ inf_le_left) inf_le_right)
-  exact inf_le_right.trans (le_infᵢ₂ fun l hl => principal_mono.2 <| Ici_subset_Ioi.2 hl)
+  exact inf_le_right.trans (le_iInf₂ fun l hl => principal_mono.2 <| Ici_subset_Ioi.2 hl)
 #align nhds_within_Ici_eq'' nhdsWithin_Ici_eq''
 
 /- warning: nhds_within_Iic_eq'' -> nhdsWithin_Iic_eq'' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l)))) (Filter.principal.{u1} α (Set.Iic.{u1} α _inst_2 a)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l)))) (Filter.principal.{u1} α (Set.Iic.{u1} α _inst_2 a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l)))) (Filter.principal.{u1} α (Set.Iic.{u1} α _inst_2 a)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l)))) (Filter.principal.{u1} α (Set.Iic.{u1} α _inst_2 a)))
 Case conversion may be inaccurate. Consider using '#align nhds_within_Iic_eq'' nhdsWithin_Iic_eq''ₓ'. -/
 theorem nhdsWithin_Iic_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology α] (a : α) :
     𝓝[≤] a = (⨅ l < a, 𝓟 (Ioi l)) ⊓ 𝓟 (Iic a) :=
@@ -1523,31 +1523,31 @@ theorem nhdsWithin_Iic_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology 
 
 /- warning: nhds_within_Ici_eq' -> nhdsWithin_Ici_eq' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u)) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (u : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Ico.{u1} α _inst_2 a u)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u)) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (u : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Ico.{u1} α _inst_2 a u)))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u)) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (u : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Ico.{u1} α _inst_2 a u)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (u : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u)) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (u : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Ico.{u1} α _inst_2 a u)))))
 Case conversion may be inaccurate. Consider using '#align nhds_within_Ici_eq' nhdsWithin_Ici_eq'ₓ'. -/
 theorem nhdsWithin_Ici_eq' [TopologicalSpace α] [Preorder α] [OrderTopology α] {a : α}
     (ha : ∃ u, a < u) : 𝓝[≥] a = ⨅ (u) (hu : a < u), 𝓟 (Ico a u) := by
-  simp only [nhdsWithin_Ici_eq'', binfᵢ_inf ha, inf_principal, Iio_inter_Ici]
+  simp only [nhdsWithin_Ici_eq'', biInf_inf ha, inf_principal, Iio_inter_Ici]
 #align nhds_within_Ici_eq' nhdsWithin_Ici_eq'
 
 /- warning: nhds_within_Iic_eq' -> nhdsWithin_Iic_eq' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a)) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioc.{u1} α _inst_2 l a)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a)) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioc.{u1} α _inst_2 l a)))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a)) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioc.{u1} α _inst_2 l a)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] {a : α}, (Exists.{succ u1} α (fun (l : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a)) -> (Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioc.{u1} α _inst_2 l a)))))
 Case conversion may be inaccurate. Consider using '#align nhds_within_Iic_eq' nhdsWithin_Iic_eq'ₓ'. -/
 theorem nhdsWithin_Iic_eq' [TopologicalSpace α] [Preorder α] [OrderTopology α] {a : α}
     (ha : ∃ l, l < a) : 𝓝[≤] a = ⨅ l < a, 𝓟 (Ioc l a) := by
-  simp only [nhdsWithin_Iic_eq'', binfᵢ_inf ha, inf_principal, Ioi_inter_Iic]
+  simp only [nhdsWithin_Iic_eq'', biInf_inf ha, inf_principal, Ioi_inter_Iic]
 #align nhds_within_Iic_eq' nhdsWithin_Iic_eq'
 
 #print nhdsWithin_Ici_basis' /-
 theorem nhdsWithin_Ici_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopology α] {a : α}
     (ha : ∃ u, a < u) : (𝓝[≥] a).HasBasis (fun u => a < u) fun u => Ico a u :=
   (nhdsWithin_Ici_eq' ha).symm ▸
-    hasBasis_binfᵢ_principal
+    hasBasis_biInf_principal
       (fun b hb c hc =>
         ⟨min b c, lt_min hb hc, Ico_subset_Ico_right (min_le_left _ _),
           Ico_subset_Ico_right (min_le_right _ _)⟩)
@@ -1580,9 +1580,9 @@ theorem nhdsWithin_Iic_basis [TopologicalSpace α] [LinearOrder α] [OrderTopolo
 
 /- warning: nhds_top_order -> nhds_top_order is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_2)] [_inst_4 : OrderTopology.{u1} α _inst_1 _inst_2], Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_2)] [_inst_4 : OrderTopology.{u1} α _inst_1 _inst_2], Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l (Top.top.{u1} α (OrderTop.toHasTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_2)] [_inst_4 : OrderTopology.{u1} α _inst_1 _inst_2], Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTop.{u1} α (Preorder.toLE.{u1} α _inst_2)] [_inst_4 : OrderTopology.{u1} α _inst_1 _inst_2], Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l (Top.top.{u1} α (OrderTop.toTop.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l))))
 Case conversion may be inaccurate. Consider using '#align nhds_top_order nhds_top_orderₓ'. -/
 theorem nhds_top_order [TopologicalSpace α] [Preorder α] [OrderTop α] [OrderTopology α] :
     𝓝 (⊤ : α) = ⨅ (l) (h₂ : l < ⊤), 𝓟 (Ioi l) := by simp [nhds_eq_order (⊤ : α)]
@@ -1590,9 +1590,9 @@ theorem nhds_top_order [TopologicalSpace α] [Preorder α] [OrderTop α] [OrderT
 
 /- warning: nhds_bot_order -> nhds_bot_order is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_2)] [_inst_4 : OrderTopology.{u1} α _inst_1 _inst_2], Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3)) l) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3)) l) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 l))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_2)] [_inst_4 : OrderTopology.{u1} α _inst_1 _inst_2], Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3)) l) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toHasBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3)) l) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 l))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_2)] [_inst_4 : OrderTopology.{u1} α _inst_1 _inst_2], Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3)) l) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3)) l) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 l))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderBot.{u1} α (Preorder.toLE.{u1} α _inst_2)] [_inst_4 : OrderTopology.{u1} α _inst_1 _inst_2], Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3))) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3)) l) (fun (h₂ : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) (Bot.bot.{u1} α (OrderBot.toBot.{u1} α (Preorder.toLE.{u1} α _inst_2) _inst_3)) l) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 l))))
 Case conversion may be inaccurate. Consider using '#align nhds_bot_order nhds_bot_orderₓ'. -/
 theorem nhds_bot_order [TopologicalSpace α] [Preorder α] [OrderBot α] [OrderTopology α] :
     𝓝 (⊥ : α) = ⨅ (l) (h₂ : ⊥ < l), 𝓟 (Iio l) := by simp [nhds_eq_order (⊥ : α)]
@@ -2656,15 +2656,15 @@ variable [TopologicalSpace α] [LinearOrderedAddCommGroup α] [OrderTopology α]
 
 variable {l : Filter β} {f g : β → α}
 
-/- warning: nhds_eq_infi_abs_sub -> nhds_eq_infᵢ_abs_sub is a dubious translation:
+/- warning: nhds_eq_infi_abs_sub -> nhds_eq_iInf_abs_sub is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (r : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) a b)) r)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (r : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) a b)) r)))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (r : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) a b)) r)))))
-Case conversion may be inaccurate. Consider using '#align nhds_eq_infi_abs_sub nhds_eq_infᵢ_abs_subₓ'. -/
-theorem nhds_eq_infᵢ_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r } :=
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (r : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) a b)) r)))))
+Case conversion may be inaccurate. Consider using '#align nhds_eq_infi_abs_sub nhds_eq_iInf_abs_subₓ'. -/
+theorem nhds_eq_iInf_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r } :=
   by
-  simp only [le_antisymm_iff, nhds_eq_order, le_inf_iff, le_infᵢ_iff, le_principal_iff, mem_Ioi,
+  simp only [le_antisymm_iff, nhds_eq_order, le_inf_iff, le_iInf_iff, le_principal_iff, mem_Ioi,
     mem_Iio, abs_sub_lt_iff, @sub_lt_iff_lt_add _ _ _ _ _ _ a, @sub_lt_comm _ _ _ _ a, set_of_and]
   refine' ⟨_, _, _⟩
   · intro ε ε0
@@ -2676,13 +2676,13 @@ theorem nhds_eq_infᵢ_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b|
     exact mem_infi_of_mem (a - b) (mem_infi_of_mem (sub_pos.2 hb) (by simp [Ioi]))
   · intro b hb
     exact mem_infi_of_mem (b - a) (mem_infi_of_mem (sub_pos.2 hb) (by simp [Iio]))
-#align nhds_eq_infi_abs_sub nhds_eq_infᵢ_abs_sub
+#align nhds_eq_infi_abs_sub nhds_eq_iInf_abs_sub
 
 /- warning: order_topology_of_nhds_abs -> orderTopology_of_nhds_abs is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} α] [_inst_5 : LinearOrderedAddCommGroup.{u1} α], (forall (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_4 a) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (r : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_5))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))) a b)) r)))))) -> (OrderTopology.{u1} α _inst_4 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))
+  forall {α : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} α] [_inst_5 : LinearOrderedAddCommGroup.{u1} α], (forall (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_4 a) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (r : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_5))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))) a b)) r)))))) -> (OrderTopology.{u1} α _inst_4 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} α] [_inst_5 : LinearOrderedAddCommGroup.{u1} α], (forall (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_4 a) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (r : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_5)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))) a b)) r)))))) -> (OrderTopology.{u1} α _inst_4 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))
+  forall {α : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} α] [_inst_5 : LinearOrderedAddCommGroup.{u1} α], (forall (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_4 a) (iInf.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (r : α) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_5)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))) a b)) r)))))) -> (OrderTopology.{u1} α _inst_4 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))
 Case conversion may be inaccurate. Consider using '#align order_topology_of_nhds_abs orderTopology_of_nhds_absₓ'. -/
 theorem orderTopology_of_nhds_abs {α : Type _} [TopologicalSpace α] [LinearOrderedAddCommGroup α]
     (h_nhds : ∀ a : α, 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r }) : OrderTopology α :=
@@ -2690,7 +2690,7 @@ theorem orderTopology_of_nhds_abs {α : Type _} [TopologicalSpace α] [LinearOrd
   refine' ⟨eq_of_nhds_eq_nhds fun a => _⟩
   rw [h_nhds]
   letI := Preorder.topology α; letI : OrderTopology α := ⟨rfl⟩
-  exact (nhds_eq_infᵢ_abs_sub a).symm
+  exact (nhds_eq_iInf_abs_sub a).symm
 #align order_topology_of_nhds_abs orderTopology_of_nhds_abs
 
 /- warning: linear_ordered_add_comm_group.tendsto_nhds -> LinearOrderedAddCommGroup.tendsto_nhds is a dubious translation:
@@ -2701,7 +2701,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align linear_ordered_add_comm_group.tendsto_nhds LinearOrderedAddCommGroup.tendsto_nhdsₓ'. -/
 theorem LinearOrderedAddCommGroup.tendsto_nhds {x : Filter β} {a : α} :
     Tendsto f x (𝓝 a) ↔ ∀ ε > (0 : α), ∀ᶠ b in x, |f b - a| < ε := by
-  simp [nhds_eq_infᵢ_abs_sub, abs_sub_comm a]
+  simp [nhds_eq_iInf_abs_sub, abs_sub_comm a]
 #align linear_ordered_add_comm_group.tendsto_nhds LinearOrderedAddCommGroup.tendsto_nhds
 
 /- warning: eventually_abs_sub_lt -> eventually_abs_sub_lt is a dubious translation:
@@ -2711,8 +2711,8 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α) {ε : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))) ε) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) x a)) ε) (nhds.{u1} α _inst_1 a))
 Case conversion may be inaccurate. Consider using '#align eventually_abs_sub_lt eventually_abs_sub_ltₓ'. -/
 theorem eventually_abs_sub_lt (a : α) {ε : α} (hε : 0 < ε) : ∀ᶠ x in 𝓝 a, |x - a| < ε :=
-  (nhds_eq_infᵢ_abs_sub a).symm ▸
-    mem_infᵢ_of_mem ε (mem_infᵢ_of_mem hε <| by simp only [abs_sub_comm, mem_principal_self])
+  (nhds_eq_iInf_abs_sub a).symm ▸
+    mem_iInf_of_mem ε (mem_iInf_of_mem hε <| by simp only [abs_sub_comm, mem_principal_self])
 #align eventually_abs_sub_lt eventually_abs_sub_lt
 
 /- warning: filter.tendsto.add_at_top -> Filter.Tendsto.add_atTop is a dubious translation:
@@ -3166,19 +3166,19 @@ theorem exists_seq_strictMono_tendsto_nhdsWithin [DenselyOrdered α] [NoMinOrder
 #align exists_seq_strict_mono_tendsto_nhds_within exists_seq_strictMono_tendsto_nhdsWithin
 -/
 
-/- warning: exists_seq_tendsto_Sup -> exists_seq_tendsto_supₛ is a dubious translation:
+/- warning: exists_seq_tendsto_Sup -> exists_seq_tendsto_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_7 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7)))))] [_inst_10 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_8] {S : Set.{u1} α}, (Set.Nonempty.{u1} α S) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7))))) S) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (Monotone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7))))) u) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α _inst_8 (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7)) S))) (forall (n : Nat), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (u n) S))))
+  forall {α : Type.{u1}} [_inst_7 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7)))))] [_inst_10 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_8] {S : Set.{u1} α}, (Set.Nonempty.{u1} α S) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7))))) S) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (Monotone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7))))) u) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α _inst_8 (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7)) S))) (forall (n : Nat), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (u n) S))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_7 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7)))))] [_inst_10 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_8] {S : Set.{u1} α}, (Set.Nonempty.{u1} α S) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7))))) S) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (Monotone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7))))) u) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α _inst_8 (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7)) S))) (forall (n : Nat), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (u n) S))))
-Case conversion may be inaccurate. Consider using '#align exists_seq_tendsto_Sup exists_seq_tendsto_supₛₓ'. -/
-theorem exists_seq_tendsto_supₛ {α : Type _} [ConditionallyCompleteLinearOrder α]
+  forall {α : Type.{u1}} [_inst_7 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7)))))] [_inst_10 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_8] {S : Set.{u1} α}, (Set.Nonempty.{u1} α S) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7))))) S) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (Monotone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7))))) u) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α _inst_8 (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7)) S))) (forall (n : Nat), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (u n) S))))
+Case conversion may be inaccurate. Consider using '#align exists_seq_tendsto_Sup exists_seq_tendsto_sSupₓ'. -/
+theorem exists_seq_tendsto_sSup {α : Type _} [ConditionallyCompleteLinearOrder α]
     [TopologicalSpace α] [OrderTopology α] [FirstCountableTopology α] {S : Set α} (hS : S.Nonempty)
-    (hS' : BddAbove S) : ∃ u : ℕ → α, Monotone u ∧ Tendsto u atTop (𝓝 (supₛ S)) ∧ ∀ n, u n ∈ S :=
+    (hS' : BddAbove S) : ∃ u : ℕ → α, Monotone u ∧ Tendsto u atTop (𝓝 (sSup S)) ∧ ∀ n, u n ∈ S :=
   by
-  rcases(isLUB_csupₛ hS hS').exists_seq_monotone_tendsto hS with ⟨u, hu⟩
+  rcases(isLUB_csSup hS hS').exists_seq_monotone_tendsto hS with ⟨u, hu⟩
   exact ⟨u, hu.1, hu.2.2⟩
-#align exists_seq_tendsto_Sup exists_seq_tendsto_supₛ
+#align exists_seq_tendsto_Sup exists_seq_tendsto_sSup
 
 #print IsGLB.exists_seq_strictAnti_tendsto_of_not_mem /-
 theorem IsGLB.exists_seq_strictAnti_tendsto_of_not_mem {t : Set α} {x : α}
@@ -3236,17 +3236,17 @@ theorem exists_seq_strictAnti_strictMono_tendsto [DenselyOrdered α] [FirstCount
 #align exists_seq_strict_anti_strict_mono_tendsto exists_seq_strictAnti_strictMono_tendsto
 -/
 
-/- warning: exists_seq_tendsto_Inf -> exists_seq_tendsto_infₛ is a dubious translation:
+/- warning: exists_seq_tendsto_Inf -> exists_seq_tendsto_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_7 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7)))))] [_inst_10 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_8] {S : Set.{u1} α}, (Set.Nonempty.{u1} α S) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7))))) S) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (Antitone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7))))) u) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α _inst_8 (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7)) S))) (forall (n : Nat), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (u n) S))))
+  forall {α : Type.{u1}} [_inst_7 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7)))))] [_inst_10 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_8] {S : Set.{u1} α}, (Set.Nonempty.{u1} α S) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7))))) S) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (Antitone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7))))) u) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α _inst_8 (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7)) S))) (forall (n : Nat), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (u n) S))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_7 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7)))))] [_inst_10 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_8] {S : Set.{u1} α}, (Set.Nonempty.{u1} α S) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7))))) S) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (Antitone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7))))) u) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α _inst_8 (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7)) S))) (forall (n : Nat), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (u n) S))))
-Case conversion may be inaccurate. Consider using '#align exists_seq_tendsto_Inf exists_seq_tendsto_infₛₓ'. -/
-theorem exists_seq_tendsto_infₛ {α : Type _} [ConditionallyCompleteLinearOrder α]
+  forall {α : Type.{u1}} [_inst_7 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7)))))] [_inst_10 : TopologicalSpace.FirstCountableTopology.{u1} α _inst_8] {S : Set.{u1} α}, (Set.Nonempty.{u1} α S) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7))))) S) -> (Exists.{succ u1} (Nat -> α) (fun (u : Nat -> α) => And (Antitone.{0, u1} Nat α (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7))))) u) (And (Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α _inst_8 (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_7)) S))) (forall (n : Nat), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (u n) S))))
+Case conversion may be inaccurate. Consider using '#align exists_seq_tendsto_Inf exists_seq_tendsto_sInfₓ'. -/
+theorem exists_seq_tendsto_sInf {α : Type _} [ConditionallyCompleteLinearOrder α]
     [TopologicalSpace α] [OrderTopology α] [FirstCountableTopology α] {S : Set α} (hS : S.Nonempty)
-    (hS' : BddBelow S) : ∃ u : ℕ → α, Antitone u ∧ Tendsto u atTop (𝓝 (infₛ S)) ∧ ∀ n, u n ∈ S :=
-  @exists_seq_tendsto_supₛ αᵒᵈ _ _ _ _ S hS hS'
-#align exists_seq_tendsto_Inf exists_seq_tendsto_infₛ
+    (hS' : BddBelow S) : ∃ u : ℕ → α, Antitone u ∧ Tendsto u atTop (𝓝 (sInf S)) ∧ ∀ n, u n ∈ S :=
+  @exists_seq_tendsto_sSup αᵒᵈ _ _ _ _ S hS hS'
+#align exists_seq_tendsto_Inf exists_seq_tendsto_sInf
 
 end OrderTopology
 
@@ -3837,272 +3837,272 @@ section CompleteLinearOrder
 variable [CompleteLinearOrder α] [TopologicalSpace α] [OrderTopology α] [CompleteLinearOrder β]
   [TopologicalSpace β] [OrderClosedTopology β] [Nonempty γ]
 
-/- warning: Sup_mem_closure -> supₛ_mem_closure is a dubious translation:
+/- warning: Sup_mem_closure -> sSup_mem_closure is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))) s) (closure.{u1} α _inst_8 s))
+  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))) s) (closure.{u1} α _inst_8 s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_9)))) s) (closure.{u1} α _inst_8 s))
-Case conversion may be inaccurate. Consider using '#align Sup_mem_closure supₛ_mem_closureₓ'. -/
-theorem supₛ_mem_closure {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
-    {s : Set α} (hs : s.Nonempty) : supₛ s ∈ closure s :=
-  (isLUB_supₛ s).mem_closure hs
-#align Sup_mem_closure supₛ_mem_closure
+  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_9)))) s) (closure.{u1} α _inst_8 s))
+Case conversion may be inaccurate. Consider using '#align Sup_mem_closure sSup_mem_closureₓ'. -/
+theorem sSup_mem_closure {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
+    {s : Set α} (hs : s.Nonempty) : sSup s ∈ closure s :=
+  (isLUB_sSup s).mem_closure hs
+#align Sup_mem_closure sSup_mem_closure
 
-/- warning: Inf_mem_closure -> infₛ_mem_closure is a dubious translation:
+/- warning: Inf_mem_closure -> sInf_mem_closure is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))) s) (closure.{u1} α _inst_8 s))
+  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))) s) (closure.{u1} α _inst_8 s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_9)))) s) (closure.{u1} α _inst_8 s))
-Case conversion may be inaccurate. Consider using '#align Inf_mem_closure infₛ_mem_closureₓ'. -/
-theorem infₛ_mem_closure {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
-    {s : Set α} (hs : s.Nonempty) : infₛ s ∈ closure s :=
-  (isGLB_infₛ s).mem_closure hs
-#align Inf_mem_closure infₛ_mem_closure
+  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_9)))) s) (closure.{u1} α _inst_8 s))
+Case conversion may be inaccurate. Consider using '#align Inf_mem_closure sInf_mem_closureₓ'. -/
+theorem sInf_mem_closure {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
+    {s : Set α} (hs : s.Nonempty) : sInf s ∈ closure s :=
+  (isGLB_sInf s).mem_closure hs
+#align Inf_mem_closure sInf_mem_closure
 
-/- warning: is_closed.Sup_mem -> IsClosed.supₛ_mem is a dubious translation:
+/- warning: is_closed.Sup_mem -> IsClosed.sSup_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (IsClosed.{u1} α _inst_8 s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))) s) s)
+  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (IsClosed.{u1} α _inst_8 s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))) s) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (IsClosed.{u1} α _inst_8 s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_9)))) s) s)
-Case conversion may be inaccurate. Consider using '#align is_closed.Sup_mem IsClosed.supₛ_memₓ'. -/
-theorem IsClosed.supₛ_mem {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α]
-    [OrderTopology α] {s : Set α} (hs : s.Nonempty) (hc : IsClosed s) : supₛ s ∈ s :=
-  (isLUB_supₛ s).mem_of_isClosed hs hc
-#align is_closed.Sup_mem IsClosed.supₛ_mem
+  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (IsClosed.{u1} α _inst_8 s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_9)))) s) s)
+Case conversion may be inaccurate. Consider using '#align is_closed.Sup_mem IsClosed.sSup_memₓ'. -/
+theorem IsClosed.sSup_mem {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α]
+    [OrderTopology α] {s : Set α} (hs : s.Nonempty) (hc : IsClosed s) : sSup s ∈ s :=
+  (isLUB_sSup s).mem_of_isClosed hs hc
+#align is_closed.Sup_mem IsClosed.sSup_mem
 
-/- warning: is_closed.Inf_mem -> IsClosed.infₛ_mem is a dubious translation:
+/- warning: is_closed.Inf_mem -> IsClosed.sInf_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (IsClosed.{u1} α _inst_8 s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))) s) s)
+  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (IsClosed.{u1} α _inst_8 s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))) s) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (IsClosed.{u1} α _inst_8 s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_9)))) s) s)
-Case conversion may be inaccurate. Consider using '#align is_closed.Inf_mem IsClosed.infₛ_memₓ'. -/
-theorem IsClosed.infₛ_mem {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α]
-    [OrderTopology α] {s : Set α} (hs : s.Nonempty) (hc : IsClosed s) : infₛ s ∈ s :=
-  (isGLB_infₛ s).mem_of_isClosed hs hc
-#align is_closed.Inf_mem IsClosed.infₛ_mem
+  forall {α : Type.{u1}} [_inst_8 : TopologicalSpace.{u1} α] [_inst_9 : CompleteLinearOrder.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_8 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_9))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (IsClosed.{u1} α _inst_8 s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_9)))) s) s)
+Case conversion may be inaccurate. Consider using '#align is_closed.Inf_mem IsClosed.sInf_memₓ'. -/
+theorem IsClosed.sInf_mem {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α]
+    [OrderTopology α] {s : Set α} (hs : s.Nonempty) (hc : IsClosed s) : sInf s ∈ s :=
+  (isGLB_sInf s).mem_of_isClosed hs hc
+#align is_closed.Inf_mem IsClosed.sInf_mem
 
-/- warning: monotone.map_Sup_of_continuous_at' -> Monotone.map_supₛ_of_continuousAt' is a dubious translation:
+/- warning: monotone.map_Sup_of_continuous_at' -> Monotone.map_sSup_of_continuousAt' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align monotone.map_Sup_of_continuous_at' Monotone.map_supₛ_of_continuousAt'ₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
+Case conversion may be inaccurate. Consider using '#align monotone.map_Sup_of_continuous_at' Monotone.map_sSup_of_continuousAt'ₓ'. -/
 /-- A monotone function continuous at the supremum of a nonempty set sends this supremum to
 the supremum of the image of this set. -/
-theorem Monotone.map_supₛ_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (supₛ s))
-    (Mf : Monotone f) (hs : s.Nonempty) : f (supₛ s) = supₛ (f '' s) :=
+theorem Monotone.map_sSup_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
+    (Mf : Monotone f) (hs : s.Nonempty) : f (sSup s) = sSup (f '' s) :=
   ((--This is a particular case of the more general is_lub.is_lub_of_tendsto
-              isLUB_supₛ
+              isLUB_sSup
               _).isLUB_of_tendsto
           (fun x hx y hy xy => Mf xy) hs <|
-        Cf.mono_left inf_le_left).supₛ_eq.symm
-#align monotone.map_Sup_of_continuous_at' Monotone.map_supₛ_of_continuousAt'
+        Cf.mono_left inf_le_left).sSup_eq.symm
+#align monotone.map_Sup_of_continuous_at' Monotone.map_sSup_of_continuousAt'
 
-/- warning: monotone.map_Sup_of_continuous_at -> Monotone.map_supₛ_of_continuousAt is a dubious translation:
+/- warning: monotone.map_Sup_of_continuous_at -> Monotone.map_sSup_of_continuousAt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) (Bot.bot.{u2} β (ConditionallyCompleteLinearOrderBot.toHasBot.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) (Bot.bot.{u2} β (ConditionallyCompleteLinearOrderBot.toHasBot.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toBot.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) (Bot.bot.{u2} β (ConditionallyCompleteLinearOrderBot.toBot.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align monotone.map_Sup_of_continuous_at Monotone.map_supₛ_of_continuousAtₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toBot.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) (Bot.bot.{u2} β (ConditionallyCompleteLinearOrderBot.toBot.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
+Case conversion may be inaccurate. Consider using '#align monotone.map_Sup_of_continuous_at Monotone.map_sSup_of_continuousAtₓ'. -/
 /-- A monotone function `f` sending `bot` to `bot` and continuous at the supremum of a set sends
 this supremum to the supremum of the image of this set. -/
-theorem Monotone.map_supₛ_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (supₛ s))
-    (Mf : Monotone f) (fbot : f ⊥ = ⊥) : f (supₛ s) = supₛ (f '' s) :=
+theorem Monotone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
+    (Mf : Monotone f) (fbot : f ⊥ = ⊥) : f (sSup s) = sSup (f '' s) :=
   by
   cases' s.eq_empty_or_nonempty with h h
   · simp [h, fbot]
   · exact Mf.map_Sup_of_continuous_at' Cf h
-#align monotone.map_Sup_of_continuous_at Monotone.map_supₛ_of_continuousAt
+#align monotone.map_Sup_of_continuous_at Monotone.map_sSup_of_continuousAt
 
-/- warning: monotone.map_supr_of_continuous_at' -> Monotone.map_supᵢ_of_continuousAt' is a dubious translation:
+/- warning: monotone.map_supr_of_continuous_at' -> Monotone.map_iSup_of_continuousAt' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} [_inst_8 : Nonempty.{u3} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (supᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (supᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι (fun (i : ι) => g i))) (supᵢ.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (fun (i : ι) => f (g i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} [_inst_8 : Nonempty.{u3} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι (fun (i : ι) => g i))) (iSup.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (fun (i : ι) => f (g i))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} [_inst_8 : Nonempty.{u1} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Monotone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι (fun (i : ι) => g i))) (supᵢ.{u3, u1} β (ConditionallyCompleteLattice.toSupSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (fun (i : ι) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align monotone.map_supr_of_continuous_at' Monotone.map_supᵢ_of_continuousAt'ₓ'. -/
+  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} [_inst_8 : Nonempty.{u1} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Monotone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι (fun (i : ι) => g i))) (iSup.{u3, u1} β (ConditionallyCompleteLattice.toSupSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (fun (i : ι) => f (g i))))
+Case conversion may be inaccurate. Consider using '#align monotone.map_supr_of_continuous_at' Monotone.map_iSup_of_continuousAt'ₓ'. -/
 /-- A monotone function continuous at the indexed supremum over a nonempty `Sort` sends this indexed
 supremum to the indexed supremum of the composition. -/
-theorem Monotone.map_supᵢ_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (supᵢ g)) (Mf : Monotone f) : f (⨆ i, g i) = ⨆ i, f (g i) := by
-  rw [supᵢ, Mf.map_Sup_of_continuous_at' Cf (range_nonempty g), ← range_comp, supᵢ]
-#align monotone.map_supr_of_continuous_at' Monotone.map_supᵢ_of_continuousAt'
+theorem Monotone.map_iSup_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iSup g)) (Mf : Monotone f) : f (⨆ i, g i) = ⨆ i, f (g i) := by
+  rw [iSup, Mf.map_Sup_of_continuous_at' Cf (range_nonempty g), ← range_comp, iSup]
+#align monotone.map_supr_of_continuous_at' Monotone.map_iSup_of_continuousAt'
 
-/- warning: monotone.map_supr_of_continuous_at -> Monotone.map_supᵢ_of_continuousAt is a dubious translation:
+/- warning: monotone.map_supr_of_continuous_at -> Monotone.map_iSup_of_continuousAt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (supᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) (Bot.bot.{u2} β (ConditionallyCompleteLinearOrderBot.toHasBot.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (supᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι (fun (i : ι) => g i))) (supᵢ.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (fun (i : ι) => f (g i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) (Bot.bot.{u2} β (ConditionallyCompleteLinearOrderBot.toHasBot.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι (fun (i : ι) => g i))) (iSup.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (fun (i : ι) => f (g i))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Monotone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (Bot.bot.{u2} α (ConditionallyCompleteLinearOrderBot.toBot.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) (Bot.bot.{u3} β (ConditionallyCompleteLinearOrderBot.toBot.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) -> (Eq.{succ u3} β (f (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι (fun (i : ι) => g i))) (supᵢ.{u3, u1} β (ConditionallyCompleteLattice.toSupSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (fun (i : ι) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align monotone.map_supr_of_continuous_at Monotone.map_supᵢ_of_continuousAtₓ'. -/
+  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Monotone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (Bot.bot.{u2} α (ConditionallyCompleteLinearOrderBot.toBot.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) (Bot.bot.{u3} β (ConditionallyCompleteLinearOrderBot.toBot.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) -> (Eq.{succ u3} β (f (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι (fun (i : ι) => g i))) (iSup.{u3, u1} β (ConditionallyCompleteLattice.toSupSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (fun (i : ι) => f (g i))))
+Case conversion may be inaccurate. Consider using '#align monotone.map_supr_of_continuous_at Monotone.map_iSup_of_continuousAtₓ'. -/
 /-- If a monotone function sending `bot` to `bot` is continuous at the indexed supremum over
 a `Sort`, then it sends this indexed supremum to the indexed supremum of the composition. -/
-theorem Monotone.map_supᵢ_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (supᵢ g)) (Mf : Monotone f) (fbot : f ⊥ = ⊥) :
+theorem Monotone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iSup g)) (Mf : Monotone f) (fbot : f ⊥ = ⊥) :
     f (⨆ i, g i) = ⨆ i, f (g i) := by
-  rw [supᵢ, Mf.map_Sup_of_continuous_at Cf fbot, ← range_comp, supᵢ]
-#align monotone.map_supr_of_continuous_at Monotone.map_supᵢ_of_continuousAt
+  rw [iSup, Mf.map_Sup_of_continuous_at Cf fbot, ← range_comp, iSup]
+#align monotone.map_supr_of_continuous_at Monotone.map_iSup_of_continuousAt
 
-/- warning: monotone.map_Inf_of_continuous_at' -> Monotone.map_infₛ_of_continuousAt' is a dubious translation:
+/- warning: monotone.map_Inf_of_continuous_at' -> Monotone.map_sInf_of_continuousAt' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align monotone.map_Inf_of_continuous_at' Monotone.map_infₛ_of_continuousAt'ₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
+Case conversion may be inaccurate. Consider using '#align monotone.map_Inf_of_continuous_at' Monotone.map_sInf_of_continuousAt'ₓ'. -/
 /-- A monotone function continuous at the infimum of a nonempty set sends this infimum to
 the infimum of the image of this set. -/
-theorem Monotone.map_infₛ_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (infₛ s))
-    (Mf : Monotone f) (hs : s.Nonempty) : f (infₛ s) = infₛ (f '' s) :=
-  @Monotone.map_supₛ_of_continuousAt' αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual hs
-#align monotone.map_Inf_of_continuous_at' Monotone.map_infₛ_of_continuousAt'
+theorem Monotone.map_sInf_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
+    (Mf : Monotone f) (hs : s.Nonempty) : f (sInf s) = sInf (f '' s) :=
+  @Monotone.map_sSup_of_continuousAt' αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual hs
+#align monotone.map_Inf_of_continuous_at' Monotone.map_sInf_of_continuousAt'
 
-/- warning: monotone.map_Inf_of_continuous_at -> Monotone.map_infₛ_of_continuousAt is a dubious translation:
+/- warning: monotone.map_Inf_of_continuous_at -> Monotone.map_sInf_of_continuousAt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Top.top.{u1} α (CompleteLattice.toTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (Top.top.{u2} β (CompleteLattice.toTop.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align monotone.map_Inf_of_continuous_at Monotone.map_infₛ_of_continuousAtₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Top.top.{u1} α (CompleteLattice.toTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (Top.top.{u2} β (CompleteLattice.toTop.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
+Case conversion may be inaccurate. Consider using '#align monotone.map_Inf_of_continuous_at Monotone.map_sInf_of_continuousAtₓ'. -/
 /-- A monotone function `f` sending `top` to `top` and continuous at the infimum of a set sends
 this infimum to the infimum of the image of this set. -/
-theorem Monotone.map_infₛ_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (infₛ s))
-    (Mf : Monotone f) (ftop : f ⊤ = ⊤) : f (infₛ s) = infₛ (f '' s) :=
-  @Monotone.map_supₛ_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual ftop
-#align monotone.map_Inf_of_continuous_at Monotone.map_infₛ_of_continuousAt
+theorem Monotone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
+    (Mf : Monotone f) (ftop : f ⊤ = ⊤) : f (sInf s) = sInf (f '' s) :=
+  @Monotone.map_sSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual ftop
+#align monotone.map_Inf_of_continuous_at Monotone.map_sInf_of_continuousAt
 
-/- warning: monotone.map_infi_of_continuous_at' -> Monotone.map_infᵢ_of_continuousAt' is a dubious translation:
+/- warning: monotone.map_infi_of_continuous_at' -> Monotone.map_iInf_of_continuousAt' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} [_inst_8 : Nonempty.{u3} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (infᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (infᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι (fun (i : ι) => g i))) (infᵢ.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (fun (i : ι) => f (g i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} [_inst_8 : Nonempty.{u3} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι (fun (i : ι) => g i))) (iInf.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (fun (i : ι) => f (g i))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} [_inst_8 : Nonempty.{u1} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (infᵢ.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Monotone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (infᵢ.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι (fun (i : ι) => g i))) (infᵢ.{u3, u1} β (ConditionallyCompleteLattice.toInfSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (fun (i : ι) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align monotone.map_infi_of_continuous_at' Monotone.map_infᵢ_of_continuousAt'ₓ'. -/
+  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} [_inst_8 : Nonempty.{u1} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Monotone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι (fun (i : ι) => g i))) (iInf.{u3, u1} β (ConditionallyCompleteLattice.toInfSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (fun (i : ι) => f (g i))))
+Case conversion may be inaccurate. Consider using '#align monotone.map_infi_of_continuous_at' Monotone.map_iInf_of_continuousAt'ₓ'. -/
 /-- A monotone function continuous at the indexed infimum over a nonempty `Sort` sends this indexed
 infimum to the indexed infimum of the composition. -/
-theorem Monotone.map_infᵢ_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (infᵢ g)) (Mf : Monotone f) : f (⨅ i, g i) = ⨅ i, f (g i) :=
-  @Monotone.map_supᵢ_of_continuousAt' αᵒᵈ βᵒᵈ _ _ _ _ _ _ ι _ f g Cf Mf.dual
-#align monotone.map_infi_of_continuous_at' Monotone.map_infᵢ_of_continuousAt'
+theorem Monotone.map_iInf_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iInf g)) (Mf : Monotone f) : f (⨅ i, g i) = ⨅ i, f (g i) :=
+  @Monotone.map_iSup_of_continuousAt' αᵒᵈ βᵒᵈ _ _ _ _ _ _ ι _ f g Cf Mf.dual
+#align monotone.map_infi_of_continuous_at' Monotone.map_iInf_of_continuousAt'
 
-/- warning: monotone.map_infi_of_continuous_at -> Monotone.map_infᵢ_of_continuousAt is a dubious translation:
+/- warning: monotone.map_infi_of_continuous_at -> Monotone.map_iInf_of_continuousAt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (infᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (infᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) (infᵢ.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (Function.comp.{u3, succ u1, succ u2} ι α β f g)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) (iInf.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (Function.comp.{u3, succ u1, succ u2} ι α β f g)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (infᵢ.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Monotone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (Top.top.{u2} α (CompleteLattice.toTop.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (Top.top.{u3} β (CompleteLattice.toTop.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) -> (Eq.{succ u3} β (f (infᵢ.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) (infᵢ.{u3, u1} β (ConditionallyCompleteLattice.toInfSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (Function.comp.{u1, succ u2, succ u3} ι α β f g)))
-Case conversion may be inaccurate. Consider using '#align monotone.map_infi_of_continuous_at Monotone.map_infᵢ_of_continuousAtₓ'. -/
+  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Monotone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (Top.top.{u2} α (CompleteLattice.toTop.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (Top.top.{u3} β (CompleteLattice.toTop.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) -> (Eq.{succ u3} β (f (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) (iInf.{u3, u1} β (ConditionallyCompleteLattice.toInfSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (Function.comp.{u1, succ u2, succ u3} ι α β f g)))
+Case conversion may be inaccurate. Consider using '#align monotone.map_infi_of_continuous_at Monotone.map_iInf_of_continuousAtₓ'. -/
 /-- If a monotone function sending `top` to `top` is continuous at the indexed infimum over
 a `Sort`, then it sends this indexed infimum to the indexed infimum of the composition. -/
-theorem Monotone.map_infᵢ_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (infᵢ g)) (Mf : Monotone f) (ftop : f ⊤ = ⊤) : f (infᵢ g) = infᵢ (f ∘ g) :=
-  @Monotone.map_supᵢ_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ ι f g Cf Mf.dual ftop
-#align monotone.map_infi_of_continuous_at Monotone.map_infᵢ_of_continuousAt
+theorem Monotone.map_iInf_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iInf g)) (Mf : Monotone f) (ftop : f ⊤ = ⊤) : f (iInf g) = iInf (f ∘ g) :=
+  @Monotone.map_iSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ ι f g Cf Mf.dual ftop
+#align monotone.map_infi_of_continuous_at Monotone.map_iInf_of_continuousAt
 
-/- warning: antitone.map_Sup_of_continuous_at' -> Antitone.map_supₛ_of_continuousAt' is a dubious translation:
+/- warning: antitone.map_Sup_of_continuous_at' -> Antitone.map_sSup_of_continuousAt' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align antitone.map_Sup_of_continuous_at' Antitone.map_supₛ_of_continuousAt'ₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
+Case conversion may be inaccurate. Consider using '#align antitone.map_Sup_of_continuous_at' Antitone.map_sSup_of_continuousAt'ₓ'. -/
 /-- An antitone function continuous at the supremum of a nonempty set sends this supremum to
 the infimum of the image of this set. -/
-theorem Antitone.map_supₛ_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (supₛ s))
-    (Af : Antitone f) (hs : s.Nonempty) : f (supₛ s) = infₛ (f '' s) :=
-  Monotone.map_supₛ_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (supₛ s) from Cf) Af
+theorem Antitone.map_sSup_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
+    (Af : Antitone f) (hs : s.Nonempty) : f (sSup s) = sInf (f '' s) :=
+  Monotone.map_sSup_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (sSup s) from Cf) Af
     hs
-#align antitone.map_Sup_of_continuous_at' Antitone.map_supₛ_of_continuousAt'
+#align antitone.map_Sup_of_continuous_at' Antitone.map_sSup_of_continuousAt'
 
-/- warning: antitone.map_Sup_of_continuous_at -> Antitone.map_supₛ_of_continuousAt is a dubious translation:
+/- warning: antitone.map_Sup_of_continuous_at -> Antitone.map_sSup_of_continuousAt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) (Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) (Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toBot.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) (Top.top.{u2} β (CompleteLattice.toTop.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align antitone.map_Sup_of_continuous_at Antitone.map_supₛ_of_continuousAtₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toBot.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) (Top.top.{u2} β (CompleteLattice.toTop.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
+Case conversion may be inaccurate. Consider using '#align antitone.map_Sup_of_continuous_at Antitone.map_sSup_of_continuousAtₓ'. -/
 /-- An antitone function `f` sending `bot` to `top` and continuous at the supremum of a set sends
 this supremum to the infimum of the image of this set. -/
-theorem Antitone.map_supₛ_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (supₛ s))
-    (Af : Antitone f) (fbot : f ⊥ = ⊤) : f (supₛ s) = infₛ (f '' s) :=
-  Monotone.map_supₛ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (supₛ s) from Cf) Af
+theorem Antitone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
+    (Af : Antitone f) (fbot : f ⊥ = ⊤) : f (sSup s) = sInf (f '' s) :=
+  Monotone.map_sSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (sSup s) from Cf) Af
     fbot
-#align antitone.map_Sup_of_continuous_at Antitone.map_supₛ_of_continuousAt
+#align antitone.map_Sup_of_continuous_at Antitone.map_sSup_of_continuousAt
 
-/- warning: antitone.map_supr_of_continuous_at' -> Antitone.map_supᵢ_of_continuousAt' is a dubious translation:
+/- warning: antitone.map_supr_of_continuous_at' -> Antitone.map_iSup_of_continuousAt' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} [_inst_8 : Nonempty.{u3} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (supᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (supᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι (fun (i : ι) => g i))) (infᵢ.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (fun (i : ι) => f (g i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} [_inst_8 : Nonempty.{u3} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι (fun (i : ι) => g i))) (iInf.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (fun (i : ι) => f (g i))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} [_inst_8 : Nonempty.{u1} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Antitone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι (fun (i : ι) => g i))) (infᵢ.{u3, u1} β (ConditionallyCompleteLattice.toInfSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (fun (i : ι) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align antitone.map_supr_of_continuous_at' Antitone.map_supᵢ_of_continuousAt'ₓ'. -/
+  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} [_inst_8 : Nonempty.{u1} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Antitone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι (fun (i : ι) => g i))) (iInf.{u3, u1} β (ConditionallyCompleteLattice.toInfSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (fun (i : ι) => f (g i))))
+Case conversion may be inaccurate. Consider using '#align antitone.map_supr_of_continuous_at' Antitone.map_iSup_of_continuousAt'ₓ'. -/
 /-- An antitone function continuous at the indexed supremum over a nonempty `Sort` sends this
 indexed supremum to the indexed infimum of the composition. -/
-theorem Antitone.map_supᵢ_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (supᵢ g)) (Af : Antitone f) : f (⨆ i, g i) = ⨅ i, f (g i) :=
-  Monotone.map_supᵢ_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (supᵢ g) from Cf) Af
-#align antitone.map_supr_of_continuous_at' Antitone.map_supᵢ_of_continuousAt'
+theorem Antitone.map_iSup_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iSup g)) (Af : Antitone f) : f (⨆ i, g i) = ⨅ i, f (g i) :=
+  Monotone.map_iSup_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (iSup g) from Cf) Af
+#align antitone.map_supr_of_continuous_at' Antitone.map_iSup_of_continuousAt'
 
-/- warning: antitone.map_supr_of_continuous_at -> Antitone.map_supᵢ_of_continuousAt is a dubious translation:
+/- warning: antitone.map_supr_of_continuous_at -> Antitone.map_iSup_of_continuousAt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (supᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) (Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (supᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι (fun (i : ι) => g i))) (infᵢ.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (fun (i : ι) => f (g i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) (Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι (fun (i : ι) => g i))) (iInf.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (fun (i : ι) => f (g i))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Antitone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (Bot.bot.{u2} α (ConditionallyCompleteLinearOrderBot.toBot.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) (Top.top.{u3} β (CompleteLattice.toTop.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) -> (Eq.{succ u3} β (f (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι (fun (i : ι) => g i))) (infᵢ.{u3, u1} β (ConditionallyCompleteLattice.toInfSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (fun (i : ι) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align antitone.map_supr_of_continuous_at Antitone.map_supᵢ_of_continuousAtₓ'. -/
+  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Antitone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (Bot.bot.{u2} α (ConditionallyCompleteLinearOrderBot.toBot.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) (Top.top.{u3} β (CompleteLattice.toTop.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) -> (Eq.{succ u3} β (f (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι (fun (i : ι) => g i))) (iInf.{u3, u1} β (ConditionallyCompleteLattice.toInfSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (fun (i : ι) => f (g i))))
+Case conversion may be inaccurate. Consider using '#align antitone.map_supr_of_continuous_at Antitone.map_iSup_of_continuousAtₓ'. -/
 /-- An antitone function sending `bot` to `top` is continuous at the indexed supremum over
 a `Sort`, then it sends this indexed supremum to the indexed supremum of the composition. -/
-theorem Antitone.map_supᵢ_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (supᵢ g)) (Af : Antitone f) (fbot : f ⊥ = ⊤) :
+theorem Antitone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iSup g)) (Af : Antitone f) (fbot : f ⊥ = ⊤) :
     f (⨆ i, g i) = ⨅ i, f (g i) :=
-  Monotone.map_supᵢ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (supᵢ g) from Cf) Af
+  Monotone.map_iSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (iSup g) from Cf) Af
     fbot
-#align antitone.map_supr_of_continuous_at Antitone.map_supᵢ_of_continuousAt
+#align antitone.map_supr_of_continuous_at Antitone.map_iSup_of_continuousAt
 
-/- warning: antitone.map_Inf_of_continuous_at' -> Antitone.map_infₛ_of_continuousAt' is a dubious translation:
+/- warning: antitone.map_Inf_of_continuous_at' -> Antitone.map_sInf_of_continuousAt' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align antitone.map_Inf_of_continuous_at' Antitone.map_infₛ_of_continuousAt'ₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
+Case conversion may be inaccurate. Consider using '#align antitone.map_Inf_of_continuous_at' Antitone.map_sInf_of_continuousAt'ₓ'. -/
 /-- An antitone function continuous at the infimum of a nonempty set sends this infimum to
 the supremum of the image of this set. -/
-theorem Antitone.map_infₛ_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (infₛ s))
-    (Af : Antitone f) (hs : s.Nonempty) : f (infₛ s) = supₛ (f '' s) :=
-  Monotone.map_infₛ_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (infₛ s) from Cf) Af
+theorem Antitone.map_sInf_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
+    (Af : Antitone f) (hs : s.Nonempty) : f (sInf s) = sSup (f '' s) :=
+  Monotone.map_sInf_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (sInf s) from Cf) Af
     hs
-#align antitone.map_Inf_of_continuous_at' Antitone.map_infₛ_of_continuousAt'
+#align antitone.map_Inf_of_continuous_at' Antitone.map_sInf_of_continuousAt'
 
-/- warning: antitone.map_Inf_of_continuous_at -> Antitone.map_infₛ_of_continuousAt is a dubious translation:
+/- warning: antitone.map_Inf_of_continuous_at -> Antitone.map_sInf_of_continuousAt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (Bot.bot.{u2} β (ConditionallyCompleteLinearOrderBot.toHasBot.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (Bot.bot.{u2} β (ConditionallyCompleteLinearOrderBot.toHasBot.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Top.top.{u1} α (CompleteLattice.toTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (Bot.bot.{u2} β (ConditionallyCompleteLinearOrderBot.toBot.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align antitone.map_Inf_of_continuous_at Antitone.map_infₛ_of_continuousAtₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Top.top.{u1} α (CompleteLattice.toTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (Bot.bot.{u2} β (ConditionallyCompleteLinearOrderBot.toBot.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u1} α _inst_1)))) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) (Set.image.{u1, u2} α β f s)))
+Case conversion may be inaccurate. Consider using '#align antitone.map_Inf_of_continuous_at Antitone.map_sInf_of_continuousAtₓ'. -/
 /-- An antitone function `f` sending `top` to `bot` and continuous at the infimum of a set sends
 this infimum to the supremum of the image of this set. -/
-theorem Antitone.map_infₛ_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (infₛ s))
-    (Af : Antitone f) (ftop : f ⊤ = ⊥) : f (infₛ s) = supₛ (f '' s) :=
-  Monotone.map_infₛ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (infₛ s) from Cf) Af
+theorem Antitone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
+    (Af : Antitone f) (ftop : f ⊤ = ⊥) : f (sInf s) = sSup (f '' s) :=
+  Monotone.map_sInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (sInf s) from Cf) Af
     ftop
-#align antitone.map_Inf_of_continuous_at Antitone.map_infₛ_of_continuousAt
+#align antitone.map_Inf_of_continuous_at Antitone.map_sInf_of_continuousAt
 
-/- warning: antitone.map_infi_of_continuous_at' -> Antitone.map_infᵢ_of_continuousAt' is a dubious translation:
+/- warning: antitone.map_infi_of_continuous_at' -> Antitone.map_iInf_of_continuousAt' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} [_inst_8 : Nonempty.{u3} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (infᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (infᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι (fun (i : ι) => g i))) (supᵢ.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (fun (i : ι) => f (g i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} [_inst_8 : Nonempty.{u3} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι (fun (i : ι) => g i))) (iSup.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (fun (i : ι) => f (g i))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} [_inst_8 : Nonempty.{u1} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (infᵢ.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Antitone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (infᵢ.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι (fun (i : ι) => g i))) (supᵢ.{u3, u1} β (ConditionallyCompleteLattice.toSupSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (fun (i : ι) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align antitone.map_infi_of_continuous_at' Antitone.map_infᵢ_of_continuousAt'ₓ'. -/
+  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} [_inst_8 : Nonempty.{u1} ι] {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Antitone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι (fun (i : ι) => g i))) (iSup.{u3, u1} β (ConditionallyCompleteLattice.toSupSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (fun (i : ι) => f (g i))))
+Case conversion may be inaccurate. Consider using '#align antitone.map_infi_of_continuous_at' Antitone.map_iInf_of_continuousAt'ₓ'. -/
 /-- An antitone function continuous at the indexed infimum over a nonempty `Sort` sends this indexed
 infimum to the indexed supremum of the composition. -/
-theorem Antitone.map_infᵢ_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (infᵢ g)) (Af : Antitone f) : f (⨅ i, g i) = ⨆ i, f (g i) :=
-  Monotone.map_infᵢ_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (infᵢ g) from Cf) Af
-#align antitone.map_infi_of_continuous_at' Antitone.map_infᵢ_of_continuousAt'
+theorem Antitone.map_iInf_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iInf g)) (Af : Antitone f) : f (⨅ i, g i) = ⨆ i, f (g i) :=
+  Monotone.map_iInf_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (iInf g) from Cf) Af
+#align antitone.map_infi_of_continuous_at' Antitone.map_iInf_of_continuousAt'
 
-/- warning: antitone.map_infi_of_continuous_at -> Antitone.map_infᵢ_of_continuousAt is a dubious translation:
+/- warning: antitone.map_infi_of_continuous_at -> Antitone.map_iInf_of_continuousAt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (infᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (Bot.bot.{u2} β (ConditionallyCompleteLinearOrderBot.toHasBot.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (infᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) (supᵢ.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (Function.comp.{u3, succ u1, succ u2} ι α β f g)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLinearOrder.{u1} α] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_2 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))))] {ι : Sort.{u3}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4)))) f) -> (Eq.{succ u2} β (f (Top.top.{u1} α (CompleteLattice.toHasTop.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1)))) (Bot.bot.{u2} β (ConditionallyCompleteLinearOrderBot.toHasBot.{u2} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} β _inst_4)))) -> (Eq.{succ u2} β (f (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_1))) ι g)) (iSup.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (CompleteLattice.toConditionallyCompleteLattice.{u2} β (CompleteLinearOrder.toCompleteLattice.{u2} β _inst_4))) ι (Function.comp.{u3, succ u1, succ u2} ι α β f g)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (infᵢ.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Antitone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (Top.top.{u2} α (CompleteLattice.toTop.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (Bot.bot.{u3} β (ConditionallyCompleteLinearOrderBot.toBot.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) -> (Eq.{succ u3} β (f (infᵢ.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) (supᵢ.{u3, u1} β (ConditionallyCompleteLattice.toSupSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (Function.comp.{u1, succ u2, succ u3} ι α β f g)))
-Case conversion may be inaccurate. Consider using '#align antitone.map_infi_of_continuous_at Antitone.map_infᵢ_of_continuousAtₓ'. -/
+  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : CompleteLinearOrder.{u2} α] [_inst_2 : TopologicalSpace.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_2 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1))))] [_inst_4 : CompleteLinearOrder.{u3} β] [_inst_5 : TopologicalSpace.{u3} β] [_inst_6 : OrderClosedTopology.{u3} β _inst_5 (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4))))] {ι : Sort.{u1}} {f : α -> β} {g : ι -> α}, (ContinuousAt.{u2, u3} α β _inst_2 _inst_5 f (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) -> (Antitone.{u2, u3} α β (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u3} β (CompleteSemilatticeInf.toPartialOrder.{u3} β (CompleteLattice.toCompleteSemilatticeInf.{u3} β (CompleteLinearOrder.toCompleteLattice.{u3} β _inst_4)))) f) -> (Eq.{succ u3} β (f (Top.top.{u2} α (CompleteLattice.toTop.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_1)))) (Bot.bot.{u3} β (ConditionallyCompleteLinearOrderBot.toBot.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) -> (Eq.{succ u3} β (f (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_1)))) ι g)) (iSup.{u3, u1} β (ConditionallyCompleteLattice.toSupSet.{u3} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} β (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u3} β (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u3} β _inst_4)))) ι (Function.comp.{u1, succ u2, succ u3} ι α β f g)))
+Case conversion may be inaccurate. Consider using '#align antitone.map_infi_of_continuous_at Antitone.map_iInf_of_continuousAtₓ'. -/
 /-- If an antitone function sending `top` to `bot` is continuous at the indexed infimum over
 a `Sort`, then it sends this indexed infimum to the indexed supremum of the composition. -/
-theorem Antitone.map_infᵢ_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (infᵢ g)) (Af : Antitone f) (ftop : f ⊤ = ⊥) : f (infᵢ g) = supᵢ (f ∘ g) :=
-  Monotone.map_infᵢ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (infᵢ g) from Cf) Af
+theorem Antitone.map_iInf_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iInf g)) (Af : Antitone f) (ftop : f ⊤ = ⊥) : f (iInf g) = iSup (f ∘ g) :=
+  Monotone.map_iInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (iInf g) from Cf) Af
     ftop
-#align antitone.map_infi_of_continuous_at Antitone.map_infᵢ_of_continuousAt
+#align antitone.map_infi_of_continuous_at Antitone.map_iInf_of_continuousAt
 
 end CompleteLinearOrder
 
@@ -4111,192 +4111,192 @@ section ConditionallyCompleteLinearOrder
 variable [ConditionallyCompleteLinearOrder α] [TopologicalSpace α] [OrderTopology α]
   [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderClosedTopology β] [Nonempty γ]
 
-/- warning: cSup_mem_closure -> csupₛ_mem_closure is a dubious translation:
+/- warning: cSup_mem_closure -> csSup_mem_closure 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}, (Set.Nonempty.{u1} α 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) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (closure.{u1} α _inst_2 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}, (Set.Nonempty.{u1} α 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) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (closure.{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)))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (closure.{u1} α _inst_2 s))
-Case conversion may be inaccurate. Consider using '#align cSup_mem_closure csupₛ_mem_closureₓ'. -/
-theorem csupₛ_mem_closure {s : Set α} (hs : s.Nonempty) (B : BddAbove s) : supₛ s ∈ closure s :=
-  (isLUB_csupₛ hs B).mem_closure hs
-#align cSup_mem_closure csupₛ_mem_closure
+  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}, (Set.Nonempty.{u1} α 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) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (closure.{u1} α _inst_2 s))
+Case conversion may be inaccurate. Consider using '#align cSup_mem_closure csSup_mem_closureₓ'. -/
+theorem csSup_mem_closure {s : Set α} (hs : s.Nonempty) (B : BddAbove s) : sSup s ∈ closure s :=
+  (isLUB_csSup hs B).mem_closure hs
+#align cSup_mem_closure csSup_mem_closure
 
-/- warning: cInf_mem_closure -> cinfₛ_mem_closure is a dubious translation:
+/- warning: cInf_mem_closure -> csInf_mem_closure 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}, (Set.Nonempty.{u1} α 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) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (closure.{u1} α _inst_2 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}, (Set.Nonempty.{u1} α 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) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (closure.{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)))))] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (closure.{u1} α _inst_2 s))
-Case conversion may be inaccurate. Consider using '#align cInf_mem_closure cinfₛ_mem_closureₓ'. -/
-theorem cinfₛ_mem_closure {s : Set α} (hs : s.Nonempty) (B : BddBelow s) : infₛ s ∈ closure s :=
-  (isGLB_cinfₛ hs B).mem_closure hs
-#align cInf_mem_closure cinfₛ_mem_closure
+  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}, (Set.Nonempty.{u1} α 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) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (closure.{u1} α _inst_2 s))
+Case conversion may be inaccurate. Consider using '#align cInf_mem_closure csInf_mem_closureₓ'. -/
+theorem csInf_mem_closure {s : Set α} (hs : s.Nonempty) (B : BddBelow s) : sInf s ∈ closure s :=
+  (isGLB_csInf hs B).mem_closure hs
+#align cInf_mem_closure csInf_mem_closure
 
-/- warning: is_closed.cSup_mem -> IsClosed.csupₛ_mem is a dubious translation:
+/- warning: is_closed.cSup_mem -> IsClosed.csSup_mem 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}, (IsClosed.{u1} α _inst_2 s) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (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}, (IsClosed.{u1} α _inst_2 s) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (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}, (IsClosed.{u1} α _inst_2 s) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (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_closed.cSup_mem IsClosed.csupₛ_memₓ'. -/
-theorem IsClosed.csupₛ_mem {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddAbove s) :
-    supₛ s ∈ s :=
-  (isLUB_csupₛ hs B).mem_of_isClosed hs hc
-#align is_closed.cSup_mem IsClosed.csupₛ_mem
+  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}, (IsClosed.{u1} α _inst_2 s) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (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_closed.cSup_mem IsClosed.csSup_memₓ'. -/
+theorem IsClosed.csSup_mem {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddAbove s) :
+    sSup s ∈ s :=
+  (isLUB_csSup hs B).mem_of_isClosed hs hc
+#align is_closed.cSup_mem IsClosed.csSup_mem
 
-/- warning: is_closed.cInf_mem -> IsClosed.cinfₛ_mem is a dubious translation:
+/- warning: is_closed.cInf_mem -> IsClosed.csInf_mem 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}, (IsClosed.{u1} α _inst_2 s) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_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}, (IsClosed.{u1} α _inst_2 s) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_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}, (IsClosed.{u1} α _inst_2 s) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
-Case conversion may be inaccurate. Consider using '#align is_closed.cInf_mem IsClosed.cinfₛ_memₓ'. -/
-theorem IsClosed.cinfₛ_mem {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddBelow s) :
-    infₛ s ∈ s :=
-  (isGLB_cinfₛ hs B).mem_of_isClosed hs hc
-#align is_closed.cInf_mem IsClosed.cinfₛ_mem
+  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}, (IsClosed.{u1} α _inst_2 s) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
+Case conversion may be inaccurate. Consider using '#align is_closed.cInf_mem IsClosed.csInf_memₓ'. -/
+theorem IsClosed.csInf_mem {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddBelow s) :
+    sInf s ∈ s :=
+  (isGLB_csInf hs B).mem_of_isClosed hs hc
+#align is_closed.cInf_mem IsClosed.csInf_mem
 
-/- warning: monotone.map_cSup_of_continuous_at -> Monotone.map_csupₛ_of_continuousAt is a dubious translation:
+/- warning: monotone.map_cSup_of_continuous_at -> Monotone.map_csSup_of_continuousAt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align monotone.map_cSup_of_continuous_at Monotone.map_csupₛ_of_continuousAtₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
+Case conversion may be inaccurate. Consider using '#align monotone.map_cSup_of_continuous_at Monotone.map_csSup_of_continuousAtₓ'. -/
 /-- If a monotone function is continuous at the supremum of a nonempty bounded above set `s`,
 then it sends this supremum to the supremum of the image of `s`. -/
-theorem Monotone.map_csupₛ_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (supₛ s))
-    (Mf : Monotone f) (ne : s.Nonempty) (H : BddAbove s) : f (supₛ s) = supₛ (f '' s) :=
+theorem Monotone.map_csSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
+    (Mf : Monotone f) (ne : s.Nonempty) (H : BddAbove s) : f (sSup s) = sSup (f '' s) :=
   by
-  refine' ((isLUB_csupₛ (ne.image f) (Mf.map_bdd_above H)).unique _).symm
-  refine' (isLUB_csupₛ Ne H).isLUB_of_tendsto (fun x hx y hy xy => Mf xy) Ne _
+  refine' ((isLUB_csSup (ne.image f) (Mf.map_bdd_above H)).unique _).symm
+  refine' (isLUB_csSup Ne H).isLUB_of_tendsto (fun x hx y hy xy => Mf xy) Ne _
   exact Cf.mono_left inf_le_left
-#align monotone.map_cSup_of_continuous_at Monotone.map_csupₛ_of_continuousAt
+#align monotone.map_cSup_of_continuous_at Monotone.map_csSup_of_continuousAt
 
-/- warning: monotone.map_csupr_of_continuous_at -> Monotone.map_csupᵢ_of_continuousAt is a dubious translation:
+/- warning: monotone.map_csupr_of_continuous_at -> Monotone.map_ciSup_of_continuousAt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (supᵢ.{u2, succ u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (iSup.{u2, succ u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (supᵢ.{u2, succ u3} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align monotone.map_csupr_of_continuous_at Monotone.map_csupᵢ_of_continuousAtₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (iSup.{u2, succ u3} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
+Case conversion may be inaccurate. Consider using '#align monotone.map_csupr_of_continuous_at Monotone.map_ciSup_of_continuousAtₓ'. -/
 /-- If a monotone function is continuous at the indexed supremum of a bounded function on
 a nonempty `Sort`, then it sends this supremum to the supremum of the composition. -/
-theorem Monotone.map_csupᵢ_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
+theorem Monotone.map_ciSup_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
     (Mf : Monotone f) (H : BddAbove (range g)) : f (⨆ i, g i) = ⨆ i, f (g i) := by
-  rw [supᵢ, Mf.map_cSup_of_continuous_at Cf (range_nonempty _) H, ← range_comp, supᵢ]
-#align monotone.map_csupr_of_continuous_at Monotone.map_csupᵢ_of_continuousAt
+  rw [iSup, Mf.map_cSup_of_continuous_at Cf (range_nonempty _) H, ← range_comp, iSup]
+#align monotone.map_csupr_of_continuous_at Monotone.map_ciSup_of_continuousAt
 
-/- warning: monotone.map_cInf_of_continuous_at -> Monotone.map_cinfₛ_of_continuousAt is a dubious translation:
+/- warning: monotone.map_cInf_of_continuous_at -> Monotone.map_csInf_of_continuousAt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align monotone.map_cInf_of_continuous_at Monotone.map_cinfₛ_of_continuousAtₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
+Case conversion may be inaccurate. Consider using '#align monotone.map_cInf_of_continuous_at Monotone.map_csInf_of_continuousAtₓ'. -/
 /-- If a monotone function is continuous at the infimum of a nonempty bounded below set `s`,
 then it sends this infimum to the infimum of the image of `s`. -/
-theorem Monotone.map_cinfₛ_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (infₛ s))
-    (Mf : Monotone f) (ne : s.Nonempty) (H : BddBelow s) : f (infₛ s) = infₛ (f '' s) :=
-  @Monotone.map_csupₛ_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual Ne H
-#align monotone.map_cInf_of_continuous_at Monotone.map_cinfₛ_of_continuousAt
+theorem Monotone.map_csInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
+    (Mf : Monotone f) (ne : s.Nonempty) (H : BddBelow s) : f (sInf s) = sInf (f '' s) :=
+  @Monotone.map_csSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual Ne H
+#align monotone.map_cInf_of_continuous_at Monotone.map_csInf_of_continuousAt
 
-/- warning: monotone.map_cinfi_of_continuous_at -> Monotone.map_cinfᵢ_of_continuousAt is a dubious translation:
+/- warning: monotone.map_cinfi_of_continuous_at -> Monotone.map_ciInf_of_continuousAt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (infᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (infᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (infᵢ.{u2, succ u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (iInf.{u2, succ u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (infᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (infᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (infᵢ.{u2, succ u3} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align monotone.map_cinfi_of_continuous_at Monotone.map_cinfᵢ_of_continuousAtₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (iInf.{u2, succ u3} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
+Case conversion may be inaccurate. Consider using '#align monotone.map_cinfi_of_continuous_at Monotone.map_ciInf_of_continuousAtₓ'. -/
 /-- A continuous monotone function sends indexed infimum to indexed infimum in conditionally
 complete linear order, under a boundedness assumption. -/
-theorem Monotone.map_cinfᵢ_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
+theorem Monotone.map_ciInf_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
     (Mf : Monotone f) (H : BddBelow (range g)) : f (⨅ i, g i) = ⨅ i, f (g i) :=
-  @Monotone.map_csupᵢ_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ _ Cf Mf.dual H
-#align monotone.map_cinfi_of_continuous_at Monotone.map_cinfᵢ_of_continuousAt
+  @Monotone.map_ciSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ _ Cf Mf.dual H
+#align monotone.map_cinfi_of_continuous_at Monotone.map_ciInf_of_continuousAt
 
-/- warning: antitone.map_cSup_of_continuous_at -> Antitone.map_csupₛ_of_continuousAt is a dubious translation:
+/- warning: antitone.map_cSup_of_continuous_at -> Antitone.map_csSup_of_continuousAt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align antitone.map_cSup_of_continuous_at Antitone.map_csupₛ_of_continuousAtₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
+Case conversion may be inaccurate. Consider using '#align antitone.map_cSup_of_continuous_at Antitone.map_csSup_of_continuousAtₓ'. -/
 /-- If an antitone function is continuous at the supremum of a nonempty bounded above set `s`,
 then it sends this supremum to the infimum of the image of `s`. -/
-theorem Antitone.map_csupₛ_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (supₛ s))
-    (Af : Antitone f) (ne : s.Nonempty) (H : BddAbove s) : f (supₛ s) = infₛ (f '' s) :=
-  Monotone.map_csupₛ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (supₛ s) from Cf) Af
+theorem Antitone.map_csSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
+    (Af : Antitone f) (ne : s.Nonempty) (H : BddAbove s) : f (sSup s) = sInf (f '' s) :=
+  Monotone.map_csSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (sSup s) from Cf) Af
     Ne H
-#align antitone.map_cSup_of_continuous_at Antitone.map_csupₛ_of_continuousAt
+#align antitone.map_cSup_of_continuous_at Antitone.map_csSup_of_continuousAt
 
-/- warning: antitone.map_csupr_of_continuous_at -> Antitone.map_csupᵢ_of_continuousAt is a dubious translation:
+/- warning: antitone.map_csupr_of_continuous_at -> Antitone.map_ciSup_of_continuousAt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (infᵢ.{u2, succ u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (iInf.{u2, succ u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (infᵢ.{u2, succ u3} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align antitone.map_csupr_of_continuous_at Antitone.map_csupᵢ_of_continuousAtₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (iInf.{u2, succ u3} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
+Case conversion may be inaccurate. Consider using '#align antitone.map_csupr_of_continuous_at Antitone.map_ciSup_of_continuousAtₓ'. -/
 /-- If an antitone function is continuous at the indexed supremum of a bounded function on
 a nonempty `Sort`, then it sends this supremum to the infimum of the composition. -/
-theorem Antitone.map_csupᵢ_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
+theorem Antitone.map_ciSup_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
     (Af : Antitone f) (H : BddAbove (range g)) : f (⨆ i, g i) = ⨅ i, f (g i) :=
-  Monotone.map_csupᵢ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (⨆ i, g i) from Cf)
+  Monotone.map_ciSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (⨆ i, g i) from Cf)
     Af H
-#align antitone.map_csupr_of_continuous_at Antitone.map_csupᵢ_of_continuousAt
+#align antitone.map_csupr_of_continuous_at Antitone.map_ciSup_of_continuousAt
 
-/- warning: antitone.map_cInf_of_continuous_at -> Antitone.map_cinfₛ_of_continuousAt is a dubious translation:
+/- warning: antitone.map_cInf_of_continuous_at -> Antitone.map_csInf_of_continuousAt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align antitone.map_cInf_of_continuous_at Antitone.map_cinfₛ_of_continuousAtₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] {f : α -> β} {s : Set.{u1} α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (Set.Nonempty.{u1} α 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) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) (Set.image.{u1, u2} α β f s)))
+Case conversion may be inaccurate. Consider using '#align antitone.map_cInf_of_continuous_at Antitone.map_csInf_of_continuousAtₓ'. -/
 /-- If an antitone function is continuous at the infimum of a nonempty bounded below set `s`,
 then it sends this infimum to the supremum of the image of `s`. -/
-theorem Antitone.map_cinfₛ_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (infₛ s))
-    (Af : Antitone f) (ne : s.Nonempty) (H : BddBelow s) : f (infₛ s) = supₛ (f '' s) :=
-  Monotone.map_cinfₛ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (infₛ s) from Cf) Af
+theorem Antitone.map_csInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
+    (Af : Antitone f) (ne : s.Nonempty) (H : BddBelow s) : f (sInf s) = sSup (f '' s) :=
+  Monotone.map_csInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (sInf s) from Cf) Af
     Ne H
-#align antitone.map_cInf_of_continuous_at Antitone.map_cinfₛ_of_continuousAt
+#align antitone.map_cInf_of_continuous_at Antitone.map_csInf_of_continuousAt
 
-/- warning: antitone.map_cinfi_of_continuous_at -> Antitone.map_cinfᵢ_of_continuousAt is a dubious translation:
+/- warning: antitone.map_cinfi_of_continuous_at -> Antitone.map_ciInf_of_continuousAt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (infᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (infᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (supᵢ.{u2, succ u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (iSup.{u2, succ u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (infᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (infᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (supᵢ.{u2, succ u3} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align antitone.map_cinfi_of_continuous_at Antitone.map_cinfᵢ_of_continuousAtₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (iSup.{u2, succ u3} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
+Case conversion may be inaccurate. Consider using '#align antitone.map_cinfi_of_continuous_at Antitone.map_ciInf_of_continuousAtₓ'. -/
 /-- A continuous antitone function sends indexed infimum to indexed supremum in conditionally
 complete linear order, under a boundedness assumption. -/
-theorem Antitone.map_cinfᵢ_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
+theorem Antitone.map_ciInf_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
     (Af : Antitone f) (H : BddBelow (range g)) : f (⨅ i, g i) = ⨆ i, f (g i) :=
-  Monotone.map_cinfᵢ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (⨅ i, g i) from Cf)
+  Monotone.map_ciInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (⨅ i, g i) from Cf)
     Af H
-#align antitone.map_cinfi_of_continuous_at Antitone.map_cinfᵢ_of_continuousAt
+#align antitone.map_cinfi_of_continuous_at Antitone.map_ciInf_of_continuousAt
 
 /- warning: monotone.tendsto_nhds_within_Iio -> Monotone.tendsto_nhdsWithin_Iio is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_8 : LinearOrder.{u1} α] [_inst_9 : TopologicalSpace.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_9 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8))))] [_inst_11 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_12 : TopologicalSpace.{u2} β] [_inst_13 : OrderTopology.{u2} β _inst_12 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11)))))] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11))))) f) -> (forall (x : α), Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_9 x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) x)) (nhds.{u2} β _inst_12 (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11)) (Set.image.{u1, u2} α β f (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) x)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_8 : LinearOrder.{u1} α] [_inst_9 : TopologicalSpace.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_9 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8))))] [_inst_11 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_12 : TopologicalSpace.{u2} β] [_inst_13 : OrderTopology.{u2} β _inst_12 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11)))))] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11))))) f) -> (forall (x : α), Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_9 x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) x)) (nhds.{u2} β _inst_12 (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11)) (Set.image.{u1, u2} α β f (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) x)))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_8 : LinearOrder.{u2} α] [_inst_9 : TopologicalSpace.{u2} α] [_inst_10 : OrderTopology.{u2} α _inst_9 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8)))))] [_inst_11 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_12 : TopologicalSpace.{u1} β] [_inst_13 : OrderTopology.{u1} β _inst_12 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11)))))] {f : α -> β}, (Monotone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11))))) f) -> (forall (x : α), Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_9 x (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) x)) (nhds.{u1} β _inst_12 (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11)) (Set.image.{u2, u1} α β f (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) x)))))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_8 : LinearOrder.{u2} α] [_inst_9 : TopologicalSpace.{u2} α] [_inst_10 : OrderTopology.{u2} α _inst_9 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8)))))] [_inst_11 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_12 : TopologicalSpace.{u1} β] [_inst_13 : OrderTopology.{u1} β _inst_12 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11)))))] {f : α -> β}, (Monotone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11))))) f) -> (forall (x : α), Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_9 x (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) x)) (nhds.{u1} β _inst_12 (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11)) (Set.image.{u2, u1} α β f (Set.Iio.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) x)))))
 Case conversion may be inaccurate. Consider using '#align monotone.tendsto_nhds_within_Iio Monotone.tendsto_nhdsWithin_Iioₓ'. -/
 /-- A monotone map has a limit to the left of any point `x`, equal to `Sup (f '' (Iio x))`. -/
 theorem Monotone.tendsto_nhdsWithin_Iio {α β : Type _} [LinearOrder α] [TopologicalSpace α]
     [OrderTopology α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderTopology β]
-    {f : α → β} (Mf : Monotone f) (x : α) : Tendsto f (𝓝[<] x) (𝓝 (supₛ (f '' Iio x))) :=
+    {f : α → β} (Mf : Monotone f) (x : α) : Tendsto f (𝓝[<] x) (𝓝 (sSup (f '' Iio x))) :=
   by
   rcases eq_empty_or_nonempty (Iio x) with (h | h); · simp [h]
   refine' tendsto_order.2 ⟨fun l hl => _, fun m hm => _⟩
   · obtain ⟨z, zx, lz⟩ : ∃ a : α, a < x ∧ l < f a := by
       simpa only [mem_image, exists_prop, exists_exists_and_eq_and] using
-        exists_lt_of_lt_csupₛ (nonempty_image_iff.2 h) hl
+        exists_lt_of_lt_csSup (nonempty_image_iff.2 h) hl
     exact
       (mem_nhdsWithin_Iio_iff_exists_Ioo_subset' zx).2 ⟨z, zx, fun y hy => lz.trans_le (Mf hy.1.le)⟩
   · filter_upwards [self_mem_nhdsWithin]with _ hy
     apply lt_of_le_of_lt _ hm
-    exact le_csupₛ (Mf.map_bdd_above bddAbove_Iio) (mem_image_of_mem _ hy)
+    exact le_csSup (Mf.map_bdd_above bddAbove_Iio) (mem_image_of_mem _ hy)
 #align monotone.tendsto_nhds_within_Iio Monotone.tendsto_nhdsWithin_Iio
 
 /- warning: monotone.tendsto_nhds_within_Ioi -> Monotone.tendsto_nhdsWithin_Ioi is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_8 : LinearOrder.{u1} α] [_inst_9 : TopologicalSpace.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_9 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8))))] [_inst_11 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_12 : TopologicalSpace.{u2} β] [_inst_13 : OrderTopology.{u2} β _inst_12 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11)))))] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11))))) f) -> (forall (x : α), Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_9 x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) x)) (nhds.{u2} β _inst_12 (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11)) (Set.image.{u1, u2} α β f (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) x)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_8 : LinearOrder.{u1} α] [_inst_9 : TopologicalSpace.{u1} α] [_inst_10 : OrderTopology.{u1} α _inst_9 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8))))] [_inst_11 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_12 : TopologicalSpace.{u2} β] [_inst_13 : OrderTopology.{u2} β _inst_12 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11)))))] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11))))) f) -> (forall (x : α), Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_9 x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) x)) (nhds.{u2} β _inst_12 (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_11)) (Set.image.{u1, u2} α β f (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_8)))) x)))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_8 : LinearOrder.{u2} α] [_inst_9 : TopologicalSpace.{u2} α] [_inst_10 : OrderTopology.{u2} α _inst_9 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8)))))] [_inst_11 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_12 : TopologicalSpace.{u1} β] [_inst_13 : OrderTopology.{u1} β _inst_12 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11)))))] {f : α -> β}, (Monotone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11))))) f) -> (forall (x : α), Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_9 x (Set.Ioi.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) x)) (nhds.{u1} β _inst_12 (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11)) (Set.image.{u2, u1} α β f (Set.Ioi.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) x)))))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_8 : LinearOrder.{u2} α] [_inst_9 : TopologicalSpace.{u2} α] [_inst_10 : OrderTopology.{u2} α _inst_9 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8)))))] [_inst_11 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_12 : TopologicalSpace.{u1} β] [_inst_13 : OrderTopology.{u1} β _inst_12 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11)))))] {f : α -> β}, (Monotone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11))))) f) -> (forall (x : α), Filter.Tendsto.{u2, u1} α β f (nhdsWithin.{u2} α _inst_9 x (Set.Ioi.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) x)) (nhds.{u1} β _inst_12 (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_11)) (Set.image.{u2, u1} α β f (Set.Ioi.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_8))))) x)))))
 Case conversion may be inaccurate. Consider using '#align monotone.tendsto_nhds_within_Ioi Monotone.tendsto_nhdsWithin_Ioiₓ'. -/
 /-- A monotone map has a limit to the right of any point `x`, equal to `Inf (f '' (Ioi x))`. -/
 theorem Monotone.tendsto_nhdsWithin_Ioi {α β : Type _} [LinearOrder α] [TopologicalSpace α]
     [OrderTopology α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderTopology β]
-    {f : α → β} (Mf : Monotone f) (x : α) : Tendsto f (𝓝[>] x) (𝓝 (infₛ (f '' Ioi x))) :=
+    {f : α → β} (Mf : Monotone f) (x : α) : Tendsto f (𝓝[>] x) (𝓝 (sInf (f '' Ioi x))) :=
   @Monotone.tendsto_nhdsWithin_Iio αᵒᵈ βᵒᵈ _ _ _ _ _ _ f Mf.dual x
 #align monotone.tendsto_nhds_within_Ioi Monotone.tendsto_nhdsWithin_Ioi
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7

@@ -4169,18 +4169,18 @@ theorem Monotone.map_csupₛ_of_continuousAt {f : α → β} {s : Set α} (Cf :
   exact Cf.mono_left inf_le_left
 #align monotone.map_cSup_of_continuous_at Monotone.map_csupₛ_of_continuousAt
 
-/- warning: monotone.map_csupr_of_continuous_at -> Monotone.map_csupr_of_continuousAt is a dubious translation:
+/- warning: monotone.map_csupr_of_continuous_at -> Monotone.map_csupᵢ_of_continuousAt is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (supᵢ.{u2, succ u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (supᵢ.{u2, succ u3} β (ConditionallyCompleteLattice.toSupSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align monotone.map_csupr_of_continuous_at Monotone.map_csupr_of_continuousAtₓ'. -/
+Case conversion may be inaccurate. Consider using '#align monotone.map_csupr_of_continuous_at Monotone.map_csupᵢ_of_continuousAtₓ'. -/
 /-- If a monotone function is continuous at the indexed supremum of a bounded function on
 a nonempty `Sort`, then it sends this supremum to the supremum of the composition. -/
-theorem Monotone.map_csupr_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
+theorem Monotone.map_csupᵢ_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
     (Mf : Monotone f) (H : BddAbove (range g)) : f (⨆ i, g i) = ⨆ i, f (g i) := by
   rw [supᵢ, Mf.map_cSup_of_continuous_at Cf (range_nonempty _) H, ← range_comp, supᵢ]
-#align monotone.map_csupr_of_continuous_at Monotone.map_csupr_of_continuousAt
+#align monotone.map_csupr_of_continuous_at Monotone.map_csupᵢ_of_continuousAt
 
 /- warning: monotone.map_cInf_of_continuous_at -> Monotone.map_cinfₛ_of_continuousAt is a dubious translation:
 lean 3 declaration is
@@ -4205,7 +4205,7 @@ Case conversion may be inaccurate. Consider using '#align monotone.map_cinfi_of_
 complete linear order, under a boundedness assumption. -/
 theorem Monotone.map_cinfᵢ_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
     (Mf : Monotone f) (H : BddBelow (range g)) : f (⨅ i, g i) = ⨅ i, f (g i) :=
-  @Monotone.map_csupr_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ _ Cf Mf.dual H
+  @Monotone.map_csupᵢ_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ _ Cf Mf.dual H
 #align monotone.map_cinfi_of_continuous_at Monotone.map_cinfᵢ_of_continuousAt
 
 /- warning: antitone.map_cSup_of_continuous_at -> Antitone.map_csupₛ_of_continuousAt is a dubious translation:
@@ -4222,19 +4222,19 @@ theorem Antitone.map_csupₛ_of_continuousAt {f : α → β} {s : Set α} (Cf :
     Ne H
 #align antitone.map_cSup_of_continuous_at Antitone.map_csupₛ_of_continuousAt
 
-/- warning: antitone.map_csupr_of_continuous_at -> Antitone.map_csupr_of_continuousAt is a dubious translation:
+/- warning: antitone.map_csupr_of_continuous_at -> Antitone.map_csupᵢ_of_continuousAt is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (infᵢ.{u2, succ u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_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_4 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_5 : TopologicalSpace.{u2} β] [_inst_6 : OrderClosedTopology.{u2} β _inst_5 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)))))] [_inst_7 : Nonempty.{succ u3} γ] {f : α -> β} {g : γ -> α}, (ContinuousAt.{u1, u2} α β _inst_2 _inst_5 f (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4))))) f) -> (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))))) (Set.range.{u1, succ u3} α γ g)) -> (Eq.{succ u2} β (f (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) γ (fun (i : γ) => g i))) (infᵢ.{u2, succ u3} β (ConditionallyCompleteLattice.toInfSet.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_4)) γ (fun (i : γ) => f (g i))))
-Case conversion may be inaccurate. Consider using '#align antitone.map_csupr_of_continuous_at Antitone.map_csupr_of_continuousAtₓ'. -/
+Case conversion may be inaccurate. Consider using '#align antitone.map_csupr_of_continuous_at Antitone.map_csupᵢ_of_continuousAtₓ'. -/
 /-- If an antitone function is continuous at the indexed supremum of a bounded function on
 a nonempty `Sort`, then it sends this supremum to the infimum of the composition. -/
-theorem Antitone.map_csupr_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
+theorem Antitone.map_csupᵢ_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
     (Af : Antitone f) (H : BddAbove (range g)) : f (⨆ i, g i) = ⨅ i, f (g i) :=
-  Monotone.map_csupr_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (⨆ i, g i) from Cf)
+  Monotone.map_csupᵢ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (⨆ i, g i) from Cf)
     Af H
-#align antitone.map_csupr_of_continuous_at Antitone.map_csupr_of_continuousAt
+#align antitone.map_csupr_of_continuous_at Antitone.map_csupᵢ_of_continuousAt
 
 /- warning: antitone.map_cInf_of_continuous_at -> Antitone.map_cinfₛ_of_continuousAt is a dubious translation:
 lean 3 declaration is

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

@@ -3463,16 +3463,12 @@ theorem frontier_Iio [NoMinOrder α] {a : α} : frontier (Iio a) = {a} :=
 #align frontier_Iio frontier_Iio
 -/
 
-/- warning: frontier_Icc -> frontier_Icc is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_6 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_6 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b)))
-Case conversion may be inaccurate. Consider using '#align frontier_Icc frontier_Iccₓ'. -/
+#print frontier_Icc /-
 @[simp]
 theorem frontier_Icc [NoMinOrder α] [NoMaxOrder α] {a b : α} (h : a ≤ b) :
     frontier (Icc a b) = {a, b} := by simp [frontier, h, Icc_diff_Ioo_same]
 #align frontier_Icc frontier_Icc
+-/
 
 #print frontier_Ioo /-
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -935,7 +935,7 @@ Case conversion may be inaccurate. Consider using '#align filter.tendsto.max_rig
 theorem Filter.Tendsto.max_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
     Tendsto (fun i => max a (f i)) l (𝓝 a) :=
   by
-  convert ((continuous_max.comp (@Continuous.Prod.mk α α _ _ a)).Tendsto a).comp h
+  convert((continuous_max.comp (@Continuous.Prod.mk α α _ _ a)).Tendsto a).comp h
   simp
 #align filter.tendsto.max_right Filter.Tendsto.max_right
 
@@ -1215,7 +1215,7 @@ include t
 
 instance : OrderTopology αᵒᵈ :=
   ⟨by
-    convert @OrderTopology.topology_eq_generate_intervals α _ _ _ <;>
+    convert@OrderTopology.topology_eq_generate_intervals α _ _ _ <;>
         conv in _ ∨ _ => rw [or_comm] <;>
       rfl⟩
 
@@ -1559,7 +1559,7 @@ theorem nhdsWithin_Ici_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopol
 theorem nhdsWithin_Iic_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopology α] {a : α}
     (ha : ∃ l, l < a) : (𝓝[≤] a).HasBasis (fun l => l < a) fun l => Ioc l a :=
   by
-  convert @nhdsWithin_Ici_basis' αᵒᵈ _ _ _ (to_dual a) ha
+  convert@nhdsWithin_Ici_basis' αᵒᵈ _ _ _ (to_dual a) ha
   exact funext fun x => (@dual_Ico _ _ _ _).symm
 #align nhds_within_Iic_basis' nhdsWithin_Iic_basis'
 -/
@@ -2020,7 +2020,7 @@ second-countable. -/
 theorem countable_of_isolated_left' [SecondCountableTopology α] :
     Set.Countable { x : α | ∃ y, y < x ∧ Ioo y x = ∅ } :=
   by
-  convert @countable_of_isolated_right' αᵒᵈ _ _ _ _
+  convert@countable_of_isolated_right' αᵒᵈ _ _ _ _
   have : ∀ x y : α, Ioo x y = { z | z < y ∧ x < z } :=
     by
     simp_rw [and_comm', Ioo]
@@ -2640,7 +2640,7 @@ with `l < a`. -/
 theorem mem_nhdsWithin_Iic_iff_exists_Icc_subset [NoMinOrder α] [DenselyOrdered α] {a : α}
     {s : Set α} : s ∈ 𝓝[≤] a ↔ ∃ l, l < a ∧ Icc l a ⊆ s :=
   by
-  convert @mem_nhdsWithin_Ici_iff_exists_Icc_subset αᵒᵈ _ _ _ _ _ _ _
+  convert@mem_nhdsWithin_Ici_iff_exists_Icc_subset αᵒᵈ _ _ _ _ _ _ _
   simp_rw [show ∀ u : αᵒᵈ, @Icc αᵒᵈ _ a u = @Icc α _ u a from fun u => dual_Icc]
   rfl
 #align mem_nhds_within_Iic_iff_exists_Icc_subset mem_nhdsWithin_Iic_iff_exists_Icc_subset

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module topology.order.basic
-! leanprover-community/mathlib commit 0a0ec35061ed9960bf0e7ffb0335f44447b58977
+! leanprover-community/mathlib commit c985ae9840e06836a71db38de372f20acb49b790
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -3463,12 +3463,16 @@ theorem frontier_Iio [NoMinOrder α] {a : α} : frontier (Iio a) = {a} :=
 #align frontier_Iio frontier_Iio
 -/
 
-#print frontier_Icc /-
+/- warning: frontier_Icc -> frontier_Icc is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] [_inst_6 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))) a b) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))) a b)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_6 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) a b) -> (Eq.{succ u1} (Set.{u1} α) (frontier.{u1} α _inst_1 (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))) a b)) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b)))
+Case conversion may be inaccurate. Consider using '#align frontier_Icc frontier_Iccₓ'. -/
 @[simp]
-theorem frontier_Icc [NoMinOrder α] [NoMaxOrder α] {a b : α} (h : a < b) :
-    frontier (Icc a b) = {a, b} := by simp [frontier, le_of_lt h, Icc_diff_Ioo_same]
+theorem frontier_Icc [NoMinOrder α] [NoMaxOrder α] {a b : α} (h : a ≤ b) :
+    frontier (Icc a b) = {a, b} := by simp [frontier, h, Icc_diff_Ioo_same]
 #align frontier_Icc frontier_Icc
--/
 
 #print frontier_Ioo /-
 @[simp]

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

@@ -216,8 +216,8 @@ theorem le_of_tendsto_of_tendsto {f g : β → α} {b : Filter β} {a₁ a₂ :
 #align le_of_tendsto_of_tendsto le_of_tendsto_of_tendsto
 -/
 
-alias le_of_tendsto_of_tendsto ← tendsto_le_of_eventuallyLe
-#align tendsto_le_of_eventually_le tendsto_le_of_eventuallyLe
+alias le_of_tendsto_of_tendsto ← tendsto_le_of_eventuallyLE
+#align tendsto_le_of_eventually_le tendsto_le_of_eventuallyLE
 
 #print le_of_tendsto_of_tendsto' /-
 theorem le_of_tendsto_of_tendsto' {f g : β → α} {b : Filter β} {a₁ a₂ : α} [NeBot b]
@@ -1650,9 +1650,9 @@ theorem nhds_bot_basis_Iic [TopologicalSpace α] [LinearOrder α] [OrderBot α]
 
 /- warning: tendsto_nhds_top_mono -> tendsto_nhds_top_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))) -> (Filter.EventuallyLe.{u1, u2} α β (Preorder.toLE.{u2} β _inst_2) l f g) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β _inst_2) l f g) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toHasTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))) -> (Filter.EventuallyLe.{u1, u2} α β (Preorder.toLE.{u2} β _inst_2) l f g) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderTop.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β _inst_2) l f g) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Top.top.{u2} β (OrderTop.toTop.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))))
 Case conversion may be inaccurate. Consider using '#align tendsto_nhds_top_mono tendsto_nhds_top_monoₓ'. -/
 theorem tendsto_nhds_top_mono [TopologicalSpace β] [Preorder β] [OrderTop β] [OrderTopology β]
     {l : Filter α} {f g : α → β} (hf : Tendsto f l (𝓝 ⊤)) (hg : f ≤ᶠ[l] g) : Tendsto g l (𝓝 ⊤) :=
@@ -1664,9 +1664,9 @@ theorem tendsto_nhds_top_mono [TopologicalSpace β] [Preorder β] [OrderTop β]
 
 /- warning: tendsto_nhds_bot_mono -> tendsto_nhds_bot_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))) -> (Filter.EventuallyLe.{u1, u2} α β (Preorder.toLE.{u2} β _inst_2) l g f) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β _inst_2) l g f) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toHasBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))) -> (Filter.EventuallyLe.{u1, u2} α β (Preorder.toLE.{u2} β _inst_2) l g f) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : Preorder.{u2} β] [_inst_3 : OrderBot.{u2} β (Preorder.toLE.{u2} β _inst_2)] [_inst_4 : OrderTopology.{u2} β _inst_1 _inst_2] {l : Filter.{u1} α} {f : α -> β} {g : α -> β}, (Filter.Tendsto.{u1, u2} α β f l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3)))) -> (Filter.EventuallyLE.{u1, u2} α β (Preorder.toLE.{u2} β _inst_2) l g f) -> (Filter.Tendsto.{u1, u2} α β g l (nhds.{u2} β _inst_1 (Bot.bot.{u2} β (OrderBot.toBot.{u2} β (Preorder.toLE.{u2} β _inst_2) _inst_3))))
 Case conversion may be inaccurate. Consider using '#align tendsto_nhds_bot_mono tendsto_nhds_bot_monoₓ'. -/
 theorem tendsto_nhds_bot_mono [TopologicalSpace β] [Preorder β] [OrderBot β] [OrderTopology β]
     {l : Filter α} {f g : α → β} (hf : Tendsto f l (𝓝 ⊥)) (hg : g ≤ᶠ[l] f) : Tendsto g l (𝓝 ⊥) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -3798,7 +3798,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] [_inst_5 : Nontrivial.{u1} α] {s : Set.{u1} α} [_inst_6 : TopologicalSpace.SeparableSpace.{u1} (Set.Elem.{u1} α s) (instTopologicalSpaceSubtype.{u1} α (fun (x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) _inst_1)], (Dense.{u1} α _inst_1 s) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) (And (Set.Countable.{u1} α t) (And (Dense.{u1} α _inst_1 t) (And (forall (x : α), (IsBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t))) (forall (x : α), (IsTop.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))) x) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t))))))))
 Case conversion may be inaccurate. Consider using '#align dense.exists_countable_dense_subset_no_bot_top Dense.exists_countable_dense_subset_no_bot_topₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 /-- Let `s` be a dense set in a nontrivial dense linear order `α`. If `s` is a
 separable space (e.g., if `α` has a second countable topology), then there exists a countable
 dense subset `t ⊆ s` such that `t` does not contain bottom/top elements of `α`. -/

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

@@ -1264,9 +1264,9 @@ theorem ge_mem_nhds {a b : α} (h : a < b) : ∀ᶠ x in 𝓝 a, x ≤ b :=
 
 /- warning: nhds_eq_order -> nhds_eq_order is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (HasInf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (b : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Iio.{u1} α _inst_2 a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Iio.{u1} α _inst_2 a)) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 b)))) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (b : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Ioi.{u1} α _inst_2 a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Ioi.{u1} α _inst_2 a)) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 b)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (b : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Iio.{u1} α _inst_2 a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Iio.{u1} α _inst_2 a)) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 b)))) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (b : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Ioi.{u1} α _inst_2 a)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Ioi.{u1} α _inst_2 a)) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 b)))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (HasInf.inf.{u1} (Filter.{u1} α) (Filter.instHasInfFilter.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (b : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Iio.{u1} α _inst_2 a)) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Iio.{u1} α _inst_2 a)) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 b)))) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (b : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Ioi.{u1} α _inst_2 a)) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Ioi.{u1} α _inst_2 a)) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 b)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [t : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (b : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Iio.{u1} α _inst_2 a)) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Iio.{u1} α _inst_2 a)) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 b)))) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (b : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Ioi.{u1} α _inst_2 a)) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Ioi.{u1} α _inst_2 a)) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 b)))))
 Case conversion may be inaccurate. Consider using '#align nhds_eq_order nhds_eq_orderₓ'. -/
 theorem nhds_eq_order (a : α) : 𝓝 a = (⨅ b ∈ Iio a, 𝓟 (Ioi b)) ⊓ ⨅ b ∈ Ioi a, 𝓟 (Iio b) := by
   rw [t.topology_eq_generate_intervals, nhds_generate_from] <;>
@@ -1498,9 +1498,9 @@ instance orderTopology_of_ordConnected {α : Type u} [ta : TopologicalSpace α]
 
 /- warning: nhds_within_Ici_eq'' -> nhdsWithin_Ici_eq'' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (HasInf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (u : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 u)))) (Filter.principal.{u1} α (Set.Ici.{u1} α _inst_2 a)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (u : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 u)))) (Filter.principal.{u1} α (Set.Ici.{u1} α _inst_2 a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (HasInf.inf.{u1} (Filter.{u1} α) (Filter.instHasInfFilter.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (u : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 u)))) (Filter.principal.{u1} α (Set.Ici.{u1} α _inst_2 a)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Ici.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (u : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) (fun (hu : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) a u) => Filter.principal.{u1} α (Set.Iio.{u1} α _inst_2 u)))) (Filter.principal.{u1} α (Set.Ici.{u1} α _inst_2 a)))
 Case conversion may be inaccurate. Consider using '#align nhds_within_Ici_eq'' nhdsWithin_Ici_eq''ₓ'. -/
 theorem nhdsWithin_Ici_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology α] (a : α) :
     𝓝[≥] a = (⨅ (u) (hu : a < u), 𝓟 (Iio u)) ⊓ 𝓟 (Ici a) :=
@@ -1512,9 +1512,9 @@ theorem nhdsWithin_Ici_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology 
 
 /- warning: nhds_within_Iic_eq'' -> nhdsWithin_Iic_eq'' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (HasInf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l)))) (Filter.principal.{u1} α (Set.Iic.{u1} α _inst_2 a)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (l : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l)))) (Filter.principal.{u1} α (Set.Iic.{u1} α _inst_2 a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (HasInf.inf.{u1} (Filter.{u1} α) (Filter.instHasInfFilter.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l)))) (Filter.principal.{u1} α (Set.Iic.{u1} α _inst_2 a)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 _inst_2] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_1 a (Set.Iic.{u1} α _inst_2 a)) (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (l : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) (fun (H : LT.lt.{u1} α (Preorder.toLT.{u1} α _inst_2) l a) => Filter.principal.{u1} α (Set.Ioi.{u1} α _inst_2 l)))) (Filter.principal.{u1} α (Set.Iic.{u1} α _inst_2 a)))
 Case conversion may be inaccurate. Consider using '#align nhds_within_Iic_eq'' nhdsWithin_Iic_eq''ₓ'. -/
 theorem nhdsWithin_Iic_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology α] (a : α) :
     𝓝[≤] a = (⨅ l < a, 𝓟 (Ioi l)) ⊓ 𝓟 (Iic a) :=
@@ -2225,9 +2225,9 @@ theorem disjoint_nhds_atTop [NoMaxOrder α] (x : α) : Disjoint (𝓝 x) atTop :
 
 /- warning: inf_nhds_at_top -> inf_nhds_atTop is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (x : α), Eq.{succ u1} (Filter.{u1} α) (HasInf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (nhds.{u1} α _inst_1 x) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (x : α), Eq.{succ u1} (Filter.{u1} α) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (nhds.{u1} α _inst_1 x) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (x : α), Eq.{succ u1} (Filter.{u1} α) (HasInf.inf.{u1} (Filter.{u1} α) (Filter.instHasInfFilter.{u1} α) (nhds.{u1} α _inst_1 x) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (x : α), Eq.{succ u1} (Filter.{u1} α) (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) (nhds.{u1} α _inst_1 x) (Filter.atTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))
 Case conversion may be inaccurate. Consider using '#align inf_nhds_at_top inf_nhds_atTopₓ'. -/
 @[simp]
 theorem inf_nhds_atTop [NoMaxOrder α] (x : α) : 𝓝 x ⊓ atTop = ⊥ :=
@@ -2246,9 +2246,9 @@ theorem disjoint_nhds_atBot [NoMinOrder α] (x : α) : Disjoint (𝓝 x) atBot :
 
 /- warning: inf_nhds_at_bot -> inf_nhds_atBot is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (x : α), Eq.{succ u1} (Filter.{u1} α) (HasInf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (nhds.{u1} α _inst_1 x) (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))] (x : α), Eq.{succ u1} (Filter.{u1} α) (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) (nhds.{u1} α _inst_1 x) (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_2)))))) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (x : α), Eq.{succ u1} (Filter.{u1} α) (HasInf.inf.{u1} (Filter.{u1} α) (Filter.instHasInfFilter.{u1} α) (nhds.{u1} α _inst_1 x) (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2)))))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))] (x : α), Eq.{succ u1} (Filter.{u1} α) (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) (nhds.{u1} α _inst_1 x) (Filter.atBot.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_2))))))) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))
 Case conversion may be inaccurate. Consider using '#align inf_nhds_at_bot inf_nhds_atBotₓ'. -/
 @[simp]
 theorem inf_nhds_atBot [NoMinOrder α] (x : α) : 𝓝 x ⊓ atBot = ⊥ :=
@@ -2660,7 +2660,7 @@ variable {l : Filter β} {f g : β → α}
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (r : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) a b)) r)))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (r : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) a b)) r)))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (r : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) a b)) r)))))
 Case conversion may be inaccurate. Consider using '#align nhds_eq_infi_abs_sub nhds_eq_infᵢ_abs_subₓ'. -/
 theorem nhds_eq_infᵢ_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r } :=
   by
@@ -2682,7 +2682,7 @@ theorem nhds_eq_infᵢ_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b|
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} α] [_inst_5 : LinearOrderedAddCommGroup.{u1} α], (forall (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_4 a) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) α (fun (r : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_5))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))) a b)) r)))))) -> (OrderTopology.{u1} α _inst_4 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} α] [_inst_5 : LinearOrderedAddCommGroup.{u1} α], (forall (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_4 a) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (r : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_5)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))) a b)) r)))))) -> (OrderTopology.{u1} α _inst_4 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))
+  forall {α : Type.{u1}} [_inst_4 : TopologicalSpace.{u1} α] [_inst_5 : LinearOrderedAddCommGroup.{u1} α], (forall (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_4 a) (infᵢ.{u1, succ u1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) α (fun (r : α) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))))))) (fun (H : GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) r (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))))))) => Filter.principal.{u1} α (setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_5)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5)))))) a b)) r)))))) -> (OrderTopology.{u1} α _inst_4 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_5))))
 Case conversion may be inaccurate. Consider using '#align order_topology_of_nhds_abs orderTopology_of_nhds_absₓ'. -/
 theorem orderTopology_of_nhds_abs {α : Type _} [TopologicalSpace α] [LinearOrderedAddCommGroup α]
     (h_nhds : ∀ a : α, 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r }) : OrderTopology α :=
@@ -2697,7 +2697,7 @@ theorem orderTopology_of_nhds_abs {α : Type _} [TopologicalSpace α] [LinearOrd
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] {f : β -> α} {x : Filter.{u2} β} {a : α}, Iff (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) (forall (ε : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) ε (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) -> (Filter.Eventually.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) (f b) a)) ε) x))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] {f : β -> α} {x : Filter.{u2} β} {a : α}, Iff (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) (forall (ε : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) ε (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) -> (Filter.Eventually.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) (f b) a)) ε) x))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] {f : β -> α} {x : Filter.{u2} β} {a : α}, Iff (Filter.Tendsto.{u2, u1} β α f x (nhds.{u1} α _inst_1 a)) (forall (ε : α), (GT.gt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) ε (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) -> (Filter.Eventually.{u2} β (fun (b : β) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) (f b) a)) ε) x))
 Case conversion may be inaccurate. Consider using '#align linear_ordered_add_comm_group.tendsto_nhds LinearOrderedAddCommGroup.tendsto_nhdsₓ'. -/
 theorem LinearOrderedAddCommGroup.tendsto_nhds {x : Filter β} {a : α} :
     Tendsto f x (𝓝 a) ↔ ∀ ε > (0 : α), ∀ᶠ b in x, |f b - a| < ε := by
@@ -2708,7 +2708,7 @@ theorem LinearOrderedAddCommGroup.tendsto_nhds {x : Filter β} {a : α} :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α) {ε : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) ε) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) x a)) ε) (nhds.{u1} α _inst_1 a))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α) {ε : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))) ε) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) x a)) ε) (nhds.{u1} α _inst_1 a))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] (a : α) {ε : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))) ε) -> (Filter.Eventually.{u1} α (fun (x : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) x a)) ε) (nhds.{u1} α _inst_1 a))
 Case conversion may be inaccurate. Consider using '#align eventually_abs_sub_lt eventually_abs_sub_ltₓ'. -/
 theorem eventually_abs_sub_lt (a : α) {ε : α} (hε : 0 < ε) : ∀ᶠ x in 𝓝 a, |x - a| < ε :=
   (nhds_eq_infᵢ_abs_sub a).symm ▸
@@ -2800,7 +2800,7 @@ theorem nhds_basis_Ioo_pos [NoMinOrder α] [NoMaxOrder α] (a : α) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] (a : α), Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 a) (fun (ε : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) ε) (fun (ε : α) => setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) b a)) ε))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] (_inst_5 : α), Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 _inst_5) (fun (ε : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))) ε) (fun (ε : α) => setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) b _inst_5)) ε))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] (_inst_5 : α), Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 _inst_5) (fun (ε : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))) ε) (fun (ε : α) => setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))) b _inst_5)) ε))
 Case conversion may be inaccurate. Consider using '#align nhds_basis_abs_sub_lt nhds_basis_abs_sub_ltₓ'. -/
 theorem nhds_basis_abs_sub_lt [NoMinOrder α] [NoMaxOrder α] (a : α) :
     (𝓝 a).HasBasis (fun ε : α => (0 : α) < ε) fun ε => { b | |b - a| < ε } :=
@@ -2817,7 +2817,7 @@ variable (α)
 lean 3 declaration is
   forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))] [_inst_5 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))))) (fun (ε : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) ε) (fun (ε : α) => setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2))))) b) ε))
 but is expected to have type
-  forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) (fun (ε : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))) ε) (fun (ε : α) => setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) b) ε))
+  forall (α : Type.{u1}) [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : LinearOrderedAddCommGroup.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))] [_inst_4 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))], Filter.HasBasis.{u1, succ u1} α α (nhds.{u1} α _inst_1 (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))))))))) (fun (ε : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))))) ε) (fun (ε : α) => setOf.{u1} α (fun (b : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_2))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_2)))))) b) ε))
 Case conversion may be inaccurate. Consider using '#align nhds_basis_zero_abs_sub_lt nhds_basis_zero_abs_sub_ltₓ'. -/
 theorem nhds_basis_zero_abs_sub_lt [NoMinOrder α] [NoMaxOrder α] :
     (𝓝 (0 : α)).HasBasis (fun ε : α => (0 : α) < ε) fun ε => { b | |b| < ε } := by
@@ -2938,9 +2938,9 @@ theorem IsGLB.nhdsWithin_neBot : ∀ {a : α} {s : Set α}, IsGLB s a → s.None
 
 /- warning: is_lub_of_mem_nhds -> isLUB_of_mem_nhds is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] {s : Set.{u1} α} {a : α} {f : Filter.{u1} α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) s)) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s f) -> (forall [_inst_7 : Filter.NeBot.{u1} α (HasInf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) f (nhds.{u1} α _inst_1 a))], IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) s a)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] {s : Set.{u1} α} {a : α} {f : Filter.{u1} α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) s)) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s f) -> (forall [_inst_7 : Filter.NeBot.{u1} α (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) f (nhds.{u1} α _inst_1 a))], IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) s a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))] {s : Set.{u1} α} {a : α} {f : Filter.{u1} α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) s)) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s f) -> (forall [_inst_7 : Filter.NeBot.{u1} α (HasInf.inf.{u1} (Filter.{u1} α) (Filter.instHasInfFilter.{u1} α) f (nhds.{u1} α _inst_1 a))], IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) s a)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))] {s : Set.{u1} α} {a : α} {f : Filter.{u1} α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) s)) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s f) -> (forall [_inst_7 : Filter.NeBot.{u1} α (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) f (nhds.{u1} α _inst_1 a))], IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) s a)
 Case conversion may be inaccurate. Consider using '#align is_lub_of_mem_nhds isLUB_of_mem_nhdsₓ'. -/
 theorem isLUB_of_mem_nhds {s : Set α} {a : α} {f : Filter α} (hsa : a ∈ upperBounds s) (hsf : s ∈ f)
     [NeBot (f ⊓ 𝓝 a)] : IsLUB s a :=
@@ -2963,9 +2963,9 @@ theorem isLUB_of_mem_closure {s : Set α} {a : α} (hsa : a ∈ upperBounds s) (
 
 /- warning: is_glb_of_mem_nhds -> isGLB_of_mem_nhds is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] {s : Set.{u1} α} {a : α} {f : Filter.{u1} α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) s)) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s f) -> (Filter.NeBot.{u1} α (HasInf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) f (nhds.{u1} α _inst_1 a))) -> (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) s a)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3))))] {s : Set.{u1} α} {a : α} {f : Filter.{u1} α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) s)) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s f) -> (Filter.NeBot.{u1} α (Inf.inf.{u1} (Filter.{u1} α) (Filter.hasInf.{u1} α) f (nhds.{u1} α _inst_1 a))) -> (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_3)))) s a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))] {s : Set.{u1} α} {a : α} {f : Filter.{u1} α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) s)) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s f) -> (Filter.NeBot.{u1} α (HasInf.inf.{u1} (Filter.{u1} α) (Filter.instHasInfFilter.{u1} α) f (nhds.{u1} α _inst_1 a))) -> (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) s a)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_3 : LinearOrder.{u1} α] [_inst_5 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3)))))] {s : Set.{u1} α} {a : α} {f : Filter.{u1} α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) s)) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s f) -> (Filter.NeBot.{u1} α (Inf.inf.{u1} (Filter.{u1} α) (Filter.instInfFilter.{u1} α) f (nhds.{u1} α _inst_1 a))) -> (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α _inst_3))))) s a)
 Case conversion may be inaccurate. Consider using '#align is_glb_of_mem_nhds isGLB_of_mem_nhdsₓ'. -/
 theorem isGLB_of_mem_nhds :
     ∀ {s : Set α} {a : α} {f : Filter α}, a ∈ lowerBounds s → s ∈ f → NeBot (f ⊓ 𝓝 a) → IsGLB s a :=

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

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

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

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

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

@@ -3,8 +3,8 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
 -/
-import Mathlib.Data.Set.Intervals.Pi
 import Mathlib.Order.Filter.Interval
+import Mathlib.Order.Interval.Set.Pi
 import Mathlib.Tactic.TFAE
 import Mathlib.Tactic.NormNum
 import Mathlib.Topology.Order.LeftRight

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

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
 -/
 import Mathlib.Data.Set.Intervals.Pi
-import Mathlib.Data.Set.Pointwise.Basic
 import Mathlib.Order.Filter.Interval
 import Mathlib.Tactic.TFAE
 import Mathlib.Tactic.NormNum
@@ -804,1352 +803,4 @@ theorem pi_Ioo_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : I
 
 end Pi
 
-/-!
-### Neighborhoods to the left and to the right on an `OrderTopology`
-
-We've seen some properties of left and right neighborhood of a point in an `OrderClosedTopology`.
-In an `OrderTopology`, such neighborhoods can be characterized as the sets containing suitable
-intervals to the right or to the left of `a`. We give now these characterizations. -/
-
-open List in
-/-- The following statements are equivalent:
-
-0. `s` is a neighborhood of `a` within `(a, +∞)`;
-1. `s` is a neighborhood of `a` within `(a, b]`;
-2. `s` is a neighborhood of `a` within `(a, b)`;
-3. `s` includes `(a, u)` for some `u ∈ (a, b]`;
-4. `s` includes `(a, u)` for some `u > a`.
--/
-theorem TFAE_mem_nhdsWithin_Ioi {a b : α} (hab : a < b) (s : Set α) :
-    TFAE [s ∈ 𝓝[>] a,
-      s ∈ 𝓝[Ioc a b] a,
-      s ∈ 𝓝[Ioo a b] a,
-      ∃ u ∈ Ioc a b, Ioo a u ⊆ s,
-      ∃ u ∈ Ioi a, Ioo a u ⊆ s] := by
-  tfae_have 1 ↔ 2
-  · rw [nhdsWithin_Ioc_eq_nhdsWithin_Ioi hab]
-  tfae_have 1 ↔ 3
-  · rw [nhdsWithin_Ioo_eq_nhdsWithin_Ioi hab]
-  tfae_have 4 → 5
-  · exact fun ⟨u, umem, hu⟩ => ⟨u, umem.1, hu⟩
-  tfae_have 5 → 1
-  · rintro ⟨u, hau, hu⟩
-    exact mem_of_superset (Ioo_mem_nhdsWithin_Ioi ⟨le_refl a, hau⟩) hu
-  tfae_have 1 → 4
-  · intro h
-    rcases mem_nhdsWithin_iff_exists_mem_nhds_inter.1 h with ⟨v, va, hv⟩
-    rcases exists_Ico_subset_of_mem_nhds' va hab with ⟨u, au, hu⟩
-    refine' ⟨u, au, fun x hx => _⟩
-    refine' hv ⟨hu ⟨le_of_lt hx.1, hx.2⟩, _⟩
-    exact hx.1
-  tfae_finish
-#align tfae_mem_nhds_within_Ioi TFAE_mem_nhdsWithin_Ioi
-
-theorem mem_nhdsWithin_Ioi_iff_exists_mem_Ioc_Ioo_subset {a u' : α} {s : Set α} (hu' : a < u') :
-    s ∈ 𝓝[>] a ↔ ∃ u ∈ Ioc a u', Ioo a u ⊆ s :=
-  (TFAE_mem_nhdsWithin_Ioi hu' s).out 0 3
-#align mem_nhds_within_Ioi_iff_exists_mem_Ioc_Ioo_subset mem_nhdsWithin_Ioi_iff_exists_mem_Ioc_Ioo_subset
-
-/-- A set is a neighborhood of `a` within `(a, +∞)` if and only if it contains an interval `(a, u)`
-with `a < u < u'`, provided `a` is not a top element. -/
-theorem mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' {a u' : α} {s : Set α} (hu' : a < u') :
-    s ∈ 𝓝[>] a ↔ ∃ u ∈ Ioi a, Ioo a u ⊆ s :=
-  (TFAE_mem_nhdsWithin_Ioi hu' s).out 0 4
-#align mem_nhds_within_Ioi_iff_exists_Ioo_subset' mem_nhdsWithin_Ioi_iff_exists_Ioo_subset'
-
-theorem nhdsWithin_Ioi_basis' {a : α} (h : ∃ b, a < b) : (𝓝[>] a).HasBasis (a < ·) (Ioo a) :=
-  let ⟨_, h⟩ := h
-  ⟨fun _ => mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' h⟩
-
-lemma nhdsWithin_Ioi_basis [NoMaxOrder α] (a : α) : (𝓝[>] a).HasBasis (a < ·) (Ioo a) :=
-  nhdsWithin_Ioi_basis' <| exists_gt a
-
-theorem nhdsWithin_Ioi_eq_bot_iff {a : α} : 𝓝[>] a = ⊥ ↔ IsTop a ∨ ∃ b, a ⋖ b := by
-  by_cases ha : IsTop a
-  · simp [ha, ha.isMax.Ioi_eq]
-  · simp only [ha, false_or]
-    rw [isTop_iff_isMax, not_isMax_iff] at ha
-    simp only [(nhdsWithin_Ioi_basis' ha).eq_bot_iff, covBy_iff_Ioo_eq]
-
-/-- A set is a neighborhood of `a` within `(a, +∞)` if and only if it contains an interval `(a, u)`
-with `a < u`. -/
-theorem mem_nhdsWithin_Ioi_iff_exists_Ioo_subset [NoMaxOrder α] {a : α} {s : Set α} :
-    s ∈ 𝓝[>] a ↔ ∃ u ∈ Ioi a, Ioo a u ⊆ s :=
-  let ⟨_u', hu'⟩ := exists_gt a
-  mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' hu'
-#align mem_nhds_within_Ioi_iff_exists_Ioo_subset mem_nhdsWithin_Ioi_iff_exists_Ioo_subset
-
-/-- The set of points which are isolated on the right is countable when the space is
-second-countable. -/
-theorem countable_setOf_isolated_right [SecondCountableTopology α] :
-    { x : α | 𝓝[>] x = ⊥ }.Countable := by
-  simp only [nhdsWithin_Ioi_eq_bot_iff, setOf_or]
-  exact (subsingleton_isTop α).countable.union countable_setOf_covBy_right
-
-/-- The set of points which are isolated on the left is countable when the space is
-second-countable. -/
-theorem countable_setOf_isolated_left [SecondCountableTopology α] :
-    { x : α | 𝓝[<] x = ⊥ }.Countable :=
-  countable_setOf_isolated_right (α := αᵒᵈ)
-
-/-- A set is a neighborhood of `a` within `(a, +∞)` if and only if it contains an interval `(a, u]`
-with `a < u`. -/
-theorem mem_nhdsWithin_Ioi_iff_exists_Ioc_subset [NoMaxOrder α] [DenselyOrdered α] {a : α}
-    {s : Set α} : s ∈ 𝓝[>] a ↔ ∃ u ∈ Ioi a, Ioc a u ⊆ s := by
-  rw [mem_nhdsWithin_Ioi_iff_exists_Ioo_subset]
-  constructor
-  · rintro ⟨u, au, as⟩
-    rcases exists_between au with ⟨v, hv⟩
-    exact ⟨v, hv.1, fun x hx => as ⟨hx.1, lt_of_le_of_lt hx.2 hv.2⟩⟩
-  · rintro ⟨u, au, as⟩
-    exact ⟨u, au, Subset.trans Ioo_subset_Ioc_self as⟩
-#align mem_nhds_within_Ioi_iff_exists_Ioc_subset mem_nhdsWithin_Ioi_iff_exists_Ioc_subset
-
-open List in
-/-- The following statements are equivalent:
-
-0. `s` is a neighborhood of `b` within `(-∞, b)`
-1. `s` is a neighborhood of `b` within `[a, b)`
-2. `s` is a neighborhood of `b` within `(a, b)`
-3. `s` includes `(l, b)` for some `l ∈ [a, b)`
-4. `s` includes `(l, b)` for some `l < b` -/
-theorem TFAE_mem_nhdsWithin_Iio {a b : α} (h : a < b) (s : Set α) :
-    TFAE [s ∈ 𝓝[<] b,-- 0 : `s` is a neighborhood of `b` within `(-∞, b)`
-        s ∈ 𝓝[Ico a b] b,-- 1 : `s` is a neighborhood of `b` within `[a, b)`
-        s ∈ 𝓝[Ioo a b] b,-- 2 : `s` is a neighborhood of `b` within `(a, b)`
-        ∃ l ∈ Ico a b, Ioo l b ⊆ s,-- 3 : `s` includes `(l, b)` for some `l ∈ [a, b)`
-        ∃ l ∈ Iio b, Ioo l b ⊆ s] := by-- 4 : `s` includes `(l, b)` for some `l < b`
-  simpa only [exists_prop, OrderDual.exists, dual_Ioi, dual_Ioc, dual_Ioo] using
-    TFAE_mem_nhdsWithin_Ioi h.dual (ofDual ⁻¹' s)
-#align tfae_mem_nhds_within_Iio TFAE_mem_nhdsWithin_Iio
-
-theorem mem_nhdsWithin_Iio_iff_exists_mem_Ico_Ioo_subset {a l' : α} {s : Set α} (hl' : l' < a) :
-    s ∈ 𝓝[<] a ↔ ∃ l ∈ Ico l' a, Ioo l a ⊆ s :=
-  (TFAE_mem_nhdsWithin_Iio hl' s).out 0 3
-#align mem_nhds_within_Iio_iff_exists_mem_Ico_Ioo_subset mem_nhdsWithin_Iio_iff_exists_mem_Ico_Ioo_subset
-
-/-- A set is a neighborhood of `a` within `(-∞, a)` if and only if it contains an interval `(l, a)`
-with `l < a`, provided `a` is not a bottom element. -/
-theorem mem_nhdsWithin_Iio_iff_exists_Ioo_subset' {a l' : α} {s : Set α} (hl' : l' < a) :
-    s ∈ 𝓝[<] a ↔ ∃ l ∈ Iio a, Ioo l a ⊆ s :=
-  (TFAE_mem_nhdsWithin_Iio hl' s).out 0 4
-#align mem_nhds_within_Iio_iff_exists_Ioo_subset' mem_nhdsWithin_Iio_iff_exists_Ioo_subset'
-
-/-- A set is a neighborhood of `a` within `(-∞, a)` if and only if it contains an interval `(l, a)`
-with `l < a`. -/
-theorem mem_nhdsWithin_Iio_iff_exists_Ioo_subset [NoMinOrder α] {a : α} {s : Set α} :
-    s ∈ 𝓝[<] a ↔ ∃ l ∈ Iio a, Ioo l a ⊆ s :=
-  let ⟨_, h⟩ := exists_lt a
-  mem_nhdsWithin_Iio_iff_exists_Ioo_subset' h
-#align mem_nhds_within_Iio_iff_exists_Ioo_subset mem_nhdsWithin_Iio_iff_exists_Ioo_subset
-
-/-- A set is a neighborhood of `a` within `(-∞, a)` if and only if it contains an interval `[l, a)`
-with `l < a`. -/
-theorem mem_nhdsWithin_Iio_iff_exists_Ico_subset [NoMinOrder α] [DenselyOrdered α] {a : α}
-    {s : Set α} : s ∈ 𝓝[<] a ↔ ∃ l ∈ Iio a, Ico l a ⊆ s := by
-  have : ofDual ⁻¹' s ∈ 𝓝[>] toDual a ↔ _ := mem_nhdsWithin_Ioi_iff_exists_Ioc_subset
-  simpa only [OrderDual.exists, exists_prop, dual_Ioc] using this
-#align mem_nhds_within_Iio_iff_exists_Ico_subset mem_nhdsWithin_Iio_iff_exists_Ico_subset
-
-theorem nhdsWithin_Iio_basis' {a : α} (h : ∃ b, b < a) : (𝓝[<] a).HasBasis (· < a) (Ioo · a) :=
-  let ⟨_, h⟩ := h
-  ⟨fun _ => mem_nhdsWithin_Iio_iff_exists_Ioo_subset' h⟩
-
-theorem nhdsWithin_Iio_eq_bot_iff {a : α} : 𝓝[<] a = ⊥ ↔ IsBot a ∨ ∃ b, b ⋖ a := by
-    convert (config := {preTransparency := .default})
-      nhdsWithin_Ioi_eq_bot_iff (a := OrderDual.toDual a) using 4
-    exact ofDual_covBy_ofDual_iff
-
-open List in
-/-- The following statements are equivalent:
-
-0. `s` is a neighborhood of `a` within `[a, +∞)`;
-1. `s` is a neighborhood of `a` within `[a, b]`;
-2. `s` is a neighborhood of `a` within `[a, b)`;
-3. `s` includes `[a, u)` for some `u ∈ (a, b]`;
-4. `s` includes `[a, u)` for some `u > a`.
--/
-theorem TFAE_mem_nhdsWithin_Ici {a b : α} (hab : a < b) (s : Set α) :
-    TFAE [s ∈ 𝓝[≥] a,
-      s ∈ 𝓝[Icc a b] a,
-      s ∈ 𝓝[Ico a b] a,
-      ∃ u ∈ Ioc a b, Ico a u ⊆ s,
-      ∃ u ∈ Ioi a , Ico a u ⊆ s] := by
-  tfae_have 1 ↔ 2
-  · rw [nhdsWithin_Icc_eq_nhdsWithin_Ici hab]
-  tfae_have 1 ↔ 3
-  · rw [nhdsWithin_Ico_eq_nhdsWithin_Ici hab]
-  tfae_have 1 ↔ 5
-  · exact (nhdsWithin_Ici_basis' ⟨b, hab⟩).mem_iff
-  tfae_have 4 → 5
-  · exact fun ⟨u, umem, hu⟩ => ⟨u, umem.1, hu⟩
-  tfae_have 5 → 4
-  · rintro ⟨u, hua, hus⟩
-    exact
-      ⟨min u b, ⟨lt_min hua hab, min_le_right _ _⟩,
-        (Ico_subset_Ico_right <| min_le_left _ _).trans hus⟩
-  tfae_finish
-#align tfae_mem_nhds_within_Ici TFAE_mem_nhdsWithin_Ici
-
-theorem mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subset {a u' : α} {s : Set α} (hu' : a < u') :
-    s ∈ 𝓝[≥] a ↔ ∃ u ∈ Ioc a u', Ico a u ⊆ s :=
-  (TFAE_mem_nhdsWithin_Ici hu' s).out 0 3 (by norm_num) (by norm_num)
-#align mem_nhds_within_Ici_iff_exists_mem_Ioc_Ico_subset mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subset
-
-/-- A set is a neighborhood of `a` within `[a, +∞)` if and only if it contains an interval `[a, u)`
-with `a < u < u'`, provided `a` is not a top element. -/
-theorem mem_nhdsWithin_Ici_iff_exists_Ico_subset' {a u' : α} {s : Set α} (hu' : a < u') :
-    s ∈ 𝓝[≥] a ↔ ∃ u ∈ Ioi a, Ico a u ⊆ s :=
-  (TFAE_mem_nhdsWithin_Ici hu' s).out 0 4 (by norm_num) (by norm_num)
-#align mem_nhds_within_Ici_iff_exists_Ico_subset' mem_nhdsWithin_Ici_iff_exists_Ico_subset'
-
-/-- A set is a neighborhood of `a` within `[a, +∞)` if and only if it contains an interval `[a, u)`
-with `a < u`. -/
-theorem mem_nhdsWithin_Ici_iff_exists_Ico_subset [NoMaxOrder α] {a : α} {s : Set α} :
-    s ∈ 𝓝[≥] a ↔ ∃ u ∈ Ioi a, Ico a u ⊆ s :=
-  let ⟨_, hu'⟩ := exists_gt a
-  mem_nhdsWithin_Ici_iff_exists_Ico_subset' hu'
-#align mem_nhds_within_Ici_iff_exists_Ico_subset mem_nhdsWithin_Ici_iff_exists_Ico_subset
-
-theorem nhdsWithin_Ici_basis_Ico [NoMaxOrder α] (a : α) :
-    (𝓝[≥] a).HasBasis (fun u => a < u) (Ico a) :=
-  ⟨fun _ => mem_nhdsWithin_Ici_iff_exists_Ico_subset⟩
-#align nhds_within_Ici_basis_Ico nhdsWithin_Ici_basis_Ico
-
-/-- The filter of right neighborhoods has a basis of closed intervals. -/
-theorem nhdsWithin_Ici_basis_Icc [NoMaxOrder α] [DenselyOrdered α] {a : α} :
-    (𝓝[≥] a).HasBasis (a < ·) (Icc a) :=
-  (nhdsWithin_Ici_basis _).to_hasBasis
-    (fun _u hu ↦ (exists_between hu).imp fun _v hv ↦ hv.imp_right Icc_subset_Ico_right)
-    fun u hu ↦ ⟨u, hu, Ico_subset_Icc_self⟩
-
-/-- A set is a neighborhood of `a` within `[a, +∞)` if and only if it contains an interval `[a, u]`
-with `a < u`. -/
-theorem mem_nhdsWithin_Ici_iff_exists_Icc_subset [NoMaxOrder α] [DenselyOrdered α] {a : α}
-    {s : Set α} : s ∈ 𝓝[≥] a ↔ ∃ u, a < u ∧ Icc a u ⊆ s :=
-  nhdsWithin_Ici_basis_Icc.mem_iff
-#align mem_nhds_within_Ici_iff_exists_Icc_subset mem_nhdsWithin_Ici_iff_exists_Icc_subset
-
-open List in
-/-- The following statements are equivalent:
-
-0. `s` is a neighborhood of `b` within `(-∞, b]`
-1. `s` is a neighborhood of `b` within `[a, b]`
-2. `s` is a neighborhood of `b` within `(a, b]`
-3. `s` includes `(l, b]` for some `l ∈ [a, b)`
-4. `s` includes `(l, b]` for some `l < b` -/
-theorem TFAE_mem_nhdsWithin_Iic {a b : α} (h : a < b) (s : Set α) :
-    TFAE [s ∈ 𝓝[≤] b,-- 0 : `s` is a neighborhood of `b` within `(-∞, b]`
-      s ∈ 𝓝[Icc a b] b,-- 1 : `s` is a neighborhood of `b` within `[a, b]`
-      s ∈ 𝓝[Ioc a b] b,-- 2 : `s` is a neighborhood of `b` within `(a, b]`
-      ∃ l ∈ Ico a b, Ioc l b ⊆ s,-- 3 : `s` includes `(l, b]` for some `l ∈ [a, b)`
-      ∃ l ∈ Iio b, Ioc l b ⊆ s] := by-- 4 : `s` includes `(l, b]` for some `l < b`
-  simpa only [exists_prop, OrderDual.exists, dual_Ici, dual_Ioc, dual_Icc, dual_Ico] using
-    TFAE_mem_nhdsWithin_Ici h.dual (ofDual ⁻¹' s)
-#align tfae_mem_nhds_within_Iic TFAE_mem_nhdsWithin_Iic
-
-theorem mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subset {a l' : α} {s : Set α} (hl' : l' < a) :
-    s ∈ 𝓝[≤] a ↔ ∃ l ∈ Ico l' a, Ioc l a ⊆ s :=
-  (TFAE_mem_nhdsWithin_Iic hl' s).out 0 3 (by norm_num) (by norm_num)
-#align mem_nhds_within_Iic_iff_exists_mem_Ico_Ioc_subset mem_nhdsWithin_Iic_iff_exists_mem_Ico_Ioc_subset
-
-/-- A set is a neighborhood of `a` within `(-∞, a]` if and only if it contains an interval `(l, a]`
-with `l < a`, provided `a` is not a bottom element. -/
-theorem mem_nhdsWithin_Iic_iff_exists_Ioc_subset' {a l' : α} {s : Set α} (hl' : l' < a) :
-    s ∈ 𝓝[≤] a ↔ ∃ l ∈ Iio a, Ioc l a ⊆ s :=
-  (TFAE_mem_nhdsWithin_Iic hl' s).out 0 4 (by norm_num) (by norm_num)
-#align mem_nhds_within_Iic_iff_exists_Ioc_subset' mem_nhdsWithin_Iic_iff_exists_Ioc_subset'
-
-/-- A set is a neighborhood of `a` within `(-∞, a]` if and only if it contains an interval `(l, a]`
-with `l < a`. -/
-theorem mem_nhdsWithin_Iic_iff_exists_Ioc_subset [NoMinOrder α] {a : α} {s : Set α} :
-    s ∈ 𝓝[≤] a ↔ ∃ l ∈ Iio a, Ioc l a ⊆ s :=
-  let ⟨_, hl'⟩ := exists_lt a
-  mem_nhdsWithin_Iic_iff_exists_Ioc_subset' hl'
-#align mem_nhds_within_Iic_iff_exists_Ioc_subset mem_nhdsWithin_Iic_iff_exists_Ioc_subset
-
-/-- A set is a neighborhood of `a` within `(-∞, a]` if and only if it contains an interval `[l, a]`
-with `l < a`. -/
-theorem mem_nhdsWithin_Iic_iff_exists_Icc_subset [NoMinOrder α] [DenselyOrdered α] {a : α}
-    {s : Set α} : s ∈ 𝓝[≤] a ↔ ∃ l, l < a ∧ Icc l a ⊆ s :=
-  calc s ∈ 𝓝[≤] a ↔ ofDual ⁻¹' s ∈ 𝓝[≥] (toDual a) := Iff.rfl
-  _ ↔ ∃ u : α, toDual a < toDual u ∧ Icc (toDual a) (toDual u) ⊆ ofDual ⁻¹' s :=
-    mem_nhdsWithin_Ici_iff_exists_Icc_subset
-  _ ↔ ∃ l, l < a ∧ Icc l a ⊆ s := by simp only [dual_Icc]; rfl
-#align mem_nhds_within_Iic_iff_exists_Icc_subset mem_nhdsWithin_Iic_iff_exists_Icc_subset
-
-/-- The filter of left neighborhoods has a basis of closed intervals. -/
-theorem nhdsWithin_Iic_basis_Icc [NoMinOrder α] [DenselyOrdered α] {a : α} :
-    (𝓝[≤] a).HasBasis (· < a) (Icc · a) :=
-  ⟨fun _ ↦ mem_nhdsWithin_Iic_iff_exists_Icc_subset⟩
-
-end OrderTopology
-
-end LinearOrder
-
-section LinearOrderedAddCommGroup
-
-variable [TopologicalSpace α] [LinearOrderedAddCommGroup α] [OrderTopology α]
-variable {l : Filter β} {f g : β → α}
-
-theorem nhds_eq_iInf_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r } := by
-  simp only [nhds_eq_order, abs_lt, setOf_and, ← inf_principal, iInf_inf_eq]
-  refine (congr_arg₂ _ ?_ ?_).trans (inf_comm ..)
-  · refine (Equiv.subLeft a).iInf_congr fun x => ?_; simp [Ioi]
-  · refine (Equiv.subRight a).iInf_congr fun x => ?_; simp [Iio]
-#align nhds_eq_infi_abs_sub nhds_eq_iInf_abs_sub
-
-theorem orderTopology_of_nhds_abs {α : Type*} [TopologicalSpace α] [LinearOrderedAddCommGroup α]
-    (h_nhds : ∀ a : α, 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r }) : OrderTopology α := by
-  refine' ⟨TopologicalSpace.ext_nhds fun a => _⟩
-  rw [h_nhds]
-  letI := Preorder.topology α; letI : OrderTopology α := ⟨rfl⟩
-  exact (nhds_eq_iInf_abs_sub a).symm
-#align order_topology_of_nhds_abs orderTopology_of_nhds_abs
-
-theorem LinearOrderedAddCommGroup.tendsto_nhds {x : Filter β} {a : α} :
-    Tendsto f x (𝓝 a) ↔ ∀ ε > (0 : α), ∀ᶠ b in x, |f b - a| < ε := by
-  simp [nhds_eq_iInf_abs_sub, abs_sub_comm a]
-#align linear_ordered_add_comm_group.tendsto_nhds LinearOrderedAddCommGroup.tendsto_nhds
-
-theorem eventually_abs_sub_lt (a : α) {ε : α} (hε : 0 < ε) : ∀ᶠ x in 𝓝 a, |x - a| < ε :=
-  (nhds_eq_iInf_abs_sub a).symm ▸
-    mem_iInf_of_mem ε (mem_iInf_of_mem hε <| by simp only [abs_sub_comm, mem_principal_self])
-#align eventually_abs_sub_lt eventually_abs_sub_lt
-
-/-- In a linearly ordered additive commutative group with the order topology, if `f` tends to `C`
-and `g` tends to `atTop` then `f + g` tends to `atTop`. -/
-theorem Filter.Tendsto.add_atTop {C : α} (hf : Tendsto f l (𝓝 C)) (hg : Tendsto g l atTop) :
-    Tendsto (fun x => f x + g x) l atTop := by
-  nontriviality α
-  obtain ⟨C', hC'⟩ : ∃ C', C' < C := exists_lt C
-  refine' tendsto_atTop_add_left_of_le' _ C' _ hg
-  exact (hf.eventually (lt_mem_nhds hC')).mono fun x => le_of_lt
-#align filter.tendsto.add_at_top Filter.Tendsto.add_atTop
-
-/-- In a linearly ordered additive commutative group with the order topology, if `f` tends to `C`
-and `g` tends to `atBot` then `f + g` tends to `atBot`. -/
-theorem Filter.Tendsto.add_atBot {C : α} (hf : Tendsto f l (𝓝 C)) (hg : Tendsto g l atBot) :
-    Tendsto (fun x => f x + g x) l atBot :=
-  Filter.Tendsto.add_atTop (α := αᵒᵈ) hf hg
-#align filter.tendsto.add_at_bot Filter.Tendsto.add_atBot
-
-/-- In a linearly ordered additive commutative group with the order topology, if `f` tends to
-`atTop` and `g` tends to `C` then `f + g` tends to `atTop`. -/
-theorem Filter.Tendsto.atTop_add {C : α} (hf : Tendsto f l atTop) (hg : Tendsto g l (𝓝 C)) :
-    Tendsto (fun x => f x + g x) l atTop := by
-  conv in _ + _ => rw [add_comm]
-  exact hg.add_atTop hf
-#align filter.tendsto.at_top_add Filter.Tendsto.atTop_add
-
-/-- In a linearly ordered additive commutative group with the order topology, if `f` tends to
-`atBot` and `g` tends to `C` then `f + g` tends to `atBot`. -/
-theorem Filter.Tendsto.atBot_add {C : α} (hf : Tendsto f l atBot) (hg : Tendsto g l (𝓝 C)) :
-    Tendsto (fun x => f x + g x) l atBot := by
-  conv in _ + _ => rw [add_comm]
-  exact hg.add_atBot hf
-#align filter.tendsto.at_bot_add Filter.Tendsto.atBot_add
-
-theorem nhds_basis_abs_sub_lt [NoMaxOrder α] (a : α) :
-    (𝓝 a).HasBasis (fun ε : α => (0 : α) < ε) fun ε => { b | |b - a| < ε } := by
-  simp only [nhds_eq_iInf_abs_sub, abs_sub_comm (a := a)]
-  refine hasBasis_biInf_principal' (fun x hx y hy => ?_) (exists_gt _)
-  exact ⟨min x y, lt_min hx hy, fun _ hz => hz.trans_le (min_le_left _ _),
-    fun _ hz => hz.trans_le (min_le_right _ _)⟩
-#align nhds_basis_abs_sub_lt nhds_basis_abs_sub_lt
-
-theorem nhds_basis_Ioo_pos [NoMaxOrder α] (a : α) :
-    (𝓝 a).HasBasis (fun ε : α => (0 : α) < ε) fun ε => Ioo (a - ε) (a + ε) := by
-  convert nhds_basis_abs_sub_lt a
-  simp only [Ioo, abs_lt, ← sub_lt_iff_lt_add, neg_lt_sub_iff_lt_add, sub_lt_comm]
-#align nhds_basis_Ioo_pos nhds_basis_Ioo_pos
-
-theorem nhds_basis_Icc_pos [NoMaxOrder α] [DenselyOrdered α] (a : α) :
-    (𝓝 a).HasBasis ((0 : α) < ·) fun ε ↦ Icc (a - ε) (a + ε) :=
-  (nhds_basis_Ioo_pos a).to_hasBasis
-    (fun _ε ε₀ ↦ let ⟨δ, δ₀, δε⟩ := exists_between ε₀
-      ⟨δ, δ₀, Icc_subset_Ioo (sub_lt_sub_left δε _) (add_lt_add_left δε _)⟩)
-    (fun ε ε₀ ↦ ⟨ε, ε₀, Ioo_subset_Icc_self⟩)
-
-variable (α)
-
-theorem nhds_basis_zero_abs_sub_lt [NoMaxOrder α] :
-    (𝓝 (0 : α)).HasBasis (fun ε : α => (0 : α) < ε) fun ε => { b | |b| < ε } := by
-  simpa using nhds_basis_abs_sub_lt (0 : α)
-#align nhds_basis_zero_abs_sub_lt nhds_basis_zero_abs_sub_lt
-
-variable {α}
-
-/-- If `a` is positive we can form a basis from only nonnegative `Set.Ioo` intervals -/
-theorem nhds_basis_Ioo_pos_of_pos [NoMaxOrder α] {a : α} (ha : 0 < a) :
-    (𝓝 a).HasBasis (fun ε : α => (0 : α) < ε ∧ ε ≤ a) fun ε => Ioo (a - ε) (a + ε) :=
-  (nhds_basis_Ioo_pos a).restrict fun ε hε => ⟨min a ε, lt_min ha hε, min_le_left _ _,
-    Ioo_subset_Ioo (sub_le_sub_left (min_le_right _ _) _) (add_le_add_left (min_le_right _ _) _)⟩
-#align nhds_basis_Ioo_pos_of_pos nhds_basis_Ioo_pos_of_pos
-
-end LinearOrderedAddCommGroup
-
-@[deprecated image_neg]
-theorem preimage_neg [AddGroup α] : preimage (Neg.neg : α → α) = image (Neg.neg : α → α) :=
-  funext fun _ => image_neg.symm
-#align preimage_neg preimage_neg
-
-@[deprecated] -- use `Filter.map_neg` from `Mathlib.Order.Filter.Pointwise`
-theorem Filter.map_neg_eq_comap_neg [AddGroup α] :
-    map (Neg.neg : α → α) = comap (Neg.neg : α → α) :=
-  funext fun _ => map_eq_comap_of_inverse (funext neg_neg) (funext neg_neg)
-#align filter.map_neg_eq_comap_neg Filter.map_neg_eq_comap_neg
-
-section OrderTopology
-
-variable [TopologicalSpace α] [TopologicalSpace β] [LinearOrder α] [LinearOrder β] [OrderTopology α]
-  [OrderTopology β]
-
-theorem IsLUB.frequently_mem {a : α} {s : Set α} (ha : IsLUB s a) (hs : s.Nonempty) :
-    ∃ᶠ x in 𝓝[≤] a, x ∈ s := by
-  rcases hs with ⟨a', ha'⟩
-  intro h
-  rcases (ha.1 ha').eq_or_lt with (rfl | ha'a)
-  · exact h.self_of_nhdsWithin le_rfl ha'
-  · rcases (mem_nhdsWithin_Iic_iff_exists_Ioc_subset' ha'a).1 h with ⟨b, hba, hb⟩
-    rcases ha.exists_between hba with ⟨b', hb's, hb'⟩
-    exact hb hb' hb's
-#align is_lub.frequently_mem IsLUB.frequently_mem
-
-theorem IsLUB.frequently_nhds_mem {a : α} {s : Set α} (ha : IsLUB s a) (hs : s.Nonempty) :
-    ∃ᶠ x in 𝓝 a, x ∈ s :=
-  (ha.frequently_mem hs).filter_mono inf_le_left
-#align is_lub.frequently_nhds_mem IsLUB.frequently_nhds_mem
-
-theorem IsGLB.frequently_mem {a : α} {s : Set α} (ha : IsGLB s a) (hs : s.Nonempty) :
-    ∃ᶠ x in 𝓝[≥] a, x ∈ s :=
-  IsLUB.frequently_mem (α := αᵒᵈ) ha hs
-#align is_glb.frequently_mem IsGLB.frequently_mem
-
-theorem IsGLB.frequently_nhds_mem {a : α} {s : Set α} (ha : IsGLB s a) (hs : s.Nonempty) :
-    ∃ᶠ x in 𝓝 a, x ∈ s :=
-  (ha.frequently_mem hs).filter_mono inf_le_left
-#align is_glb.frequently_nhds_mem IsGLB.frequently_nhds_mem
-
-theorem IsLUB.mem_closure {a : α} {s : Set α} (ha : IsLUB s a) (hs : s.Nonempty) : a ∈ closure s :=
-  (ha.frequently_nhds_mem hs).mem_closure
-#align is_lub.mem_closure IsLUB.mem_closure
-
-theorem IsGLB.mem_closure {a : α} {s : Set α} (ha : IsGLB s a) (hs : s.Nonempty) : a ∈ closure s :=
-  (ha.frequently_nhds_mem hs).mem_closure
-#align is_glb.mem_closure IsGLB.mem_closure
-
-theorem IsLUB.nhdsWithin_neBot {a : α} {s : Set α} (ha : IsLUB s a) (hs : s.Nonempty) :
-    NeBot (𝓝[s] a) :=
-  mem_closure_iff_nhdsWithin_neBot.1 (ha.mem_closure hs)
-#align is_lub.nhds_within_ne_bot IsLUB.nhdsWithin_neBot
-
-theorem IsGLB.nhdsWithin_neBot : ∀ {a : α} {s : Set α}, IsGLB s a → s.Nonempty → NeBot (𝓝[s] a) :=
-  IsLUB.nhdsWithin_neBot (α := αᵒᵈ)
-#align is_glb.nhds_within_ne_bot IsGLB.nhdsWithin_neBot
-
-theorem isLUB_of_mem_nhds {s : Set α} {a : α} {f : Filter α} (hsa : a ∈ upperBounds s) (hsf : s ∈ f)
-    [NeBot (f ⊓ 𝓝 a)] : IsLUB s a :=
-  ⟨hsa, fun b hb =>
-    not_lt.1 fun hba =>
-      have : s ∩ { a | b < a } ∈ f ⊓ 𝓝 a := inter_mem_inf hsf (IsOpen.mem_nhds (isOpen_lt' _) hba)
-      let ⟨_x, ⟨hxs, hxb⟩⟩ := Filter.nonempty_of_mem this
-      have : b < b := lt_of_lt_of_le hxb <| hb hxs
-      lt_irrefl b this⟩
-#align is_lub_of_mem_nhds isLUB_of_mem_nhds
-
-theorem isLUB_of_mem_closure {s : Set α} {a : α} (hsa : a ∈ upperBounds s) (hsf : a ∈ closure s) :
-    IsLUB s a := by
-  rw [mem_closure_iff_clusterPt, ClusterPt, inf_comm] at hsf
-  exact isLUB_of_mem_nhds hsa (mem_principal_self s)
-#align is_lub_of_mem_closure isLUB_of_mem_closure
-
-theorem isGLB_of_mem_nhds :
-    ∀ {s : Set α} {a : α} {f : Filter α}, a ∈ lowerBounds s → s ∈ f → NeBot (f ⊓ 𝓝 a) → IsGLB s a :=
-  isLUB_of_mem_nhds (α := αᵒᵈ)
-#align is_glb_of_mem_nhds isGLB_of_mem_nhds
-
-theorem isGLB_of_mem_closure {s : Set α} {a : α} (hsa : a ∈ lowerBounds s) (hsf : a ∈ closure s) :
-    IsGLB s a :=
-  isLUB_of_mem_closure (α := αᵒᵈ) hsa hsf
-#align is_glb_of_mem_closure isGLB_of_mem_closure
-
-theorem IsLUB.mem_upperBounds_of_tendsto [Preorder γ] [TopologicalSpace γ] [OrderClosedTopology γ]
-    {f : α → γ} {s : Set α} {a : α} {b : γ} (hf : MonotoneOn f s) (ha : IsLUB s a)
-    (hb : Tendsto f (𝓝[s] a) (𝓝 b)) : b ∈ upperBounds (f '' s) := by
-  rintro _ ⟨x, hx, rfl⟩
-  replace ha := ha.inter_Ici_of_mem hx
-  haveI := ha.nhdsWithin_neBot ⟨x, hx, le_rfl⟩
-  refine' ge_of_tendsto (hb.mono_left (nhdsWithin_mono _ (inter_subset_left s (Ici x)))) _
-  exact mem_of_superset self_mem_nhdsWithin fun y hy => hf hx hy.1 hy.2
-#align is_lub.mem_upper_bounds_of_tendsto IsLUB.mem_upperBounds_of_tendsto
-
--- For a version of this theorem in which the convergence considered on the domain `α` is as `x : α`
--- tends to infinity, rather than tending to a point `x` in `α`, see `isLUB_of_tendsto_atTop`
-theorem IsLUB.isLUB_of_tendsto [Preorder γ] [TopologicalSpace γ] [OrderClosedTopology γ] {f : α → γ}
-    {s : Set α} {a : α} {b : γ} (hf : MonotoneOn f s) (ha : IsLUB s a) (hs : s.Nonempty)
-    (hb : Tendsto f (𝓝[s] a) (𝓝 b)) : IsLUB (f '' s) b :=
-  haveI := ha.nhdsWithin_neBot hs
-  ⟨ha.mem_upperBounds_of_tendsto hf hb, fun _b' hb' =>
-    le_of_tendsto hb (mem_of_superset self_mem_nhdsWithin fun _ hx => hb' <| mem_image_of_mem _ hx)⟩
-#align is_lub.is_lub_of_tendsto IsLUB.isLUB_of_tendsto
-
-theorem IsGLB.mem_lowerBounds_of_tendsto [Preorder γ] [TopologicalSpace γ] [OrderClosedTopology γ]
-    {f : α → γ} {s : Set α} {a : α} {b : γ} (hf : MonotoneOn f s) (ha : IsGLB s a)
-    (hb : Tendsto f (𝓝[s] a) (𝓝 b)) : b ∈ lowerBounds (f '' s) :=
-  IsLUB.mem_upperBounds_of_tendsto (α := αᵒᵈ) (γ := γᵒᵈ) hf.dual ha hb
-#align is_glb.mem_lower_bounds_of_tendsto IsGLB.mem_lowerBounds_of_tendsto
-
--- For a version of this theorem in which the convergence considered on the domain `α` is as
--- `x : α` tends to negative infinity, rather than tending to a point `x` in `α`, see
--- `isGLB_of_tendsto_atBot`
-theorem IsGLB.isGLB_of_tendsto [Preorder γ] [TopologicalSpace γ] [OrderClosedTopology γ] {f : α → γ}
-    {s : Set α} {a : α} {b : γ} (hf : MonotoneOn f s) :
-    IsGLB s a → s.Nonempty → Tendsto f (𝓝[s] a) (𝓝 b) → IsGLB (f '' s) b :=
-  IsLUB.isLUB_of_tendsto (α := αᵒᵈ) (γ := γᵒᵈ) hf.dual
-#align is_glb.is_glb_of_tendsto IsGLB.isGLB_of_tendsto
-
-theorem IsLUB.mem_lowerBounds_of_tendsto [Preorder γ] [TopologicalSpace γ] [OrderClosedTopology γ]
-    {f : α → γ} {s : Set α} {a : α} {b : γ} (hf : AntitoneOn f s) (ha : IsLUB s a)
-    (hb : Tendsto f (𝓝[s] a) (𝓝 b)) : b ∈ lowerBounds (f '' s) :=
-  IsLUB.mem_upperBounds_of_tendsto (γ := γᵒᵈ) hf ha hb
-#align is_lub.mem_lower_bounds_of_tendsto IsLUB.mem_lowerBounds_of_tendsto
-
-theorem IsLUB.isGLB_of_tendsto [Preorder γ] [TopologicalSpace γ] [OrderClosedTopology γ] :
-    ∀ {f : α → γ} {s : Set α} {a : α} {b : γ},
-      AntitoneOn f s → IsLUB s a → s.Nonempty → Tendsto f (𝓝[s] a) (𝓝 b) → IsGLB (f '' s) b :=
-  IsLUB.isLUB_of_tendsto (γ := γᵒᵈ)
-#align is_lub.is_glb_of_tendsto IsLUB.isGLB_of_tendsto
-
-theorem IsGLB.mem_upperBounds_of_tendsto [Preorder γ] [TopologicalSpace γ] [OrderClosedTopology γ]
-    {f : α → γ} {s : Set α} {a : α} {b : γ} (hf : AntitoneOn f s) (ha : IsGLB s a)
-    (hb : Tendsto f (𝓝[s] a) (𝓝 b)) : b ∈ upperBounds (f '' s) :=
-  IsGLB.mem_lowerBounds_of_tendsto (γ := γᵒᵈ) hf ha hb
-#align is_glb.mem_upper_bounds_of_tendsto IsGLB.mem_upperBounds_of_tendsto
-
-theorem IsGLB.isLUB_of_tendsto [Preorder γ] [TopologicalSpace γ] [OrderClosedTopology γ] :
-    ∀ {f : α → γ} {s : Set α} {a : α} {b : γ},
-      AntitoneOn f s → IsGLB s a → s.Nonempty → Tendsto f (𝓝[s] a) (𝓝 b) → IsLUB (f '' s) b :=
-  IsGLB.isGLB_of_tendsto (γ := γᵒᵈ)
-#align is_glb.is_lub_of_tendsto IsGLB.isLUB_of_tendsto
-
-theorem IsLUB.mem_of_isClosed {a : α} {s : Set α} (ha : IsLUB s a) (hs : s.Nonempty)
-    (sc : IsClosed s) : a ∈ s :=
-  sc.closure_subset <| ha.mem_closure hs
-#align is_lub.mem_of_is_closed IsLUB.mem_of_isClosed
-
-alias IsClosed.isLUB_mem := IsLUB.mem_of_isClosed
-#align is_closed.is_lub_mem IsClosed.isLUB_mem
-
-theorem IsGLB.mem_of_isClosed {a : α} {s : Set α} (ha : IsGLB s a) (hs : s.Nonempty)
-    (sc : IsClosed s) : a ∈ s :=
-  sc.closure_subset <| ha.mem_closure hs
-#align is_glb.mem_of_is_closed IsGLB.mem_of_isClosed
-
-alias IsClosed.isGLB_mem := IsGLB.mem_of_isClosed
-#align is_closed.is_glb_mem IsClosed.isGLB_mem
-
-/-!
-### Existence of sequences tending to `sInf` or `sSup` of a given set
--/
-
-theorem IsLUB.exists_seq_strictMono_tendsto_of_not_mem {t : Set α} {x : α}
-    [IsCountablyGenerated (𝓝 x)] (htx : IsLUB t x) (not_mem : x ∉ t) (ht : t.Nonempty) :
-    ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n < x) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t := by
-  obtain ⟨v, hvx, hvt⟩ := exists_seq_forall_of_frequently (htx.frequently_mem ht)
-  replace hvx := hvx.mono_right nhdsWithin_le_nhds
-  have hvx' : ∀ {n}, v n < x := (htx.1 (hvt _)).lt_of_ne (ne_of_mem_of_not_mem (hvt _) not_mem)
-  have : ∀ k, ∀ᶠ l in atTop, v k < v l := fun k => hvx.eventually (lt_mem_nhds hvx')
-  choose N hN hvN using fun k => ((eventually_gt_atTop k).and (this k)).exists
-  refine ⟨fun k => v (N^[k] 0), strictMono_nat_of_lt_succ fun _ => ?_, fun _ => hvx',
-    hvx.comp (strictMono_nat_of_lt_succ fun _ => ?_).tendsto_atTop, fun _ => hvt _⟩
-  · rw [iterate_succ_apply']; exact hvN _
-  · rw [iterate_succ_apply']; exact hN _
-#align is_lub.exists_seq_strict_mono_tendsto_of_not_mem IsLUB.exists_seq_strictMono_tendsto_of_not_mem
-
-theorem IsLUB.exists_seq_monotone_tendsto {t : Set α} {x : α} [IsCountablyGenerated (𝓝 x)]
-    (htx : IsLUB t x) (ht : t.Nonempty) :
-    ∃ u : ℕ → α, Monotone u ∧ (∀ n, u n ≤ x) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t := by
-  by_cases h : x ∈ t
-  · exact ⟨fun _ => x, monotone_const, fun n => le_rfl, tendsto_const_nhds, fun _ => h⟩
-  · rcases htx.exists_seq_strictMono_tendsto_of_not_mem h ht with ⟨u, hu⟩
-    exact ⟨u, hu.1.monotone, fun n => (hu.2.1 n).le, hu.2.2⟩
-#align is_lub.exists_seq_monotone_tendsto IsLUB.exists_seq_monotone_tendsto
-
-theorem exists_seq_strictMono_tendsto' {α : Type*} [LinearOrder α] [TopologicalSpace α]
-    [DenselyOrdered α] [OrderTopology α] [FirstCountableTopology α] {x y : α} (hy : y < x) :
-    ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n ∈ Ioo y x) ∧ Tendsto u atTop (𝓝 x) := by
-  have hx : x ∉ Ioo y x := fun h => (lt_irrefl x h.2).elim
-  have ht : Set.Nonempty (Ioo y x) := nonempty_Ioo.2 hy
-  rcases (isLUB_Ioo hy).exists_seq_strictMono_tendsto_of_not_mem hx ht with ⟨u, hu⟩
-  exact ⟨u, hu.1, hu.2.2.symm⟩
-#align exists_seq_strict_mono_tendsto' exists_seq_strictMono_tendsto'
-
-theorem exists_seq_strictMono_tendsto [DenselyOrdered α] [NoMinOrder α] [FirstCountableTopology α]
-    (x : α) : ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n < x) ∧ Tendsto u atTop (𝓝 x) := by
-  obtain ⟨y, hy⟩ : ∃ y, y < x := exists_lt x
-  rcases exists_seq_strictMono_tendsto' hy with ⟨u, hu_mono, hu_mem, hux⟩
-  exact ⟨u, hu_mono, fun n => (hu_mem n).2, hux⟩
-#align exists_seq_strict_mono_tendsto exists_seq_strictMono_tendsto
-
-theorem exists_seq_strictMono_tendsto_nhdsWithin [DenselyOrdered α] [NoMinOrder α]
-    [FirstCountableTopology α] (x : α) :
-    ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n < x) ∧ Tendsto u atTop (𝓝[<] x) :=
-  let ⟨u, hu, hx, h⟩ := exists_seq_strictMono_tendsto x
-  ⟨u, hu, hx, tendsto_nhdsWithin_mono_right (range_subset_iff.2 hx) <| tendsto_nhdsWithin_range.2 h⟩
-#align exists_seq_strict_mono_tendsto_nhds_within exists_seq_strictMono_tendsto_nhdsWithin
-
-theorem exists_seq_tendsto_sSup {α : Type*} [ConditionallyCompleteLinearOrder α]
-    [TopologicalSpace α] [OrderTopology α] [FirstCountableTopology α] {S : Set α} (hS : S.Nonempty)
-    (hS' : BddAbove S) : ∃ u : ℕ → α, Monotone u ∧ Tendsto u atTop (𝓝 (sSup S)) ∧ ∀ n, u n ∈ S := by
-  rcases (isLUB_csSup hS hS').exists_seq_monotone_tendsto hS with ⟨u, hu⟩
-  exact ⟨u, hu.1, hu.2.2⟩
-#align exists_seq_tendsto_Sup exists_seq_tendsto_sSup
-
-theorem IsGLB.exists_seq_strictAnti_tendsto_of_not_mem {t : Set α} {x : α}
-    [IsCountablyGenerated (𝓝 x)] (htx : IsGLB t x) (not_mem : x ∉ t) (ht : t.Nonempty) :
-    ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, x < u n) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t :=
-  IsLUB.exists_seq_strictMono_tendsto_of_not_mem (α := αᵒᵈ) htx not_mem ht
-#align is_glb.exists_seq_strict_anti_tendsto_of_not_mem IsGLB.exists_seq_strictAnti_tendsto_of_not_mem
-
-theorem IsGLB.exists_seq_antitone_tendsto {t : Set α} {x : α} [IsCountablyGenerated (𝓝 x)]
-    (htx : IsGLB t x) (ht : t.Nonempty) :
-    ∃ u : ℕ → α, Antitone u ∧ (∀ n, x ≤ u n) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t :=
-  IsLUB.exists_seq_monotone_tendsto (α := αᵒᵈ) htx ht
-#align is_glb.exists_seq_antitone_tendsto IsGLB.exists_seq_antitone_tendsto
-
-theorem exists_seq_strictAnti_tendsto' [DenselyOrdered α] [FirstCountableTopology α] {x y : α}
-    (hy : x < y) : ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, u n ∈ Ioo x y) ∧ Tendsto u atTop (𝓝 x) := by
-  simpa only [dual_Ioo]
-    using exists_seq_strictMono_tendsto' (α := αᵒᵈ) (OrderDual.toDual_lt_toDual.2 hy)
-#align exists_seq_strict_anti_tendsto' exists_seq_strictAnti_tendsto'
-
-theorem exists_seq_strictAnti_tendsto [DenselyOrdered α] [NoMaxOrder α] [FirstCountableTopology α]
-    (x : α) : ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, x < u n) ∧ Tendsto u atTop (𝓝 x) :=
-  exists_seq_strictMono_tendsto (α := αᵒᵈ) x
-#align exists_seq_strict_anti_tendsto exists_seq_strictAnti_tendsto
-
-theorem exists_seq_strictAnti_tendsto_nhdsWithin [DenselyOrdered α] [NoMaxOrder α]
-    [FirstCountableTopology α] (x : α) :
-    ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, x < u n) ∧ Tendsto u atTop (𝓝[>] x) :=
-  exists_seq_strictMono_tendsto_nhdsWithin (α := αᵒᵈ) _
-#align exists_seq_strict_anti_tendsto_nhds_within exists_seq_strictAnti_tendsto_nhdsWithin
-
-theorem exists_seq_strictAnti_strictMono_tendsto [DenselyOrdered α] [FirstCountableTopology α]
-    {x y : α} (h : x < y) :
-    ∃ u v : ℕ → α, StrictAnti u ∧ StrictMono v ∧ (∀ k, u k ∈ Ioo x y) ∧ (∀ l, v l ∈ Ioo x y) ∧
-      (∀ k l, u k < v l) ∧ Tendsto u atTop (𝓝 x) ∧ Tendsto v atTop (𝓝 y) := by
-  rcases exists_seq_strictAnti_tendsto' h with ⟨u, hu_anti, hu_mem, hux⟩
-  rcases exists_seq_strictMono_tendsto' (hu_mem 0).2 with ⟨v, hv_mono, hv_mem, hvy⟩
-  exact
-    ⟨u, v, hu_anti, hv_mono, hu_mem, fun l => ⟨(hu_mem 0).1.trans (hv_mem l).1, (hv_mem l).2⟩,
-      fun k l => (hu_anti.antitone (zero_le k)).trans_lt (hv_mem l).1, hux, hvy⟩
-#align exists_seq_strict_anti_strict_mono_tendsto exists_seq_strictAnti_strictMono_tendsto
-
-theorem exists_seq_tendsto_sInf {α : Type*} [ConditionallyCompleteLinearOrder α]
-    [TopologicalSpace α] [OrderTopology α] [FirstCountableTopology α] {S : Set α} (hS : S.Nonempty)
-    (hS' : BddBelow S) : ∃ u : ℕ → α, Antitone u ∧ Tendsto u atTop (𝓝 (sInf S)) ∧ ∀ n, u n ∈ S :=
-  exists_seq_tendsto_sSup (α := αᵒᵈ) hS hS'
-#align exists_seq_tendsto_Inf exists_seq_tendsto_sInf
-
-end OrderTopology
-
-section DenselyOrdered
-
-variable [TopologicalSpace α] [LinearOrder α] [OrderTopology α] [DenselyOrdered α] {a b : α}
-  {s : Set α}
-
-/-- The closure of the interval `(a, +∞)` is the closed interval `[a, +∞)`, unless `a` is a top
-element. -/
-theorem closure_Ioi' {a : α} (h : (Ioi a).Nonempty) : closure (Ioi a) = Ici a := by
-  apply Subset.antisymm
-  · exact closure_minimal Ioi_subset_Ici_self isClosed_Ici
-  · rw [← diff_subset_closure_iff, Ici_diff_Ioi_same, singleton_subset_iff]
-    exact isGLB_Ioi.mem_closure h
-#align closure_Ioi' closure_Ioi'
-
-/-- The closure of the interval `(a, +∞)` is the closed interval `[a, +∞)`. -/
-@[simp]
-theorem closure_Ioi (a : α) [NoMaxOrder α] : closure (Ioi a) = Ici a :=
-  closure_Ioi' nonempty_Ioi
-#align closure_Ioi closure_Ioi
-
-/-- The closure of the interval `(-∞, a)` is the closed interval `(-∞, a]`, unless `a` is a bottom
-element. -/
-theorem closure_Iio' (h : (Iio a).Nonempty) : closure (Iio a) = Iic a :=
-  closure_Ioi' (α := αᵒᵈ) h
-#align closure_Iio' closure_Iio'
-
-/-- The closure of the interval `(-∞, a)` is the interval `(-∞, a]`. -/
-@[simp]
-theorem closure_Iio (a : α) [NoMinOrder α] : closure (Iio a) = Iic a :=
-  closure_Iio' nonempty_Iio
-#align closure_Iio closure_Iio
-
-/-- The closure of the open interval `(a, b)` is the closed interval `[a, b]`. -/
-@[simp]
-theorem closure_Ioo {a b : α} (hab : a ≠ b) : closure (Ioo a b) = Icc a b := by
-  apply Subset.antisymm
-  · exact closure_minimal Ioo_subset_Icc_self isClosed_Icc
-  · cases' hab.lt_or_lt with hab hab
-    · rw [← diff_subset_closure_iff, Icc_diff_Ioo_same hab.le]
-      have hab' : (Ioo a b).Nonempty := nonempty_Ioo.2 hab
-      simp only [insert_subset_iff, singleton_subset_iff]
-      exact ⟨(isGLB_Ioo hab).mem_closure hab', (isLUB_Ioo hab).mem_closure hab'⟩
-    · rw [Icc_eq_empty_of_lt hab]
-      exact empty_subset _
-#align closure_Ioo closure_Ioo
-
-/-- The closure of the interval `(a, b]` is the closed interval `[a, b]`. -/
-@[simp]
-theorem closure_Ioc {a b : α} (hab : a ≠ b) : closure (Ioc a b) = Icc a b := by
-  apply Subset.antisymm
-  · exact closure_minimal Ioc_subset_Icc_self isClosed_Icc
-  · apply Subset.trans _ (closure_mono Ioo_subset_Ioc_self)
-    rw [closure_Ioo hab]
-#align closure_Ioc closure_Ioc
-
-/-- The closure of the interval `[a, b)` is the closed interval `[a, b]`. -/
-@[simp]
-theorem closure_Ico {a b : α} (hab : a ≠ b) : closure (Ico a b) = Icc a b := by
-  apply Subset.antisymm
-  · exact closure_minimal Ico_subset_Icc_self isClosed_Icc
-  · apply Subset.trans _ (closure_mono Ioo_subset_Ico_self)
-    rw [closure_Ioo hab]
-#align closure_Ico closure_Ico
-
-@[simp]
-theorem interior_Ici' {a : α} (ha : (Iio a).Nonempty) : interior (Ici a) = Ioi a := by
-  rw [← compl_Iio, interior_compl, closure_Iio' ha, compl_Iic]
-#align interior_Ici' interior_Ici'
-
-theorem interior_Ici [NoMinOrder α] {a : α} : interior (Ici a) = Ioi a :=
-  interior_Ici' nonempty_Iio
-#align interior_Ici interior_Ici
-
-@[simp]
-theorem interior_Iic' {a : α} (ha : (Ioi a).Nonempty) : interior (Iic a) = Iio a :=
-  interior_Ici' (α := αᵒᵈ) ha
-#align interior_Iic' interior_Iic'
-
-theorem interior_Iic [NoMaxOrder α] {a : α} : interior (Iic a) = Iio a :=
-  interior_Iic' nonempty_Ioi
-#align interior_Iic interior_Iic
-
-@[simp]
-theorem interior_Icc [NoMinOrder α] [NoMaxOrder α] {a b : α} : interior (Icc a b) = Ioo a b := by
-  rw [← Ici_inter_Iic, interior_inter, interior_Ici, interior_Iic, Ioi_inter_Iio]
-#align interior_Icc interior_Icc
-
-@[simp]
-theorem Icc_mem_nhds_iff [NoMinOrder α] [NoMaxOrder α] {a b x : α} :
-    Icc a b ∈ 𝓝 x ↔ x ∈ Ioo a b := by
-  rw [← interior_Icc, mem_interior_iff_mem_nhds]
-
-@[simp]
-theorem interior_Ico [NoMinOrder α] {a b : α} : interior (Ico a b) = Ioo a b := by
-  rw [← Ici_inter_Iio, interior_inter, interior_Ici, interior_Iio, Ioi_inter_Iio]
-#align interior_Ico interior_Ico
-
-@[simp]
-theorem Ico_mem_nhds_iff [NoMinOrder α] {a b x : α} : Ico a b ∈ 𝓝 x ↔ x ∈ Ioo a b := by
-  rw [← interior_Ico, mem_interior_iff_mem_nhds]
-
-@[simp]
-theorem interior_Ioc [NoMaxOrder α] {a b : α} : interior (Ioc a b) = Ioo a b := by
-  rw [← Ioi_inter_Iic, interior_inter, interior_Ioi, interior_Iic, Ioi_inter_Iio]
-#align interior_Ioc interior_Ioc
-
-@[simp]
-theorem Ioc_mem_nhds_iff [NoMaxOrder α] {a b x : α} : Ioc a b ∈ 𝓝 x ↔ x ∈ Ioo a b := by
-  rw [← interior_Ioc, mem_interior_iff_mem_nhds]
-
-theorem closure_interior_Icc {a b : α} (h : a ≠ b) : closure (interior (Icc a b)) = Icc a b :=
-  (closure_minimal interior_subset isClosed_Icc).antisymm <|
-    calc
-      Icc a b = closure (Ioo a b) := (closure_Ioo h).symm
-      _ ⊆ closure (interior (Icc a b)) :=
-        closure_mono (interior_maximal Ioo_subset_Icc_self isOpen_Ioo)
-#align closure_interior_Icc closure_interior_Icc
-
-theorem Ioc_subset_closure_interior (a b : α) : Ioc a b ⊆ closure (interior (Ioc a b)) := by
-  rcases eq_or_ne a b with (rfl | h)
-  · simp
-  · calc
-      Ioc a b ⊆ Icc a b := Ioc_subset_Icc_self
-      _ = closure (Ioo a b) := (closure_Ioo h).symm
-      _ ⊆ closure (interior (Ioc a b)) :=
-        closure_mono (interior_maximal Ioo_subset_Ioc_self isOpen_Ioo)
-#align Ioc_subset_closure_interior Ioc_subset_closure_interior
-
-theorem Ico_subset_closure_interior (a b : α) : Ico a b ⊆ closure (interior (Ico a b)) := by
-  simpa only [dual_Ioc] using Ioc_subset_closure_interior (OrderDual.toDual b) (OrderDual.toDual a)
-#align Ico_subset_closure_interior Ico_subset_closure_interior
-
-@[simp]
-theorem frontier_Ici' {a : α} (ha : (Iio a).Nonempty) : frontier (Ici a) = {a} := by
-  simp [frontier, ha]
-#align frontier_Ici' frontier_Ici'
-
-theorem frontier_Ici [NoMinOrder α] {a : α} : frontier (Ici a) = {a} :=
-  frontier_Ici' nonempty_Iio
-#align frontier_Ici frontier_Ici
-
-@[simp]
-theorem frontier_Iic' {a : α} (ha : (Ioi a).Nonempty) : frontier (Iic a) = {a} := by
-  simp [frontier, ha]
-#align frontier_Iic' frontier_Iic'
-
-theorem frontier_Iic [NoMaxOrder α] {a : α} : frontier (Iic a) = {a} :=
-  frontier_Iic' nonempty_Ioi
-#align frontier_Iic frontier_Iic
-
-@[simp]
-theorem frontier_Ioi' {a : α} (ha : (Ioi a).Nonempty) : frontier (Ioi a) = {a} := by
-  simp [frontier, closure_Ioi' ha, Iic_diff_Iio, Icc_self]
-#align frontier_Ioi' frontier_Ioi'
-
-theorem frontier_Ioi [NoMaxOrder α] {a : α} : frontier (Ioi a) = {a} :=
-  frontier_Ioi' nonempty_Ioi
-#align frontier_Ioi frontier_Ioi
-
-@[simp]
-theorem frontier_Iio' {a : α} (ha : (Iio a).Nonempty) : frontier (Iio a) = {a} := by
-  simp [frontier, closure_Iio' ha, Iic_diff_Iio, Icc_self]
-#align frontier_Iio' frontier_Iio'
-
-theorem frontier_Iio [NoMinOrder α] {a : α} : frontier (Iio a) = {a} :=
-  frontier_Iio' nonempty_Iio
-#align frontier_Iio frontier_Iio
-
-@[simp]
-theorem frontier_Icc [NoMinOrder α] [NoMaxOrder α] {a b : α} (h : a ≤ b) :
-    frontier (Icc a b) = {a, b} := by simp [frontier, h, Icc_diff_Ioo_same]
-#align frontier_Icc frontier_Icc
-
-@[simp]
-theorem frontier_Ioo {a b : α} (h : a < b) : frontier (Ioo a b) = {a, b} := by
-  rw [frontier, closure_Ioo h.ne, interior_Ioo, Icc_diff_Ioo_same h.le]
-#align frontier_Ioo frontier_Ioo
-
-@[simp]
-theorem frontier_Ico [NoMinOrder α] {a b : α} (h : a < b) : frontier (Ico a b) = {a, b} := by
-  rw [frontier, closure_Ico h.ne, interior_Ico, Icc_diff_Ioo_same h.le]
-#align frontier_Ico frontier_Ico
-
-@[simp]
-theorem frontier_Ioc [NoMaxOrder α] {a b : α} (h : a < b) : frontier (Ioc a b) = {a, b} := by
-  rw [frontier, closure_Ioc h.ne, interior_Ioc, Icc_diff_Ioo_same h.le]
-#align frontier_Ioc frontier_Ioc
-
-theorem nhdsWithin_Ioi_neBot' {a b : α} (H₁ : (Ioi a).Nonempty) (H₂ : a ≤ b) :
-    NeBot (𝓝[Ioi a] b) :=
-  mem_closure_iff_nhdsWithin_neBot.1 <| by rwa [closure_Ioi' H₁]
-#align nhds_within_Ioi_ne_bot' nhdsWithin_Ioi_neBot'
-
-theorem nhdsWithin_Ioi_neBot [NoMaxOrder α] {a b : α} (H : a ≤ b) : NeBot (𝓝[Ioi a] b) :=
-  nhdsWithin_Ioi_neBot' nonempty_Ioi H
-#align nhds_within_Ioi_ne_bot nhdsWithin_Ioi_neBot
-
-theorem nhdsWithin_Ioi_self_neBot' {a : α} (H : (Ioi a).Nonempty) : NeBot (𝓝[>] a) :=
-  nhdsWithin_Ioi_neBot' H (le_refl a)
-#align nhds_within_Ioi_self_ne_bot' nhdsWithin_Ioi_self_neBot'
-
-instance nhdsWithin_Ioi_self_neBot [NoMaxOrder α] (a : α) : NeBot (𝓝[>] a) :=
-  nhdsWithin_Ioi_neBot (le_refl a)
-#align nhds_within_Ioi_self_ne_bot nhdsWithin_Ioi_self_neBot
-
-theorem nhdsWithin_Iio_neBot' {b c : α} (H₁ : (Iio c).Nonempty) (H₂ : b ≤ c) :
-    NeBot (𝓝[Iio c] b) :=
-  mem_closure_iff_nhdsWithin_neBot.1 <| by rwa [closure_Iio' H₁]
-#align nhds_within_Iio_ne_bot' nhdsWithin_Iio_neBot'
-
-theorem nhdsWithin_Iio_neBot [NoMinOrder α] {a b : α} (H : a ≤ b) : NeBot (𝓝[Iio b] a) :=
-  nhdsWithin_Iio_neBot' nonempty_Iio H
-#align nhds_within_Iio_ne_bot nhdsWithin_Iio_neBot
-
-theorem nhdsWithin_Iio_self_neBot' {b : α} (H : (Iio b).Nonempty) : NeBot (𝓝[<] b) :=
-  nhdsWithin_Iio_neBot' H (le_refl b)
-#align nhds_within_Iio_self_ne_bot' nhdsWithin_Iio_self_neBot'
-
-instance nhdsWithin_Iio_self_neBot [NoMinOrder α] (a : α) : NeBot (𝓝[<] a) :=
-  nhdsWithin_Iio_neBot (le_refl a)
-#align nhds_within_Iio_self_ne_bot nhdsWithin_Iio_self_neBot
-
-theorem right_nhdsWithin_Ico_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ico a b] b) :=
-  (isLUB_Ico H).nhdsWithin_neBot (nonempty_Ico.2 H)
-#align right_nhds_within_Ico_ne_bot right_nhdsWithin_Ico_neBot
-
-theorem left_nhdsWithin_Ioc_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ioc a b] a) :=
-  (isGLB_Ioc H).nhdsWithin_neBot (nonempty_Ioc.2 H)
-#align left_nhds_within_Ioc_ne_bot left_nhdsWithin_Ioc_neBot
-
-theorem left_nhdsWithin_Ioo_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ioo a b] a) :=
-  (isGLB_Ioo H).nhdsWithin_neBot (nonempty_Ioo.2 H)
-#align left_nhds_within_Ioo_ne_bot left_nhdsWithin_Ioo_neBot
-
-theorem right_nhdsWithin_Ioo_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ioo a b] b) :=
-  (isLUB_Ioo H).nhdsWithin_neBot (nonempty_Ioo.2 H)
-#align right_nhds_within_Ioo_ne_bot right_nhdsWithin_Ioo_neBot
-
-theorem comap_coe_nhdsWithin_Iio_of_Ioo_subset (hb : s ⊆ Iio b)
-    (hs : s.Nonempty → ∃ a < b, Ioo a b ⊆ s) : comap ((↑) : s → α) (𝓝[<] b) = atTop := by
-  nontriviality
-  haveI : Nonempty s := nontrivial_iff_nonempty.1 ‹_›
-  rcases hs (nonempty_subtype.1 ‹_›) with ⟨a, h, hs⟩
-  ext u; constructor
-  · rintro ⟨t, ht, hts⟩
-    obtain ⟨x, ⟨hxa : a ≤ x, hxb : x < b⟩, hxt : Ioo x b ⊆ t⟩ :=
-      (mem_nhdsWithin_Iio_iff_exists_mem_Ico_Ioo_subset h).mp ht
-    obtain ⟨y, hxy, hyb⟩ := exists_between hxb
-    refine' mem_of_superset (mem_atTop ⟨y, hs ⟨hxa.trans_lt hxy, hyb⟩⟩) _
-    rintro ⟨z, hzs⟩ (hyz : y ≤ z)
-    exact hts (hxt ⟨hxy.trans_le hyz, hb hzs⟩)
-  · intro hu
-    obtain ⟨x : s, hx : ∀ z, x ≤ z → z ∈ u⟩ := mem_atTop_sets.1 hu
-    exact ⟨Ioo x b, Ioo_mem_nhdsWithin_Iio' (hb x.2), fun z hz => hx _ hz.1.le⟩
-#align comap_coe_nhds_within_Iio_of_Ioo_subset comap_coe_nhdsWithin_Iio_of_Ioo_subset
-
-theorem comap_coe_nhdsWithin_Ioi_of_Ioo_subset (ha : s ⊆ Ioi a)
-    (hs : s.Nonempty → ∃ b > a, Ioo a b ⊆ s) : comap ((↑) : s → α) (𝓝[>] a) = atBot :=
-  comap_coe_nhdsWithin_Iio_of_Ioo_subset (show ofDual ⁻¹' s ⊆ Iio (toDual a) from ha) fun h => by
-    simpa only [OrderDual.exists, dual_Ioo] using hs h
-#align comap_coe_nhds_within_Ioi_of_Ioo_subset comap_coe_nhdsWithin_Ioi_of_Ioo_subset
-
-theorem map_coe_atTop_of_Ioo_subset (hb : s ⊆ Iio b) (hs : ∀ a' < b, ∃ a < b, Ioo a b ⊆ s) :
-    map ((↑) : s → α) atTop = 𝓝[<] b := by
-  rcases eq_empty_or_nonempty (Iio b) with (hb' | ⟨a, ha⟩)
-  · have : IsEmpty s := ⟨fun x => hb'.subset (hb x.2)⟩
-    rw [filter_eq_bot_of_isEmpty atTop, Filter.map_bot, hb', nhdsWithin_empty]
-  · rw [← comap_coe_nhdsWithin_Iio_of_Ioo_subset hb fun _ => hs a ha, map_comap_of_mem]
-    rw [Subtype.range_val]
-    exact (mem_nhdsWithin_Iio_iff_exists_Ioo_subset' ha).2 (hs a ha)
-#align map_coe_at_top_of_Ioo_subset map_coe_atTop_of_Ioo_subset
-
-theorem map_coe_atBot_of_Ioo_subset (ha : s ⊆ Ioi a) (hs : ∀ b' > a, ∃ b > a, Ioo a b ⊆ s) :
-    map ((↑) : s → α) atBot = 𝓝[>] a := by
-  -- the elaborator gets stuck without `(... : _)`
-  refine' (map_coe_atTop_of_Ioo_subset (show ofDual ⁻¹' s ⊆ Iio (toDual a) from ha)
-    fun b' hb' => _ : _)
-  simpa only [OrderDual.exists, dual_Ioo] using hs b' hb'
-#align map_coe_at_bot_of_Ioo_subset map_coe_atBot_of_Ioo_subset
-
-/-- The `atTop` filter for an open interval `Ioo a b` comes from the left-neighbourhoods filter at
-the right endpoint in the ambient order. -/
-theorem comap_coe_Ioo_nhdsWithin_Iio (a b : α) : comap ((↑) : Ioo a b → α) (𝓝[<] b) = atTop :=
-  comap_coe_nhdsWithin_Iio_of_Ioo_subset Ioo_subset_Iio_self fun h =>
-    ⟨a, nonempty_Ioo.1 h, Subset.refl _⟩
-#align comap_coe_Ioo_nhds_within_Iio comap_coe_Ioo_nhdsWithin_Iio
-
-/-- The `atBot` filter for an open interval `Ioo a b` comes from the right-neighbourhoods filter at
-the left endpoint in the ambient order. -/
-theorem comap_coe_Ioo_nhdsWithin_Ioi (a b : α) : comap ((↑) : Ioo a b → α) (𝓝[>] a) = atBot :=
-  comap_coe_nhdsWithin_Ioi_of_Ioo_subset Ioo_subset_Ioi_self fun h =>
-    ⟨b, nonempty_Ioo.1 h, Subset.refl _⟩
-#align comap_coe_Ioo_nhds_within_Ioi comap_coe_Ioo_nhdsWithin_Ioi
-
-theorem comap_coe_Ioi_nhdsWithin_Ioi (a : α) : comap ((↑) : Ioi a → α) (𝓝[>] a) = atBot :=
-  comap_coe_nhdsWithin_Ioi_of_Ioo_subset (Subset.refl _) fun ⟨x, hx⟩ => ⟨x, hx, Ioo_subset_Ioi_self⟩
-#align comap_coe_Ioi_nhds_within_Ioi comap_coe_Ioi_nhdsWithin_Ioi
-
-theorem comap_coe_Iio_nhdsWithin_Iio (a : α) : comap ((↑) : Iio a → α) (𝓝[<] a) = atTop :=
-  comap_coe_Ioi_nhdsWithin_Ioi (α := αᵒᵈ) a
-#align comap_coe_Iio_nhds_within_Iio comap_coe_Iio_nhdsWithin_Iio
-
-@[simp]
-theorem map_coe_Ioo_atTop {a b : α} (h : a < b) : map ((↑) : Ioo a b → α) atTop = 𝓝[<] b :=
-  map_coe_atTop_of_Ioo_subset Ioo_subset_Iio_self fun _ _ => ⟨_, h, Subset.refl _⟩
-#align map_coe_Ioo_at_top map_coe_Ioo_atTop
-
-@[simp]
-theorem map_coe_Ioo_atBot {a b : α} (h : a < b) : map ((↑) : Ioo a b → α) atBot = 𝓝[>] a :=
-  map_coe_atBot_of_Ioo_subset Ioo_subset_Ioi_self fun _ _ => ⟨_, h, Subset.refl _⟩
-#align map_coe_Ioo_at_bot map_coe_Ioo_atBot
-
-@[simp]
-theorem map_coe_Ioi_atBot (a : α) : map ((↑) : Ioi a → α) atBot = 𝓝[>] a :=
-  map_coe_atBot_of_Ioo_subset (Subset.refl _) fun b hb => ⟨b, hb, Ioo_subset_Ioi_self⟩
-#align map_coe_Ioi_at_bot map_coe_Ioi_atBot
-
-@[simp]
-theorem map_coe_Iio_atTop (a : α) : map ((↑) : Iio a → α) atTop = 𝓝[<] a :=
-  map_coe_Ioi_atBot (α := αᵒᵈ) _
-#align map_coe_Iio_at_top map_coe_Iio_atTop
-
-variable {l : Filter β} {f : α → β}
-
-@[simp]
-theorem tendsto_comp_coe_Ioo_atTop (h : a < b) :
-    Tendsto (fun x : Ioo a b => f x) atTop l ↔ Tendsto f (𝓝[<] b) l := by
-  rw [← map_coe_Ioo_atTop h, tendsto_map'_iff]; rfl
-#align tendsto_comp_coe_Ioo_at_top tendsto_comp_coe_Ioo_atTop
-
-@[simp]
-theorem tendsto_comp_coe_Ioo_atBot (h : a < b) :
-    Tendsto (fun x : Ioo a b => f x) atBot l ↔ Tendsto f (𝓝[>] a) l := by
-  rw [← map_coe_Ioo_atBot h, tendsto_map'_iff]; rfl
-#align tendsto_comp_coe_Ioo_at_bot tendsto_comp_coe_Ioo_atBot
-
--- Porting note (#11215): TODO: `simpNF` claims that `simp` can't use
--- this lemma to simplify LHS but it can
-@[simp, nolint simpNF]
-theorem tendsto_comp_coe_Ioi_atBot :
-    Tendsto (fun x : Ioi a => f x) atBot l ↔ Tendsto f (𝓝[>] a) l := by
-  rw [← map_coe_Ioi_atBot, tendsto_map'_iff]; rfl
-#align tendsto_comp_coe_Ioi_at_bot tendsto_comp_coe_Ioi_atBot
-
--- Porting note (#11215): TODO: `simpNF` claims that `simp` can't use
--- this lemma to simplify LHS but it can
-@[simp, nolint simpNF]
-theorem tendsto_comp_coe_Iio_atTop :
-    Tendsto (fun x : Iio a => f x) atTop l ↔ Tendsto f (𝓝[<] a) l := by
-  rw [← map_coe_Iio_atTop, tendsto_map'_iff]; rfl
-#align tendsto_comp_coe_Iio_at_top tendsto_comp_coe_Iio_atTop
-
-@[simp]
-theorem tendsto_Ioo_atTop {f : β → Ioo a b} :
-    Tendsto f l atTop ↔ Tendsto (fun x => (f x : α)) l (𝓝[<] b) := by
-  rw [← comap_coe_Ioo_nhdsWithin_Iio, tendsto_comap_iff]; rfl
-#align tendsto_Ioo_at_top tendsto_Ioo_atTop
-
-@[simp]
-theorem tendsto_Ioo_atBot {f : β → Ioo a b} :
-    Tendsto f l atBot ↔ Tendsto (fun x => (f x : α)) l (𝓝[>] a) := by
-  rw [← comap_coe_Ioo_nhdsWithin_Ioi, tendsto_comap_iff]; rfl
-#align tendsto_Ioo_at_bot tendsto_Ioo_atBot
-
-@[simp]
-theorem tendsto_Ioi_atBot {f : β → Ioi a} :
-    Tendsto f l atBot ↔ Tendsto (fun x => (f x : α)) l (𝓝[>] a) := by
-  rw [← comap_coe_Ioi_nhdsWithin_Ioi, tendsto_comap_iff]; rfl
-#align tendsto_Ioi_at_bot tendsto_Ioi_atBot
-
-@[simp]
-theorem tendsto_Iio_atTop {f : β → Iio a} :
-    Tendsto f l atTop ↔ Tendsto (fun x => (f x : α)) l (𝓝[<] a) := by
-  rw [← comap_coe_Iio_nhdsWithin_Iio, tendsto_comap_iff]; rfl
-#align tendsto_Iio_at_top tendsto_Iio_atTop
-
-instance (x : α) [Nontrivial α] : NeBot (𝓝[≠] x) := by
-  refine forall_mem_nonempty_iff_neBot.1 fun s hs => ?_
-  obtain ⟨u, u_open, xu, us⟩ : ∃ u : Set α, IsOpen u ∧ x ∈ u ∧ u ∩ {x}ᶜ ⊆ s := mem_nhdsWithin.1 hs
-  obtain ⟨a, b, a_lt_b, hab⟩ : ∃ a b : α, a < b ∧ Ioo a b ⊆ u := u_open.exists_Ioo_subset ⟨x, xu⟩
-  obtain ⟨y, hy⟩ : ∃ y, a < y ∧ y < b := exists_between a_lt_b
-  rcases ne_or_eq x y with (xy | rfl)
-  · exact ⟨y, us ⟨hab hy, xy.symm⟩⟩
-  obtain ⟨z, hz⟩ : ∃ z, a < z ∧ z < x := exists_between hy.1
-  exact ⟨z, us ⟨hab ⟨hz.1, hz.2.trans hy.2⟩, hz.2.ne⟩⟩
-
-/-- Let `s` be a dense set in a nontrivial dense linear order `α`. If `s` is a
-separable space (e.g., if `α` has a second countable topology), then there exists a countable
-dense subset `t ⊆ s` such that `t` does not contain bottom/top elements of `α`. -/
-theorem Dense.exists_countable_dense_subset_no_bot_top [Nontrivial α] {s : Set α} [SeparableSpace s]
-    (hs : Dense s) :
-    ∃ t, t ⊆ s ∧ t.Countable ∧ Dense t ∧ (∀ x, IsBot x → x ∉ t) ∧ ∀ x, IsTop x → x ∉ t := by
-  rcases hs.exists_countable_dense_subset with ⟨t, hts, htc, htd⟩
-  refine' ⟨t \ ({ x | IsBot x } ∪ { x | IsTop x }), _, _, _, fun x hx => _, fun x hx => _⟩
-  · exact (diff_subset _ _).trans hts
-  · exact htc.mono (diff_subset _ _)
-  · exact htd.diff_finite ((subsingleton_isBot α).finite.union (subsingleton_isTop α).finite)
-  · simp [hx]
-  · simp [hx]
-#align dense.exists_countable_dense_subset_no_bot_top Dense.exists_countable_dense_subset_no_bot_top
-
-variable (α)
-
-/-- If `α` is a nontrivial separable dense linear order, then there exists a
-countable dense set `s : Set α` that contains neither top nor bottom elements of `α`.
-For a dense set containing both bot and top elements, see
-`exists_countable_dense_bot_top`. -/
-theorem exists_countable_dense_no_bot_top [SeparableSpace α] [Nontrivial α] :
-    ∃ s : Set α, s.Countable ∧ Dense s ∧ (∀ x, IsBot x → x ∉ s) ∧ ∀ x, IsTop x → x ∉ s := by
-  simpa using dense_univ.exists_countable_dense_subset_no_bot_top
-#align exists_countable_dense_no_bot_top exists_countable_dense_no_bot_top
-
-end DenselyOrdered
-
-section ConditionallyCompleteLinearOrder
-
-variable [ConditionallyCompleteLinearOrder α] [TopologicalSpace α] [OrderTopology α]
-  [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderClosedTopology β] [Nonempty γ]
-
-/-- A monotone function continuous at the supremum of a nonempty set sends this supremum to
-the supremum of the image of this set. -/
-theorem Monotone.map_sSup_of_continuousAt' {f : α → β} {A : Set α} (Cf : ContinuousAt f (sSup A))
-    (Mf : Monotone f) (A_nonemp : A.Nonempty) (A_bdd : BddAbove A := by bddDefault) :
-    f (sSup A) = sSup (f '' A) :=
-  --This is a particular case of the more general `IsLUB.isLUB_of_tendsto`
-  .symm <| ((isLUB_csSup A_nonemp A_bdd).isLUB_of_tendsto (Mf.monotoneOn _) A_nonemp <|
-    Cf.mono_left inf_le_left).csSup_eq (A_nonemp.image f)
-#align monotone.map_Sup_of_continuous_at' Monotone.map_sSup_of_continuousAt'
-
-/-- A monotone function continuous at the indexed supremum over a nonempty `Sort` sends this indexed
-supremum to the indexed supremum of the composition. -/
-theorem Monotone.map_iSup_of_continuousAt' {ι : Sort*} [Nonempty ι] {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (iSup g)) (Mf : Monotone f)
-    (bdd : BddAbove (range g) := by bddDefault) : f (⨆ i, g i) = ⨆ i, f (g i) := by
-  rw [iSup, Monotone.map_sSup_of_continuousAt' Cf Mf (range_nonempty g) bdd, ← range_comp, iSup]
-  rfl
-#align monotone.map_supr_of_continuous_at' Monotone.map_iSup_of_continuousAt'
-
-/-- A monotone function continuous at the infimum of a nonempty set sends this infimum to
-the infimum of the image of this set. -/
-theorem Monotone.map_sInf_of_continuousAt' {f : α → β} {A : Set α} (Cf : ContinuousAt f (sInf A))
-    (Mf : Monotone f) (A_nonemp : A.Nonempty) (A_bdd : BddBelow A := by bddDefault) :
-    f (sInf A) = sInf (f '' A) :=
-  Monotone.map_sSup_of_continuousAt' (α := αᵒᵈ) (β := βᵒᵈ) Cf Mf.dual A_nonemp A_bdd
-#align monotone.map_Inf_of_continuous_at' Monotone.map_sInf_of_continuousAt'
-
-/-- A monotone function continuous at the indexed infimum over a nonempty `Sort` sends this indexed
-infimum to the indexed infimum of the composition. -/
-theorem Monotone.map_iInf_of_continuousAt' {ι : Sort*} [Nonempty ι] {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (iInf g)) (Mf : Monotone f)
-    (bdd : BddBelow (range g) := by bddDefault) : f (⨅ i, g i) = ⨅ i, f (g i) := by
-  rw [iInf, Monotone.map_sInf_of_continuousAt' Cf Mf (range_nonempty g) bdd, ← range_comp, iInf]
-  rfl
-#align monotone.map_infi_of_continuous_at' Monotone.map_iInf_of_continuousAt'
-
-/-- An antitone function continuous at the infimum of a nonempty set sends this infimum to
-the supremum of the image of this set. -/
-theorem Antitone.map_sInf_of_continuousAt' {f : α → β} {A : Set α} (Cf : ContinuousAt f (sInf A))
-    (Af : Antitone f) (A_nonemp : A.Nonempty) (A_bdd : BddBelow A := by bddDefault) :
-    f (sInf A) = sSup (f '' A) :=
-  Monotone.map_sInf_of_continuousAt' (β := βᵒᵈ) Cf Af.dual_right A_nonemp A_bdd
-#align antitone.map_Inf_of_continuous_at' Antitone.map_sInf_of_continuousAt'
-
-/-- An antitone function continuous at the indexed infimum over a nonempty `Sort` sends this indexed
-infimum to the indexed supremum of the composition. -/
-theorem Antitone.map_iInf_of_continuousAt' {ι : Sort*} [Nonempty ι] {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (iInf g)) (Af : Antitone f)
-    (bdd : BddBelow (range g) := by bddDefault) : f (⨅ i, g i) = ⨆ i, f (g i) := by
-  rw [iInf, Antitone.map_sInf_of_continuousAt' Cf Af (range_nonempty g) bdd, ← range_comp, iSup]
-  rfl
-#align antitone.map_infi_of_continuous_at' Antitone.map_iInf_of_continuousAt'
-
-/-- An antitone function continuous at the supremum of a nonempty set sends this supremum to
-the infimum of the image of this set. -/
-theorem Antitone.map_sSup_of_continuousAt' {f : α → β} {A : Set α} (Cf : ContinuousAt f (sSup A))
-    (Af : Antitone f) (A_nonemp : A.Nonempty) (A_bdd : BddAbove A := by bddDefault) :
-    f (sSup A) = sInf (f '' A) :=
-  Monotone.map_sSup_of_continuousAt' (β := βᵒᵈ) Cf Af.dual_right A_nonemp A_bdd
-#align antitone.map_Sup_of_continuous_at' Antitone.map_sSup_of_continuousAt'
-
-/-- An antitone function continuous at the indexed supremum over a nonempty `Sort` sends this
-indexed supremum to the indexed infimum of the composition. -/
-theorem Antitone.map_iSup_of_continuousAt' {ι : Sort*} [Nonempty ι] {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (iSup g)) (Af : Antitone f)
-    (bdd : BddAbove (range g) := by bddDefault) : f (⨆ i, g i) = ⨅ i, f (g i) := by
-  rw [iSup, Antitone.map_sSup_of_continuousAt' Cf Af (range_nonempty g) bdd, ← range_comp, iInf]
-  rfl
-#align antitone.map_supr_of_continuous_at' Antitone.map_iSup_of_continuousAt'
-
-end ConditionallyCompleteLinearOrder
-
-section CompleteLinearOrder
-
-variable [CompleteLinearOrder α] [TopologicalSpace α] [OrderTopology α] [CompleteLinearOrder β]
-  [TopologicalSpace β] [OrderClosedTopology β] [Nonempty γ]
-
-theorem sSup_mem_closure {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
-    {s : Set α} (hs : s.Nonempty) : sSup s ∈ closure s :=
-  (isLUB_sSup s).mem_closure hs
-#align Sup_mem_closure sSup_mem_closure
-
-theorem sInf_mem_closure {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
-    {s : Set α} (hs : s.Nonempty) : sInf s ∈ closure s :=
-  (isGLB_sInf s).mem_closure hs
-#align Inf_mem_closure sInf_mem_closure
-
-theorem IsClosed.sSup_mem {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α]
-    [OrderTopology α] {s : Set α} (hs : s.Nonempty) (hc : IsClosed s) : sSup s ∈ s :=
-  (isLUB_sSup s).mem_of_isClosed hs hc
-#align is_closed.Sup_mem IsClosed.sSup_mem
-
-theorem IsClosed.sInf_mem {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α]
-    [OrderTopology α] {s : Set α} (hs : s.Nonempty) (hc : IsClosed s) : sInf s ∈ s :=
-  (isGLB_sInf s).mem_of_isClosed hs hc
-#align is_closed.Inf_mem IsClosed.sInf_mem
-
-/-- A monotone function `f` sending `bot` to `bot` and continuous at the supremum of a set sends
-this supremum to the supremum of the image of this set. -/
-theorem Monotone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
-    (Mf : Monotone f) (fbot : f ⊥ = ⊥) : f (sSup s) = sSup (f '' s) := by
-  rcases s.eq_empty_or_nonempty with h | h
-  · simp [h, fbot]
-  · exact Mf.map_sSup_of_continuousAt' Cf h
-#align monotone.map_Sup_of_continuous_at Monotone.map_sSup_of_continuousAt
-
-/-- If a monotone function sending `bot` to `bot` is continuous at the indexed supremum over
-a `Sort`, then it sends this indexed supremum to the indexed supremum of the composition. -/
-theorem Monotone.map_iSup_of_continuousAt {ι : Sort*} {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (iSup g)) (Mf : Monotone f) (fbot : f ⊥ = ⊥) :
-    f (⨆ i, g i) = ⨆ i, f (g i) := by
-  rw [iSup, Mf.map_sSup_of_continuousAt Cf fbot, ← range_comp, iSup]; rfl
-#align monotone.map_supr_of_continuous_at Monotone.map_iSup_of_continuousAt
-
-/-- A monotone function `f` sending `top` to `top` and continuous at the infimum of a set sends
-this infimum to the infimum of the image of this set. -/
-theorem Monotone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
-    (Mf : Monotone f) (ftop : f ⊤ = ⊤) : f (sInf s) = sInf (f '' s) :=
-  Monotone.map_sSup_of_continuousAt (α := αᵒᵈ) (β := βᵒᵈ) Cf Mf.dual ftop
-#align monotone.map_Inf_of_continuous_at Monotone.map_sInf_of_continuousAt
-
-/-- If a monotone function sending `top` to `top` is continuous at the indexed infimum over
-a `Sort`, then it sends this indexed infimum to the indexed infimum of the composition. -/
-theorem Monotone.map_iInf_of_continuousAt {ι : Sort*} {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (iInf g)) (Mf : Monotone f) (ftop : f ⊤ = ⊤) : f (iInf g) = iInf (f ∘ g) :=
-  Monotone.map_iSup_of_continuousAt (α := αᵒᵈ) (β := βᵒᵈ) Cf Mf.dual ftop
-#align monotone.map_infi_of_continuous_at Monotone.map_iInf_of_continuousAt
-
-/-- An antitone function `f` sending `bot` to `top` and continuous at the supremum of a set sends
-this supremum to the infimum of the image of this set. -/
-theorem Antitone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
-    (Af : Antitone f) (fbot : f ⊥ = ⊤) : f (sSup s) = sInf (f '' s) :=
-  Monotone.map_sSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (sSup s) from Cf) Af
-    fbot
-#align antitone.map_Sup_of_continuous_at Antitone.map_sSup_of_continuousAt
-
-/-- An antitone function sending `bot` to `top` is continuous at the indexed supremum over
-a `Sort`, then it sends this indexed supremum to the indexed supremum of the composition. -/
-theorem Antitone.map_iSup_of_continuousAt {ι : Sort*} {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (iSup g)) (Af : Antitone f) (fbot : f ⊥ = ⊤) :
-    f (⨆ i, g i) = ⨅ i, f (g i) :=
-  Monotone.map_iSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (iSup g) from Cf) Af
-    fbot
-#align antitone.map_supr_of_continuous_at Antitone.map_iSup_of_continuousAt
-
-/-- An antitone function `f` sending `top` to `bot` and continuous at the infimum of a set sends
-this infimum to the supremum of the image of this set. -/
-theorem Antitone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
-    (Af : Antitone f) (ftop : f ⊤ = ⊥) : f (sInf s) = sSup (f '' s) :=
-  Monotone.map_sInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (sInf s) from Cf) Af
-    ftop
-#align antitone.map_Inf_of_continuous_at Antitone.map_sInf_of_continuousAt
-
-/-- If an antitone function sending `top` to `bot` is continuous at the indexed infimum over
-a `Sort`, then it sends this indexed infimum to the indexed supremum of the composition. -/
-theorem Antitone.map_iInf_of_continuousAt {ι : Sort*} {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (iInf g)) (Af : Antitone f) (ftop : f ⊤ = ⊥) : f (iInf g) = iSup (f ∘ g) :=
-  Monotone.map_iInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (iInf g) from Cf) Af
-    ftop
-#align antitone.map_infi_of_continuous_at Antitone.map_iInf_of_continuousAt
-
-end CompleteLinearOrder
-
-section ConditionallyCompleteLinearOrder
-
-variable [ConditionallyCompleteLinearOrder α] [TopologicalSpace α] [OrderTopology α]
-  [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderClosedTopology β] [Nonempty γ]
-
-theorem csSup_mem_closure {s : Set α} (hs : s.Nonempty) (B : BddAbove s) : sSup s ∈ closure s :=
-  (isLUB_csSup hs B).mem_closure hs
-#align cSup_mem_closure csSup_mem_closure
-
-theorem csInf_mem_closure {s : Set α} (hs : s.Nonempty) (B : BddBelow s) : sInf s ∈ closure s :=
-  (isGLB_csInf hs B).mem_closure hs
-#align cInf_mem_closure csInf_mem_closure
-
-theorem IsClosed.csSup_mem {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddAbove s) :
-    sSup s ∈ s :=
-  (isLUB_csSup hs B).mem_of_isClosed hs hc
-#align is_closed.cSup_mem IsClosed.csSup_mem
-
-theorem IsClosed.csInf_mem {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddBelow s) :
-    sInf s ∈ s :=
-  (isGLB_csInf hs B).mem_of_isClosed hs hc
-#align is_closed.cInf_mem IsClosed.csInf_mem
-
-theorem IsClosed.isLeast_csInf {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddBelow s) :
-    IsLeast s (sInf s) :=
-  ⟨hc.csInf_mem hs B, (isGLB_csInf hs B).1⟩
-
-theorem IsClosed.isGreatest_csSup {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddAbove s) :
-    IsGreatest s (sSup s) :=
-  IsClosed.isLeast_csInf (α := αᵒᵈ) hc hs B
-
-/-- If a monotone function is continuous at the supremum of a nonempty bounded above set `s`,
-then it sends this supremum to the supremum of the image of `s`. -/
-theorem Monotone.map_csSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
-    (Mf : Monotone f) (ne : s.Nonempty) (H : BddAbove s) : f (sSup s) = sSup (f '' s) := by
-  refine' ((isLUB_csSup (ne.image f) (Mf.map_bddAbove H)).unique _).symm
-  refine' (isLUB_csSup ne H).isLUB_of_tendsto (fun x _ y _ xy => Mf xy) ne _
-  exact Cf.mono_left inf_le_left
-#align monotone.map_cSup_of_continuous_at Monotone.map_csSup_of_continuousAt
-
-/-- If a monotone function is continuous at the indexed supremum of a bounded function on
-a nonempty `Sort`, then it sends this supremum to the supremum of the composition. -/
-theorem Monotone.map_ciSup_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
-    (Mf : Monotone f) (H : BddAbove (range g)) : f (⨆ i, g i) = ⨆ i, f (g i) := by
-  rw [iSup, Mf.map_csSup_of_continuousAt Cf (range_nonempty _) H, ← range_comp, iSup]; rfl
-#align monotone.map_csupr_of_continuous_at Monotone.map_ciSup_of_continuousAt
-
-/-- If a monotone function is continuous at the infimum of a nonempty bounded below set `s`,
-then it sends this infimum to the infimum of the image of `s`. -/
-theorem Monotone.map_csInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
-    (Mf : Monotone f) (ne : s.Nonempty) (H : BddBelow s) : f (sInf s) = sInf (f '' s) :=
-  Monotone.map_csSup_of_continuousAt (α := αᵒᵈ) (β := βᵒᵈ) Cf Mf.dual ne H
-#align monotone.map_cInf_of_continuous_at Monotone.map_csInf_of_continuousAt
-
-/-- A continuous monotone function sends indexed infimum to indexed infimum in conditionally
-complete linear order, under a boundedness assumption. -/
-theorem Monotone.map_ciInf_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
-    (Mf : Monotone f) (H : BddBelow (range g)) : f (⨅ i, g i) = ⨅ i, f (g i) :=
-  Monotone.map_ciSup_of_continuousAt (α := αᵒᵈ) (β := βᵒᵈ) Cf Mf.dual H
-#align monotone.map_cinfi_of_continuous_at Monotone.map_ciInf_of_continuousAt
-
-/-- If an antitone function is continuous at the supremum of a nonempty bounded above set `s`,
-then it sends this supremum to the infimum of the image of `s`. -/
-theorem Antitone.map_csSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
-    (Af : Antitone f) (ne : s.Nonempty) (H : BddAbove s) : f (sSup s) = sInf (f '' s) :=
-  Monotone.map_csSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (sSup s) from Cf) Af
-    ne H
-#align antitone.map_cSup_of_continuous_at Antitone.map_csSup_of_continuousAt
-
-/-- If an antitone function is continuous at the indexed supremum of a bounded function on
-a nonempty `Sort`, then it sends this supremum to the infimum of the composition. -/
-theorem Antitone.map_ciSup_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
-    (Af : Antitone f) (H : BddAbove (range g)) : f (⨆ i, g i) = ⨅ i, f (g i) :=
-  Monotone.map_ciSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (⨆ i, g i) from Cf)
-    Af H
-#align antitone.map_csupr_of_continuous_at Antitone.map_ciSup_of_continuousAt
-
-/-- If an antitone function is continuous at the infimum of a nonempty bounded below set `s`,
-then it sends this infimum to the supremum of the image of `s`. -/
-theorem Antitone.map_csInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
-    (Af : Antitone f) (ne : s.Nonempty) (H : BddBelow s) : f (sInf s) = sSup (f '' s) :=
-  Monotone.map_csInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (sInf s) from Cf) Af
-    ne H
-#align antitone.map_cInf_of_continuous_at Antitone.map_csInf_of_continuousAt
-
-/-- A continuous antitone function sends indexed infimum to indexed supremum in conditionally
-complete linear order, under a boundedness assumption. -/
-theorem Antitone.map_ciInf_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
-    (Af : Antitone f) (H : BddBelow (range g)) : f (⨅ i, g i) = ⨆ i, f (g i) :=
-  Monotone.map_ciInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (⨅ i, g i) from Cf)
-    Af H
-#align antitone.map_cinfi_of_continuous_at Antitone.map_ciInf_of_continuousAt
-
-/-- A monotone map has a limit to the left of any point `x`, equal to `sSup (f '' (Iio x))`. -/
-theorem Monotone.tendsto_nhdsWithin_Iio {α β : Type*} [LinearOrder α] [TopologicalSpace α]
-    [OrderTopology α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderTopology β]
-    {f : α → β} (Mf : Monotone f) (x : α) : Tendsto f (𝓝[<] x) (𝓝 (sSup (f '' Iio x))) := by
-  rcases eq_empty_or_nonempty (Iio x) with (h | h); · simp [h]
-  refine' tendsto_order.2 ⟨fun l hl => _, fun m hm => _⟩
-  · obtain ⟨z, zx, lz⟩ : ∃ a : α, a < x ∧ l < f a := by
-      simpa only [mem_image, exists_prop, exists_exists_and_eq_and] using
-        exists_lt_of_lt_csSup (h.image _) hl
-    exact mem_of_superset (Ioo_mem_nhdsWithin_Iio' zx) fun y hy => lz.trans_le (Mf hy.1.le)
-  · refine mem_of_superset self_mem_nhdsWithin fun _ hy => lt_of_le_of_lt ?_ hm
-    exact le_csSup (Mf.map_bddAbove bddAbove_Iio) (mem_image_of_mem _ hy)
-#align monotone.tendsto_nhds_within_Iio Monotone.tendsto_nhdsWithin_Iio
-
-/-- A monotone map has a limit to the right of any point `x`, equal to `sInf (f '' (Ioi x))`. -/
-theorem Monotone.tendsto_nhdsWithin_Ioi {α β : Type*} [LinearOrder α] [TopologicalSpace α]
-    [OrderTopology α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderTopology β]
-    {f : α → β} (Mf : Monotone f) (x : α) : Tendsto f (𝓝[>] x) (𝓝 (sInf (f '' Ioi x))) :=
-  Monotone.tendsto_nhdsWithin_Iio (α := αᵒᵈ) (β := βᵒᵈ) Mf.dual x
-#align monotone.tendsto_nhds_within_Ioi Monotone.tendsto_nhdsWithin_Ioi
-
-end ConditionallyCompleteLinearOrder
-
 end OrderTopology

Move files from Topology.Algebra.Order to Topology.Order when they do not contain any algebra. Also move Topology.LocalExtr to Topology.Order.LocalExtr.

According to git, the moves are:

• Mathlib/Topology/{Algebra => }/Order/ExtendFrom.lean
• Mathlib/Topology/{Algebra => }/Order/ExtrClosure.lean
• Mathlib/Topology/{Algebra => }/Order/Filter.lean
• Mathlib/Topology/{Algebra => }/Order/IntermediateValue.lean
• Mathlib/Topology/{Algebra => }/Order/LeftRight.lean
• Mathlib/Topology/{Algebra => }/Order/LeftRightLim.lean
• Mathlib/Topology/{Algebra => }/Order/MonotoneContinuity.lean
• Mathlib/Topology/{Algebra => }/Order/MonotoneConvergence.lean
• Mathlib/Topology/{Algebra => }/Order/ProjIcc.lean
• Mathlib/Topology/{Algebra => }/Order/T5.lean
• Mathlib/Topology/{ => Order}/LocalExtr.lean

@@ -8,8 +8,8 @@ import Mathlib.Data.Set.Pointwise.Basic
 import Mathlib.Order.Filter.Interval
 import Mathlib.Tactic.TFAE
 import Mathlib.Tactic.NormNum
+import Mathlib.Topology.Order.LeftRight
 import Mathlib.Topology.Order.OrderClosed
-import Mathlib.Topology.Algebra.Order.LeftRight
 
 #align_import topology.order.basic from "leanprover-community/mathlib"@"3efd324a3a31eaa40c9d5bfc669c4fafee5f9423"
 

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -1090,7 +1090,6 @@ end LinearOrder
 section LinearOrderedAddCommGroup
 
 variable [TopologicalSpace α] [LinearOrderedAddCommGroup α] [OrderTopology α]
-
 variable {l : Filter β} {f g : β → α}
 
 theorem nhds_eq_iInf_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r } := by

The main addition is IsTopologicalBasis.inf (see https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/Inf.20of.20a.20pair.20of.20topologies/near/419989448), and I also reordered things to be in the more typical order (deducing the Pi version from the iInf version rather than the converse).

Also a few extra golfs and variations.

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com>

@@ -1102,7 +1102,7 @@ theorem nhds_eq_iInf_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| <
 
 theorem orderTopology_of_nhds_abs {α : Type*} [TopologicalSpace α] [LinearOrderedAddCommGroup α]
     (h_nhds : ∀ a : α, 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r }) : OrderTopology α := by
-  refine' ⟨eq_of_nhds_eq_nhds fun a => _⟩
+  refine' ⟨TopologicalSpace.ext_nhds fun a => _⟩
   rw [h_nhds]
   letI := Preorder.topology α; letI : OrderTopology α := ⟨rfl⟩
   exact (nhds_eq_iInf_abs_sub a).symm

Currently doesn't simplify since interior_Icc goes the other way.

We were using it in PrimeNumberTheoremAnd for things like "point does not lie on boundary of rectangle".

Co-authored-by: L Lllvvuu <git@llllvvuu.dev>

@@ -1542,16 +1542,29 @@ theorem interior_Icc [NoMinOrder α] [NoMaxOrder α] {a b : α} : interior (Icc
   rw [← Ici_inter_Iic, interior_inter, interior_Ici, interior_Iic, Ioi_inter_Iio]
 #align interior_Icc interior_Icc
 
+@[simp]
+theorem Icc_mem_nhds_iff [NoMinOrder α] [NoMaxOrder α] {a b x : α} :
+    Icc a b ∈ 𝓝 x ↔ x ∈ Ioo a b := by
+  rw [← interior_Icc, mem_interior_iff_mem_nhds]
+
 @[simp]
 theorem interior_Ico [NoMinOrder α] {a b : α} : interior (Ico a b) = Ioo a b := by
   rw [← Ici_inter_Iio, interior_inter, interior_Ici, interior_Iio, Ioi_inter_Iio]
 #align interior_Ico interior_Ico
 
+@[simp]
+theorem Ico_mem_nhds_iff [NoMinOrder α] {a b x : α} : Ico a b ∈ 𝓝 x ↔ x ∈ Ioo a b := by
+  rw [← interior_Ico, mem_interior_iff_mem_nhds]
+
 @[simp]
 theorem interior_Ioc [NoMaxOrder α] {a b : α} : interior (Ioc a b) = Ioo a b := by
   rw [← Ioi_inter_Iic, interior_inter, interior_Ioi, interior_Iic, Ioi_inter_Iio]
 #align interior_Ioc interior_Ioc
 
+@[simp]
+theorem Ioc_mem_nhds_iff [NoMaxOrder α] {a b x : α} : Ioc a b ∈ 𝓝 x ↔ x ∈ Ioo a b := by
+  rw [← interior_Ioc, mem_interior_iff_mem_nhds]
+
 theorem closure_interior_Icc {a b : α} (h : a ≠ b) : closure (interior (Icc a b)) = Icc a b :=
   (closure_minimal interior_subset isClosed_Icc).antisymm <|
     calc

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

• "new lemma"
• "added lemma"

@@ -200,7 +200,7 @@ instance tendstoIccClassNhdsPi {ι : Type*} {α : ι → Type*} [∀ i, Preorder
   exact fun p hp g hg => hp ⟨hg.1 _, hg.2 _⟩
 #align tendsto_Icc_class_nhds_pi tendstoIccClassNhdsPi
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 theorem induced_topology_le_preorder [Preorder α] [Preorder β] [TopologicalSpace β]
     [OrderTopology β] {f : α → β} (hf : ∀ {x y}, f x < f y ↔ x < y) :
     induced f ‹TopologicalSpace β› ≤ Preorder.topology α := by
@@ -210,7 +210,7 @@ theorem induced_topology_le_preorder [Preorder α] [Preorder β] [TopologicalSpa
   refine inf_le_inf (le_iInf₂ fun a ha => ?_) (le_iInf₂ fun a ha => ?_)
   exacts [iInf₂_le (f a) ha, iInf₂_le (f a) ha]
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 theorem induced_topology_eq_preorder [Preorder α] [Preorder β] [TopologicalSpace β]
     [OrderTopology β] {f : α → β} (hf : ∀ {x y}, f x < f y ↔ x < y)
     (H₁ : ∀ {a b x}, b < f a → ¬(b < f x) → ∃ y, y < a ∧ b ≤ f y)
@@ -554,7 +554,7 @@ theorem SecondCountableTopology.of_separableSpace_orderTopology [DenselyOrdered
 
 variable {α}
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 /-- The set of points which are isolated on the right is countable when the space is
 second-countable. -/
 theorem countable_setOf_covBy_right [SecondCountableTopology α] :

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

@@ -60,7 +60,7 @@ universe u v w
 
 variable {α : Type u} {β : Type v} {γ : Type w}
 
--- Porting note: todo: define `Preorder.topology` before `OrderTopology` and reuse the def
+-- Porting note (#11215): TODO: define `Preorder.topology` before `OrderTopology` and reuse the def
 /-- The order topology on an ordered type is the topology generated by open intervals. We register
 it on a preorder, but it is mostly interesting in linear orders, where it is also order-closed.
 We define it as a mixin. If you want to introduce the order topology on a preorder, use
@@ -1778,14 +1778,16 @@ theorem tendsto_comp_coe_Ioo_atBot (h : a < b) :
   rw [← map_coe_Ioo_atBot h, tendsto_map'_iff]; rfl
 #align tendsto_comp_coe_Ioo_at_bot tendsto_comp_coe_Ioo_atBot
 
--- Porting note: todo: `simpNF` claims that `simp` can't use this lemma to simplify LHS but it can
+-- Porting note (#11215): TODO: `simpNF` claims that `simp` can't use
+-- this lemma to simplify LHS but it can
 @[simp, nolint simpNF]
 theorem tendsto_comp_coe_Ioi_atBot :
     Tendsto (fun x : Ioi a => f x) atBot l ↔ Tendsto f (𝓝[>] a) l := by
   rw [← map_coe_Ioi_atBot, tendsto_map'_iff]; rfl
 #align tendsto_comp_coe_Ioi_at_bot tendsto_comp_coe_Ioi_atBot
 
--- Porting note: todo: `simpNF` claims that `simp` can't use this lemma to simplify LHS but it can
+-- Porting note (#11215): TODO: `simpNF` claims that `simp` can't use
+-- this lemma to simplify LHS but it can
 @[simp, nolint simpNF]
 theorem tendsto_comp_coe_Iio_atTop :
     Tendsto (fun x : Iio a => f x) atTop l ↔ Tendsto f (𝓝[<] a) l := by

Those lemmas have historically been very annoying to use in rw since all their arguments were implicit. One too many people complained about it on Zulip, so I'm changing them.

Downstream code broken by this change can fix it by adding appropriately many _s.

Also marks CauSeq.ext @[ext].

Order.BoundedOrder

• top_sup_eq
• sup_top_eq
• bot_sup_eq
• sup_bot_eq
• top_inf_eq
• inf_top_eq
• bot_inf_eq
• inf_bot_eq

Order.Lattice

• sup_idem
• sup_comm
• sup_assoc
• sup_left_idem
• sup_right_idem
• inf_idem
• inf_comm
• inf_assoc
• inf_left_idem
• inf_right_idem
• sup_inf_left
• sup_inf_right
• inf_sup_left
• inf_sup_right

Order.MinMax

• max_min_distrib_left
• max_min_distrib_right
• min_max_distrib_left
• min_max_distrib_right

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

@@ -1095,7 +1095,7 @@ variable {l : Filter β} {f g : β → α}
 
 theorem nhds_eq_iInf_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r } := by
   simp only [nhds_eq_order, abs_lt, setOf_and, ← inf_principal, iInf_inf_eq]
-  refine (congr_arg₂ _ ?_ ?_).trans inf_comm
+  refine (congr_arg₂ _ ?_ ?_).trans (inf_comm ..)
   · refine (Equiv.subLeft a).iInf_congr fun x => ?_; simp [Ioi]
   · refine (Equiv.subRight a).iInf_congr fun x => ?_; simp [Iio]
 #align nhds_eq_infi_abs_sub nhds_eq_iInf_abs_sub

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -60,7 +60,7 @@ universe u v w
 
 variable {α : Type u} {β : Type v} {γ : Type w}
 
--- porting note: todo: define `Preorder.topology` before `OrderTopology` and reuse the def
+-- Porting note: todo: define `Preorder.topology` before `OrderTopology` and reuse the def
 /-- The order topology on an ordered type is the topology generated by open intervals. We register
 it on a preorder, but it is mostly interesting in linear orders, where it is also order-closed.
 We define it as a mixin. If you want to introduce the order topology on a preorder, use
@@ -200,7 +200,7 @@ instance tendstoIccClassNhdsPi {ι : Type*} {α : ι → Type*} [∀ i, Preorder
   exact fun p hp g hg => hp ⟨hg.1 _, hg.2 _⟩
 #align tendsto_Icc_class_nhds_pi tendstoIccClassNhdsPi
 
--- porting note: new lemma
+-- Porting note: new lemma
 theorem induced_topology_le_preorder [Preorder α] [Preorder β] [TopologicalSpace β]
     [OrderTopology β] {f : α → β} (hf : ∀ {x y}, f x < f y ↔ x < y) :
     induced f ‹TopologicalSpace β› ≤ Preorder.topology α := by
@@ -210,7 +210,7 @@ theorem induced_topology_le_preorder [Preorder α] [Preorder β] [TopologicalSpa
   refine inf_le_inf (le_iInf₂ fun a ha => ?_) (le_iInf₂ fun a ha => ?_)
   exacts [iInf₂_le (f a) ha, iInf₂_le (f a) ha]
 
--- porting note: new lemma
+-- Porting note: new lemma
 theorem induced_topology_eq_preorder [Preorder α] [Preorder β] [TopologicalSpace β]
     [OrderTopology β] {f : α → β} (hf : ∀ {x y}, f x < f y ↔ x < y)
     (H₁ : ∀ {a b x}, b < f a → ¬(b < f x) → ∃ y, y < a ∧ b ≤ f y)
@@ -554,7 +554,7 @@ theorem SecondCountableTopology.of_separableSpace_orderTopology [DenselyOrdered
 
 variable {α}
 
--- porting note: new lemma
+-- Porting note: new lemma
 /-- The set of points which are isolated on the right is countable when the space is
 second-countable. -/
 theorem countable_setOf_covBy_right [SecondCountableTopology α] :
@@ -1778,14 +1778,14 @@ theorem tendsto_comp_coe_Ioo_atBot (h : a < b) :
   rw [← map_coe_Ioo_atBot h, tendsto_map'_iff]; rfl
 #align tendsto_comp_coe_Ioo_at_bot tendsto_comp_coe_Ioo_atBot
 
--- porting note: todo: `simpNF` claims that `simp` can't use this lemma to simplify LHS but it can
+-- Porting note: todo: `simpNF` claims that `simp` can't use this lemma to simplify LHS but it can
 @[simp, nolint simpNF]
 theorem tendsto_comp_coe_Ioi_atBot :
     Tendsto (fun x : Ioi a => f x) atBot l ↔ Tendsto f (𝓝[>] a) l := by
   rw [← map_coe_Ioi_atBot, tendsto_map'_iff]; rfl
 #align tendsto_comp_coe_Ioi_at_bot tendsto_comp_coe_Ioi_atBot
 
--- porting note: todo: `simpNF` claims that `simp` can't use this lemma to simplify LHS but it can
+-- Porting note: todo: `simpNF` claims that `simp` can't use this lemma to simplify LHS but it can
 @[simp, nolint simpNF]
 theorem tendsto_comp_coe_Iio_atTop :
     Tendsto (fun x : Iio a => f x) atTop l ↔ Tendsto f (𝓝[<] a) l := by

Generalize to a Preorder, add an Iff version.

@@ -804,46 +804,6 @@ theorem pi_Ioo_mem_nhds' (ha : ∀ i, a' i < x' i) (hb : ∀ i, x' i < b' i) : I
 
 end Pi
 
-theorem disjoint_nhds_atTop [NoMaxOrder α] (x : α) : Disjoint (𝓝 x) atTop := by
-  rcases exists_gt x with ⟨y, hy : x < y⟩
-  refine' disjoint_of_disjoint_of_mem _ (Iio_mem_nhds hy) (mem_atTop y)
-  exact disjoint_left.mpr fun z => not_le.2
-#align disjoint_nhds_at_top disjoint_nhds_atTop
-
-@[simp]
-theorem inf_nhds_atTop [NoMaxOrder α] (x : α) : 𝓝 x ⊓ atTop = ⊥ :=
-  disjoint_iff.1 (disjoint_nhds_atTop x)
-#align inf_nhds_at_top inf_nhds_atTop
-
-theorem disjoint_nhds_atBot [NoMinOrder α] (x : α) : Disjoint (𝓝 x) atBot :=
-  disjoint_nhds_atTop (α := αᵒᵈ) x
-#align disjoint_nhds_at_bot disjoint_nhds_atBot
-
-@[simp]
-theorem inf_nhds_atBot [NoMinOrder α] (x : α) : 𝓝 x ⊓ atBot = ⊥ :=
-  inf_nhds_atTop (α := αᵒᵈ) x
-#align inf_nhds_at_bot inf_nhds_atBot
-
-theorem not_tendsto_nhds_of_tendsto_atTop [NoMaxOrder α] {F : Filter β} [NeBot F] {f : β → α}
-    (hf : Tendsto f F atTop) (x : α) : ¬Tendsto f F (𝓝 x) :=
-  hf.not_tendsto (disjoint_nhds_atTop x).symm
-#align not_tendsto_nhds_of_tendsto_at_top not_tendsto_nhds_of_tendsto_atTop
-
-theorem not_tendsto_atTop_of_tendsto_nhds [NoMaxOrder α] {F : Filter β} [NeBot F] {f : β → α}
-    {x : α} (hf : Tendsto f F (𝓝 x)) : ¬Tendsto f F atTop :=
-  hf.not_tendsto (disjoint_nhds_atTop x)
-#align not_tendsto_at_top_of_tendsto_nhds not_tendsto_atTop_of_tendsto_nhds
-
-theorem not_tendsto_nhds_of_tendsto_atBot [NoMinOrder α] {F : Filter β} [NeBot F] {f : β → α}
-    (hf : Tendsto f F atBot) (x : α) : ¬Tendsto f F (𝓝 x) :=
-  hf.not_tendsto (disjoint_nhds_atBot x).symm
-#align not_tendsto_nhds_of_tendsto_at_bot not_tendsto_nhds_of_tendsto_atBot
-
-theorem not_tendsto_atBot_of_tendsto_nhds [NoMinOrder α] {F : Filter β} [NeBot F] {f : β → α}
-    {x : α} (hf : Tendsto f F (𝓝 x)) : ¬Tendsto f F atBot :=
-  hf.not_tendsto (disjoint_nhds_atBot x)
-#align not_tendsto_at_bot_of_tendsto_nhds not_tendsto_atBot_of_tendsto_nhds
-
 /-!
 ### Neighborhoods to the left and to the right on an `OrderTopology`
 

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>

@@ -564,16 +564,16 @@ theorem countable_setOf_covBy_right [SecondCountableTopology α] :
   have : ∀ x ∈ s, ∃ y, x ⋖ y := fun x => id
   choose! y hy using this
   have Hy : ∀ x z, x ∈ s → z < y x → z ≤ x := fun x z hx => (hy x hx).le_of_lt
-  suffices H : ∀ a : Set α, IsOpen a → Set.Countable { x | x ∈ s ∧ x ∈ a ∧ y x ∉ a }
-  · have : s ⊆ ⋃ a ∈ countableBasis α, { x | x ∈ s ∧ x ∈ a ∧ y x ∉ a } := fun x hx => by
+  suffices H : ∀ a : Set α, IsOpen a → Set.Countable { x | x ∈ s ∧ x ∈ a ∧ y x ∉ a } by
+    have : s ⊆ ⋃ a ∈ countableBasis α, { x | x ∈ s ∧ x ∈ a ∧ y x ∉ a } := fun x hx => by
       rcases (isBasis_countableBasis α).exists_mem_of_ne (hy x hx).ne with ⟨a, ab, xa, ya⟩
       exact mem_iUnion₂.2 ⟨a, ab, hx, xa, ya⟩
     refine Set.Countable.mono this ?_
     refine' Countable.biUnion (countable_countableBasis α) fun a ha => H _ _
     exact isOpen_of_mem_countableBasis ha
   intro a ha
-  suffices H : Set.Countable { x | (x ∈ s ∧ x ∈ a ∧ y x ∉ a) ∧ ¬IsBot x }
-  · exact H.of_diff (subsingleton_isBot α).countable
+  suffices H : Set.Countable { x | (x ∈ s ∧ x ∈ a ∧ y x ∉ a) ∧ ¬IsBot x } from
+    H.of_diff (subsingleton_isBot α).countable
   simp only [and_assoc]
   let t := { x | x ∈ s ∧ x ∈ a ∧ y x ∉ a ∧ ¬IsBot x }
   have : ∀ x ∈ t, ∃ z < x, Ioc z x ⊆ a := by
@@ -592,8 +592,8 @@ theorem countable_setOf_covBy_right [SecondCountableTopology α] :
       by_contra! H
       exact lt_irrefl _ ((Hy _ _ x't.1 H).trans_lt h')
   refine' this.countable_of_isOpen (fun x hx => _) fun x hx => ⟨x, hz x hx, le_rfl⟩
-  suffices H : Ioc (z x) x = Ioo (z x) (y x)
-  · rw [H]
+  suffices H : Ioc (z x) x = Ioo (z x) (y x) by
+    rw [H]
     exact isOpen_Ioo
   exact Subset.antisymm (Ioc_subset_Ioo_right (hy x hx.1).lt) fun u hu => ⟨hu.1, Hy _ _ hx.1 hu.2⟩
 

They were deprecated since the file was ported in #2052

@@ -2178,24 +2178,4 @@ theorem Monotone.tendsto_nhdsWithin_Ioi {α β : Type*} [LinearOrder α] [Topolo
 
 end ConditionallyCompleteLinearOrder
 
-section NhdsWithPos
-
-section LinearOrderedAddCommGroup
-
-variable [LinearOrder α] [Zero α] [TopologicalSpace α] [OrderTopology α]
-
-@[deprecated Ioo_mem_nhdsWithin_Ioi']
-theorem eventually_nhdsWithin_pos_mem_Ioo {ε : α} (h : 0 < ε) : ∀ᶠ x in 𝓝[>] 0, x ∈ Ioo 0 ε :=
-  Ioo_mem_nhdsWithin_Ioi' h
-#align eventually_nhds_within_pos_mem_Ioo eventually_nhdsWithin_pos_mem_Ioo
-
-@[deprecated Ioc_mem_nhdsWithin_Ioi']
-theorem eventually_nhdsWithin_pos_mem_Ioc {ε : α} (h : 0 < ε) : ∀ᶠ x in 𝓝[>] 0, x ∈ Ioc 0 ε :=
-  Ioc_mem_nhdsWithin_Ioi' h
-#align eventually_nhds_within_pos_mem_Ioc eventually_nhdsWithin_pos_mem_Ioc
-
-end LinearOrderedAddCommGroup
-
-end NhdsWithPos
-
 end OrderTopology

• golf atBot_le_nhds_bot and atTop_le_nhds_top;
• deprecate them;
• use tendsto_atTop_iInf instead in CondCdf.

@@ -530,21 +530,15 @@ theorem Dense.topology_eq_generateFrom [DenselyOrdered α] {s : Set α} (hs : De
       let _ := generateFrom (Ioi '' s ∪ Iio '' s)
       exact isOpen_iUnion fun x ↦ isOpen_iUnion fun h ↦ .basic _ <| .inr <| mem_image_of_mem _ h.1
 
+@[deprecated OrderBot.atBot_eq] -- 2024-02-14
 theorem atBot_le_nhds_bot [OrderBot α] : (atBot : Filter α) ≤ 𝓝 ⊥ := by
-  cases subsingleton_or_nontrivial α
-  · simp only [nhds_discrete, le_pure_iff, mem_atBot_sets, mem_singleton_iff,
-      eq_iff_true_of_subsingleton, imp_true_iff, exists_const]
-  have h : atBot.HasBasis (fun _ : α => True) Iic := @atBot_basis α _ _
-  have h_nhds : (𝓝 ⊥).HasBasis (fun a : α => ⊥ < a) fun a => Iio a := @nhds_bot_basis α _ _ _ _ _
-  intro s
-  rw [h.mem_iff, h_nhds.mem_iff]
-  rintro ⟨a, ha_bot_lt, h_Iio_a_subset_s⟩
-  refine' ⟨⊥, trivial, _root_.trans _ h_Iio_a_subset_s⟩
-  simpa only [Iic_bot, singleton_subset_iff, mem_Iio]
+  rw [OrderBot.atBot_eq]
+  apply pure_le_nhds
 #align at_bot_le_nhds_bot atBot_le_nhds_bot
 
+@[deprecated OrderTop.atTop_eq] -- 2024-02-14
 theorem atTop_le_nhds_top [OrderTop α] : (atTop : Filter α) ≤ 𝓝 ⊤ :=
-  @atBot_le_nhds_bot αᵒᵈ _ _ _ _
+  set_option linter.deprecated false in @atBot_le_nhds_bot αᵒᵈ _ _ _
 #align at_top_le_nhds_top atTop_le_nhds_top
 
 variable (α)

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

@@ -530,6 +530,23 @@ theorem Dense.topology_eq_generateFrom [DenselyOrdered α] {s : Set α} (hs : De
       let _ := generateFrom (Ioi '' s ∪ Iio '' s)
       exact isOpen_iUnion fun x ↦ isOpen_iUnion fun h ↦ .basic _ <| .inr <| mem_image_of_mem _ h.1
 
+theorem atBot_le_nhds_bot [OrderBot α] : (atBot : Filter α) ≤ 𝓝 ⊥ := by
+  cases subsingleton_or_nontrivial α
+  · simp only [nhds_discrete, le_pure_iff, mem_atBot_sets, mem_singleton_iff,
+      eq_iff_true_of_subsingleton, imp_true_iff, exists_const]
+  have h : atBot.HasBasis (fun _ : α => True) Iic := @atBot_basis α _ _
+  have h_nhds : (𝓝 ⊥).HasBasis (fun a : α => ⊥ < a) fun a => Iio a := @nhds_bot_basis α _ _ _ _ _
+  intro s
+  rw [h.mem_iff, h_nhds.mem_iff]
+  rintro ⟨a, ha_bot_lt, h_Iio_a_subset_s⟩
+  refine' ⟨⊥, trivial, _root_.trans _ h_Iio_a_subset_s⟩
+  simpa only [Iic_bot, singleton_subset_iff, mem_Iio]
+#align at_bot_le_nhds_bot atBot_le_nhds_bot
+
+theorem atTop_le_nhds_top [OrderTop α] : (atTop : Filter α) ≤ 𝓝 ⊤ :=
+  @atBot_le_nhds_bot αᵒᵈ _ _ _ _
+#align at_top_le_nhds_top atTop_le_nhds_top
+
 variable (α)
 
 /-- Let `α` be a densely ordered linear order with order topology. If `α` is a separable space, then

@@ -8,7 +8,7 @@ import Mathlib.Data.Set.Pointwise.Basic
 import Mathlib.Order.Filter.Interval
 import Mathlib.Tactic.TFAE
 import Mathlib.Tactic.NormNum
-import Mathlib.Topology.Separation
+import Mathlib.Topology.Order.OrderClosed
 import Mathlib.Topology.Algebra.Order.LeftRight
 
 #align_import topology.order.basic from "leanprover-community/mathlib"@"3efd324a3a31eaa40c9d5bfc669c4fafee5f9423"
@@ -26,10 +26,6 @@ we introduce a class `OrderTopology α` (which is a `Prop`, also known as a mixi
 the type `α` having already a topological space structure and a preorder structure, the topological
 structure is equal to the order topology.
 
-We also introduce another (mixin) class `OrderClosedTopology α` saying that the set of points
-`(x, y)` with `x ≤ y` is closed in the product space. This is automatically satisfied on a linear
-order with the order topology.
-
 We prove many basic properties of such topologies.
 
 ## Main statements
@@ -38,32 +34,9 @@ This file contains the proofs of the following facts. For exact requirements
 (`OrderClosedTopology` vs `OrderTopology`, `Preorder` vs `PartialOrder` vs `LinearOrder` etc)
 see their statements.
 
-### Open / closed sets
-
-* `isOpen_lt` : if `f` and `g` are continuous functions, then `{x | f x < g x}` is open;
-* `isOpen_Iio`, `isOpen_Ioi`, `isOpen_Ioo` : open intervals are open;
-* `isClosed_le` : if `f` and `g` are continuous functions, then `{x | f x ≤ g x}` is closed;
-* `isClosed_Iic`, `isClosed_Ici`, `isClosed_Icc` : closed intervals are closed;
-* `frontier_le_subset_eq`, `frontier_lt_subset_eq` : frontiers of both `{x | f x ≤ g x}`
-  and `{x | f x < g x}` are included by `{x | f x = g x}`;
 * `exists_Ioc_subset_of_mem_nhds`, `exists_Ico_subset_of_mem_nhds` : if `x < y`, then any
   neighborhood of `x` includes an interval `[x, z)` for some `z ∈ (x, y]`, and any neighborhood
   of `y` includes an interval `(z, y]` for some `z ∈ [x, y)`.
-
-### Convergence and inequalities
-
-* `le_of_tendsto_of_tendsto` : if `f` converges to `a`, `g` converges to `b`, and eventually
-  `f x ≤ g x`, then `a ≤ b`
-* `le_of_tendsto`, `ge_of_tendsto` : if `f` converges to `a` and eventually `f x ≤ b`
-  (resp., `b ≤ f x`), then `a ≤ b` (resp., `b ≤ a`); we also provide primed versions
-  that assume the inequalities to hold for all `x`.
-
-### Min, max, `sSup` and `sInf`
-
-* `Continuous.min`, `Continuous.max`: pointwise `min`/`max` of two continuous functions is
-  continuous.
-* `Tendsto.min`, `Tendsto.max` : if `f` tends to `a` and `g` tends to `b`, then their pointwise
-  `min`/`max` tend to `min a b` and `max a b`, respectively.
 * `tendsto_of_tendsto_of_tendsto_of_le_of_le` : theorem known as squeeze theorem,
   sandwich theorem, theorem of Carabinieri, and two policemen (and a drunk) theorem; if `g` and `h`
   both converge to `a`, and eventually `g x ≤ f x ≤ h x`, then `f` converges to `a`.
@@ -87,761 +60,6 @@ universe u v w
 
 variable {α : Type u} {β : Type v} {γ : Type w}
 
-/-- If `α` is a topological space and a preorder, `ClosedIicTopology α` means that `Iic a` is
-closed for all `a : α`. -/
-class ClosedIicTopology (α : Type*) [TopologicalSpace α] [Preorder α] : Prop where
-  /-- For any `a`, the set `{b | b ≤ a}` is closed. -/
-  isClosed_le' (a : α) : IsClosed { b : α | b ≤ a }
-
-export ClosedIicTopology (isClosed_le')
-#align is_closed_le' ClosedIicTopology.isClosed_le'
-
-/-- If `α` is a topological space and a preorder, `ClosedIciTopology α` means that `Ici a` is
-closed for all `a : α`. -/
-class ClosedIciTopology (α : Type*) [TopologicalSpace α] [Preorder α] : Prop where
-  /-- For any `a`, the set `{b | a ≤ b}` is closed. -/
-  isClosed_ge' (a : α) : IsClosed { b : α | a ≤ b }
-
-export ClosedIciTopology (isClosed_ge')
-#align is_closed_ge' ClosedIciTopology.isClosed_ge'
-
-/-- A topology on a set which is both a topological space and a preorder is _order-closed_ if the
-set of points `(x, y)` with `x ≤ y` is closed in the product space. We introduce this as a mixin.
-This property is satisfied for the order topology on a linear order, but it can be satisfied more
-generally, and suffices to derive many interesting properties relating order and topology. -/
-class OrderClosedTopology (α : Type*) [TopologicalSpace α] [Preorder α] : Prop where
-  /-- The set `{ (x, y) | x ≤ y }` is a closed set. -/
-  isClosed_le' : IsClosed { p : α × α | p.1 ≤ p.2 }
-#align order_closed_topology OrderClosedTopology
-
-instance [TopologicalSpace α] [h : FirstCountableTopology α] : FirstCountableTopology αᵒᵈ := h
-instance [TopologicalSpace α] [h : SecondCountableTopology α] : SecondCountableTopology αᵒᵈ := h
-
-theorem Dense.orderDual [TopologicalSpace α] {s : Set α} (hs : Dense s) :
-    Dense (OrderDual.ofDual ⁻¹' s) :=
-  hs
-#align dense.order_dual Dense.orderDual
-
-section ClosedIicTopology
-
-variable [TopologicalSpace α] [Preorder α] [t : ClosedIicTopology α]
-
-instance : ClosedIciTopology αᵒᵈ where
-  isClosed_ge' a := isClosed_le' (α := α) a
-
-theorem isClosed_Iic {a : α} : IsClosed (Iic a) :=
-  isClosed_le' a
-#align is_closed_Iic isClosed_Iic
-
-@[simp]
-theorem closure_Iic (a : α) : closure (Iic a) = Iic a :=
-  isClosed_Iic.closure_eq
-#align closure_Iic closure_Iic
-
-theorem le_of_tendsto_of_frequently {f : β → α} {a b : α} {x : Filter β} (lim : Tendsto f x (𝓝 a))
-    (h : ∃ᶠ c in x, f c ≤ b) : a ≤ b :=
-  (isClosed_le' b).mem_of_frequently_of_tendsto h lim
-
-theorem le_of_tendsto {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
-    (h : ∀ᶠ c in x, f c ≤ b) : a ≤ b :=
-  (isClosed_le' b).mem_of_tendsto lim h
-#align le_of_tendsto le_of_tendsto
-
-theorem le_of_tendsto' {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
-    (h : ∀ c, f c ≤ b) : a ≤ b :=
-  le_of_tendsto lim (eventually_of_forall h)
-#align le_of_tendsto' le_of_tendsto'
-
-end ClosedIicTopology
-
-section ClosedIciTopology
-
-variable [TopologicalSpace α] [Preorder α] [t : ClosedIciTopology α]
-
-instance : ClosedIicTopology αᵒᵈ where
-  isClosed_le' a := isClosed_ge' (α := α) a
-
-theorem isClosed_Ici {a : α} : IsClosed (Ici a) :=
-  isClosed_ge' a
-#align is_closed_Ici isClosed_Ici
-
-@[simp]
-theorem closure_Ici (a : α) : closure (Ici a) = Ici a :=
-  isClosed_Ici.closure_eq
-#align closure_Ici closure_Ici
-
-lemma ge_of_tendsto_of_frequently {f : β → α} {a b : α} {x : Filter β} (lim : Tendsto f x (𝓝 a))
-    (h : ∃ᶠ c in x, b ≤ f c) : b ≤ a :=
-  (isClosed_ge' b).mem_of_frequently_of_tendsto h lim
-
-theorem ge_of_tendsto {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
-    (h : ∀ᶠ c in x, b ≤ f c) : b ≤ a :=
-  (isClosed_ge' b).mem_of_tendsto lim h
-#align ge_of_tendsto ge_of_tendsto
-
-theorem ge_of_tendsto' {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
-    (h : ∀ c, b ≤ f c) : b ≤ a :=
-  ge_of_tendsto lim (eventually_of_forall h)
-#align ge_of_tendsto' ge_of_tendsto'
-
-end ClosedIciTopology
-
-section OrderClosedTopology
-
-section Preorder
-
-variable [TopologicalSpace α] [Preorder α] [t : OrderClosedTopology α]
-
-namespace Subtype
-
--- todo: add `OrderEmbedding.orderClosedTopology`
-instance {p : α → Prop} : OrderClosedTopology (Subtype p) :=
-  have this : Continuous fun p : Subtype p × Subtype p => ((p.fst : α), (p.snd : α)) :=
-    continuous_subtype_val.prod_map continuous_subtype_val
-  OrderClosedTopology.mk (t.isClosed_le'.preimage this)
-
-end Subtype
-
-theorem isClosed_le_prod : IsClosed { p : α × α | p.1 ≤ p.2 } :=
-  t.isClosed_le'
-#align is_closed_le_prod isClosed_le_prod
-
-theorem isClosed_le [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
-    IsClosed { b | f b ≤ g b } :=
-  continuous_iff_isClosed.mp (hf.prod_mk hg) _ isClosed_le_prod
-#align is_closed_le isClosed_le
-
-instance : ClosedIicTopology α where
-  isClosed_le' _ := isClosed_le continuous_id continuous_const
-
-instance : ClosedIciTopology α where
-  isClosed_ge' _ := isClosed_le continuous_const continuous_id
-
-instance : OrderClosedTopology αᵒᵈ :=
-  ⟨(OrderClosedTopology.isClosed_le' (α := α)).preimage continuous_swap⟩
-
-theorem isClosed_Icc {a b : α} : IsClosed (Icc a b) :=
-  IsClosed.inter isClosed_Ici isClosed_Iic
-#align is_closed_Icc isClosed_Icc
-
-@[simp]
-theorem closure_Icc (a b : α) : closure (Icc a b) = Icc a b :=
-  isClosed_Icc.closure_eq
-#align closure_Icc closure_Icc
-
-theorem le_of_tendsto_of_tendsto {f g : β → α} {b : Filter β} {a₁ a₂ : α} [NeBot b]
-    (hf : Tendsto f b (𝓝 a₁)) (hg : Tendsto g b (𝓝 a₂)) (h : f ≤ᶠ[b] g) : a₁ ≤ a₂ :=
-  have : Tendsto (fun b => (f b, g b)) b (𝓝 (a₁, a₂)) := hf.prod_mk_nhds hg
-  show (a₁, a₂) ∈ { p : α × α | p.1 ≤ p.2 } from t.isClosed_le'.mem_of_tendsto this h
-#align le_of_tendsto_of_tendsto le_of_tendsto_of_tendsto
-
-alias tendsto_le_of_eventuallyLE := le_of_tendsto_of_tendsto
-#align tendsto_le_of_eventually_le tendsto_le_of_eventuallyLE
-
-theorem le_of_tendsto_of_tendsto' {f g : β → α} {b : Filter β} {a₁ a₂ : α} [NeBot b]
-    (hf : Tendsto f b (𝓝 a₁)) (hg : Tendsto g b (𝓝 a₂)) (h : ∀ x, f x ≤ g x) : a₁ ≤ a₂ :=
-  le_of_tendsto_of_tendsto hf hg (eventually_of_forall h)
-#align le_of_tendsto_of_tendsto' le_of_tendsto_of_tendsto'
-
-@[simp]
-theorem closure_le_eq [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
-    closure { b | f b ≤ g b } = { b | f b ≤ g b } :=
-  (isClosed_le hf hg).closure_eq
-#align closure_le_eq closure_le_eq
-
-theorem closure_lt_subset_le [TopologicalSpace β] {f g : β → α} (hf : Continuous f)
-    (hg : Continuous g) : closure { b | f b < g b } ⊆ { b | f b ≤ g b } :=
-  (closure_minimal fun _ => le_of_lt) <| isClosed_le hf hg
-#align closure_lt_subset_le closure_lt_subset_le
-
-theorem ContinuousWithinAt.closure_le [TopologicalSpace β] {f g : β → α} {s : Set β} {x : β}
-    (hx : x ∈ closure s) (hf : ContinuousWithinAt f s x) (hg : ContinuousWithinAt g s x)
-    (h : ∀ y ∈ s, f y ≤ g y) : f x ≤ g x :=
-  show (f x, g x) ∈ { p : α × α | p.1 ≤ p.2 } from
-    OrderClosedTopology.isClosed_le'.closure_subset ((hf.prod hg).mem_closure hx h)
-#align continuous_within_at.closure_le ContinuousWithinAt.closure_le
-
-/-- If `s` is a closed set and two functions `f` and `g` are continuous on `s`,
-then the set `{x ∈ s | f x ≤ g x}` is a closed set. -/
-theorem IsClosed.isClosed_le [TopologicalSpace β] {f g : β → α} {s : Set β} (hs : IsClosed s)
-    (hf : ContinuousOn f s) (hg : ContinuousOn g s) : IsClosed ({ x ∈ s | f x ≤ g x }) :=
-  (hf.prod hg).preimage_isClosed_of_isClosed hs OrderClosedTopology.isClosed_le'
-#align is_closed.is_closed_le IsClosed.isClosed_le
-
-theorem le_on_closure [TopologicalSpace β] {f g : β → α} {s : Set β} (h : ∀ x ∈ s, f x ≤ g x)
-    (hf : ContinuousOn f (closure s)) (hg : ContinuousOn g (closure s)) ⦃x⦄ (hx : x ∈ closure s) :
-    f x ≤ g x :=
-  have : s ⊆ { y ∈ closure s | f y ≤ g y } := fun y hy => ⟨subset_closure hy, h y hy⟩
-  (closure_minimal this (isClosed_closure.isClosed_le hf hg) hx).2
-#align le_on_closure le_on_closure
-
-theorem IsClosed.epigraph [TopologicalSpace β] {f : β → α} {s : Set β} (hs : IsClosed s)
-    (hf : ContinuousOn f s) : IsClosed { p : β × α | p.1 ∈ s ∧ f p.1 ≤ p.2 } :=
-  (hs.preimage continuous_fst).isClosed_le (hf.comp continuousOn_fst Subset.rfl) continuousOn_snd
-#align is_closed.epigraph IsClosed.epigraph
-
-theorem IsClosed.hypograph [TopologicalSpace β] {f : β → α} {s : Set β} (hs : IsClosed s)
-    (hf : ContinuousOn f s) : IsClosed { p : β × α | p.1 ∈ s ∧ p.2 ≤ f p.1 } :=
-  (hs.preimage continuous_fst).isClosed_le continuousOn_snd (hf.comp continuousOn_fst Subset.rfl)
-#align is_closed.hypograph IsClosed.hypograph
-
-end Preorder
-
-section PartialOrder
-
-variable [TopologicalSpace α] [PartialOrder α] [t : OrderClosedTopology α]
-
--- see Note [lower instance priority]
-instance (priority := 90) OrderClosedTopology.to_t2Space : T2Space α :=
-  t2_iff_isClosed_diagonal.2 <| by
-    simpa only [diagonal, le_antisymm_iff] using
-      t.isClosed_le'.inter (isClosed_le continuous_snd continuous_fst)
-#align order_closed_topology.to_t2_space OrderClosedTopology.to_t2Space
-
-end PartialOrder
-
-section LinearOrder
-
-variable [TopologicalSpace α] [LinearOrder α] [OrderClosedTopology α]
-
-theorem isOpen_lt [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
-    IsOpen { b | f b < g b } := by
-  simpa only [lt_iff_not_le] using (isClosed_le hg hf).isOpen_compl
-#align is_open_lt isOpen_lt
-
-theorem isOpen_lt_prod : IsOpen { p : α × α | p.1 < p.2 } :=
-  isOpen_lt continuous_fst continuous_snd
-#align is_open_lt_prod isOpen_lt_prod
-
-variable {a b : α}
-
-theorem isOpen_Iio : IsOpen (Iio a) :=
-  isOpen_lt continuous_id continuous_const
-#align is_open_Iio isOpen_Iio
-
-theorem isOpen_Ioi : IsOpen (Ioi a) :=
-  isOpen_lt continuous_const continuous_id
-#align is_open_Ioi isOpen_Ioi
-
-theorem isOpen_Ioo : IsOpen (Ioo a b) :=
-  IsOpen.inter isOpen_Ioi isOpen_Iio
-#align is_open_Ioo isOpen_Ioo
-
-@[simp]
-theorem interior_Ioi : interior (Ioi a) = Ioi a :=
-  isOpen_Ioi.interior_eq
-#align interior_Ioi interior_Ioi
-
-@[simp]
-theorem interior_Iio : interior (Iio a) = Iio a :=
-  isOpen_Iio.interior_eq
-#align interior_Iio interior_Iio
-
-@[simp]
-theorem interior_Ioo : interior (Ioo a b) = Ioo a b :=
-  isOpen_Ioo.interior_eq
-#align interior_Ioo interior_Ioo
-
-theorem Ioo_subset_closure_interior : Ioo a b ⊆ closure (interior (Ioo a b)) := by
-  simp only [interior_Ioo, subset_closure]
-#align Ioo_subset_closure_interior Ioo_subset_closure_interior
-
-theorem Iio_mem_nhds {a b : α} (h : a < b) : Iio b ∈ 𝓝 a :=
-  IsOpen.mem_nhds isOpen_Iio h
-#align Iio_mem_nhds Iio_mem_nhds
-
-theorem Ioi_mem_nhds {a b : α} (h : a < b) : Ioi a ∈ 𝓝 b :=
-  IsOpen.mem_nhds isOpen_Ioi h
-#align Ioi_mem_nhds Ioi_mem_nhds
-
-theorem Iic_mem_nhds {a b : α} (h : a < b) : Iic b ∈ 𝓝 a :=
-  mem_of_superset (Iio_mem_nhds h) Iio_subset_Iic_self
-#align Iic_mem_nhds Iic_mem_nhds
-
-theorem Ici_mem_nhds {a b : α} (h : a < b) : Ici a ∈ 𝓝 b :=
-  mem_of_superset (Ioi_mem_nhds h) Ioi_subset_Ici_self
-#align Ici_mem_nhds Ici_mem_nhds
-
-theorem Ioo_mem_nhds {a b x : α} (ha : a < x) (hb : x < b) : Ioo a b ∈ 𝓝 x :=
-  IsOpen.mem_nhds isOpen_Ioo ⟨ha, hb⟩
-#align Ioo_mem_nhds Ioo_mem_nhds
-
-theorem Ioc_mem_nhds {a b x : α} (ha : a < x) (hb : x < b) : Ioc a b ∈ 𝓝 x :=
-  mem_of_superset (Ioo_mem_nhds ha hb) Ioo_subset_Ioc_self
-#align Ioc_mem_nhds Ioc_mem_nhds
-
-theorem Ico_mem_nhds {a b x : α} (ha : a < x) (hb : x < b) : Ico a b ∈ 𝓝 x :=
-  mem_of_superset (Ioo_mem_nhds ha hb) Ioo_subset_Ico_self
-#align Ico_mem_nhds Ico_mem_nhds
-
-theorem Icc_mem_nhds {a b x : α} (ha : a < x) (hb : x < b) : Icc a b ∈ 𝓝 x :=
-  mem_of_superset (Ioo_mem_nhds ha hb) Ioo_subset_Icc_self
-#align Icc_mem_nhds Icc_mem_nhds
-
-theorem eventually_lt_of_tendsto_lt {l : Filter γ} {f : γ → α} {u v : α} (hv : v < u)
-    (h : Filter.Tendsto f l (𝓝 v)) : ∀ᶠ a in l, f a < u :=
-  tendsto_nhds.1 h (· < u) isOpen_Iio hv
-#align eventually_lt_of_tendsto_lt eventually_lt_of_tendsto_lt
-
-theorem eventually_gt_of_tendsto_gt {l : Filter γ} {f : γ → α} {u v : α} (hv : u < v)
-    (h : Filter.Tendsto f l (𝓝 v)) : ∀ᶠ a in l, u < f a :=
-  tendsto_nhds.1 h (· > u) isOpen_Ioi hv
-#align eventually_gt_of_tendsto_gt eventually_gt_of_tendsto_gt
-
-theorem eventually_le_of_tendsto_lt {l : Filter γ} {f : γ → α} {u v : α} (hv : v < u)
-    (h : Tendsto f l (𝓝 v)) : ∀ᶠ a in l, f a ≤ u :=
-  (eventually_lt_of_tendsto_lt hv h).mono fun _ => le_of_lt
-#align eventually_le_of_tendsto_lt eventually_le_of_tendsto_lt
-
-theorem eventually_ge_of_tendsto_gt {l : Filter γ} {f : γ → α} {u v : α} (hv : u < v)
-    (h : Tendsto f l (𝓝 v)) : ∀ᶠ a in l, u ≤ f a :=
-  (eventually_gt_of_tendsto_gt hv h).mono fun _ => le_of_lt
-#align eventually_ge_of_tendsto_gt eventually_ge_of_tendsto_gt
-
-variable [TopologicalSpace γ]
-
-/-!
-### Neighborhoods to the left and to the right on an `OrderClosedTopology`
-
-Limits to the left and to the right of real functions are defined in terms of neighborhoods to
-the left and to the right, either open or closed, i.e., members of `𝓝[>] a` and
-`𝓝[≥] a` on the right, and similarly on the left. Here we simply prove that all
-right-neighborhoods of a point are equal, and we'll prove later other useful characterizations which
-require the stronger hypothesis `OrderTopology α` -/
-
-
-/-!
-#### Right neighborhoods, point excluded
--/
-
-theorem Ioo_mem_nhdsWithin_Ioi {a b c : α} (H : b ∈ Ico a c) : Ioo a c ∈ 𝓝[>] b :=
-  mem_nhdsWithin.2
-    ⟨Iio c, isOpen_Iio, H.2, by rw [inter_comm, Ioi_inter_Iio]; exact Ioo_subset_Ioo_left H.1⟩
-#align Ioo_mem_nhds_within_Ioi Ioo_mem_nhdsWithin_Ioi
-
--- porting note: new lemma; todo: swap `'`?
-theorem Ioo_mem_nhdsWithin_Ioi' {a b : α} (H : a < b) : Ioo a b ∈ 𝓝[>] a :=
-  Ioo_mem_nhdsWithin_Ioi ⟨le_rfl, H⟩
-
-theorem CovBy.nhdsWithin_Ioi {a b : α} (h : a ⋖ b) : 𝓝[>] a = ⊥ :=
-  empty_mem_iff_bot.mp <| h.Ioo_eq ▸ Ioo_mem_nhdsWithin_Ioi' h.1
-
-theorem Ioc_mem_nhdsWithin_Ioi {a b c : α} (H : b ∈ Ico a c) : Ioc a c ∈ 𝓝[>] b :=
-  mem_of_superset (Ioo_mem_nhdsWithin_Ioi H) Ioo_subset_Ioc_self
-#align Ioc_mem_nhds_within_Ioi Ioc_mem_nhdsWithin_Ioi
-
--- porting note: new lemma; todo: swap `'`?
-theorem Ioc_mem_nhdsWithin_Ioi' {a b : α} (H : a < b) : Ioc a b ∈ 𝓝[>] a :=
-  Ioc_mem_nhdsWithin_Ioi ⟨le_rfl, H⟩
-
-theorem Ico_mem_nhdsWithin_Ioi {a b c : α} (H : b ∈ Ico a c) : Ico a c ∈ 𝓝[>] b :=
-  mem_of_superset (Ioo_mem_nhdsWithin_Ioi H) Ioo_subset_Ico_self
-#align Ico_mem_nhds_within_Ioi Ico_mem_nhdsWithin_Ioi
-
--- porting note: new lemma; todo: swap `'`?
-theorem Ico_mem_nhdsWithin_Ioi' {a b : α} (H : a < b) : Ico a b ∈ 𝓝[>] a :=
-  Ico_mem_nhdsWithin_Ioi ⟨le_rfl, H⟩
-
-theorem Icc_mem_nhdsWithin_Ioi {a b c : α} (H : b ∈ Ico a c) : Icc a c ∈ 𝓝[>] b :=
-  mem_of_superset (Ioo_mem_nhdsWithin_Ioi H) Ioo_subset_Icc_self
-#align Icc_mem_nhds_within_Ioi Icc_mem_nhdsWithin_Ioi
-
--- porting note: new lemma; todo: swap `'`?
-theorem Icc_mem_nhdsWithin_Ioi' {a b : α} (H : a < b) : Icc a b ∈ 𝓝[>] a :=
-  Icc_mem_nhdsWithin_Ioi ⟨le_rfl, H⟩
-
-@[simp]
-theorem nhdsWithin_Ioc_eq_nhdsWithin_Ioi {a b : α} (h : a < b) : 𝓝[Ioc a b] a = 𝓝[>] a :=
-  nhdsWithin_inter_of_mem' <| nhdsWithin_le_nhds <| Iic_mem_nhds h
-#align nhds_within_Ioc_eq_nhds_within_Ioi nhdsWithin_Ioc_eq_nhdsWithin_Ioi
-
-@[simp]
-theorem nhdsWithin_Ioo_eq_nhdsWithin_Ioi {a b : α} (h : a < b) : 𝓝[Ioo a b] a = 𝓝[>] a :=
-  nhdsWithin_inter_of_mem' <| nhdsWithin_le_nhds <| Iio_mem_nhds h
-#align nhds_within_Ioo_eq_nhds_within_Ioi nhdsWithin_Ioo_eq_nhdsWithin_Ioi
-
-@[simp]
-theorem continuousWithinAt_Ioc_iff_Ioi [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
-    ContinuousWithinAt f (Ioc a b) a ↔ ContinuousWithinAt f (Ioi a) a := by
-  simp only [ContinuousWithinAt, nhdsWithin_Ioc_eq_nhdsWithin_Ioi h]
-#align continuous_within_at_Ioc_iff_Ioi continuousWithinAt_Ioc_iff_Ioi
-
-@[simp]
-theorem continuousWithinAt_Ioo_iff_Ioi [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
-    ContinuousWithinAt f (Ioo a b) a ↔ ContinuousWithinAt f (Ioi a) a := by
-  simp only [ContinuousWithinAt, nhdsWithin_Ioo_eq_nhdsWithin_Ioi h]
-#align continuous_within_at_Ioo_iff_Ioi continuousWithinAt_Ioo_iff_Ioi
-
-/-!
-#### Left neighborhoods, point excluded
--/
-
-theorem Ioo_mem_nhdsWithin_Iio {a b c : α} (H : b ∈ Ioc a c) : Ioo a c ∈ 𝓝[<] b := by
-  simpa only [dual_Ioo] using
-    Ioo_mem_nhdsWithin_Ioi (show toDual b ∈ Ico (toDual c) (toDual a) from H.symm)
-#align Ioo_mem_nhds_within_Iio Ioo_mem_nhdsWithin_Iio
-
--- porting note: new lemma; todo: swap `'`?
-theorem Ioo_mem_nhdsWithin_Iio' {a b : α} (H : a < b) : Ioo a b ∈ 𝓝[<] b :=
-  Ioo_mem_nhdsWithin_Iio ⟨H, le_rfl⟩
-
-theorem CovBy.nhdsWithin_Iio {a b : α} (h : a ⋖ b) : 𝓝[<] b = ⊥ :=
-  empty_mem_iff_bot.mp <| h.Ioo_eq ▸ Ioo_mem_nhdsWithin_Iio' h.1
-
-theorem Ico_mem_nhdsWithin_Iio {a b c : α} (H : b ∈ Ioc a c) : Ico a c ∈ 𝓝[<] b :=
-  mem_of_superset (Ioo_mem_nhdsWithin_Iio H) Ioo_subset_Ico_self
-#align Ico_mem_nhds_within_Iio Ico_mem_nhdsWithin_Iio
-
--- porting note: new lemma; todo: swap `'`?
-theorem Ico_mem_nhdsWithin_Iio' {a b : α} (H : a < b) : Ico a b ∈ 𝓝[<] b :=
-  Ico_mem_nhdsWithin_Iio ⟨H, le_rfl⟩
-
-theorem Ioc_mem_nhdsWithin_Iio {a b c : α} (H : b ∈ Ioc a c) : Ioc a c ∈ 𝓝[<] b :=
-  mem_of_superset (Ioo_mem_nhdsWithin_Iio H) Ioo_subset_Ioc_self
-#align Ioc_mem_nhds_within_Iio Ioc_mem_nhdsWithin_Iio
-
--- porting note: new lemma; todo: swap `'`?
-theorem Ioc_mem_nhdsWithin_Iio' {a b : α} (H : a < b) : Ioc a b ∈ 𝓝[<] b :=
-  Ioc_mem_nhdsWithin_Iio ⟨H, le_rfl⟩
-
-theorem Icc_mem_nhdsWithin_Iio {a b c : α} (H : b ∈ Ioc a c) : Icc a c ∈ 𝓝[<] b :=
-  mem_of_superset (Ioo_mem_nhdsWithin_Iio H) Ioo_subset_Icc_self
-#align Icc_mem_nhds_within_Iio Icc_mem_nhdsWithin_Iio
-
-theorem Icc_mem_nhdsWithin_Iio' {a b : α} (H : a < b) : Icc a b ∈ 𝓝[<] b :=
-  Icc_mem_nhdsWithin_Iio ⟨H, le_rfl⟩
-
-@[simp]
-theorem nhdsWithin_Ico_eq_nhdsWithin_Iio {a b : α} (h : a < b) : 𝓝[Ico a b] b = 𝓝[<] b := by
-  simpa only [dual_Ioc] using nhdsWithin_Ioc_eq_nhdsWithin_Ioi h.dual
-#align nhds_within_Ico_eq_nhds_within_Iio nhdsWithin_Ico_eq_nhdsWithin_Iio
-
-@[simp]
-theorem nhdsWithin_Ioo_eq_nhdsWithin_Iio {a b : α} (h : a < b) : 𝓝[Ioo a b] b = 𝓝[<] b := by
-  simpa only [dual_Ioo] using nhdsWithin_Ioo_eq_nhdsWithin_Ioi h.dual
-#align nhds_within_Ioo_eq_nhds_within_Iio nhdsWithin_Ioo_eq_nhdsWithin_Iio
-
-@[simp]
-theorem continuousWithinAt_Ico_iff_Iio {a b : α} {f : α → γ} (h : a < b) :
-    ContinuousWithinAt f (Ico a b) b ↔ ContinuousWithinAt f (Iio b) b := by
-  simp only [ContinuousWithinAt, nhdsWithin_Ico_eq_nhdsWithin_Iio h]
-#align continuous_within_at_Ico_iff_Iio continuousWithinAt_Ico_iff_Iio
-
-@[simp]
-theorem continuousWithinAt_Ioo_iff_Iio {a b : α} {f : α → γ} (h : a < b) :
-    ContinuousWithinAt f (Ioo a b) b ↔ ContinuousWithinAt f (Iio b) b := by
-  simp only [ContinuousWithinAt, nhdsWithin_Ioo_eq_nhdsWithin_Iio h]
-#align continuous_within_at_Ioo_iff_Iio continuousWithinAt_Ioo_iff_Iio
-
-/-!
-#### Right neighborhoods, point included
--/
-
-theorem Ioo_mem_nhdsWithin_Ici {a b c : α} (H : b ∈ Ioo a c) : Ioo a c ∈ 𝓝[≥] b :=
-  mem_nhdsWithin_of_mem_nhds <| IsOpen.mem_nhds isOpen_Ioo H
-#align Ioo_mem_nhds_within_Ici Ioo_mem_nhdsWithin_Ici
-
-theorem Ioc_mem_nhdsWithin_Ici {a b c : α} (H : b ∈ Ioo a c) : Ioc a c ∈ 𝓝[≥] b :=
-  mem_of_superset (Ioo_mem_nhdsWithin_Ici H) Ioo_subset_Ioc_self
-#align Ioc_mem_nhds_within_Ici Ioc_mem_nhdsWithin_Ici
-
-theorem Ico_mem_nhdsWithin_Ici {a b c : α} (H : b ∈ Ico a c) : Ico a c ∈ 𝓝[≥] b :=
-  mem_nhdsWithin.2
-    ⟨Iio c, isOpen_Iio, H.2, by simp only [inter_comm, Ici_inter_Iio, Ico_subset_Ico_left H.1]⟩
-#align Ico_mem_nhds_within_Ici Ico_mem_nhdsWithin_Ici
-
-theorem Ico_mem_nhdsWithin_Ici' {a b : α} (H : a < b) : Ico a b ∈ 𝓝[≥] a :=
-  Ico_mem_nhdsWithin_Ici ⟨le_rfl, H⟩
-
-theorem Icc_mem_nhdsWithin_Ici {a b c : α} (H : b ∈ Ico a c) : Icc a c ∈ 𝓝[≥] b :=
-  mem_of_superset (Ico_mem_nhdsWithin_Ici H) Ico_subset_Icc_self
-#align Icc_mem_nhds_within_Ici Icc_mem_nhdsWithin_Ici
-
-theorem Icc_mem_nhdsWithin_Ici' {a b : α} (H : a < b) : Icc a b ∈ 𝓝[≥] a :=
-  Icc_mem_nhdsWithin_Ici ⟨le_rfl, H⟩
-
-@[simp]
-theorem nhdsWithin_Icc_eq_nhdsWithin_Ici {a b : α} (h : a < b) : 𝓝[Icc a b] a = 𝓝[≥] a :=
-  nhdsWithin_inter_of_mem' <| nhdsWithin_le_nhds <| Iic_mem_nhds h
-#align nhds_within_Icc_eq_nhds_within_Ici nhdsWithin_Icc_eq_nhdsWithin_Ici
-
-@[simp]
-theorem nhdsWithin_Ico_eq_nhdsWithin_Ici {a b : α} (h : a < b) : 𝓝[Ico a b] a = 𝓝[≥] a :=
-  nhdsWithin_inter_of_mem' <| nhdsWithin_le_nhds <| Iio_mem_nhds h
-#align nhds_within_Ico_eq_nhds_within_Ici nhdsWithin_Ico_eq_nhdsWithin_Ici
-
-@[simp]
-theorem continuousWithinAt_Icc_iff_Ici [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
-    ContinuousWithinAt f (Icc a b) a ↔ ContinuousWithinAt f (Ici a) a := by
-  simp only [ContinuousWithinAt, nhdsWithin_Icc_eq_nhdsWithin_Ici h]
-#align continuous_within_at_Icc_iff_Ici continuousWithinAt_Icc_iff_Ici
-
-@[simp]
-theorem continuousWithinAt_Ico_iff_Ici [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
-    ContinuousWithinAt f (Ico a b) a ↔ ContinuousWithinAt f (Ici a) a := by
-  simp only [ContinuousWithinAt, nhdsWithin_Ico_eq_nhdsWithin_Ici h]
-#align continuous_within_at_Ico_iff_Ici continuousWithinAt_Ico_iff_Ici
-
-/-!
-#### Left neighborhoods, point included
--/
-
-
-theorem Ioo_mem_nhdsWithin_Iic {a b c : α} (H : b ∈ Ioo a c) : Ioo a c ∈ 𝓝[≤] b :=
-  mem_nhdsWithin_of_mem_nhds <| IsOpen.mem_nhds isOpen_Ioo H
-#align Ioo_mem_nhds_within_Iic Ioo_mem_nhdsWithin_Iic
-
-theorem Ico_mem_nhdsWithin_Iic {a b c : α} (H : b ∈ Ioo a c) : Ico a c ∈ 𝓝[≤] b :=
-  mem_of_superset (Ioo_mem_nhdsWithin_Iic H) Ioo_subset_Ico_self
-#align Ico_mem_nhds_within_Iic Ico_mem_nhdsWithin_Iic
-
-theorem Ioc_mem_nhdsWithin_Iic {a b c : α} (H : b ∈ Ioc a c) : Ioc a c ∈ 𝓝[≤] b := by
-  simpa only [dual_Ico] using
-    Ico_mem_nhdsWithin_Ici (show toDual b ∈ Ico (toDual c) (toDual a) from H.symm)
-#align Ioc_mem_nhds_within_Iic Ioc_mem_nhdsWithin_Iic
-
-theorem Ioc_mem_nhdsWithin_Iic' {a b : α} (H : a < b) : Ioc a b ∈ 𝓝[≤] b :=
-  Ioc_mem_nhdsWithin_Iic ⟨H, le_rfl⟩
-
-theorem Icc_mem_nhdsWithin_Iic {a b c : α} (H : b ∈ Ioc a c) : Icc a c ∈ 𝓝[≤] b :=
-  mem_of_superset (Ioc_mem_nhdsWithin_Iic H) Ioc_subset_Icc_self
-#align Icc_mem_nhds_within_Iic Icc_mem_nhdsWithin_Iic
-
-theorem Icc_mem_nhdsWithin_Iic' {a b : α} (H : a < b) : Icc a b ∈ 𝓝[≤] b :=
-  Icc_mem_nhdsWithin_Iic ⟨H, le_rfl⟩
-
-@[simp]
-theorem nhdsWithin_Icc_eq_nhdsWithin_Iic {a b : α} (h : a < b) : 𝓝[Icc a b] b = 𝓝[≤] b := by
-  simpa only [dual_Icc] using nhdsWithin_Icc_eq_nhdsWithin_Ici h.dual
-#align nhds_within_Icc_eq_nhds_within_Iic nhdsWithin_Icc_eq_nhdsWithin_Iic
-
-@[simp]
-theorem nhdsWithin_Ioc_eq_nhdsWithin_Iic {a b : α} (h : a < b) : 𝓝[Ioc a b] b = 𝓝[≤] b := by
-  simpa only [dual_Ico] using nhdsWithin_Ico_eq_nhdsWithin_Ici h.dual
-#align nhds_within_Ioc_eq_nhds_within_Iic nhdsWithin_Ioc_eq_nhdsWithin_Iic
-
-@[simp]
-theorem continuousWithinAt_Icc_iff_Iic [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
-    ContinuousWithinAt f (Icc a b) b ↔ ContinuousWithinAt f (Iic b) b := by
-  simp only [ContinuousWithinAt, nhdsWithin_Icc_eq_nhdsWithin_Iic h]
-#align continuous_within_at_Icc_iff_Iic continuousWithinAt_Icc_iff_Iic
-
-@[simp]
-theorem continuousWithinAt_Ioc_iff_Iic [TopologicalSpace β] {a b : α} {f : α → β} (h : a < b) :
-    ContinuousWithinAt f (Ioc a b) b ↔ ContinuousWithinAt f (Iic b) b := by
-  simp only [ContinuousWithinAt, nhdsWithin_Ioc_eq_nhdsWithin_Iic h]
-#align continuous_within_at_Ioc_iff_Iic continuousWithinAt_Ioc_iff_Iic
-
-end LinearOrder
-
-section LinearOrder
-
-variable [TopologicalSpace α] [LinearOrder α] [OrderClosedTopology α] {f g : β → α}
-
-section
-
-variable [TopologicalSpace β]
-
-theorem lt_subset_interior_le (hf : Continuous f) (hg : Continuous g) :
-    { b | f b < g b } ⊆ interior { b | f b ≤ g b } :=
-  (interior_maximal fun _ => le_of_lt) <| isOpen_lt hf hg
-#align lt_subset_interior_le lt_subset_interior_le
-
-theorem frontier_le_subset_eq (hf : Continuous f) (hg : Continuous g) :
-    frontier { b | f b ≤ g b } ⊆ { b | f b = g b } := by
-  rw [frontier_eq_closure_inter_closure, closure_le_eq hf hg]
-  rintro b ⟨hb₁, hb₂⟩
-  refine' le_antisymm hb₁ (closure_lt_subset_le hg hf _)
-  convert hb₂ using 2; simp only [not_le.symm]; rfl
-#align frontier_le_subset_eq frontier_le_subset_eq
-
-theorem frontier_Iic_subset (a : α) : frontier (Iic a) ⊆ {a} :=
-  frontier_le_subset_eq (@continuous_id α _) continuous_const
-#align frontier_Iic_subset frontier_Iic_subset
-
-theorem frontier_Ici_subset (a : α) : frontier (Ici a) ⊆ {a} :=
-  frontier_Iic_subset (α := αᵒᵈ) _
-#align frontier_Ici_subset frontier_Ici_subset
-
-theorem frontier_lt_subset_eq (hf : Continuous f) (hg : Continuous g) :
-    frontier { b | f b < g b } ⊆ { b | f b = g b } := by
-  simpa only [← not_lt, ← compl_setOf, frontier_compl, eq_comm] using frontier_le_subset_eq hg hf
-#align frontier_lt_subset_eq frontier_lt_subset_eq
-
-theorem continuous_if_le [TopologicalSpace γ] [∀ x, Decidable (f x ≤ g x)] {f' g' : β → γ}
-    (hf : Continuous f) (hg : Continuous g) (hf' : ContinuousOn f' { x | f x ≤ g x })
-    (hg' : ContinuousOn g' { x | g x ≤ f x }) (hfg : ∀ x, f x = g x → f' x = g' x) :
-    Continuous fun x => if f x ≤ g x then f' x else g' x := by
-  refine' continuous_if (fun a ha => hfg _ (frontier_le_subset_eq hf hg ha)) _ (hg'.mono _)
-  · rwa [(isClosed_le hf hg).closure_eq]
-  · simp only [not_le]
-    exact closure_lt_subset_le hg hf
-#align continuous_if_le continuous_if_le
-
-theorem Continuous.if_le [TopologicalSpace γ] [∀ x, Decidable (f x ≤ g x)] {f' g' : β → γ}
-    (hf' : Continuous f') (hg' : Continuous g') (hf : Continuous f) (hg : Continuous g)
-    (hfg : ∀ x, f x = g x → f' x = g' x) : Continuous fun x => if f x ≤ g x then f' x else g' x :=
-  continuous_if_le hf hg hf'.continuousOn hg'.continuousOn hfg
-#align continuous.if_le Continuous.if_le
-
-theorem Filter.Tendsto.eventually_lt {l : Filter γ} {f g : γ → α} {y z : α} (hf : Tendsto f l (𝓝 y))
-    (hg : Tendsto g l (𝓝 z)) (hyz : y < z) : ∀ᶠ x in l, f x < g x :=
-  let ⟨_a, ha, _b, hb, h⟩ := hyz.exists_disjoint_Iio_Ioi
-  (hg.eventually (Ioi_mem_nhds hb)).mp <| (hf.eventually (Iio_mem_nhds ha)).mono fun _ h₁ h₂ =>
-    h _ h₁ _ h₂
-#align tendsto.eventually_lt Filter.Tendsto.eventually_lt
-
-nonrec theorem ContinuousAt.eventually_lt {x₀ : β} (hf : ContinuousAt f x₀) (hg : ContinuousAt g x₀)
-    (hfg : f x₀ < g x₀) : ∀ᶠ x in 𝓝 x₀, f x < g x :=
-  hf.eventually_lt hg hfg
-#align continuous_at.eventually_lt ContinuousAt.eventually_lt
-
-@[continuity]
-protected theorem Continuous.min (hf : Continuous f) (hg : Continuous g) :
-    Continuous fun b => min (f b) (g b) := by
-  simp only [min_def]
-  exact hf.if_le hg hf hg fun x => id
-#align continuous.min Continuous.min
-
-@[continuity]
-protected theorem Continuous.max (hf : Continuous f) (hg : Continuous g) :
-    Continuous fun b => max (f b) (g b) :=
-  Continuous.min (α := αᵒᵈ) hf hg
-#align continuous.max Continuous.max
-
-end
-
-theorem continuous_min : Continuous fun p : α × α => min p.1 p.2 :=
-  continuous_fst.min continuous_snd
-#align continuous_min continuous_min
-
-theorem continuous_max : Continuous fun p : α × α => max p.1 p.2 :=
-  continuous_fst.max continuous_snd
-#align continuous_max continuous_max
-
-protected theorem Filter.Tendsto.max {b : Filter β} {a₁ a₂ : α} (hf : Tendsto f b (𝓝 a₁))
-    (hg : Tendsto g b (𝓝 a₂)) : Tendsto (fun b => max (f b) (g b)) b (𝓝 (max a₁ a₂)) :=
-  (continuous_max.tendsto (a₁, a₂)).comp (hf.prod_mk_nhds hg)
-#align filter.tendsto.max Filter.Tendsto.max
-
-protected theorem Filter.Tendsto.min {b : Filter β} {a₁ a₂ : α} (hf : Tendsto f b (𝓝 a₁))
-    (hg : Tendsto g b (𝓝 a₂)) : Tendsto (fun b => min (f b) (g b)) b (𝓝 (min a₁ a₂)) :=
-  (continuous_min.tendsto (a₁, a₂)).comp (hf.prod_mk_nhds hg)
-#align filter.tendsto.min Filter.Tendsto.min
-
-protected theorem Filter.Tendsto.max_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
-    Tendsto (fun i => max a (f i)) l (𝓝 a) := by
-  convert ((continuous_max.comp (@Continuous.Prod.mk α α _ _ a)).tendsto a).comp h
-  simp
-#align filter.tendsto.max_right Filter.Tendsto.max_right
-
-protected theorem Filter.Tendsto.max_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
-    Tendsto (fun i => max (f i) a) l (𝓝 a) := by
-  simp_rw [max_comm _ a]
-  exact h.max_right
-#align filter.tendsto.max_left Filter.Tendsto.max_left
-
-theorem Filter.tendsto_nhds_max_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝[>] a)) :
-    Tendsto (fun i => max a (f i)) l (𝓝[>] a) := by
-  obtain ⟨h₁ : Tendsto f l (𝓝 a), h₂ : ∀ᶠ i in l, f i ∈ Ioi a⟩ := tendsto_nhdsWithin_iff.mp h
-  exact tendsto_nhdsWithin_iff.mpr ⟨h₁.max_right, h₂.mono fun i hi => lt_max_of_lt_right hi⟩
-#align filter.tendsto_nhds_max_right Filter.tendsto_nhds_max_right
-
-theorem Filter.tendsto_nhds_max_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝[>] a)) :
-    Tendsto (fun i => max (f i) a) l (𝓝[>] a) := by
-  simp_rw [max_comm _ a]
-  exact Filter.tendsto_nhds_max_right h
-#align filter.tendsto_nhds_max_left Filter.tendsto_nhds_max_left
-
-theorem Filter.Tendsto.min_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
-    Tendsto (fun i => min a (f i)) l (𝓝 a) :=
-  Filter.Tendsto.max_right (α := αᵒᵈ) h
-#align filter.tendsto.min_right Filter.Tendsto.min_right
-
-theorem Filter.Tendsto.min_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
-    Tendsto (fun i => min (f i) a) l (𝓝 a) :=
-  Filter.Tendsto.max_left (α := αᵒᵈ) h
-#align filter.tendsto.min_left Filter.Tendsto.min_left
-
-theorem Filter.tendsto_nhds_min_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝[<] a)) :
-    Tendsto (fun i => min a (f i)) l (𝓝[<] a) :=
-  Filter.tendsto_nhds_max_right (α := αᵒᵈ) h
-#align filter.tendsto_nhds_min_right Filter.tendsto_nhds_min_right
-
-theorem Filter.tendsto_nhds_min_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝[<] a)) :
-    Tendsto (fun i => min (f i) a) l (𝓝[<] a) :=
-  Filter.tendsto_nhds_max_left (α := αᵒᵈ) h
-#align filter.tendsto_nhds_min_left Filter.tendsto_nhds_min_left
-
-protected theorem Dense.exists_lt [NoMinOrder α] {s : Set α} (hs : Dense s) (x : α) :
-    ∃ y ∈ s, y < x :=
-  hs.exists_mem_open isOpen_Iio (exists_lt x)
-#align dense.exists_lt Dense.exists_lt
-
-protected theorem Dense.exists_gt [NoMaxOrder α] {s : Set α} (hs : Dense s) (x : α) :
-    ∃ y ∈ s, x < y :=
-  hs.orderDual.exists_lt x
-#align dense.exists_gt Dense.exists_gt
-
-protected theorem Dense.exists_le [NoMinOrder α] {s : Set α} (hs : Dense s) (x : α) :
-    ∃ y ∈ s, y ≤ x :=
-  (hs.exists_lt x).imp fun _ h => ⟨h.1, h.2.le⟩
-#align dense.exists_le Dense.exists_le
-
-protected theorem Dense.exists_ge [NoMaxOrder α] {s : Set α} (hs : Dense s) (x : α) :
-    ∃ y ∈ s, x ≤ y :=
-  hs.orderDual.exists_le x
-#align dense.exists_ge Dense.exists_ge
-
-theorem Dense.exists_le' {s : Set α} (hs : Dense s) (hbot : ∀ x, IsBot x → x ∈ s) (x : α) :
-    ∃ y ∈ s, y ≤ x := by
-  by_cases hx : IsBot x
-  · exact ⟨x, hbot x hx, le_rfl⟩
-  · simp only [IsBot, not_forall, not_le] at hx
-    rcases hs.exists_mem_open isOpen_Iio hx with ⟨y, hys, hy : y < x⟩
-    exact ⟨y, hys, hy.le⟩
-#align dense.exists_le' Dense.exists_le'
-
-theorem Dense.exists_ge' {s : Set α} (hs : Dense s) (htop : ∀ x, IsTop x → x ∈ s) (x : α) :
-    ∃ y ∈ s, x ≤ y :=
-  hs.orderDual.exists_le' htop x
-#align dense.exists_ge' Dense.exists_ge'
-
-theorem Dense.exists_between [DenselyOrdered α] {s : Set α} (hs : Dense s) {x y : α} (h : x < y) :
-    ∃ z ∈ s, z ∈ Ioo x y :=
-  hs.exists_mem_open isOpen_Ioo (nonempty_Ioo.2 h)
-#align dense.exists_between Dense.exists_between
-
-theorem Dense.Ioi_eq_biUnion [DenselyOrdered α] {s : Set α} (hs : Dense s) (x : α) :
-    Ioi x = ⋃ y ∈ s ∩ Ioi x, Ioi y := by
-  refine Subset.antisymm (fun z hz ↦ ?_) (iUnion₂_subset fun y hy ↦ Ioi_subset_Ioi (le_of_lt hy.2))
-  rcases hs.exists_between hz with ⟨y, hys, hxy, hyz⟩
-  exact mem_iUnion₂.2 ⟨y, ⟨hys, hxy⟩, hyz⟩
-
-theorem Dense.Iio_eq_biUnion [DenselyOrdered α] {s : Set α} (hs : Dense s) (x : α) :
-    Iio x = ⋃ y ∈ s ∩ Iio x, Iio y :=
-  Dense.Ioi_eq_biUnion (α := αᵒᵈ) hs x
-
-end LinearOrder
-
-end OrderClosedTopology
-
-instance [Preorder α] [TopologicalSpace α] [OrderClosedTopology α] [Preorder β] [TopologicalSpace β]
-    [OrderClosedTopology β] : OrderClosedTopology (α × β) :=
-  ⟨(isClosed_le continuous_fst.fst continuous_snd.fst).inter
-    (isClosed_le continuous_fst.snd continuous_snd.snd)⟩
-
-instance {ι : Type*} {α : ι → Type*} [∀ i, Preorder (α i)] [∀ i, TopologicalSpace (α i)]
-    [∀ i, OrderClosedTopology (α i)] : OrderClosedTopology (∀ i, α i) := by
-  constructor
-  simp only [Pi.le_def, setOf_forall]
-  exact isClosed_iInter fun i => isClosed_le (continuous_apply i).fst' (continuous_apply i).snd'
-
-instance Pi.orderClosedTopology' [Preorder β] [TopologicalSpace β] [OrderClosedTopology β] :
-    OrderClosedTopology (α → β) :=
-  inferInstance
-#align pi.order_closed_topology' Pi.orderClosedTopology'
-
 -- porting note: todo: define `Preorder.topology` before `OrderTopology` and reuse the def
 /-- The order topology on an ordered type is the topology generated by open intervals. We register
 it on a preorder, but it is mostly interesting in linear orders, where it is also order-closed.
@@ -1160,24 +378,6 @@ section LinearOrder
 
 variable [TopologicalSpace α] [LinearOrder α]
 
-section OrderClosedTopology
-
-variable [OrderClosedTopology α] {a b : α}
-
-theorem eventually_le_nhds (hab : a < b) : ∀ᶠ x in 𝓝 a, x ≤ b := Iic_mem_nhds hab
-#align eventually_le_nhds eventually_le_nhds
-
-theorem eventually_lt_nhds (hab : a < b) : ∀ᶠ x in 𝓝 a, x < b := Iio_mem_nhds hab
-#align eventually_lt_nhds eventually_lt_nhds
-
-theorem eventually_ge_nhds (hab : b < a) : ∀ᶠ x in 𝓝 a, b ≤ x := Ici_mem_nhds hab
-#align eventually_ge_nhds eventually_ge_nhds
-
-theorem eventually_gt_nhds (hab : b < a) : ∀ᶠ x in 𝓝 a, b < x := Ioi_mem_nhds hab
-#align eventually_gt_nhds eventually_gt_nhds
-
-end OrderClosedTopology
-
 section OrderTopology
 
 variable [OrderTopology α]

Some of these are already transitively imported, others aren't used at all (but not handled by noshake in #9772).

Mostly I wanted to avoid needing all of algebra imported (but unused!) in FilteredColimitCommutesFiniteLimit; there are now some assert_not_exists to preserve this.

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

@@ -7,6 +7,7 @@ import Mathlib.Data.Set.Intervals.Pi
 import Mathlib.Data.Set.Pointwise.Basic
 import Mathlib.Order.Filter.Interval
 import Mathlib.Tactic.TFAE
+import Mathlib.Tactic.NormNum
 import Mathlib.Topology.Separation
 import Mathlib.Topology.Algebra.Order.LeftRight
 

@@ -1844,17 +1844,18 @@ theorem nhdsWithin_Ici_basis_Ico [NoMaxOrder α] (a : α) :
   ⟨fun _ => mem_nhdsWithin_Ici_iff_exists_Ico_subset⟩
 #align nhds_within_Ici_basis_Ico nhdsWithin_Ici_basis_Ico
 
+/-- The filter of right neighborhoods has a basis of closed intervals. -/
+theorem nhdsWithin_Ici_basis_Icc [NoMaxOrder α] [DenselyOrdered α] {a : α} :
+    (𝓝[≥] a).HasBasis (a < ·) (Icc a) :=
+  (nhdsWithin_Ici_basis _).to_hasBasis
+    (fun _u hu ↦ (exists_between hu).imp fun _v hv ↦ hv.imp_right Icc_subset_Ico_right)
+    fun u hu ↦ ⟨u, hu, Ico_subset_Icc_self⟩
+
 /-- A set is a neighborhood of `a` within `[a, +∞)` if and only if it contains an interval `[a, u]`
 with `a < u`. -/
 theorem mem_nhdsWithin_Ici_iff_exists_Icc_subset [NoMaxOrder α] [DenselyOrdered α] {a : α}
-    {s : Set α} : s ∈ 𝓝[≥] a ↔ ∃ u, a < u ∧ Icc a u ⊆ s := by
-  rw [mem_nhdsWithin_Ici_iff_exists_Ico_subset]
-  constructor
-  · rintro ⟨u, au, as⟩
-    rcases exists_between au with ⟨v, hv⟩
-    exact ⟨v, hv.1, fun x hx => as ⟨hx.1, lt_of_le_of_lt hx.2 hv.2⟩⟩
-  · rintro ⟨u, au, as⟩
-    exact ⟨u, au, Subset.trans Ico_subset_Icc_self as⟩
+    {s : Set α} : s ∈ 𝓝[≥] a ↔ ∃ u, a < u ∧ Icc a u ⊆ s :=
+  nhdsWithin_Ici_basis_Icc.mem_iff
 #align mem_nhds_within_Ici_iff_exists_Icc_subset mem_nhdsWithin_Ici_iff_exists_Icc_subset
 
 open List in
@@ -1905,6 +1906,11 @@ theorem mem_nhdsWithin_Iic_iff_exists_Icc_subset [NoMinOrder α] [DenselyOrdered
   _ ↔ ∃ l, l < a ∧ Icc l a ⊆ s := by simp only [dual_Icc]; rfl
 #align mem_nhds_within_Iic_iff_exists_Icc_subset mem_nhdsWithin_Iic_iff_exists_Icc_subset
 
+/-- The filter of left neighborhoods has a basis of closed intervals. -/
+theorem nhdsWithin_Iic_basis_Icc [NoMinOrder α] [DenselyOrdered α] {a : α} :
+    (𝓝[≤] a).HasBasis (· < a) (Icc · a) :=
+  ⟨fun _ ↦ mem_nhdsWithin_Iic_iff_exists_Icc_subset⟩
+
 end OrderTopology
 
 end LinearOrder

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -4,10 +4,10 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
 -/
 import Mathlib.Data.Set.Intervals.Pi
-import Mathlib.Data.Set.Pointwise.Interval
+import Mathlib.Data.Set.Pointwise.Basic
 import Mathlib.Order.Filter.Interval
 import Mathlib.Tactic.TFAE
-import Mathlib.Topology.Support
+import Mathlib.Topology.Separation
 import Mathlib.Topology.Algebra.Order.LeftRight
 
 #align_import topology.order.basic from "leanprover-community/mathlib"@"3efd324a3a31eaa40c9d5bfc669c4fafee5f9423"

Also add ge_of_tendsto_of_frequently

@@ -137,6 +137,10 @@ theorem closure_Iic (a : α) : closure (Iic a) = Iic a :=
   isClosed_Iic.closure_eq
 #align closure_Iic closure_Iic
 
+theorem le_of_tendsto_of_frequently {f : β → α} {a b : α} {x : Filter β} (lim : Tendsto f x (𝓝 a))
+    (h : ∃ᶠ c in x, f c ≤ b) : a ≤ b :=
+  (isClosed_le' b).mem_of_frequently_of_tendsto h lim
+
 theorem le_of_tendsto {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
     (h : ∀ᶠ c in x, f c ≤ b) : a ≤ b :=
   (isClosed_le' b).mem_of_tendsto lim h
@@ -165,6 +169,10 @@ theorem closure_Ici (a : α) : closure (Ici a) = Ici a :=
   isClosed_Ici.closure_eq
 #align closure_Ici closure_Ici
 
+lemma ge_of_tendsto_of_frequently {f : β → α} {a b : α} {x : Filter β} (lim : Tendsto f x (𝓝 a))
+    (h : ∃ᶠ c in x, b ≤ f c) : b ≤ a :=
+  (isClosed_ge' b).mem_of_frequently_of_tendsto h lim
+
 theorem ge_of_tendsto {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
     (h : ∀ᶠ c in x, b ≤ f c) : b ≤ a :=
   (isClosed_ge' b).mem_of_tendsto lim h

Rename

• Covby → CovBy, Wcovby → WCovBy
• *covby* → *covBy*
• wcovby.finset_val → WCovBy.finset_val, wcovby.finset_coe → WCovBy.finset_coe
• Covby.is_coatom → CovBy.isCoatom

@@ -414,7 +414,7 @@ theorem Ioo_mem_nhdsWithin_Ioi {a b c : α} (H : b ∈ Ico a c) : Ioo a c ∈ 
 theorem Ioo_mem_nhdsWithin_Ioi' {a b : α} (H : a < b) : Ioo a b ∈ 𝓝[>] a :=
   Ioo_mem_nhdsWithin_Ioi ⟨le_rfl, H⟩
 
-theorem Covby.nhdsWithin_Ioi {a b : α} (h : a ⋖ b) : 𝓝[>] a = ⊥ :=
+theorem CovBy.nhdsWithin_Ioi {a b : α} (h : a ⋖ b) : 𝓝[>] a = ⊥ :=
   empty_mem_iff_bot.mp <| h.Ioo_eq ▸ Ioo_mem_nhdsWithin_Ioi' h.1
 
 theorem Ioc_mem_nhdsWithin_Ioi {a b c : α} (H : b ∈ Ico a c) : Ioc a c ∈ 𝓝[>] b :=
@@ -476,7 +476,7 @@ theorem Ioo_mem_nhdsWithin_Iio {a b c : α} (H : b ∈ Ioc a c) : Ioo a c ∈ 
 theorem Ioo_mem_nhdsWithin_Iio' {a b : α} (H : a < b) : Ioo a b ∈ 𝓝[<] b :=
   Ioo_mem_nhdsWithin_Iio ⟨H, le_rfl⟩
 
-theorem Covby.nhdsWithin_Iio {a b : α} (h : a ⋖ b) : 𝓝[<] b = ⊥ :=
+theorem CovBy.nhdsWithin_Iio {a b : α} (h : a ⋖ b) : 𝓝[<] b = ⊥ :=
   empty_mem_iff_bot.mp <| h.Ioo_eq ▸ Ioo_mem_nhdsWithin_Iio' h.1
 
 theorem Ico_mem_nhdsWithin_Iio {a b c : α} (H : b ∈ Ioc a c) : Ico a c ∈ 𝓝[<] b :=
@@ -1337,7 +1337,7 @@ variable {α}
 -- porting note: new lemma
 /-- The set of points which are isolated on the right is countable when the space is
 second-countable. -/
-theorem countable_setOf_covby_right [SecondCountableTopology α] :
+theorem countable_setOf_covBy_right [SecondCountableTopology α] :
     Set.Countable { x : α | ∃ y, x ⋖ y } := by
   nontriviality α
   let s := { x : α | ∃ y, x ⋖ y }
@@ -1379,24 +1379,24 @@ theorem countable_setOf_covby_right [SecondCountableTopology α] :
 
 /-- The set of points which are isolated on the right is countable when the space is
 second-countable. -/
-@[deprecated countable_setOf_covby_right]
+@[deprecated countable_setOf_covBy_right]
 theorem countable_of_isolated_right' [SecondCountableTopology α] :
     Set.Countable { x : α | ∃ y, x < y ∧ Ioo x y = ∅ } := by
-  simpa only [← covby_iff_Ioo_eq] using countable_setOf_covby_right
+  simpa only [← covBy_iff_Ioo_eq] using countable_setOf_covBy_right
 #align countable_of_isolated_right countable_of_isolated_right'
 
 /-- The set of points which are isolated on the left is countable when the space is
 second-countable. -/
-theorem countable_setOf_covby_left [SecondCountableTopology α] :
+theorem countable_setOf_covBy_left [SecondCountableTopology α] :
     Set.Countable { x : α | ∃ y, y ⋖ x } := by
-  convert countable_setOf_covby_right (α := αᵒᵈ) using 5
-  exact toDual_covby_toDual_iff.symm
+  convert countable_setOf_covBy_right (α := αᵒᵈ) using 5
+  exact toDual_covBy_toDual_iff.symm
 
 /-- The set of points which are isolated on the left is countable when the space is
 second-countable. -/
 theorem countable_of_isolated_left' [SecondCountableTopology α] :
     Set.Countable { x : α | ∃ y, y < x ∧ Ioo y x = ∅ } := by
-  simpa only [← covby_iff_Ioo_eq] using countable_setOf_covby_left
+  simpa only [← covBy_iff_Ioo_eq] using countable_setOf_covBy_left
 #align countable_of_isolated_left countable_of_isolated_left'
 
 /-- Consider a disjoint family of intervals `(x, y)` with `x < y` in a second-countable space.
@@ -1408,7 +1408,7 @@ theorem Set.PairwiseDisjoint.countable_of_Ioo [SecondCountableTopology α] {y :
   have : (s \ { x | ∃ y, x ⋖ y }).Countable :=
     (h.subset (diff_subset _ _)).countable_of_isOpen (fun _ _ => isOpen_Ioo)
       fun x hx => (h' _ hx.1).exists_lt_lt (mt (Exists.intro (y x)) hx.2)
-  this.of_diff countable_setOf_covby_right
+  this.of_diff countable_setOf_covBy_right
 #align set.pairwise_disjoint.countable_of_Ioo Set.PairwiseDisjoint.countable_of_Ioo
 
 /-- For a function taking values in a second countable space, the set of points `x` for
@@ -1689,7 +1689,7 @@ theorem nhdsWithin_Ioi_eq_bot_iff {a : α} : 𝓝[>] a = ⊥ ↔ IsTop a ∨ ∃
   · simp [ha, ha.isMax.Ioi_eq]
   · simp only [ha, false_or]
     rw [isTop_iff_isMax, not_isMax_iff] at ha
-    simp only [(nhdsWithin_Ioi_basis' ha).eq_bot_iff, covby_iff_Ioo_eq]
+    simp only [(nhdsWithin_Ioi_basis' ha).eq_bot_iff, covBy_iff_Ioo_eq]
 
 /-- A set is a neighborhood of `a` within `(a, +∞)` if and only if it contains an interval `(a, u)`
 with `a < u`. -/
@@ -1704,7 +1704,7 @@ second-countable. -/
 theorem countable_setOf_isolated_right [SecondCountableTopology α] :
     { x : α | 𝓝[>] x = ⊥ }.Countable := by
   simp only [nhdsWithin_Ioi_eq_bot_iff, setOf_or]
-  exact (subsingleton_isTop α).countable.union countable_setOf_covby_right
+  exact (subsingleton_isTop α).countable.union countable_setOf_covBy_right
 
 /-- The set of points which are isolated on the left is countable when the space is
 second-countable. -/
@@ -1778,7 +1778,7 @@ theorem nhdsWithin_Iio_basis' {a : α} (h : ∃ b, b < a) : (𝓝[<] a).HasBasis
 theorem nhdsWithin_Iio_eq_bot_iff {a : α} : 𝓝[<] a = ⊥ ↔ IsBot a ∨ ∃ b, b ⋖ a := by
     convert (config := {preTransparency := .default})
       nhdsWithin_Ioi_eq_bot_iff (a := OrderDual.toDual a) using 4
-    exact ofDual_covby_ofDual_iff
+    exact ofDual_covBy_ofDual_iff
 
 open List in
 /-- The following statements are equivalent:

See Zulip thread for the discussion.

@@ -1043,7 +1043,7 @@ theorem StrictMono.embedding_of_ordConnected {α β : Type*} [LinearOrder α] [L
 order is the same as the restriction to the subset of the order topology. -/
 instance orderTopology_of_ordConnected {α : Type u} [TopologicalSpace α] [LinearOrder α]
     [OrderTopology α] {t : Set α} [ht : OrdConnected t] : OrderTopology t :=
-  ⟨(Subtype.strictMono_coe t).induced_topology_eq_preorder $ by
+  ⟨(Subtype.strictMono_coe t).induced_topology_eq_preorder <| by
     rwa [← @Subtype.range_val _ t] at ht⟩
 #align order_topology_of_ord_connected orderTopology_of_ordConnected
 

• rename Finset.Nonempty.image_iff to Finset.image_nonempty, deprecate the old version;
• rename Set.nonempty_image_iff to Set.image_nonempty, deprecate the old version;
• drop unneeded Finset.Nonempty arguments here and there;
• add versions of some lemmas that assume Nonempty s instead of Nonempty (s.image f) or Nonempty (s.map f).

@@ -2937,7 +2937,7 @@ theorem Monotone.tendsto_nhdsWithin_Iio {α β : Type*} [LinearOrder α] [Topolo
   refine' tendsto_order.2 ⟨fun l hl => _, fun m hm => _⟩
   · obtain ⟨z, zx, lz⟩ : ∃ a : α, a < x ∧ l < f a := by
       simpa only [mem_image, exists_prop, exists_exists_and_eq_and] using
-        exists_lt_of_lt_csSup (nonempty_image_iff.2 h) hl
+        exists_lt_of_lt_csSup (h.image _) hl
     exact mem_of_superset (Ioo_mem_nhdsWithin_Iio' zx) fun y hy => lz.trans_le (Mf hy.1.le)
   · refine mem_of_superset self_mem_nhdsWithin fun _ hy => lt_of_le_of_lt ?_ hm
     exact le_csSup (Mf.map_bddAbove bddAbove_Iio) (mem_image_of_mem _ hy)

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.

@@ -2774,7 +2774,7 @@ theorem IsClosed.sInf_mem {α : Type u} [TopologicalSpace α] [CompleteLinearOrd
 this supremum to the supremum of the image of this set. -/
 theorem Monotone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
     (Mf : Monotone f) (fbot : f ⊥ = ⊥) : f (sSup s) = sSup (f '' s) := by
-  cases' s.eq_empty_or_nonempty with h h
+  rcases s.eq_empty_or_nonempty with h | h
   · simp [h, fbot]
   · exact Mf.map_sSup_of_continuousAt' Cf h
 #align monotone.map_Sup_of_continuous_at Monotone.map_sSup_of_continuousAt

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

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

@@ -1365,11 +1365,11 @@ theorem countable_setOf_covby_right [SecondCountableTopology α] :
     rcases hxx'.lt_or_lt with (h' | h')
     · refine' disjoint_left.2 fun u ux ux' => xt.2.2.1 _
       refine' h'z x' x't ⟨ux'.1.trans_le (ux.2.trans (hy x xt.1).le), _⟩
-      by_contra' H
+      by_contra! H
       exact lt_irrefl _ ((Hy _ _ xt.1 H).trans_lt h')
     · refine' disjoint_left.2 fun u ux ux' => x't.2.2.1 _
       refine' h'z x xt ⟨ux.1.trans_le (ux'.2.trans (hy x' x't.1).le), _⟩
-      by_contra' H
+      by_contra! H
       exact lt_irrefl _ ((Hy _ _ x't.1 H).trans_lt h')
   refine' this.countable_of_isOpen (fun x hx => _) fun x hx => ⟨x, hz x hx, le_rfl⟩
   suffices H : Ioc (z x) x = Ioo (z x) (y x)

This PR renames the field Clopens.clopen' -> Clopens.isClopen', and the lemmas

• preimage_closed_of_closed -> ContinuousOn.preimage_isClosed_of_isClosed

as well as: ClopenUpperSet.clopen -> ClopenUpperSet.isClopen connectedComponent_eq_iInter_clopen -> connectedComponent_eq_iInter_isClopen connectedComponent_subset_iInter_clopen -> connectedComponent_subset_iInter_isClopen continuous_boolIndicator_iff_clopen -> continuous_boolIndicator_iff_isClopen continuousOn_boolIndicator_iff_clopen -> continuousOn_boolIndicator_iff_isClopen DiscreteQuotient.ofClopen -> DiscreteQuotient.ofIsClopen disjoint_or_subset_of_clopen -> disjoint_or_subset_of_isClopen exists_clopen_{lower,upper}of_not_le -> exists_isClopen{lower,upper}_of_not_le exists_clopen_of_cofiltered -> exists_isClopen_of_cofiltered exists_clopen_of_totally_separated -> exists_isClopen_of_totally_separated exists_clopen_upper_or_lower_of_ne -> exists_isClopen_upper_or_lower_of_ne IsPreconnected.subset_clopen -> IsPreconnected.subset_isClopen isTotallyDisconnected_of_clopen_set -> isTotallyDisconnected_of_isClopen_set LocallyConstant.ofClopen_fiber_one -> LocallyConstant.ofIsClopen_fiber_one LocallyConstant.ofClopen_fiber_zero -> LocallyConstant.ofIsClopen_fiber_zero LocallyConstant.ofClopen -> LocallyConstant.ofIsClopen preimage_clopen_of_clopen -> preimage_isClopen_of_isClopen TopologicalSpace.Clopens.clopen -> TopologicalSpace.Clopens.isClopen

@@ -256,7 +256,7 @@ theorem ContinuousWithinAt.closure_le [TopologicalSpace β] {f g : β → α} {s
 then the set `{x ∈ s | f x ≤ g x}` is a closed set. -/
 theorem IsClosed.isClosed_le [TopologicalSpace β] {f g : β → α} {s : Set β} (hs : IsClosed s)
     (hf : ContinuousOn f s) (hg : ContinuousOn g s) : IsClosed ({ x ∈ s | f x ≤ g x }) :=
-  (hf.prod hg).preimage_closed_of_closed hs OrderClosedTopology.isClosed_le'
+  (hf.prod hg).preimage_isClosed_of_isClosed hs OrderClosedTopology.isClosed_le'
 #align is_closed.is_closed_le IsClosed.isClosed_le
 
 theorem le_on_closure [TopologicalSpace β] {f g : β → α} {s : Set β} (h : ∀ x ∈ s, f x ≤ g x)

These are split from #8226 (and subsequent changes in #8366), and arise from the fact the latest Lean is better at detecting these due to better abstraction.

I can't comment on whether any of these should be concerning, but putting them in a small commit makes it easier for someone to find and review them later.

Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -954,7 +954,7 @@ theorem tendsto_order_unbounded {f : β → α} {a : α} {x : Filter β} (hu : 
 
 end Preorder
 
-instance tendstoIxxNhdsWithin {α : Type*} [Preorder α] [TopologicalSpace α] (a : α) {s t : Set α}
+instance tendstoIxxNhdsWithin {α : Type*} [TopologicalSpace α] (a : α) {s t : Set α}
     {Ixx} [TendstoIxxClass Ixx (𝓝 a) (𝓝 a)] [TendstoIxxClass Ixx (𝓟 s) (𝓟 t)] :
     TendstoIxxClass Ixx (𝓝[s] a) (𝓝[t] a) :=
   Filter.tendstoIxxClass_inf

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

@@ -1681,6 +1681,9 @@ theorem nhdsWithin_Ioi_basis' {a : α} (h : ∃ b, a < b) : (𝓝[>] a).HasBasis
   let ⟨_, h⟩ := h
   ⟨fun _ => mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' h⟩
 
+lemma nhdsWithin_Ioi_basis [NoMaxOrder α] (a : α) : (𝓝[>] a).HasBasis (a < ·) (Ioo a) :=
+  nhdsWithin_Ioi_basis' <| exists_gt a
+
 theorem nhdsWithin_Ioi_eq_bot_iff {a : α} : 𝓝[>] a = ⊥ ↔ IsTop a ∨ ∃ b, a ⋖ b := by
   by_cases ha : IsTop a
   · simp [ha, ha.isMax.Ioi_eq]

All the other properties of topological spaces like T0Space or RegularSpace are in the root namespace. Many files were opening TopologicalSpace just for the sake of shortening TopologicalSpace.SecondCountableTopology...

@@ -1326,7 +1326,7 @@ variable (α)
 /-- Let `α` be a densely ordered linear order with order topology. If `α` is a separable space, then
 it has second countable topology. Note that the "densely ordered" assumption cannot be dropped, see
 [double arrow space](https://topology.pi-base.org/spaces/S000093) for a counterexample. -/
-theorem TopologicalSpace.SecondCountableTopology.of_separableSpace_orderTopology [DenselyOrdered α]
+theorem SecondCountableTopology.of_separableSpace_orderTopology [DenselyOrdered α]
     [SeparableSpace α] : SecondCountableTopology α := by
   rcases exists_countable_dense α with ⟨s, hc, hd⟩
   refine ⟨⟨_, ?_, hd.topology_eq_generateFrom⟩⟩

• Add frequently_lt_nhds and frequently_gt_nhds.
• Move some lemmas from Topology/Order/Basic to Topology/Algebra/Order/LeftRight.
• Relax TC assumptions in Filter.Eventually.exists_lt (and *_gt). New versions assume NeBot (𝓝[<] a) and NeBot (𝓝[>] a), so the latter one can be applied, e.g., to ((a : ℝ≥0) : ℝ≥0∞).

From the Mandelbrot set connectedness project.

Co-Authored-By: @girving

@@ -276,25 +276,6 @@ theorem IsClosed.hypograph [TopologicalSpace β] {f : β → α} {s : Set β} (h
   (hs.preimage continuous_fst).isClosed_le continuousOn_snd (hf.comp continuousOn_fst Subset.rfl)
 #align is_closed.hypograph IsClosed.hypograph
 
--- Porting note: todo: move these lemmas to `Topology.Algebra.Order.LeftRight`
-theorem nhdsWithin_Ici_neBot {a b : α} (H₂ : a ≤ b) : NeBot (𝓝[Ici a] b) :=
-  nhdsWithin_neBot_of_mem H₂
-#align nhds_within_Ici_ne_bot nhdsWithin_Ici_neBot
-
-@[instance]
-theorem nhdsWithin_Ici_self_neBot (a : α) : NeBot (𝓝[≥] a) :=
-  nhdsWithin_Ici_neBot (le_refl a)
-#align nhds_within_Ici_self_ne_bot nhdsWithin_Ici_self_neBot
-
-theorem nhdsWithin_Iic_neBot {a b : α} (H : a ≤ b) : NeBot (𝓝[Iic b] a) :=
-  nhdsWithin_neBot_of_mem H
-#align nhds_within_Iic_ne_bot nhdsWithin_Iic_neBot
-
-@[instance]
-theorem nhdsWithin_Iic_self_neBot (a : α) : NeBot (𝓝[≤] a) :=
-  nhdsWithin_Iic_neBot (le_refl a)
-#align nhds_within_Iic_self_ne_bot nhdsWithin_Iic_self_neBot
-
 end Preorder
 
 section PartialOrder
@@ -2477,12 +2458,6 @@ instance nhdsWithin_Ioi_self_neBot [NoMaxOrder α] (a : α) : NeBot (𝓝[>] a)
   nhdsWithin_Ioi_neBot (le_refl a)
 #align nhds_within_Ioi_self_ne_bot nhdsWithin_Ioi_self_neBot
 
-theorem Filter.Eventually.exists_gt [NoMaxOrder α] {a : α} {p : α → Prop} (h : ∀ᶠ x in 𝓝 a, p x) :
-    ∃ b > a, p b := by
-  simpa only [exists_prop, gt_iff_lt, and_comm] using
-    ((h.filter_mono (@nhdsWithin_le_nhds _ _ a (Ioi a))).and self_mem_nhdsWithin).exists
-#align filter.eventually.exists_gt Filter.Eventually.exists_gt
-
 theorem nhdsWithin_Iio_neBot' {b c : α} (H₁ : (Iio c).Nonempty) (H₂ : b ≤ c) :
     NeBot (𝓝[Iio c] b) :=
   mem_closure_iff_nhdsWithin_neBot.1 <| by rwa [closure_Iio' H₁]
@@ -2500,11 +2475,6 @@ instance nhdsWithin_Iio_self_neBot [NoMinOrder α] (a : α) : NeBot (𝓝[<] a)
   nhdsWithin_Iio_neBot (le_refl a)
 #align nhds_within_Iio_self_ne_bot nhdsWithin_Iio_self_neBot
 
-theorem Filter.Eventually.exists_lt [NoMinOrder α] {a : α} {p : α → Prop} (h : ∀ᶠ x in 𝓝 a, p x) :
-    ∃ b < a, p b :=
-  Filter.Eventually.exists_gt (α := αᵒᵈ) h
-#align filter.eventually.exists_lt Filter.Eventually.exists_lt
-
 theorem right_nhdsWithin_Ico_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ico a b] b) :=
   (isLUB_Ico H).nhdsWithin_neBot (nonempty_Ico.2 H)
 #align right_nhds_within_Ico_ne_bot right_nhdsWithin_Ico_neBot

Currently, the layercake formula for the Lebesgue integral assumes sigma-finiteness of the measure, while the layercake formula for the Bochner integral (and integrable functions) doesn't. At the cost of a more complicated proof, we remove the sigma-finiteness also from the Lebesgue measure case.

Co-authored-by: Kalle <kalle.kytola@aalto.fi>

@@ -1430,6 +1430,60 @@ theorem Set.PairwiseDisjoint.countable_of_Ioo [SecondCountableTopology α] {y :
   this.of_diff countable_setOf_covby_right
 #align set.pairwise_disjoint.countable_of_Ioo Set.PairwiseDisjoint.countable_of_Ioo
 
+/-- For a function taking values in a second countable space, the set of points `x` for
+which the image under `f` of `(x, ∞)` is separated above from `f x` is countable. -/
+theorem countable_image_lt_image_Ioi [LinearOrder β] (f : β → α) [SecondCountableTopology α] :
+    Set.Countable {x | ∃ z, f x < z ∧ ∀ y, x < y → z ≤ f y} := by
+  /- If the values of `f` are separated above on the right of `x`, there is an interval `(f x, z x)`
+    which is not reached by `f`. This gives a family of disjoint open intervals in `α`. Such a
+    family can only be countable as `α` is second-countable. -/
+  nontriviality β
+  have : Nonempty α := Nonempty.map f (by infer_instance)
+  let s := {x | ∃ z, f x < z ∧ ∀ y, x < y → z ≤ f y}
+  have : ∀ x, x ∈ s → ∃ z, f x < z ∧ ∀ y, x < y → z ≤ f y := fun x hx ↦ hx
+  -- choose `z x` such that `f` does not take the values in `(f x, z x)`.
+  choose! z hz using this
+  have I : InjOn f s := by
+    apply StrictMonoOn.injOn
+    intro x hx y _ hxy
+    calc
+      f x < z x := (hz x hx).1
+      _ ≤ f y := (hz x hx).2 y hxy
+  -- show that `f s` is countable by arguing that a disjoint family of disjoint open intervals
+  -- (the intervals `(f x, z x)`) is at most countable.
+  have fs_count : (f '' s).Countable := by
+    have A : (f '' s).PairwiseDisjoint fun x => Ioo x (z (invFunOn f s x)) := by
+      rintro _ ⟨u, us, rfl⟩ _ ⟨v, vs, rfl⟩ huv
+      wlog hle : u ≤ v generalizing u v
+      · exact (this v vs u us huv.symm (le_of_not_le hle)).symm
+      have hlt : u < v := hle.lt_of_ne (ne_of_apply_ne _ huv)
+      apply disjoint_iff_forall_ne.2
+      rintro a ha b hb rfl
+      simp only [I.leftInvOn_invFunOn us, I.leftInvOn_invFunOn vs] at ha hb
+      exact lt_irrefl _ ((ha.2.trans_le ((hz u us).2 v hlt)).trans hb.1)
+    apply Set.PairwiseDisjoint.countable_of_Ioo A
+    rintro _ ⟨y, ys, rfl⟩
+    simpa only [I.leftInvOn_invFunOn ys] using (hz y ys).1
+  exact MapsTo.countable_of_injOn (mapsTo_image f s) I fs_count
+
+/-- For a function taking values in a second countable space, the set of points `x` for
+which the image under `f` of `(x, ∞)` is separated below from `f x` is countable. -/
+theorem countable_image_gt_image_Ioi [LinearOrder β] (f : β → α) [SecondCountableTopology α] :
+    Set.Countable {x | ∃ z, z < f x ∧ ∀ y, x < y → f y ≤ z} :=
+  countable_image_lt_image_Ioi (α := αᵒᵈ) f
+
+/-- For a function taking values in a second countable space, the set of points `x` for
+which the image under `f` of `(-∞, x)` is separated above from `f x` is countable. -/
+theorem countable_image_lt_image_Iio [LinearOrder β] (f : β → α) [SecondCountableTopology α] :
+    Set.Countable {x | ∃ z, f x < z ∧ ∀ y, y < x → z ≤ f y} :=
+  countable_image_lt_image_Ioi (β := βᵒᵈ) f
+
+/-- For a function taking values in a second countable space, the set of points `x` for
+which the image under `f` of `(-∞, x)` is separated below from `f x` is countable. -/
+theorem countable_image_gt_image_Iio [LinearOrder β] (f : β → α) [SecondCountableTopology α] :
+    Set.Countable {x | ∃ z, z < f x ∧ ∀ y, y < x → f y ≤ z} :=
+  countable_image_lt_image_Ioi (α := αᵒᵈ) (β := βᵒᵈ) f
+
 instance instIsCountablyGenerated_atTop [SecondCountableTopology α] :
     IsCountablyGenerated (atTop : Filter α) := by
   by_cases h : ∃ (x : α), IsTop x

Also add IsClosed.isGreatest_csSup.

@@ -2832,6 +2832,14 @@ theorem IsClosed.csInf_mem {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B :
   (isGLB_csInf hs B).mem_of_isClosed hs hc
 #align is_closed.cInf_mem IsClosed.csInf_mem
 
+theorem IsClosed.isLeast_csInf {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddBelow s) :
+    IsLeast s (sInf s) :=
+  ⟨hc.csInf_mem hs B, (isGLB_csInf hs B).1⟩
+
+theorem IsClosed.isGreatest_csSup {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddAbove s) :
+    IsGreatest s (sSup s) :=
+  IsClosed.isLeast_csInf (α := αᵒᵈ) hc hs B
+
 /-- If a monotone function is continuous at the supremum of a nonempty bounded above set `s`,
 then it sends this supremum to the supremum of the image of `s`. -/
 theorem Monotone.map_csSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))

@@ -1430,6 +1430,40 @@ theorem Set.PairwiseDisjoint.countable_of_Ioo [SecondCountableTopology α] {y :
   this.of_diff countable_setOf_covby_right
 #align set.pairwise_disjoint.countable_of_Ioo Set.PairwiseDisjoint.countable_of_Ioo
 
+instance instIsCountablyGenerated_atTop [SecondCountableTopology α] :
+    IsCountablyGenerated (atTop : Filter α) := by
+  by_cases h : ∃ (x : α), IsTop x
+  · rcases h with ⟨x, hx⟩
+    rw [atTop_eq_pure_of_isTop hx]
+    exact isCountablyGenerated_pure x
+  · rcases exists_countable_basis α with ⟨b, b_count, b_ne, hb⟩
+    have : Countable b := by exact Iff.mpr countable_coe_iff b_count
+    have A : ∀ (s : b), ∃ (x : α), x ∈ (s : Set α) := by
+      intro s
+      have : (s : Set α) ≠ ∅ := by
+        intro H
+        apply b_ne
+        convert s.2
+        exact H.symm
+      exact Iff.mp nmem_singleton_empty this
+    choose a ha using A
+    have : (atTop : Filter α) = (generate (Ici '' (range a))) := by
+      apply atTop_eq_generate_of_not_bddAbove
+      intro ⟨x, hx⟩
+      simp only [IsTop, not_exists, not_forall, not_le] at h
+      rcases h x with ⟨y, hy⟩
+      obtain ⟨s, sb, -, hs⟩ : ∃ s, s ∈ b ∧ y ∈ s ∧ s ⊆ Ioi x :=
+        hb.exists_subset_of_mem_open hy isOpen_Ioi
+      have I : a ⟨s, sb⟩ ≤ x := hx (mem_range_self _)
+      have J : x < a ⟨s, sb⟩ := hs (ha ⟨s, sb⟩)
+      exact lt_irrefl _ (I.trans_lt J)
+    rw [this]
+    exact ⟨_, (countable_range _).image _, rfl⟩
+
+instance instIsCountablyGenerated_atBot [SecondCountableTopology α] :
+    IsCountablyGenerated (atBot : Filter α) :=
+  @instIsCountablyGenerated_atTop αᵒᵈ _ _ _ _
+
 section Pi
 
 /-!

@@ -226,7 +226,7 @@ theorem le_of_tendsto_of_tendsto {f g : β → α} {b : Filter β} {a₁ a₂ :
   show (a₁, a₂) ∈ { p : α × α | p.1 ≤ p.2 } from t.isClosed_le'.mem_of_tendsto this h
 #align le_of_tendsto_of_tendsto le_of_tendsto_of_tendsto
 
-alias le_of_tendsto_of_tendsto ← tendsto_le_of_eventuallyLE
+alias tendsto_le_of_eventuallyLE := le_of_tendsto_of_tendsto
 #align tendsto_le_of_eventually_le tendsto_le_of_eventuallyLE
 
 theorem le_of_tendsto_of_tendsto' {f g : β → α} {b : Filter β} {a₁ a₂ : α} [NeBot b]
@@ -2081,7 +2081,7 @@ theorem IsLUB.mem_of_isClosed {a : α} {s : Set α} (ha : IsLUB s a) (hs : s.Non
   sc.closure_subset <| ha.mem_closure hs
 #align is_lub.mem_of_is_closed IsLUB.mem_of_isClosed
 
-alias IsLUB.mem_of_isClosed ← IsClosed.isLUB_mem
+alias IsClosed.isLUB_mem := IsLUB.mem_of_isClosed
 #align is_closed.is_lub_mem IsClosed.isLUB_mem
 
 theorem IsGLB.mem_of_isClosed {a : α} {s : Set α} (ha : IsGLB s a) (hs : s.Nonempty)
@@ -2089,7 +2089,7 @@ theorem IsGLB.mem_of_isClosed {a : α} {s : Set α} (ha : IsGLB s a) (hs : s.Non
   sc.closure_subset <| ha.mem_closure hs
 #align is_glb.mem_of_is_closed IsGLB.mem_of_isClosed
 
-alias IsGLB.mem_of_isClosed ← IsClosed.isGLB_mem
+alias IsClosed.isGLB_mem := IsGLB.mem_of_isClosed
 #align is_closed.is_glb_mem IsClosed.isGLB_mem
 
 /-!

As discussed a while ago on Zulip, we introduce classes expressing that a certain topology has closed Icis/Iics, which is sufficient to get boundedness of compacts on the desired side. The main application is that these now apply to types satisfying UpperTopology/LowerTopology, which will allow us to apply these compactness results to semicontinuous functions.

The naming was discussed here

@@ -86,6 +86,24 @@ universe u v w
 
 variable {α : Type u} {β : Type v} {γ : Type w}
 
+/-- If `α` is a topological space and a preorder, `ClosedIicTopology α` means that `Iic a` is
+closed for all `a : α`. -/
+class ClosedIicTopology (α : Type*) [TopologicalSpace α] [Preorder α] : Prop where
+  /-- For any `a`, the set `{b | b ≤ a}` is closed. -/
+  isClosed_le' (a : α) : IsClosed { b : α | b ≤ a }
+
+export ClosedIicTopology (isClosed_le')
+#align is_closed_le' ClosedIicTopology.isClosed_le'
+
+/-- If `α` is a topological space and a preorder, `ClosedIciTopology α` means that `Ici a` is
+closed for all `a : α`. -/
+class ClosedIciTopology (α : Type*) [TopologicalSpace α] [Preorder α] : Prop where
+  /-- For any `a`, the set `{b | a ≤ b}` is closed. -/
+  isClosed_ge' (a : α) : IsClosed { b : α | a ≤ b }
+
+export ClosedIciTopology (isClosed_ge')
+#align is_closed_ge' ClosedIciTopology.isClosed_ge'
+
 /-- A topology on a set which is both a topological space and a preorder is _order-closed_ if the
 set of points `(x, y)` with `x ≤ y` is closed in the product space. We introduce this as a mixin.
 This property is satisfied for the order topology on a linear order, but it can be satisfied more
@@ -103,6 +121,62 @@ theorem Dense.orderDual [TopologicalSpace α] {s : Set α} (hs : Dense s) :
   hs
 #align dense.order_dual Dense.orderDual
 
+section ClosedIicTopology
+
+variable [TopologicalSpace α] [Preorder α] [t : ClosedIicTopology α]
+
+instance : ClosedIciTopology αᵒᵈ where
+  isClosed_ge' a := isClosed_le' (α := α) a
+
+theorem isClosed_Iic {a : α} : IsClosed (Iic a) :=
+  isClosed_le' a
+#align is_closed_Iic isClosed_Iic
+
+@[simp]
+theorem closure_Iic (a : α) : closure (Iic a) = Iic a :=
+  isClosed_Iic.closure_eq
+#align closure_Iic closure_Iic
+
+theorem le_of_tendsto {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
+    (h : ∀ᶠ c in x, f c ≤ b) : a ≤ b :=
+  (isClosed_le' b).mem_of_tendsto lim h
+#align le_of_tendsto le_of_tendsto
+
+theorem le_of_tendsto' {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
+    (h : ∀ c, f c ≤ b) : a ≤ b :=
+  le_of_tendsto lim (eventually_of_forall h)
+#align le_of_tendsto' le_of_tendsto'
+
+end ClosedIicTopology
+
+section ClosedIciTopology
+
+variable [TopologicalSpace α] [Preorder α] [t : ClosedIciTopology α]
+
+instance : ClosedIicTopology αᵒᵈ where
+  isClosed_le' a := isClosed_ge' (α := α) a
+
+theorem isClosed_Ici {a : α} : IsClosed (Ici a) :=
+  isClosed_ge' a
+#align is_closed_Ici isClosed_Ici
+
+@[simp]
+theorem closure_Ici (a : α) : closure (Ici a) = Ici a :=
+  isClosed_Ici.closure_eq
+#align closure_Ici closure_Ici
+
+theorem ge_of_tendsto {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
+    (h : ∀ᶠ c in x, b ≤ f c) : b ≤ a :=
+  (isClosed_ge' b).mem_of_tendsto lim h
+#align ge_of_tendsto ge_of_tendsto
+
+theorem ge_of_tendsto' {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
+    (h : ∀ c, b ≤ f c) : b ≤ a :=
+  ge_of_tendsto lim (eventually_of_forall h)
+#align ge_of_tendsto' ge_of_tendsto'
+
+end ClosedIciTopology
+
 section OrderClosedTopology
 
 section Preorder
@@ -128,21 +202,11 @@ theorem isClosed_le [TopologicalSpace β] {f g : β → α} (hf : Continuous f)
   continuous_iff_isClosed.mp (hf.prod_mk hg) _ isClosed_le_prod
 #align is_closed_le isClosed_le
 
-theorem isClosed_le' (a : α) : IsClosed { b | b ≤ a } :=
-  isClosed_le continuous_id continuous_const
-#align is_closed_le' isClosed_le'
+instance : ClosedIicTopology α where
+  isClosed_le' _ := isClosed_le continuous_id continuous_const
 
-theorem isClosed_Iic {a : α} : IsClosed (Iic a) :=
-  isClosed_le' a
-#align is_closed_Iic isClosed_Iic
-
-theorem isClosed_ge' (a : α) : IsClosed { b | a ≤ b } :=
-  isClosed_le continuous_const continuous_id
-#align is_closed_ge' isClosed_ge'
-
-theorem isClosed_Ici {a : α} : IsClosed (Ici a) :=
-  isClosed_ge' a
-#align is_closed_Ici isClosed_Ici
+instance : ClosedIciTopology α where
+  isClosed_ge' _ := isClosed_le continuous_const continuous_id
 
 instance : OrderClosedTopology αᵒᵈ :=
   ⟨(OrderClosedTopology.isClosed_le' (α := α)).preimage continuous_swap⟩
@@ -156,16 +220,6 @@ theorem closure_Icc (a b : α) : closure (Icc a b) = Icc a b :=
   isClosed_Icc.closure_eq
 #align closure_Icc closure_Icc
 
-@[simp]
-theorem closure_Iic (a : α) : closure (Iic a) = Iic a :=
-  isClosed_Iic.closure_eq
-#align closure_Iic closure_Iic
-
-@[simp]
-theorem closure_Ici (a : α) : closure (Ici a) = Ici a :=
-  isClosed_Ici.closure_eq
-#align closure_Ici closure_Ici
-
 theorem le_of_tendsto_of_tendsto {f g : β → α} {b : Filter β} {a₁ a₂ : α} [NeBot b]
     (hf : Tendsto f b (𝓝 a₁)) (hg : Tendsto g b (𝓝 a₂)) (h : f ≤ᶠ[b] g) : a₁ ≤ a₂ :=
   have : Tendsto (fun b => (f b, g b)) b (𝓝 (a₁, a₂)) := hf.prod_mk_nhds hg
@@ -180,26 +234,6 @@ theorem le_of_tendsto_of_tendsto' {f g : β → α} {b : Filter β} {a₁ a₂ :
   le_of_tendsto_of_tendsto hf hg (eventually_of_forall h)
 #align le_of_tendsto_of_tendsto' le_of_tendsto_of_tendsto'
 
-theorem le_of_tendsto {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
-    (h : ∀ᶠ c in x, f c ≤ b) : a ≤ b :=
-  le_of_tendsto_of_tendsto lim tendsto_const_nhds h
-#align le_of_tendsto le_of_tendsto
-
-theorem le_of_tendsto' {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
-    (h : ∀ c, f c ≤ b) : a ≤ b :=
-  le_of_tendsto lim (eventually_of_forall h)
-#align le_of_tendsto' le_of_tendsto'
-
-theorem ge_of_tendsto {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
-    (h : ∀ᶠ c in x, b ≤ f c) : b ≤ a :=
-  le_of_tendsto_of_tendsto tendsto_const_nhds lim h
-#align ge_of_tendsto ge_of_tendsto
-
-theorem ge_of_tendsto' {f : β → α} {a b : α} {x : Filter β} [NeBot x] (lim : Tendsto f x (𝓝 a))
-    (h : ∀ c, b ≤ f c) : b ≤ a :=
-  ge_of_tendsto lim (eventually_of_forall h)
-#align ge_of_tendsto' ge_of_tendsto'
-
 @[simp]
 theorem closure_le_eq [TopologicalSpace β] {f g : β → α} (hf : Continuous f) (hg : Continuous g) :
     closure { b | f b ≤ g b } = { b | f b ≤ g b } :=

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

This has nice performance benefits.

@@ -90,7 +90,7 @@ variable {α : Type u} {β : Type v} {γ : Type w}
 set of points `(x, y)` with `x ≤ y` is closed in the product space. We introduce this as a mixin.
 This property is satisfied for the order topology on a linear order, but it can be satisfied more
 generally, and suffices to derive many interesting properties relating order and topology. -/
-class OrderClosedTopology (α : Type _) [TopologicalSpace α] [Preorder α] : Prop where
+class OrderClosedTopology (α : Type*) [TopologicalSpace α] [Preorder α] : Prop where
   /-- The set `{ (x, y) | x ≤ y }` is a closed set. -/
   isClosed_le' : IsClosed { p : α × α | p.1 ≤ p.2 }
 #align order_closed_topology OrderClosedTopology
@@ -807,7 +807,7 @@ instance [Preorder α] [TopologicalSpace α] [OrderClosedTopology α] [Preorder
   ⟨(isClosed_le continuous_fst.fst continuous_snd.fst).inter
     (isClosed_le continuous_fst.snd continuous_snd.snd)⟩
 
-instance {ι : Type _} {α : ι → Type _} [∀ i, Preorder (α i)] [∀ i, TopologicalSpace (α i)]
+instance {ι : Type*} {α : ι → Type*} [∀ i, Preorder (α i)] [∀ i, TopologicalSpace (α i)]
     [∀ i, OrderClosedTopology (α i)] : OrderClosedTopology (∀ i, α i) := by
   constructor
   simp only [Pi.le_def, setOf_forall]
@@ -823,7 +823,7 @@ instance Pi.orderClosedTopology' [Preorder β] [TopologicalSpace β] [OrderClose
 it on a preorder, but it is mostly interesting in linear orders, where it is also order-closed.
 We define it as a mixin. If you want to introduce the order topology on a preorder, use
 `Preorder.topology`. -/
-class OrderTopology (α : Type _) [t : TopologicalSpace α] [Preorder α] : Prop where
+class OrderTopology (α : Type*) [t : TopologicalSpace α] [Preorder α] : Prop where
   /-- The topology is generated by open intervals `Set.Ioi _` and `Set.Iio _`. -/
   topology_eq_generate_intervals : t = generateFrom { s | ∃ a, s = Ioi a ∨ s = Iio a }
 #align order_topology OrderTopology
@@ -832,7 +832,7 @@ class OrderTopology (α : Type _) [t : TopologicalSpace α] [Preorder α] : Prop
 `(a, ∞) = { x ∣ a < x }, (-∞ , b) = {x ∣ x < b}` for all `a, b` in `α`. We do not register it as an
 instance as many ordered sets are already endowed with the same topology, most often in a non-defeq
 way though. Register as a local instance when necessary. -/
-def Preorder.topology (α : Type _) [Preorder α] : TopologicalSpace α :=
+def Preorder.topology (α : Type*) [Preorder α] : TopologicalSpace α :=
   generateFrom { s : Set α | ∃ a : α, s = { b : α | a < b } ∨ s = { b : α | b < a } }
 #align preorder.topology Preorder.topology
 
@@ -939,13 +939,13 @@ theorem tendsto_order_unbounded {f : β → α} {a : α} {x : Filter β} (hu : 
 
 end Preorder
 
-instance tendstoIxxNhdsWithin {α : Type _} [Preorder α] [TopologicalSpace α] (a : α) {s t : Set α}
+instance tendstoIxxNhdsWithin {α : Type*} [Preorder α] [TopologicalSpace α] (a : α) {s t : Set α}
     {Ixx} [TendstoIxxClass Ixx (𝓝 a) (𝓝 a)] [TendstoIxxClass Ixx (𝓟 s) (𝓟 t)] :
     TendstoIxxClass Ixx (𝓝[s] a) (𝓝[t] a) :=
   Filter.tendstoIxxClass_inf
 #align tendsto_Ixx_nhds_within tendstoIxxNhdsWithin
 
-instance tendstoIccClassNhdsPi {ι : Type _} {α : ι → Type _} [∀ i, Preorder (α i)]
+instance tendstoIccClassNhdsPi {ι : Type*} {α : ι → Type*} [∀ i, Preorder (α i)]
     [∀ i, TopologicalSpace (α i)] [∀ i, OrderTopology (α i)] (f : ∀ i, α i) :
     TendstoIxxClass Icc (𝓝 f) (𝓝 f) := by
   constructor
@@ -1008,7 +1008,7 @@ theorem induced_orderTopology {α : Type u} {β : Type v} [Preorder α] [ta : To
 
 /-- The topology induced by a strictly monotone function with order-connected range is the preorder
 topology. -/
-nonrec theorem StrictMono.induced_topology_eq_preorder {α β : Type _} [LinearOrder α]
+nonrec theorem StrictMono.induced_topology_eq_preorder {α β : Type*} [LinearOrder α]
     [LinearOrder β] [t : TopologicalSpace β] [OrderTopology β] {f : α → β}
     (hf : StrictMono f) (hc : OrdConnected (range f)) : t.induced f = Preorder.topology α := by
   refine induced_topology_eq_preorder hf.lt_iff_lt (fun h₁ h₂ => ?_) fun h₁ h₂ => ?_
@@ -1019,7 +1019,7 @@ nonrec theorem StrictMono.induced_topology_eq_preorder {α β : Type _} [LinearO
 
 /-- A strictly monotone function between linear orders with order topology is a topological
 embedding provided that the range of `f` is order-connected. -/
-theorem StrictMono.embedding_of_ordConnected {α β : Type _} [LinearOrder α] [LinearOrder β]
+theorem StrictMono.embedding_of_ordConnected {α β : Type*} [LinearOrder α] [LinearOrder β]
     [TopologicalSpace α] [h : OrderTopology α] [TopologicalSpace β] [OrderTopology β] {f : α → β}
     (hf : StrictMono f) (hc : OrdConnected (range f)) : Embedding f :=
   ⟨⟨h.1.trans <| Eq.symm <| hf.induced_topology_eq_preorder hc⟩, hf.injective⟩
@@ -1406,7 +1406,7 @@ sometimes Lean fails to unify different instances while trying to apply the depe
 e.g., `ι → ℝ`.
 -/
 
-variable {ι : Type _} {π : ι → Type _} [Finite ι] [∀ i, LinearOrder (π i)]
+variable {ι : Type*} {π : ι → Type*} [Finite ι] [∀ i, LinearOrder (π i)]
   [∀ i, TopologicalSpace (π i)] [∀ i, OrderTopology (π i)] {a b x : ∀ i, π i} {a' b' x' : ι → α}
 
 theorem pi_Iic_mem_nhds (ha : ∀ i, x i < a i) : Iic a ∈ 𝓝 x :=
@@ -1808,7 +1808,7 @@ theorem nhds_eq_iInf_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| <
   · refine (Equiv.subRight a).iInf_congr fun x => ?_; simp [Iio]
 #align nhds_eq_infi_abs_sub nhds_eq_iInf_abs_sub
 
-theorem orderTopology_of_nhds_abs {α : Type _} [TopologicalSpace α] [LinearOrderedAddCommGroup α]
+theorem orderTopology_of_nhds_abs {α : Type*} [TopologicalSpace α] [LinearOrderedAddCommGroup α]
     (h_nhds : ∀ a : α, 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r }) : OrderTopology α := by
   refine' ⟨eq_of_nhds_eq_nhds fun a => _⟩
   rw [h_nhds]
@@ -2085,7 +2085,7 @@ theorem IsLUB.exists_seq_monotone_tendsto {t : Set α} {x : α} [IsCountablyGene
     exact ⟨u, hu.1.monotone, fun n => (hu.2.1 n).le, hu.2.2⟩
 #align is_lub.exists_seq_monotone_tendsto IsLUB.exists_seq_monotone_tendsto
 
-theorem exists_seq_strictMono_tendsto' {α : Type _} [LinearOrder α] [TopologicalSpace α]
+theorem exists_seq_strictMono_tendsto' {α : Type*} [LinearOrder α] [TopologicalSpace α]
     [DenselyOrdered α] [OrderTopology α] [FirstCountableTopology α] {x y : α} (hy : y < x) :
     ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n ∈ Ioo y x) ∧ Tendsto u atTop (𝓝 x) := by
   have hx : x ∉ Ioo y x := fun h => (lt_irrefl x h.2).elim
@@ -2108,7 +2108,7 @@ theorem exists_seq_strictMono_tendsto_nhdsWithin [DenselyOrdered α] [NoMinOrder
   ⟨u, hu, hx, tendsto_nhdsWithin_mono_right (range_subset_iff.2 hx) <| tendsto_nhdsWithin_range.2 h⟩
 #align exists_seq_strict_mono_tendsto_nhds_within exists_seq_strictMono_tendsto_nhdsWithin
 
-theorem exists_seq_tendsto_sSup {α : Type _} [ConditionallyCompleteLinearOrder α]
+theorem exists_seq_tendsto_sSup {α : Type*} [ConditionallyCompleteLinearOrder α]
     [TopologicalSpace α] [OrderTopology α] [FirstCountableTopology α] {S : Set α} (hS : S.Nonempty)
     (hS' : BddAbove S) : ∃ u : ℕ → α, Monotone u ∧ Tendsto u atTop (𝓝 (sSup S)) ∧ ∀ n, u n ∈ S := by
   rcases (isLUB_csSup hS hS').exists_seq_monotone_tendsto hS with ⟨u, hu⟩
@@ -2155,7 +2155,7 @@ theorem exists_seq_strictAnti_strictMono_tendsto [DenselyOrdered α] [FirstCount
       fun k l => (hu_anti.antitone (zero_le k)).trans_lt (hv_mem l).1, hux, hvy⟩
 #align exists_seq_strict_anti_strict_mono_tendsto exists_seq_strictAnti_strictMono_tendsto
 
-theorem exists_seq_tendsto_sInf {α : Type _} [ConditionallyCompleteLinearOrder α]
+theorem exists_seq_tendsto_sInf {α : Type*} [ConditionallyCompleteLinearOrder α]
     [TopologicalSpace α] [OrderTopology α] [FirstCountableTopology α] {S : Set α} (hS : S.Nonempty)
     (hS' : BddBelow S) : ∃ u : ℕ → α, Antitone u ∧ Tendsto u atTop (𝓝 (sInf S)) ∧ ∀ n, u n ∈ S :=
   exists_seq_tendsto_sSup (α := αᵒᵈ) hS hS'
@@ -2590,7 +2590,7 @@ theorem Monotone.map_sSup_of_continuousAt' {f : α → β} {A : Set α} (Cf : Co
 
 /-- A monotone function continuous at the indexed supremum over a nonempty `Sort` sends this indexed
 supremum to the indexed supremum of the composition. -/
-theorem Monotone.map_iSup_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
+theorem Monotone.map_iSup_of_continuousAt' {ι : Sort*} [Nonempty ι] {f : α → β} {g : ι → α}
     (Cf : ContinuousAt f (iSup g)) (Mf : Monotone f)
     (bdd : BddAbove (range g) := by bddDefault) : f (⨆ i, g i) = ⨆ i, f (g i) := by
   rw [iSup, Monotone.map_sSup_of_continuousAt' Cf Mf (range_nonempty g) bdd, ← range_comp, iSup]
@@ -2607,7 +2607,7 @@ theorem Monotone.map_sInf_of_continuousAt' {f : α → β} {A : Set α} (Cf : Co
 
 /-- A monotone function continuous at the indexed infimum over a nonempty `Sort` sends this indexed
 infimum to the indexed infimum of the composition. -/
-theorem Monotone.map_iInf_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
+theorem Monotone.map_iInf_of_continuousAt' {ι : Sort*} [Nonempty ι] {f : α → β} {g : ι → α}
     (Cf : ContinuousAt f (iInf g)) (Mf : Monotone f)
     (bdd : BddBelow (range g) := by bddDefault) : f (⨅ i, g i) = ⨅ i, f (g i) := by
   rw [iInf, Monotone.map_sInf_of_continuousAt' Cf Mf (range_nonempty g) bdd, ← range_comp, iInf]
@@ -2624,7 +2624,7 @@ theorem Antitone.map_sInf_of_continuousAt' {f : α → β} {A : Set α} (Cf : Co
 
 /-- An antitone function continuous at the indexed infimum over a nonempty `Sort` sends this indexed
 infimum to the indexed supremum of the composition. -/
-theorem Antitone.map_iInf_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
+theorem Antitone.map_iInf_of_continuousAt' {ι : Sort*} [Nonempty ι] {f : α → β} {g : ι → α}
     (Cf : ContinuousAt f (iInf g)) (Af : Antitone f)
     (bdd : BddBelow (range g) := by bddDefault) : f (⨅ i, g i) = ⨆ i, f (g i) := by
   rw [iInf, Antitone.map_sInf_of_continuousAt' Cf Af (range_nonempty g) bdd, ← range_comp, iSup]
@@ -2641,7 +2641,7 @@ theorem Antitone.map_sSup_of_continuousAt' {f : α → β} {A : Set α} (Cf : Co
 
 /-- An antitone function continuous at the indexed supremum over a nonempty `Sort` sends this
 indexed supremum to the indexed infimum of the composition. -/
-theorem Antitone.map_iSup_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
+theorem Antitone.map_iSup_of_continuousAt' {ι : Sort*} [Nonempty ι] {f : α → β} {g : ι → α}
     (Cf : ContinuousAt f (iSup g)) (Af : Antitone f)
     (bdd : BddAbove (range g) := by bddDefault) : f (⨆ i, g i) = ⨅ i, f (g i) := by
   rw [iSup, Antitone.map_sSup_of_continuousAt' Cf Af (range_nonempty g) bdd, ← range_comp, iInf]
@@ -2686,7 +2686,7 @@ theorem Monotone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : Con
 
 /-- If a monotone function sending `bot` to `bot` is continuous at the indexed supremum over
 a `Sort`, then it sends this indexed supremum to the indexed supremum of the composition. -/
-theorem Monotone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
+theorem Monotone.map_iSup_of_continuousAt {ι : Sort*} {f : α → β} {g : ι → α}
     (Cf : ContinuousAt f (iSup g)) (Mf : Monotone f) (fbot : f ⊥ = ⊥) :
     f (⨆ i, g i) = ⨆ i, f (g i) := by
   rw [iSup, Mf.map_sSup_of_continuousAt Cf fbot, ← range_comp, iSup]; rfl
@@ -2701,7 +2701,7 @@ theorem Monotone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : Con
 
 /-- If a monotone function sending `top` to `top` is continuous at the indexed infimum over
 a `Sort`, then it sends this indexed infimum to the indexed infimum of the composition. -/
-theorem Monotone.map_iInf_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
+theorem Monotone.map_iInf_of_continuousAt {ι : Sort*} {f : α → β} {g : ι → α}
     (Cf : ContinuousAt f (iInf g)) (Mf : Monotone f) (ftop : f ⊤ = ⊤) : f (iInf g) = iInf (f ∘ g) :=
   Monotone.map_iSup_of_continuousAt (α := αᵒᵈ) (β := βᵒᵈ) Cf Mf.dual ftop
 #align monotone.map_infi_of_continuous_at Monotone.map_iInf_of_continuousAt
@@ -2716,7 +2716,7 @@ theorem Antitone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : Con
 
 /-- An antitone function sending `bot` to `top` is continuous at the indexed supremum over
 a `Sort`, then it sends this indexed supremum to the indexed supremum of the composition. -/
-theorem Antitone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
+theorem Antitone.map_iSup_of_continuousAt {ι : Sort*} {f : α → β} {g : ι → α}
     (Cf : ContinuousAt f (iSup g)) (Af : Antitone f) (fbot : f ⊥ = ⊤) :
     f (⨆ i, g i) = ⨅ i, f (g i) :=
   Monotone.map_iSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (iSup g) from Cf) Af
@@ -2733,7 +2733,7 @@ theorem Antitone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : Con
 
 /-- If an antitone function sending `top` to `bot` is continuous at the indexed infimum over
 a `Sort`, then it sends this indexed infimum to the indexed supremum of the composition. -/
-theorem Antitone.map_iInf_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
+theorem Antitone.map_iInf_of_continuousAt {ι : Sort*} {f : α → β} {g : ι → α}
     (Cf : ContinuousAt f (iInf g)) (Af : Antitone f) (ftop : f ⊤ = ⊥) : f (iInf g) = iSup (f ∘ g) :=
   Monotone.map_iInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (iInf g) from Cf) Af
     ftop
@@ -2827,7 +2827,7 @@ theorem Antitone.map_ciInf_of_continuousAt {f : α → β} {g : γ → α} (Cf :
 #align antitone.map_cinfi_of_continuous_at Antitone.map_ciInf_of_continuousAt
 
 /-- A monotone map has a limit to the left of any point `x`, equal to `sSup (f '' (Iio x))`. -/
-theorem Monotone.tendsto_nhdsWithin_Iio {α β : Type _} [LinearOrder α] [TopologicalSpace α]
+theorem Monotone.tendsto_nhdsWithin_Iio {α β : Type*} [LinearOrder α] [TopologicalSpace α]
     [OrderTopology α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderTopology β]
     {f : α → β} (Mf : Monotone f) (x : α) : Tendsto f (𝓝[<] x) (𝓝 (sSup (f '' Iio x))) := by
   rcases eq_empty_or_nonempty (Iio x) with (h | h); · simp [h]
@@ -2841,7 +2841,7 @@ theorem Monotone.tendsto_nhdsWithin_Iio {α β : Type _} [LinearOrder α] [Topol
 #align monotone.tendsto_nhds_within_Iio Monotone.tendsto_nhdsWithin_Iio
 
 /-- A monotone map has a limit to the right of any point `x`, equal to `sInf (f '' (Ioi x))`. -/
-theorem Monotone.tendsto_nhdsWithin_Ioi {α β : Type _} [LinearOrder α] [TopologicalSpace α]
+theorem Monotone.tendsto_nhdsWithin_Ioi {α β : Type*} [LinearOrder α] [TopologicalSpace α]
     [OrderTopology α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderTopology β]
     {f : α → β} (Mf : Monotone f) (x : α) : Tendsto f (𝓝[>] x) (𝓝 (sInf (f '' Ioi x))) :=
   Monotone.tendsto_nhdsWithin_Iio (α := αᵒᵈ) (β := βᵒᵈ) Mf.dual x

Generalize some existing lemmas from CompleteLinearOrders to ConditionallyCompleteLinearOrders, adding the appropriate boundedness assumptions:

• Monotone.map_limsSup_of_continuousAt + its 3 order-dual variants
• Monotone.map_limsup_of_continuousAt + its 3 order-dual variants
• Monotone.map_sSup_of_continuousAt' + its 3 order-dual variants
• Monotone.map_iSup_of_continuousAt' + its 3 order-dual variants

For the first two to work automatically still on CompleteLinearOrders, the existing macro tactic isBoundedDefault about boundedness of filters is used. For the last two to work automatically still on CompleteLinearOrders, a similar new macro tactic bddDefault about boundedness of sets is included in the PR.

Co-authored-by: kkytola <39528102+kkytola@users.noreply.github.com>

@@ -145,7 +145,7 @@ theorem isClosed_Ici {a : α} : IsClosed (Ici a) :=
 #align is_closed_Ici isClosed_Ici
 
 instance : OrderClosedTopology αᵒᵈ :=
-  ⟨(@OrderClosedTopology.isClosed_le' α _ _ _).preimage continuous_swap⟩
+  ⟨(OrderClosedTopology.isClosed_le' (α := α)).preimage continuous_swap⟩
 
 theorem isClosed_Icc {a b : α} : IsClosed (Icc a b) :=
   IsClosed.inter isClosed_Ici isClosed_Iic
@@ -636,7 +636,7 @@ theorem frontier_Iic_subset (a : α) : frontier (Iic a) ⊆ {a} :=
 #align frontier_Iic_subset frontier_Iic_subset
 
 theorem frontier_Ici_subset (a : α) : frontier (Ici a) ⊆ {a} :=
-  @frontier_Iic_subset αᵒᵈ _ _ _ _
+  frontier_Iic_subset (α := αᵒᵈ) _
 #align frontier_Ici_subset frontier_Ici_subset
 
 theorem frontier_lt_subset_eq (hf : Continuous f) (hg : Continuous g) :
@@ -682,7 +682,7 @@ protected theorem Continuous.min (hf : Continuous f) (hg : Continuous g) :
 @[continuity]
 protected theorem Continuous.max (hf : Continuous f) (hg : Continuous g) :
     Continuous fun b => max (f b) (g b) :=
-  @Continuous.min αᵒᵈ _ _ _ _ _ _ _ hf hg
+  Continuous.min (α := αᵒᵈ) hf hg
 #align continuous.max Continuous.max
 
 end
@@ -731,22 +731,22 @@ theorem Filter.tendsto_nhds_max_left {l : Filter β} {a : α} (h : Tendsto f l (
 
 theorem Filter.Tendsto.min_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
     Tendsto (fun i => min a (f i)) l (𝓝 a) :=
-  @Filter.Tendsto.max_right αᵒᵈ β _ _ _ f l a h
+  Filter.Tendsto.max_right (α := αᵒᵈ) h
 #align filter.tendsto.min_right Filter.Tendsto.min_right
 
 theorem Filter.Tendsto.min_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝 a)) :
     Tendsto (fun i => min (f i) a) l (𝓝 a) :=
-  @Filter.Tendsto.max_left αᵒᵈ β _ _ _ f l a h
+  Filter.Tendsto.max_left (α := αᵒᵈ) h
 #align filter.tendsto.min_left Filter.Tendsto.min_left
 
 theorem Filter.tendsto_nhds_min_right {l : Filter β} {a : α} (h : Tendsto f l (𝓝[<] a)) :
     Tendsto (fun i => min a (f i)) l (𝓝[<] a) :=
-  @Filter.tendsto_nhds_max_right αᵒᵈ β _ _ _ f l a h
+  Filter.tendsto_nhds_max_right (α := αᵒᵈ) h
 #align filter.tendsto_nhds_min_right Filter.tendsto_nhds_min_right
 
 theorem Filter.tendsto_nhds_min_left {l : Filter β} {a : α} (h : Tendsto f l (𝓝[<] a)) :
     Tendsto (fun i => min (f i) a) l (𝓝[<] a) :=
-  @Filter.tendsto_nhds_max_left αᵒᵈ β _ _ _ f l a h
+  Filter.tendsto_nhds_max_left (α := αᵒᵈ) h
 #align filter.tendsto_nhds_min_left Filter.tendsto_nhds_min_left
 
 protected theorem Dense.exists_lt [NoMinOrder α] {s : Set α} (hs : Dense s) (x : α) :
@@ -844,7 +844,7 @@ variable [TopologicalSpace α] [Preorder α] [t : OrderTopology α]
 
 instance : OrderTopology αᵒᵈ :=
   ⟨by
-    convert @OrderTopology.topology_eq_generate_intervals α _ _ _ using 6
+    convert OrderTopology.topology_eq_generate_intervals (α := α) using 6
     apply or_comm⟩
 
 theorem isOpen_iff_generate_intervals {s : Set α} :
@@ -1065,8 +1065,8 @@ theorem nhdsWithin_Ici_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopol
 
 theorem nhdsWithin_Iic_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopology α] {a : α}
     (ha : ∃ l, l < a) : (𝓝[≤] a).HasBasis (fun l => l < a) fun l => Ioc l a := by
-  convert @nhdsWithin_Ici_basis' αᵒᵈ _ _ _ (toDual a) ha using 2
-  exact (@dual_Ico _ _ _ _).symm
+  convert nhdsWithin_Ici_basis' (α := αᵒᵈ) ha using 2
+  exact dual_Ico.symm
 #align nhds_within_Iic_basis' nhdsWithin_Iic_basis'
 
 theorem nhdsWithin_Ici_basis [TopologicalSpace α] [LinearOrder α] [OrderTopology α] [NoMaxOrder α]
@@ -1095,7 +1095,7 @@ theorem nhds_top_basis [TopologicalSpace α] [LinearOrder α] [OrderTop α] [Ord
 
 theorem nhds_bot_basis [TopologicalSpace α] [LinearOrder α] [OrderBot α] [OrderTopology α]
     [Nontrivial α] : (𝓝 ⊥).HasBasis (fun a : α => ⊥ < a) fun a : α => Iio a :=
-  @nhds_top_basis αᵒᵈ _ _ _ _ _
+  nhds_top_basis (α := αᵒᵈ)
 #align nhds_bot_basis nhds_bot_basis
 
 theorem nhds_top_basis_Ici [TopologicalSpace α] [LinearOrder α] [OrderTop α] [OrderTopology α]
@@ -1107,7 +1107,7 @@ theorem nhds_top_basis_Ici [TopologicalSpace α] [LinearOrder α] [OrderTop α]
 
 theorem nhds_bot_basis_Iic [TopologicalSpace α] [LinearOrder α] [OrderBot α] [OrderTopology α]
     [Nontrivial α] [DenselyOrdered α] : (𝓝 ⊥).HasBasis (fun a : α => ⊥ < a) Iic :=
-  @nhds_top_basis_Ici αᵒᵈ _ _ _ _ _ _
+  nhds_top_basis_Ici (α := αᵒᵈ)
 #align nhds_bot_basis_Iic nhds_bot_basis_Iic
 
 theorem tendsto_nhds_top_mono [TopologicalSpace β] [Preorder β] [OrderTop β] [OrderTopology β]
@@ -1119,7 +1119,7 @@ theorem tendsto_nhds_top_mono [TopologicalSpace β] [Preorder β] [OrderTop β]
 
 theorem tendsto_nhds_bot_mono [TopologicalSpace β] [Preorder β] [OrderBot β] [OrderTopology β]
     {l : Filter α} {f g : α → β} (hf : Tendsto f l (𝓝 ⊥)) (hg : g ≤ᶠ[l] f) : Tendsto g l (𝓝 ⊥) :=
-  @tendsto_nhds_top_mono α βᵒᵈ _ _ _ _ _ _ _ hf hg
+  tendsto_nhds_top_mono (β := βᵒᵈ) hf hg
 #align tendsto_nhds_bot_mono tendsto_nhds_bot_mono
 
 theorem tendsto_nhds_top_mono' [TopologicalSpace β] [Preorder β] [OrderTop β] [OrderTopology β]
@@ -1213,7 +1213,7 @@ theorem exists_Icc_mem_subset_of_mem_nhdsWithin_Ici {a : α} {s : Set α} (hs :
 theorem exists_Icc_mem_subset_of_mem_nhdsWithin_Iic {a : α} {s : Set α} (hs : s ∈ 𝓝[≤] a) :
     ∃ b ≤ a, Icc b a ∈ 𝓝[≤] a ∧ Icc b a ⊆ s := by
   simpa only [dual_Icc, toDual.surjective.exists] using
-    @exists_Icc_mem_subset_of_mem_nhdsWithin_Ici αᵒᵈ _ _ _ (toDual a) _ hs
+    exists_Icc_mem_subset_of_mem_nhdsWithin_Ici (α := αᵒᵈ) (a := toDual a) hs
 #align exists_Icc_mem_subset_of_mem_nhds_within_Iic exists_Icc_mem_subset_of_mem_nhdsWithin_Iic
 
 theorem exists_Icc_mem_subset_of_mem_nhds {a : α} {s : Set α} (hs : s ∈ 𝓝 a) :
@@ -1374,7 +1374,7 @@ theorem countable_of_isolated_right' [SecondCountableTopology α] :
 second-countable. -/
 theorem countable_setOf_covby_left [SecondCountableTopology α] :
     Set.Countable { x : α | ∃ y, y ⋖ x } := by
-  convert @countable_setOf_covby_right αᵒᵈ _ _ _ _ using 5
+  convert countable_setOf_covby_right (α := αᵒᵈ) using 5
   exact toDual_covby_toDual_iff.symm
 
 /-- The set of points which are isolated on the left is countable when the space is
@@ -1493,12 +1493,12 @@ theorem inf_nhds_atTop [NoMaxOrder α] (x : α) : 𝓝 x ⊓ atTop = ⊥ :=
 #align inf_nhds_at_top inf_nhds_atTop
 
 theorem disjoint_nhds_atBot [NoMinOrder α] (x : α) : Disjoint (𝓝 x) atBot :=
-  @disjoint_nhds_atTop αᵒᵈ _ _ _ _ x
+  disjoint_nhds_atTop (α := αᵒᵈ) x
 #align disjoint_nhds_at_bot disjoint_nhds_atBot
 
 @[simp]
 theorem inf_nhds_atBot [NoMinOrder α] (x : α) : 𝓝 x ⊓ atBot = ⊥ :=
-  @inf_nhds_atTop αᵒᵈ _ _ _ _ x
+  inf_nhds_atTop (α := αᵒᵈ) x
 #align inf_nhds_at_bot inf_nhds_atBot
 
 theorem not_tendsto_nhds_of_tendsto_atTop [NoMaxOrder α] {F : Filter β} [NeBot F] {f : β → α}
@@ -1840,7 +1840,7 @@ theorem Filter.Tendsto.add_atTop {C : α} (hf : Tendsto f l (𝓝 C)) (hg : Tend
 and `g` tends to `atBot` then `f + g` tends to `atBot`. -/
 theorem Filter.Tendsto.add_atBot {C : α} (hf : Tendsto f l (𝓝 C)) (hg : Tendsto g l atBot) :
     Tendsto (fun x => f x + g x) l atBot :=
-  @Filter.Tendsto.add_atTop αᵒᵈ _ _ _ _ _ _ _ _ hf hg
+  Filter.Tendsto.add_atTop (α := αᵒᵈ) hf hg
 #align filter.tendsto.add_at_bot Filter.Tendsto.add_atBot
 
 /-- In a linearly ordered additive commutative group with the order topology, if `f` tends to
@@ -1932,7 +1932,7 @@ theorem IsLUB.frequently_nhds_mem {a : α} {s : Set α} (ha : IsLUB s a) (hs : s
 
 theorem IsGLB.frequently_mem {a : α} {s : Set α} (ha : IsGLB s a) (hs : s.Nonempty) :
     ∃ᶠ x in 𝓝[≥] a, x ∈ s :=
-  @IsLUB.frequently_mem αᵒᵈ _ _ _ _ _ ha hs
+  IsLUB.frequently_mem (α := αᵒᵈ) ha hs
 #align is_glb.frequently_mem IsGLB.frequently_mem
 
 theorem IsGLB.frequently_nhds_mem {a : α} {s : Set α} (ha : IsGLB s a) (hs : s.Nonempty) :
@@ -1954,7 +1954,7 @@ theorem IsLUB.nhdsWithin_neBot {a : α} {s : Set α} (ha : IsLUB s a) (hs : s.No
 #align is_lub.nhds_within_ne_bot IsLUB.nhdsWithin_neBot
 
 theorem IsGLB.nhdsWithin_neBot : ∀ {a : α} {s : Set α}, IsGLB s a → s.Nonempty → NeBot (𝓝[s] a) :=
-  @IsLUB.nhdsWithin_neBot αᵒᵈ _ _ _
+  IsLUB.nhdsWithin_neBot (α := αᵒᵈ)
 #align is_glb.nhds_within_ne_bot IsGLB.nhdsWithin_neBot
 
 theorem isLUB_of_mem_nhds {s : Set α} {a : α} {f : Filter α} (hsa : a ∈ upperBounds s) (hsf : s ∈ f)
@@ -1975,12 +1975,12 @@ theorem isLUB_of_mem_closure {s : Set α} {a : α} (hsa : a ∈ upperBounds s) (
 
 theorem isGLB_of_mem_nhds :
     ∀ {s : Set α} {a : α} {f : Filter α}, a ∈ lowerBounds s → s ∈ f → NeBot (f ⊓ 𝓝 a) → IsGLB s a :=
-  @isLUB_of_mem_nhds αᵒᵈ _ _ _
+  isLUB_of_mem_nhds (α := αᵒᵈ)
 #align is_glb_of_mem_nhds isGLB_of_mem_nhds
 
 theorem isGLB_of_mem_closure {s : Set α} {a : α} (hsa : a ∈ lowerBounds s) (hsf : a ∈ closure s) :
     IsGLB s a :=
-  @isLUB_of_mem_closure αᵒᵈ _ _ _ s a hsa hsf
+  isLUB_of_mem_closure (α := αᵒᵈ) hsa hsf
 #align is_glb_of_mem_closure isGLB_of_mem_closure
 
 theorem IsLUB.mem_upperBounds_of_tendsto [Preorder γ] [TopologicalSpace γ] [OrderClosedTopology γ]
@@ -2006,7 +2006,7 @@ theorem IsLUB.isLUB_of_tendsto [Preorder γ] [TopologicalSpace γ] [OrderClosedT
 theorem IsGLB.mem_lowerBounds_of_tendsto [Preorder γ] [TopologicalSpace γ] [OrderClosedTopology γ]
     {f : α → γ} {s : Set α} {a : α} {b : γ} (hf : MonotoneOn f s) (ha : IsGLB s a)
     (hb : Tendsto f (𝓝[s] a) (𝓝 b)) : b ∈ lowerBounds (f '' s) :=
-  @IsLUB.mem_upperBounds_of_tendsto αᵒᵈ γᵒᵈ _ _ _ _ _ _ _ _ _ _ hf.dual ha hb
+  IsLUB.mem_upperBounds_of_tendsto (α := αᵒᵈ) (γ := γᵒᵈ) hf.dual ha hb
 #align is_glb.mem_lower_bounds_of_tendsto IsGLB.mem_lowerBounds_of_tendsto
 
 -- For a version of this theorem in which the convergence considered on the domain `α` is as
@@ -2015,31 +2015,31 @@ theorem IsGLB.mem_lowerBounds_of_tendsto [Preorder γ] [TopologicalSpace γ] [Or
 theorem IsGLB.isGLB_of_tendsto [Preorder γ] [TopologicalSpace γ] [OrderClosedTopology γ] {f : α → γ}
     {s : Set α} {a : α} {b : γ} (hf : MonotoneOn f s) :
     IsGLB s a → s.Nonempty → Tendsto f (𝓝[s] a) (𝓝 b) → IsGLB (f '' s) b :=
-  @IsLUB.isLUB_of_tendsto αᵒᵈ γᵒᵈ _ _ _ _ _ _ f s a b hf.dual
+  IsLUB.isLUB_of_tendsto (α := αᵒᵈ) (γ := γᵒᵈ) hf.dual
 #align is_glb.is_glb_of_tendsto IsGLB.isGLB_of_tendsto
 
 theorem IsLUB.mem_lowerBounds_of_tendsto [Preorder γ] [TopologicalSpace γ] [OrderClosedTopology γ]
     {f : α → γ} {s : Set α} {a : α} {b : γ} (hf : AntitoneOn f s) (ha : IsLUB s a)
     (hb : Tendsto f (𝓝[s] a) (𝓝 b)) : b ∈ lowerBounds (f '' s) :=
-  @IsLUB.mem_upperBounds_of_tendsto α γᵒᵈ _ _ _ _ _ _ _ _ _ _ hf ha hb
+  IsLUB.mem_upperBounds_of_tendsto (γ := γᵒᵈ) hf ha hb
 #align is_lub.mem_lower_bounds_of_tendsto IsLUB.mem_lowerBounds_of_tendsto
 
 theorem IsLUB.isGLB_of_tendsto [Preorder γ] [TopologicalSpace γ] [OrderClosedTopology γ] :
     ∀ {f : α → γ} {s : Set α} {a : α} {b : γ},
       AntitoneOn f s → IsLUB s a → s.Nonempty → Tendsto f (𝓝[s] a) (𝓝 b) → IsGLB (f '' s) b :=
-  @IsLUB.isLUB_of_tendsto α γᵒᵈ _ _ _ _ _ _
+  IsLUB.isLUB_of_tendsto (γ := γᵒᵈ)
 #align is_lub.is_glb_of_tendsto IsLUB.isGLB_of_tendsto
 
 theorem IsGLB.mem_upperBounds_of_tendsto [Preorder γ] [TopologicalSpace γ] [OrderClosedTopology γ]
     {f : α → γ} {s : Set α} {a : α} {b : γ} (hf : AntitoneOn f s) (ha : IsGLB s a)
     (hb : Tendsto f (𝓝[s] a) (𝓝 b)) : b ∈ upperBounds (f '' s) :=
-  @IsGLB.mem_lowerBounds_of_tendsto α γᵒᵈ _ _ _ _ _ _ _ _ _ _ hf ha hb
+  IsGLB.mem_lowerBounds_of_tendsto (γ := γᵒᵈ) hf ha hb
 #align is_glb.mem_upper_bounds_of_tendsto IsGLB.mem_upperBounds_of_tendsto
 
 theorem IsGLB.isLUB_of_tendsto [Preorder γ] [TopologicalSpace γ] [OrderClosedTopology γ] :
     ∀ {f : α → γ} {s : Set α} {a : α} {b : γ},
       AntitoneOn f s → IsGLB s a → s.Nonempty → Tendsto f (𝓝[s] a) (𝓝 b) → IsLUB (f '' s) b :=
-  @IsGLB.isGLB_of_tendsto α γᵒᵈ _ _ _ _ _ _
+  IsGLB.isGLB_of_tendsto (γ := γᵒᵈ)
 #align is_glb.is_lub_of_tendsto IsGLB.isLUB_of_tendsto
 
 theorem IsLUB.mem_of_isClosed {a : α} {s : Set α} (ha : IsLUB s a) (hs : s.Nonempty)
@@ -2118,13 +2118,13 @@ theorem exists_seq_tendsto_sSup {α : Type _} [ConditionallyCompleteLinearOrder
 theorem IsGLB.exists_seq_strictAnti_tendsto_of_not_mem {t : Set α} {x : α}
     [IsCountablyGenerated (𝓝 x)] (htx : IsGLB t x) (not_mem : x ∉ t) (ht : t.Nonempty) :
     ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, x < u n) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t :=
-  @IsLUB.exists_seq_strictMono_tendsto_of_not_mem αᵒᵈ _ _ _ t x _ htx not_mem ht
+  IsLUB.exists_seq_strictMono_tendsto_of_not_mem (α := αᵒᵈ) htx not_mem ht
 #align is_glb.exists_seq_strict_anti_tendsto_of_not_mem IsGLB.exists_seq_strictAnti_tendsto_of_not_mem
 
 theorem IsGLB.exists_seq_antitone_tendsto {t : Set α} {x : α} [IsCountablyGenerated (𝓝 x)]
     (htx : IsGLB t x) (ht : t.Nonempty) :
     ∃ u : ℕ → α, Antitone u ∧ (∀ n, x ≤ u n) ∧ Tendsto u atTop (𝓝 x) ∧ ∀ n, u n ∈ t :=
-  @IsLUB.exists_seq_monotone_tendsto αᵒᵈ _ _ _ t x _ htx ht
+  IsLUB.exists_seq_monotone_tendsto (α := αᵒᵈ) htx ht
 #align is_glb.exists_seq_antitone_tendsto IsGLB.exists_seq_antitone_tendsto
 
 theorem exists_seq_strictAnti_tendsto' [DenselyOrdered α] [FirstCountableTopology α] {x y : α}
@@ -2135,13 +2135,13 @@ theorem exists_seq_strictAnti_tendsto' [DenselyOrdered α] [FirstCountableTopolo
 
 theorem exists_seq_strictAnti_tendsto [DenselyOrdered α] [NoMaxOrder α] [FirstCountableTopology α]
     (x : α) : ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, x < u n) ∧ Tendsto u atTop (𝓝 x) :=
-  @exists_seq_strictMono_tendsto αᵒᵈ _ _ _ _ _ _ x
+  exists_seq_strictMono_tendsto (α := αᵒᵈ) x
 #align exists_seq_strict_anti_tendsto exists_seq_strictAnti_tendsto
 
 theorem exists_seq_strictAnti_tendsto_nhdsWithin [DenselyOrdered α] [NoMaxOrder α]
     [FirstCountableTopology α] (x : α) :
     ∃ u : ℕ → α, StrictAnti u ∧ (∀ n, x < u n) ∧ Tendsto u atTop (𝓝[>] x) :=
-  @exists_seq_strictMono_tendsto_nhdsWithin αᵒᵈ _ _ _ _ _ _ _
+  exists_seq_strictMono_tendsto_nhdsWithin (α := αᵒᵈ) _
 #align exists_seq_strict_anti_tendsto_nhds_within exists_seq_strictAnti_tendsto_nhdsWithin
 
 theorem exists_seq_strictAnti_strictMono_tendsto [DenselyOrdered α] [FirstCountableTopology α]
@@ -2158,7 +2158,7 @@ theorem exists_seq_strictAnti_strictMono_tendsto [DenselyOrdered α] [FirstCount
 theorem exists_seq_tendsto_sInf {α : Type _} [ConditionallyCompleteLinearOrder α]
     [TopologicalSpace α] [OrderTopology α] [FirstCountableTopology α] {S : Set α} (hS : S.Nonempty)
     (hS' : BddBelow S) : ∃ u : ℕ → α, Antitone u ∧ Tendsto u atTop (𝓝 (sInf S)) ∧ ∀ n, u n ∈ S :=
-  @exists_seq_tendsto_sSup αᵒᵈ _ _ _ _ S hS hS'
+  exists_seq_tendsto_sSup (α := αᵒᵈ) hS hS'
 #align exists_seq_tendsto_Inf exists_seq_tendsto_sInf
 
 end OrderTopology
@@ -2186,7 +2186,7 @@ theorem closure_Ioi (a : α) [NoMaxOrder α] : closure (Ioi a) = Ici a :=
 /-- The closure of the interval `(-∞, a)` is the closed interval `(-∞, a]`, unless `a` is a bottom
 element. -/
 theorem closure_Iio' (h : (Iio a).Nonempty) : closure (Iio a) = Iic a :=
-  @closure_Ioi' αᵒᵈ _ _ _ _ _ h
+  closure_Ioi' (α := αᵒᵈ) h
 #align closure_Iio' closure_Iio'
 
 /-- The closure of the interval `(-∞, a)` is the interval `(-∞, a]`. -/
@@ -2238,7 +2238,7 @@ theorem interior_Ici [NoMinOrder α] {a : α} : interior (Ici a) = Ioi a :=
 
 @[simp]
 theorem interior_Iic' {a : α} (ha : (Ioi a).Nonempty) : interior (Iic a) = Iio a :=
-  @interior_Ici' αᵒᵈ _ _ _ _ _ ha
+  interior_Ici' (α := αᵒᵈ) ha
 #align interior_Iic' interior_Iic'
 
 theorem interior_Iic [NoMaxOrder α] {a : α} : interior (Iic a) = Iio a :=
@@ -2380,7 +2380,7 @@ instance nhdsWithin_Iio_self_neBot [NoMinOrder α] (a : α) : NeBot (𝓝[<] a)
 
 theorem Filter.Eventually.exists_lt [NoMinOrder α] {a : α} {p : α → Prop} (h : ∀ᶠ x in 𝓝 a, p x) :
     ∃ b < a, p b :=
-  @Filter.Eventually.exists_gt αᵒᵈ _ _ _ _ _ _ _ h
+  Filter.Eventually.exists_gt (α := αᵒᵈ) h
 #align filter.eventually.exists_lt Filter.Eventually.exists_lt
 
 theorem right_nhdsWithin_Ico_neBot {a b : α} (H : a < b) : NeBot (𝓝[Ico a b] b) :=
@@ -2460,7 +2460,7 @@ theorem comap_coe_Ioi_nhdsWithin_Ioi (a : α) : comap ((↑) : Ioi a → α) (
 #align comap_coe_Ioi_nhds_within_Ioi comap_coe_Ioi_nhdsWithin_Ioi
 
 theorem comap_coe_Iio_nhdsWithin_Iio (a : α) : comap ((↑) : Iio a → α) (𝓝[<] a) = atTop :=
-  @comap_coe_Ioi_nhdsWithin_Ioi αᵒᵈ _ _ _ _ a
+  comap_coe_Ioi_nhdsWithin_Ioi (α := αᵒᵈ) a
 #align comap_coe_Iio_nhds_within_Iio comap_coe_Iio_nhdsWithin_Iio
 
 @[simp]
@@ -2480,7 +2480,7 @@ theorem map_coe_Ioi_atBot (a : α) : map ((↑) : Ioi a → α) atBot = 𝓝[>]
 
 @[simp]
 theorem map_coe_Iio_atTop (a : α) : map ((↑) : Iio a → α) atTop = 𝓝[<] a :=
-  @map_coe_Ioi_atBot αᵒᵈ _ _ _ _ _
+  map_coe_Ioi_atBot (α := αᵒᵈ) _
 #align map_coe_Iio_at_top map_coe_Iio_atTop
 
 variable {l : Filter β} {f : α → β}
@@ -2573,6 +2573,83 @@ theorem exists_countable_dense_no_bot_top [SeparableSpace α] [Nontrivial α] :
 
 end DenselyOrdered
 
+section ConditionallyCompleteLinearOrder
+
+variable [ConditionallyCompleteLinearOrder α] [TopologicalSpace α] [OrderTopology α]
+  [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderClosedTopology β] [Nonempty γ]
+
+/-- A monotone function continuous at the supremum of a nonempty set sends this supremum to
+the supremum of the image of this set. -/
+theorem Monotone.map_sSup_of_continuousAt' {f : α → β} {A : Set α} (Cf : ContinuousAt f (sSup A))
+    (Mf : Monotone f) (A_nonemp : A.Nonempty) (A_bdd : BddAbove A := by bddDefault) :
+    f (sSup A) = sSup (f '' A) :=
+  --This is a particular case of the more general `IsLUB.isLUB_of_tendsto`
+  .symm <| ((isLUB_csSup A_nonemp A_bdd).isLUB_of_tendsto (Mf.monotoneOn _) A_nonemp <|
+    Cf.mono_left inf_le_left).csSup_eq (A_nonemp.image f)
+#align monotone.map_Sup_of_continuous_at' Monotone.map_sSup_of_continuousAt'
+
+/-- A monotone function continuous at the indexed supremum over a nonempty `Sort` sends this indexed
+supremum to the indexed supremum of the composition. -/
+theorem Monotone.map_iSup_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iSup g)) (Mf : Monotone f)
+    (bdd : BddAbove (range g) := by bddDefault) : f (⨆ i, g i) = ⨆ i, f (g i) := by
+  rw [iSup, Monotone.map_sSup_of_continuousAt' Cf Mf (range_nonempty g) bdd, ← range_comp, iSup]
+  rfl
+#align monotone.map_supr_of_continuous_at' Monotone.map_iSup_of_continuousAt'
+
+/-- A monotone function continuous at the infimum of a nonempty set sends this infimum to
+the infimum of the image of this set. -/
+theorem Monotone.map_sInf_of_continuousAt' {f : α → β} {A : Set α} (Cf : ContinuousAt f (sInf A))
+    (Mf : Monotone f) (A_nonemp : A.Nonempty) (A_bdd : BddBelow A := by bddDefault) :
+    f (sInf A) = sInf (f '' A) :=
+  Monotone.map_sSup_of_continuousAt' (α := αᵒᵈ) (β := βᵒᵈ) Cf Mf.dual A_nonemp A_bdd
+#align monotone.map_Inf_of_continuous_at' Monotone.map_sInf_of_continuousAt'
+
+/-- A monotone function continuous at the indexed infimum over a nonempty `Sort` sends this indexed
+infimum to the indexed infimum of the composition. -/
+theorem Monotone.map_iInf_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iInf g)) (Mf : Monotone f)
+    (bdd : BddBelow (range g) := by bddDefault) : f (⨅ i, g i) = ⨅ i, f (g i) := by
+  rw [iInf, Monotone.map_sInf_of_continuousAt' Cf Mf (range_nonempty g) bdd, ← range_comp, iInf]
+  rfl
+#align monotone.map_infi_of_continuous_at' Monotone.map_iInf_of_continuousAt'
+
+/-- An antitone function continuous at the infimum of a nonempty set sends this infimum to
+the supremum of the image of this set. -/
+theorem Antitone.map_sInf_of_continuousAt' {f : α → β} {A : Set α} (Cf : ContinuousAt f (sInf A))
+    (Af : Antitone f) (A_nonemp : A.Nonempty) (A_bdd : BddBelow A := by bddDefault) :
+    f (sInf A) = sSup (f '' A) :=
+  Monotone.map_sInf_of_continuousAt' (β := βᵒᵈ) Cf Af.dual_right A_nonemp A_bdd
+#align antitone.map_Inf_of_continuous_at' Antitone.map_sInf_of_continuousAt'
+
+/-- An antitone function continuous at the indexed infimum over a nonempty `Sort` sends this indexed
+infimum to the indexed supremum of the composition. -/
+theorem Antitone.map_iInf_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iInf g)) (Af : Antitone f)
+    (bdd : BddBelow (range g) := by bddDefault) : f (⨅ i, g i) = ⨆ i, f (g i) := by
+  rw [iInf, Antitone.map_sInf_of_continuousAt' Cf Af (range_nonempty g) bdd, ← range_comp, iSup]
+  rfl
+#align antitone.map_infi_of_continuous_at' Antitone.map_iInf_of_continuousAt'
+
+/-- An antitone function continuous at the supremum of a nonempty set sends this supremum to
+the infimum of the image of this set. -/
+theorem Antitone.map_sSup_of_continuousAt' {f : α → β} {A : Set α} (Cf : ContinuousAt f (sSup A))
+    (Af : Antitone f) (A_nonemp : A.Nonempty) (A_bdd : BddAbove A := by bddDefault) :
+    f (sSup A) = sInf (f '' A) :=
+  Monotone.map_sSup_of_continuousAt' (β := βᵒᵈ) Cf Af.dual_right A_nonemp A_bdd
+#align antitone.map_Sup_of_continuous_at' Antitone.map_sSup_of_continuousAt'
+
+/-- An antitone function continuous at the indexed supremum over a nonempty `Sort` sends this
+indexed supremum to the indexed infimum of the composition. -/
+theorem Antitone.map_iSup_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iSup g)) (Af : Antitone f)
+    (bdd : BddAbove (range g) := by bddDefault) : f (⨆ i, g i) = ⨅ i, f (g i) := by
+  rw [iSup, Antitone.map_sSup_of_continuousAt' Cf Af (range_nonempty g) bdd, ← range_comp, iInf]
+  rfl
+#align antitone.map_supr_of_continuous_at' Antitone.map_iSup_of_continuousAt'
+
+end ConditionallyCompleteLinearOrder
+
 section CompleteLinearOrder
 
 variable [CompleteLinearOrder α] [TopologicalSpace α] [OrderTopology α] [CompleteLinearOrder β]
@@ -2598,15 +2675,6 @@ theorem IsClosed.sInf_mem {α : Type u} [TopologicalSpace α] [CompleteLinearOrd
   (isGLB_sInf s).mem_of_isClosed hs hc
 #align is_closed.Inf_mem IsClosed.sInf_mem
 
-/-- A monotone function continuous at the supremum of a nonempty set sends this supremum to
-the supremum of the image of this set. -/
-theorem Monotone.map_sSup_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
-    (Mf : Monotone f) (hs : s.Nonempty) : f (sSup s) = sSup (f '' s) :=
-  --This is a particular case of the more general `IsLUB.isLUB_of_tendsto`
-  ((isLUB_sSup _).isLUB_of_tendsto (fun _ _ _ _ xy => Mf xy) hs <|
-    Cf.mono_left inf_le_left).sSup_eq.symm
-#align monotone.map_Sup_of_continuous_at' Monotone.map_sSup_of_continuousAt'
-
 /-- A monotone function `f` sending `bot` to `bot` and continuous at the supremum of a set sends
 this supremum to the supremum of the image of this set. -/
 theorem Monotone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
@@ -2616,13 +2684,6 @@ theorem Monotone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : Con
   · exact Mf.map_sSup_of_continuousAt' Cf h
 #align monotone.map_Sup_of_continuous_at Monotone.map_sSup_of_continuousAt
 
-/-- A monotone function continuous at the indexed supremum over a nonempty `Sort` sends this indexed
-supremum to the indexed supremum of the composition. -/
-theorem Monotone.map_iSup_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (iSup g)) (Mf : Monotone f) : f (⨆ i, g i) = ⨆ i, f (g i) := by
-  rw [iSup, Mf.map_sSup_of_continuousAt' Cf (range_nonempty g), ← range_comp, iSup]; rfl
-#align monotone.map_supr_of_continuous_at' Monotone.map_iSup_of_continuousAt'
-
 /-- If a monotone function sending `bot` to `bot` is continuous at the indexed supremum over
 a `Sort`, then it sends this indexed supremum to the indexed supremum of the composition. -/
 theorem Monotone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
@@ -2631,42 +2692,20 @@ theorem Monotone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι
   rw [iSup, Mf.map_sSup_of_continuousAt Cf fbot, ← range_comp, iSup]; rfl
 #align monotone.map_supr_of_continuous_at Monotone.map_iSup_of_continuousAt
 
-/-- A monotone function continuous at the infimum of a nonempty set sends this infimum to
-the infimum of the image of this set. -/
-theorem Monotone.map_sInf_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
-    (Mf : Monotone f) (hs : s.Nonempty) : f (sInf s) = sInf (f '' s) :=
-  @Monotone.map_sSup_of_continuousAt' αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual hs
-#align monotone.map_Inf_of_continuous_at' Monotone.map_sInf_of_continuousAt'
-
 /-- A monotone function `f` sending `top` to `top` and continuous at the infimum of a set sends
 this infimum to the infimum of the image of this set. -/
 theorem Monotone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
     (Mf : Monotone f) (ftop : f ⊤ = ⊤) : f (sInf s) = sInf (f '' s) :=
-  @Monotone.map_sSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual ftop
+  Monotone.map_sSup_of_continuousAt (α := αᵒᵈ) (β := βᵒᵈ) Cf Mf.dual ftop
 #align monotone.map_Inf_of_continuous_at Monotone.map_sInf_of_continuousAt
 
-/-- A monotone function continuous at the indexed infimum over a nonempty `Sort` sends this indexed
-infimum to the indexed infimum of the composition. -/
-theorem Monotone.map_iInf_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (iInf g)) (Mf : Monotone f) : f (⨅ i, g i) = ⨅ i, f (g i) :=
-  @Monotone.map_iSup_of_continuousAt' αᵒᵈ βᵒᵈ _ _ _ _ _ _ ι _ f g Cf Mf.dual
-#align monotone.map_infi_of_continuous_at' Monotone.map_iInf_of_continuousAt'
-
 /-- If a monotone function sending `top` to `top` is continuous at the indexed infimum over
 a `Sort`, then it sends this indexed infimum to the indexed infimum of the composition. -/
 theorem Monotone.map_iInf_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
     (Cf : ContinuousAt f (iInf g)) (Mf : Monotone f) (ftop : f ⊤ = ⊤) : f (iInf g) = iInf (f ∘ g) :=
-  @Monotone.map_iSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ ι f g Cf Mf.dual ftop
+  Monotone.map_iSup_of_continuousAt (α := αᵒᵈ) (β := βᵒᵈ) Cf Mf.dual ftop
 #align monotone.map_infi_of_continuous_at Monotone.map_iInf_of_continuousAt
 
-/-- An antitone function continuous at the supremum of a nonempty set sends this supremum to
-the infimum of the image of this set. -/
-theorem Antitone.map_sSup_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
-    (Af : Antitone f) (hs : s.Nonempty) : f (sSup s) = sInf (f '' s) :=
-  Monotone.map_sSup_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (sSup s) from Cf) Af
-    hs
-#align antitone.map_Sup_of_continuous_at' Antitone.map_sSup_of_continuousAt'
-
 /-- An antitone function `f` sending `bot` to `top` and continuous at the supremum of a set sends
 this supremum to the infimum of the image of this set. -/
 theorem Antitone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
@@ -2675,13 +2714,6 @@ theorem Antitone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : Con
     fbot
 #align antitone.map_Sup_of_continuous_at Antitone.map_sSup_of_continuousAt
 
-/-- An antitone function continuous at the indexed supremum over a nonempty `Sort` sends this
-indexed supremum to the indexed infimum of the composition. -/
-theorem Antitone.map_iSup_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (iSup g)) (Af : Antitone f) : f (⨆ i, g i) = ⨅ i, f (g i) :=
-  Monotone.map_iSup_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (iSup g) from Cf) Af
-#align antitone.map_supr_of_continuous_at' Antitone.map_iSup_of_continuousAt'
-
 /-- An antitone function sending `bot` to `top` is continuous at the indexed supremum over
 a `Sort`, then it sends this indexed supremum to the indexed supremum of the composition. -/
 theorem Antitone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
@@ -2691,14 +2723,6 @@ theorem Antitone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι
     fbot
 #align antitone.map_supr_of_continuous_at Antitone.map_iSup_of_continuousAt
 
-/-- An antitone function continuous at the infimum of a nonempty set sends this infimum to
-the supremum of the image of this set. -/
-theorem Antitone.map_sInf_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
-    (Af : Antitone f) (hs : s.Nonempty) : f (sInf s) = sSup (f '' s) :=
-  Monotone.map_sInf_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (sInf s) from Cf) Af
-    hs
-#align antitone.map_Inf_of_continuous_at' Antitone.map_sInf_of_continuousAt'
-
 /-- An antitone function `f` sending `top` to `bot` and continuous at the infimum of a set sends
 this infimum to the supremum of the image of this set. -/
 theorem Antitone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
@@ -2707,13 +2731,6 @@ theorem Antitone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : Con
     ftop
 #align antitone.map_Inf_of_continuous_at Antitone.map_sInf_of_continuousAt
 
-/-- An antitone function continuous at the indexed infimum over a nonempty `Sort` sends this indexed
-infimum to the indexed supremum of the composition. -/
-theorem Antitone.map_iInf_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (iInf g)) (Af : Antitone f) : f (⨅ i, g i) = ⨆ i, f (g i) :=
-  Monotone.map_iInf_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (iInf g) from Cf) Af
-#align antitone.map_infi_of_continuous_at' Antitone.map_iInf_of_continuousAt'
-
 /-- If an antitone function sending `top` to `bot` is continuous at the indexed infimum over
 a `Sort`, then it sends this indexed infimum to the indexed supremum of the composition. -/
 theorem Antitone.map_iInf_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
@@ -2767,14 +2784,14 @@ theorem Monotone.map_ciSup_of_continuousAt {f : α → β} {g : γ → α} (Cf :
 then it sends this infimum to the infimum of the image of `s`. -/
 theorem Monotone.map_csInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
     (Mf : Monotone f) (ne : s.Nonempty) (H : BddBelow s) : f (sInf s) = sInf (f '' s) :=
-  @Monotone.map_csSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual ne H
+  Monotone.map_csSup_of_continuousAt (α := αᵒᵈ) (β := βᵒᵈ) Cf Mf.dual ne H
 #align monotone.map_cInf_of_continuous_at Monotone.map_csInf_of_continuousAt
 
 /-- A continuous monotone function sends indexed infimum to indexed infimum in conditionally
 complete linear order, under a boundedness assumption. -/
 theorem Monotone.map_ciInf_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
     (Mf : Monotone f) (H : BddBelow (range g)) : f (⨅ i, g i) = ⨅ i, f (g i) :=
-  @Monotone.map_ciSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ _ Cf Mf.dual H
+  Monotone.map_ciSup_of_continuousAt (α := αᵒᵈ) (β := βᵒᵈ) Cf Mf.dual H
 #align monotone.map_cinfi_of_continuous_at Monotone.map_ciInf_of_continuousAt
 
 /-- If an antitone function is continuous at the supremum of a nonempty bounded above set `s`,
@@ -2827,7 +2844,7 @@ theorem Monotone.tendsto_nhdsWithin_Iio {α β : Type _} [LinearOrder α] [Topol
 theorem Monotone.tendsto_nhdsWithin_Ioi {α β : Type _} [LinearOrder α] [TopologicalSpace α]
     [OrderTopology α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderTopology β]
     {f : α → β} (Mf : Monotone f) (x : α) : Tendsto f (𝓝[>] x) (𝓝 (sInf (f '' Ioi x))) :=
-  @Monotone.tendsto_nhdsWithin_Iio αᵒᵈ βᵒᵈ _ _ _ _ _ _ f Mf.dual x
+  Monotone.tendsto_nhdsWithin_Iio (α := αᵒᵈ) (β := βᵒᵈ) Mf.dual x
 #align monotone.tendsto_nhds_within_Ioi Monotone.tendsto_nhdsWithin_Ioi
 
 end ConditionallyCompleteLinearOrder

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
-
-! This file was ported from Lean 3 source module topology.order.basic
-! leanprover-community/mathlib commit 3efd324a3a31eaa40c9d5bfc669c4fafee5f9423
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Set.Intervals.Pi
 import Mathlib.Data.Set.Pointwise.Interval
@@ -15,6 +10,8 @@ import Mathlib.Tactic.TFAE
 import Mathlib.Topology.Support
 import Mathlib.Topology.Algebra.Order.LeftRight
 
+#align_import topology.order.basic from "leanprover-community/mathlib"@"3efd324a3a31eaa40c9d5bfc669c4fafee5f9423"
+
 /-!
 # Theory of topology on ordered spaces
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -1021,7 +1021,7 @@ nonrec theorem StrictMono.induced_topology_eq_preorder {α β : Type _} [LinearO
     exact ⟨y, hf.lt_iff_lt.1 h₁, le_rfl⟩
 
 /-- A strictly monotone function between linear orders with order topology is a topological
-embedding provided that the range of `f` is  order-connected. -/
+embedding provided that the range of `f` is order-connected. -/
 theorem StrictMono.embedding_of_ordConnected {α β : Type _} [LinearOrder α] [LinearOrder β]
     [TopologicalSpace α] [h : OrderTopology α] [TopologicalSpace β] [OrderTopology β] {f : α → β}
     (hf : StrictMono f) (hc : OrdConnected (range f)) : Embedding f :=

@@ -2073,7 +2073,7 @@ theorem IsLUB.exists_seq_strictMono_tendsto_of_not_mem {t : Set α} {x : α}
   have hvx' : ∀ {n}, v n < x := (htx.1 (hvt _)).lt_of_ne (ne_of_mem_of_not_mem (hvt _) not_mem)
   have : ∀ k, ∀ᶠ l in atTop, v k < v l := fun k => hvx.eventually (lt_mem_nhds hvx')
   choose N hN hvN using fun k => ((eventually_gt_atTop k).and (this k)).exists
-  refine ⟨fun k => v ((N^[k]) 0), strictMono_nat_of_lt_succ fun _ => ?_, fun _ => hvx',
+  refine ⟨fun k => v (N^[k] 0), strictMono_nat_of_lt_succ fun _ => ?_, fun _ => hvx',
     hvx.comp (strictMono_nat_of_lt_succ fun _ => ?_).tendsto_atTop, fun _ => hvt _⟩
   · rw [iterate_succ_apply']; exact hvN _
   · rw [iterate_succ_apply']; exact hN _

Currently, (for both Set and Finset) insert_subset is an iff lemma stating that insert a s ⊆ t if and only if a ∈ t and s ⊆ t. For both types, this PR renames this lemma to insert_subset_iff, and adds an insert_subset lemma that gives the implication just in the reverse direction : namely theorem insert_subset (ha : a ∈ t) (hs : s ⊆ t) : insert a s ⊆ t .

This both aligns the naming with union_subset and union_subset_iff, and removes the need for the awkward insert_subset.mpr ⟨_,_⟩ idiom. It touches a lot of files (too many to list), but in a trivial way.

@@ -2206,7 +2206,7 @@ theorem closure_Ioo {a b : α} (hab : a ≠ b) : closure (Ioo a b) = Icc a b :=
   · cases' hab.lt_or_lt with hab hab
     · rw [← diff_subset_closure_iff, Icc_diff_Ioo_same hab.le]
       have hab' : (Ioo a b).Nonempty := nonempty_Ioo.2 hab
-      simp only [insert_subset, singleton_subset_iff]
+      simp only [insert_subset_iff, singleton_subset_iff]
       exact ⟨(isGLB_Ioo hab).mem_closure hab', (isLUB_Ioo hab).mem_closure hab'⟩
     · rw [Icc_eq_empty_of_lt hab]
       exact empty_subset _

@@ -1354,11 +1354,11 @@ theorem countable_setOf_covby_right [SecondCountableTopology α] :
     · refine' disjoint_left.2 fun u ux ux' => xt.2.2.1 _
       refine' h'z x' x't ⟨ux'.1.trans_le (ux.2.trans (hy x xt.1).le), _⟩
       by_contra' H
-      exact False.elim (lt_irrefl _ ((Hy _ _ xt.1 H).trans_lt h'))
+      exact lt_irrefl _ ((Hy _ _ xt.1 H).trans_lt h')
     · refine' disjoint_left.2 fun u ux ux' => x't.2.2.1 _
       refine' h'z x xt ⟨ux.1.trans_le (ux'.2.trans (hy x' x't.1).le), _⟩
       by_contra' H
-      exact False.elim (lt_irrefl _ ((Hy _ _ x't.1 H).trans_lt h'))
+      exact lt_irrefl _ ((Hy _ _ x't.1 H).trans_lt h')
   refine' this.countable_of_isOpen (fun x hx => _) fun x hx => ⟨x, hz x hx, le_rfl⟩
   suffices H : Ioc (z x) x = Ioo (z x) (y x)
   · rw [H]

Also rename 2 lemmas

• IsCompact.exists_local_min_mem_open -> IsCompact.exists_isLocalMin_mem_open;
• Metric.exists_local_min_mem_ball -> Metric.exists_isLocal_min_mem_ball.

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module topology.order.basic
-! leanprover-community/mathlib commit c985ae9840e06836a71db38de372f20acb49b790
+! leanprover-community/mathlib commit 3efd324a3a31eaa40c9d5bfc669c4fafee5f9423
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -801,51 +801,6 @@ theorem Dense.Iio_eq_biUnion [DenselyOrdered α] {s : Set α} (hs : Dense s) (x
     Iio x = ⋃ y ∈ s ∩ Iio x, Iio y :=
   Dense.Ioi_eq_biUnion (α := αᵒᵈ) hs x
 
-variable [Nonempty α] [TopologicalSpace β]
-
-/-- A compact set is bounded below -/
-theorem IsCompact.bddBelow {s : Set α} (hs : IsCompact s) : BddBelow s := by
-  cases' botOrderOrNoBotOrder α with h h; exact OrderBot.bddBelow s
-  have : s ⊆ ⋃ a : α, Ioi a := (@iUnion_Ioi α _ (NoBotOrder.to_noMinOrder α)).symm ▸ subset_univ s
-  rcases hs.elim_finite_subcover _ (fun _ => isOpen_Ioi) this with ⟨t, ht⟩
-  refine t.bddBelow.imp fun C hC y hy => ?_
-  rcases mem_iUnion₂.1 (ht hy) with ⟨a, ha, hay⟩
-  exact (hC ha).trans (le_of_lt hay)
-#align is_compact.bdd_below IsCompact.bddBelow
-
-/-- A compact set is bounded above -/
-theorem IsCompact.bddAbove {s : Set α} (hs : IsCompact s) : BddAbove s :=
-  @IsCompact.bddBelow αᵒᵈ _ _ _ _ _ hs
-#align is_compact.bdd_above IsCompact.bddAbove
-
-/-- A continuous function is bounded below on a compact set. -/
-theorem IsCompact.bddBelow_image {f : β → α} {K : Set β} (hK : IsCompact K)
-    (hf : ContinuousOn f K) : BddBelow (f '' K) :=
-  (hK.image_of_continuousOn hf).bddBelow
-#align is_compact.bdd_below_image IsCompact.bddBelow_image
-
-/-- A continuous function is bounded above on a compact set. -/
-theorem IsCompact.bddAbove_image {f : β → α} {K : Set β} (hK : IsCompact K)
-    (hf : ContinuousOn f K) : BddAbove (f '' K) :=
-  @IsCompact.bddBelow_image αᵒᵈ _ _ _ _ _ _ _ _ hK hf
-#align is_compact.bdd_above_image IsCompact.bddAbove_image
-
-/-- A continuous function with compact support is bounded below. -/
-@[to_additive " A continuous function with compact support is bounded below. "]
-theorem Continuous.bddBelow_range_of_hasCompactMulSupport [One α] {f : β → α} (hf : Continuous f)
-    (h : HasCompactMulSupport f) : BddBelow (range f) :=
-  (h.isCompact_range hf).bddBelow
-#align continuous.bdd_below_range_of_has_compact_mul_support Continuous.bddBelow_range_of_hasCompactMulSupport
-#align continuous.bdd_below_range_of_has_compact_support Continuous.bddBelow_range_of_hasCompactSupport
-
-/-- A continuous function with compact support is bounded above. -/
-@[to_additive " A continuous function with compact support is bounded above. "]
-theorem Continuous.bddAbove_range_of_hasCompactMulSupport [One α] {f : β → α} (hf : Continuous f)
-    (h : HasCompactMulSupport f) : BddAbove (range f) :=
-  @Continuous.bddBelow_range_of_hasCompactMulSupport αᵒᵈ _ _ _ _ _ _ _ _ hf h
-#align continuous.bdd_above_range_of_has_compact_mul_support Continuous.bddAbove_range_of_hasCompactMulSupport
-#align continuous.bdd_above_range_of_has_compact_support Continuous.bddAbove_range_of_hasCompactSupport
-
 end LinearOrder
 
 end OrderClosedTopology

@@ -1921,6 +1921,13 @@ theorem nhds_basis_Ioo_pos [NoMaxOrder α] (a : α) :
   simp only [Ioo, abs_lt, ← sub_lt_iff_lt_add, neg_lt_sub_iff_lt_add, sub_lt_comm]
 #align nhds_basis_Ioo_pos nhds_basis_Ioo_pos
 
+theorem nhds_basis_Icc_pos [NoMaxOrder α] [DenselyOrdered α] (a : α) :
+    (𝓝 a).HasBasis ((0 : α) < ·) fun ε ↦ Icc (a - ε) (a + ε) :=
+  (nhds_basis_Ioo_pos a).to_hasBasis
+    (fun _ε ε₀ ↦ let ⟨δ, δ₀, δε⟩ := exists_between ε₀
+      ⟨δ, δ₀, Icc_subset_Ioo (sub_lt_sub_left δε _) (add_lt_add_left δε _)⟩)
+    (fun ε ε₀ ↦ ⟨ε, ε₀, Ioo_subset_Icc_self⟩)
+
 variable (α)
 
 theorem nhds_basis_zero_abs_sub_lt [NoMaxOrder α] :

@@ -245,7 +245,7 @@ theorem IsClosed.hypograph [TopologicalSpace β] {f : β → α} {s : Set β} (h
   (hs.preimage continuous_fst).isClosed_le continuousOn_snd (hf.comp continuousOn_fst Subset.rfl)
 #align is_closed.hypograph IsClosed.hypograph
 
--- todo: move these lemmas to `Topology.Algebra.Order.LeftRight`
+-- Porting note: todo: move these lemmas to `Topology.Algebra.Order.LeftRight`
 theorem nhdsWithin_Ici_neBot {a b : α} (H₂ : a ≤ b) : NeBot (𝓝[Ici a] b) :=
   nhdsWithin_neBot_of_mem H₂
 #align nhds_within_Ici_ne_bot nhdsWithin_Ici_neBot
@@ -1250,7 +1250,7 @@ theorem exists_Icc_mem_subset_of_mem_nhdsWithin_Ici {a : α} {s : Set α} (hs :
   rcases (em (IsMax a)).imp_right not_isMax_iff.mp with (ha | ha)
   · use a
     simpa [ha.Ici_eq] using hs
-  · rcases(nhdsWithin_Ici_basis' ha).mem_iff.mp hs with ⟨b, hab, hbs⟩
+  · rcases (nhdsWithin_Ici_basis' ha).mem_iff.mp hs with ⟨b, hab, hbs⟩
     rcases eq_empty_or_nonempty (Ioo a b) with (H | ⟨c, hac, hcb⟩)
     · have : Ico a b = Icc a a := by rw [← Icc_union_Ioo_eq_Ico le_rfl hab, H, union_empty]
       exact ⟨a, le_rfl, this ▸ ⟨Ico_mem_nhdsWithin_Ici' hab, hbs⟩⟩
@@ -1959,7 +1959,7 @@ theorem IsLUB.frequently_mem {a : α} {s : Set α} (ha : IsLUB s a) (hs : s.None
     ∃ᶠ x in 𝓝[≤] a, x ∈ s := by
   rcases hs with ⟨a', ha'⟩
   intro h
-  rcases(ha.1 ha').eq_or_lt with (rfl | ha'a)
+  rcases (ha.1 ha').eq_or_lt with (rfl | ha'a)
   · exact h.self_of_nhdsWithin le_rfl ha'
   · rcases (mem_nhdsWithin_Iic_iff_exists_Ioc_subset' ha'a).1 h with ⟨b, hba, hb⟩
     rcases ha.exists_between hba with ⟨b', hb's, hb'⟩
@@ -2131,7 +2131,7 @@ theorem exists_seq_strictMono_tendsto' {α : Type _} [LinearOrder α] [Topologic
     ∃ u : ℕ → α, StrictMono u ∧ (∀ n, u n ∈ Ioo y x) ∧ Tendsto u atTop (𝓝 x) := by
   have hx : x ∉ Ioo y x := fun h => (lt_irrefl x h.2).elim
   have ht : Set.Nonempty (Ioo y x) := nonempty_Ioo.2 hy
-  rcases(isLUB_Ioo hy).exists_seq_strictMono_tendsto_of_not_mem hx ht with ⟨u, hu⟩
+  rcases (isLUB_Ioo hy).exists_seq_strictMono_tendsto_of_not_mem hx ht with ⟨u, hu⟩
   exact ⟨u, hu.1, hu.2.2.symm⟩
 #align exists_seq_strict_mono_tendsto' exists_seq_strictMono_tendsto'
 
@@ -2152,7 +2152,7 @@ theorem exists_seq_strictMono_tendsto_nhdsWithin [DenselyOrdered α] [NoMinOrder
 theorem exists_seq_tendsto_sSup {α : Type _} [ConditionallyCompleteLinearOrder α]
     [TopologicalSpace α] [OrderTopology α] [FirstCountableTopology α] {S : Set α} (hS : S.Nonempty)
     (hS' : BddAbove S) : ∃ u : ℕ → α, Monotone u ∧ Tendsto u atTop (𝓝 (sSup S)) ∧ ∀ n, u n ∈ S := by
-  rcases(isLUB_csSup hS hS').exists_seq_monotone_tendsto hS with ⟨u, hu⟩
+  rcases (isLUB_csSup hS hS').exists_seq_monotone_tendsto hS with ⟨u, hu⟩
   exact ⟨u, hu.1, hu.2.2⟩
 #align exists_seq_tendsto_Sup exists_seq_tendsto_sSup
 
@@ -2392,8 +2392,7 @@ theorem nhdsWithin_Ioi_self_neBot' {a : α} (H : (Ioi a).Nonempty) : NeBot (𝓝
   nhdsWithin_Ioi_neBot' H (le_refl a)
 #align nhds_within_Ioi_self_ne_bot' nhdsWithin_Ioi_self_neBot'
 
-@[instance]
-theorem nhdsWithin_Ioi_self_neBot [NoMaxOrder α] (a : α) : NeBot (𝓝[>] a) :=
+instance nhdsWithin_Ioi_self_neBot [NoMaxOrder α] (a : α) : NeBot (𝓝[>] a) :=
   nhdsWithin_Ioi_neBot (le_refl a)
 #align nhds_within_Ioi_self_ne_bot nhdsWithin_Ioi_self_neBot
 
@@ -2416,8 +2415,7 @@ theorem nhdsWithin_Iio_self_neBot' {b : α} (H : (Iio b).Nonempty) : NeBot (𝓝
   nhdsWithin_Iio_neBot' H (le_refl b)
 #align nhds_within_Iio_self_ne_bot' nhdsWithin_Iio_self_neBot'
 
-@[instance]
-theorem nhdsWithin_Iio_self_neBot [NoMinOrder α] (a : α) : NeBot (𝓝[<] a) :=
+instance nhdsWithin_Iio_self_neBot [NoMinOrder α] (a : α) : NeBot (𝓝[<] a) :=
   nhdsWithin_Iio_neBot (le_refl a)
 #align nhds_within_Iio_self_ne_bot nhdsWithin_Iio_self_neBot
 

I wrote a script to find lines that contain an odd number of backticks

@@ -57,7 +57,7 @@ see their statements.
 * `le_of_tendsto_of_tendsto` : if `f` converges to `a`, `g` converges to `b`, and eventually
   `f x ≤ g x`, then `a ≤ b`
 * `le_of_tendsto`, `ge_of_tendsto` : if `f` converges to `a` and eventually `f x ≤ b`
-  (resp., `b ≤ f x`), then `a ≤ b` (resp., `b ≤ a); we also provide primed versions
+  (resp., `b ≤ f x`), then `a ≤ b` (resp., `b ≤ a`); we also provide primed versions
   that assume the inequalities to hold for all `x`.
 
 ### Min, max, `sSup` and `sInf`

Part 3 of #5001

@@ -1072,7 +1072,7 @@ theorem StrictMono.embedding_of_ordConnected {α β : Type _} [LinearOrder α] [
     (hf : StrictMono f) (hc : OrdConnected (range f)) : Embedding f :=
   ⟨⟨h.1.trans <| Eq.symm <| hf.induced_topology_eq_preorder hc⟩, hf.injective⟩
 
-/-- On an `Set.OrdConnected` subset of a linear order, the order topology for the restriction of the
+/-- On a `Set.OrdConnected` subset of a linear order, the order topology for the restriction of the
 order is the same as the restriction to the subset of the order topology. -/
 instance orderTopology_of_ordConnected {α : Type u} [TopologicalSpace α] [LinearOrder α]
     [OrderTopology α] {t : Set α} [ht : OrdConnected t] : OrderTopology t :=

These are all doc fixes

@@ -114,7 +114,7 @@ variable [TopologicalSpace α] [Preorder α] [t : OrderClosedTopology α]
 
 namespace Subtype
 
--- todo: add `OrderEmbedding.orderClosedtopology`
+-- todo: add `OrderEmbedding.orderClosedTopology`
 instance {p : α → Prop} : OrderClosedTopology (Subtype p) :=
   have this : Continuous fun p : Subtype p × Subtype p => ((p.fst : α), (p.snd : α)) :=
     continuous_subtype_val.prod_map continuous_subtype_val

@@ -974,7 +974,7 @@ theorem tendsto_of_tendsto_of_tendsto_of_le_of_le {f g h : β → α} {b : Filte
 #align tendsto_of_tendsto_of_tendsto_of_le_of_le tendsto_of_tendsto_of_tendsto_of_le_of_le
 
 theorem nhds_order_unbounded {a : α} (hu : ∃ u, a < u) (hl : ∃ l, l < a) :
-    𝓝 a = ⨅ (l) (_h₂ : l < a) (u) (_h₂ : a < u), 𝓟 (Ioo l u) := by
+    𝓝 a = ⨅ (l) (_ : l < a) (u) (_ : a < u), 𝓟 (Ioo l u) := by
   simp only [nhds_eq_order, ← inf_biInf, ← biInf_inf, *, ← inf_principal, ← Ioi_inter_Iio]; rfl
 #align nhds_order_unbounded nhds_order_unbounded
 
@@ -1081,7 +1081,7 @@ instance orderTopology_of_ordConnected {α : Type u} [TopologicalSpace α] [Line
 #align order_topology_of_ord_connected orderTopology_of_ordConnected
 
 theorem nhdsWithin_Ici_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology α] (a : α) :
-    𝓝[≥] a = (⨅ (u) (_hu : a < u), 𝓟 (Iio u)) ⊓ 𝓟 (Ici a) := by
+    𝓝[≥] a = (⨅ (u) (_ : a < u), 𝓟 (Iio u)) ⊓ 𝓟 (Ici a) := by
   rw [nhdsWithin, nhds_eq_order]
   refine' le_antisymm (inf_le_inf_right _ inf_le_right) (le_inf (le_inf _ inf_le_left) inf_le_right)
   exact inf_le_right.trans (le_iInf₂ fun l hl => principal_mono.2 <| Ici_subset_Ioi.2 hl)
@@ -1093,7 +1093,7 @@ theorem nhdsWithin_Iic_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology 
 #align nhds_within_Iic_eq'' nhdsWithin_Iic_eq''
 
 theorem nhdsWithin_Ici_eq' [TopologicalSpace α] [Preorder α] [OrderTopology α] {a : α}
-    (ha : ∃ u, a < u) : 𝓝[≥] a = ⨅ (u) (_hu : a < u), 𝓟 (Ico a u) := by
+    (ha : ∃ u, a < u) : 𝓝[≥] a = ⨅ (u) (_ : a < u), 𝓟 (Ico a u) := by
   simp only [nhdsWithin_Ici_eq'', biInf_inf ha, inf_principal, Iio_inter_Ici]
 #align nhds_within_Ici_eq' nhdsWithin_Ici_eq'
 

@@ -11,6 +11,7 @@ Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
 import Mathlib.Data.Set.Intervals.Pi
 import Mathlib.Data.Set.Pointwise.Interval
 import Mathlib.Order.Filter.Interval
+import Mathlib.Tactic.TFAE
 import Mathlib.Topology.Support
 import Mathlib.Topology.Algebra.Order.LeftRight
 
@@ -1590,16 +1591,23 @@ theorem TFAE_mem_nhdsWithin_Ioi {a b : α} (hab : a < b) (s : Set α) :
       s ∈ 𝓝[Ioo a b] a,
       ∃ u ∈ Ioc a b, Ioo a u ⊆ s,
       ∃ u ∈ Ioi a, Ioo a u ⊆ s] := by
-  rw [nhdsWithin_Ioc_eq_nhdsWithin_Ioi hab, nhdsWithin_Ioo_eq_nhdsWithin_Ioi hab]
-  apply_rules [tfae_of_cycle, Chain.cons, Chain.nil] <;> try { exact id }
-  · rw [nhdsWithin, mem_inf_principal]
-    intro h
-    rcases exists_Ico_subset_of_mem_nhds' h hab with ⟨u, au, hu⟩
-    exact ⟨u, au, fun x hx => hu (Ioo_subset_Ico_self hx) hx.1⟩
-  · rintro ⟨u, hu, hs⟩
-    exact ⟨u, hu.1, hs⟩
-  · rintro ⟨u, hu, hs⟩
-    exact mem_of_superset (Ioo_mem_nhdsWithin_Ioi' hu) hs
+  tfae_have 1 ↔ 2
+  · rw [nhdsWithin_Ioc_eq_nhdsWithin_Ioi hab]
+  tfae_have 1 ↔ 3
+  · rw [nhdsWithin_Ioo_eq_nhdsWithin_Ioi hab]
+  tfae_have 4 → 5
+  · exact fun ⟨u, umem, hu⟩ => ⟨u, umem.1, hu⟩
+  tfae_have 5 → 1
+  · rintro ⟨u, hau, hu⟩
+    exact mem_of_superset (Ioo_mem_nhdsWithin_Ioi ⟨le_refl a, hau⟩) hu
+  tfae_have 1 → 4
+  · intro h
+    rcases mem_nhdsWithin_iff_exists_mem_nhds_inter.1 h with ⟨v, va, hv⟩
+    rcases exists_Ico_subset_of_mem_nhds' va hab with ⟨u, au, hu⟩
+    refine' ⟨u, au, fun x hx => _⟩
+    refine' hv ⟨hu ⟨le_of_lt hx.1, hx.2⟩, _⟩
+    exact hx.1
+  tfae_finish
 #align tfae_mem_nhds_within_Ioi TFAE_mem_nhdsWithin_Ioi
 
 theorem mem_nhdsWithin_Ioi_iff_exists_mem_Ioc_Ioo_subset {a u' : α} {s : Set α} (hu' : a < u') :
@@ -1729,14 +1737,20 @@ theorem TFAE_mem_nhdsWithin_Ici {a b : α} (hab : a < b) (s : Set α) :
       s ∈ 𝓝[Ico a b] a,
       ∃ u ∈ Ioc a b, Ico a u ⊆ s,
       ∃ u ∈ Ioi a , Ico a u ⊆ s] := by
-  rw [nhdsWithin_Icc_eq_nhdsWithin_Ici hab, nhdsWithin_Ico_eq_nhdsWithin_Ici hab]
-  apply_rules [tfae_of_cycle, Chain.cons, Chain.nil] <;> try { exact id }
-  · rw [nhdsWithin, mem_inf_principal]
-    intro h
-    rcases exists_Ico_subset_of_mem_nhds' h hab with ⟨u, au, hu⟩
-    exact ⟨u, au, fun x hx => hu hx hx.1⟩
-  · rintro ⟨u, hu, hs⟩; exact ⟨u, hu.1, hs⟩
-  · rintro ⟨u, hu, hs⟩; exact mem_of_superset (Ico_mem_nhdsWithin_Ici' hu) hs
+  tfae_have 1 ↔ 2
+  · rw [nhdsWithin_Icc_eq_nhdsWithin_Ici hab]
+  tfae_have 1 ↔ 3
+  · rw [nhdsWithin_Ico_eq_nhdsWithin_Ici hab]
+  tfae_have 1 ↔ 5
+  · exact (nhdsWithin_Ici_basis' ⟨b, hab⟩).mem_iff
+  tfae_have 4 → 5
+  · exact fun ⟨u, umem, hu⟩ => ⟨u, umem.1, hu⟩
+  tfae_have 5 → 4
+  · rintro ⟨u, hua, hus⟩
+    exact
+      ⟨min u b, ⟨lt_min hua hab, min_le_right _ _⟩,
+        (Ico_subset_Ico_right <| min_le_left _ _).trans hus⟩
+  tfae_finish
 #align tfae_mem_nhds_within_Ici TFAE_mem_nhdsWithin_Ici
 
 theorem mem_nhdsWithin_Ici_iff_exists_mem_Ioc_Ico_subset {a u' : α} {s : Set α} (hu' : a < u') :

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>

@@ -59,7 +59,7 @@ see their statements.
   (resp., `b ≤ f x`), then `a ≤ b` (resp., `b ≤ a); we also provide primed versions
   that assume the inequalities to hold for all `x`.
 
-### Min, max, `supₛ` and `infₛ`
+### Min, max, `sSup` and `sInf`
 
 * `Continuous.min`, `Continuous.max`: pointwise `min`/`max` of two continuous functions is
   continuous.
@@ -790,25 +790,25 @@ theorem Dense.exists_between [DenselyOrdered α] {s : Set α} (hs : Dense s) {x
   hs.exists_mem_open isOpen_Ioo (nonempty_Ioo.2 h)
 #align dense.exists_between Dense.exists_between
 
-theorem Dense.Ioi_eq_bunionᵢ [DenselyOrdered α] {s : Set α} (hs : Dense s) (x : α) :
+theorem Dense.Ioi_eq_biUnion [DenselyOrdered α] {s : Set α} (hs : Dense s) (x : α) :
     Ioi x = ⋃ y ∈ s ∩ Ioi x, Ioi y := by
-  refine Subset.antisymm (fun z hz ↦ ?_) (unionᵢ₂_subset fun y hy ↦ Ioi_subset_Ioi (le_of_lt hy.2))
+  refine Subset.antisymm (fun z hz ↦ ?_) (iUnion₂_subset fun y hy ↦ Ioi_subset_Ioi (le_of_lt hy.2))
   rcases hs.exists_between hz with ⟨y, hys, hxy, hyz⟩
-  exact mem_unionᵢ₂.2 ⟨y, ⟨hys, hxy⟩, hyz⟩
+  exact mem_iUnion₂.2 ⟨y, ⟨hys, hxy⟩, hyz⟩
 
-theorem Dense.Iio_eq_bunionᵢ [DenselyOrdered α] {s : Set α} (hs : Dense s) (x : α) :
+theorem Dense.Iio_eq_biUnion [DenselyOrdered α] {s : Set α} (hs : Dense s) (x : α) :
     Iio x = ⋃ y ∈ s ∩ Iio x, Iio y :=
-  Dense.Ioi_eq_bunionᵢ (α := αᵒᵈ) hs x
+  Dense.Ioi_eq_biUnion (α := αᵒᵈ) hs x
 
 variable [Nonempty α] [TopologicalSpace β]
 
 /-- A compact set is bounded below -/
 theorem IsCompact.bddBelow {s : Set α} (hs : IsCompact s) : BddBelow s := by
   cases' botOrderOrNoBotOrder α with h h; exact OrderBot.bddBelow s
-  have : s ⊆ ⋃ a : α, Ioi a := (@unionᵢ_Ioi α _ (NoBotOrder.to_noMinOrder α)).symm ▸ subset_univ s
+  have : s ⊆ ⋃ a : α, Ioi a := (@iUnion_Ioi α _ (NoBotOrder.to_noMinOrder α)).symm ▸ subset_univ s
   rcases hs.elim_finite_subcover _ (fun _ => isOpen_Ioi) this with ⟨t, ht⟩
   refine t.bddBelow.imp fun C hC y hy => ?_
-  rcases mem_unionᵢ₂.1 (ht hy) with ⟨a, ha, hay⟩
+  rcases mem_iUnion₂.1 (ht hy) with ⟨a, ha, hay⟩
   exact (hC ha).trans (le_of_lt hay)
 #align is_compact.bdd_below IsCompact.bddBelow
 
@@ -858,7 +858,7 @@ instance {ι : Type _} {α : ι → Type _} [∀ i, Preorder (α i)] [∀ i, Top
     [∀ i, OrderClosedTopology (α i)] : OrderClosedTopology (∀ i, α i) := by
   constructor
   simp only [Pi.le_def, setOf_forall]
-  exact isClosed_interᵢ fun i => isClosed_le (continuous_apply i).fst' (continuous_apply i).snd'
+  exact isClosed_iInter fun i => isClosed_le (continuous_apply i).fst' (continuous_apply i).snd'
 
 instance Pi.orderClosedTopology' [Preorder β] [TopologicalSpace β] [OrderClosedTopology β] :
     OrderClosedTopology (α → β) :=
@@ -925,21 +925,21 @@ theorem ge_mem_nhds {a b : α} (h : a < b) : ∀ᶠ x in 𝓝 a, x ≤ b :=
 
 theorem nhds_eq_order (a : α) : 𝓝 a = (⨅ b ∈ Iio a, 𝓟 (Ioi b)) ⊓ ⨅ b ∈ Ioi a, 𝓟 (Iio b) := by
   rw [t.topology_eq_generate_intervals, nhds_generateFrom]
-  simp_rw [mem_setOf_eq, @and_comm (a ∈ _), exists_or, or_and_right, infᵢ_or, infᵢ_and, infᵢ_exists,
-    infᵢ_inf_eq, infᵢ_comm (ι := Set α), infᵢ_infᵢ_eq_left, mem_Ioi, mem_Iio]
+  simp_rw [mem_setOf_eq, @and_comm (a ∈ _), exists_or, or_and_right, iInf_or, iInf_and, iInf_exists,
+    iInf_inf_eq, iInf_comm (ι := Set α), iInf_iInf_eq_left, mem_Ioi, mem_Iio]
 #align nhds_eq_order nhds_eq_order
 
 theorem tendsto_order {f : β → α} {a : α} {x : Filter β} :
     Tendsto f x (𝓝 a) ↔ (∀ a' < a, ∀ᶠ b in x, a' < f b) ∧ ∀ a' > a, ∀ᶠ b in x, f b < a' := by
-  simp only [nhds_eq_order a, tendsto_inf, tendsto_infᵢ, tendsto_principal]; rfl
+  simp only [nhds_eq_order a, tendsto_inf, tendsto_iInf, tendsto_principal]; rfl
 #align tendsto_order tendsto_order
 
 instance tendstoIccClassNhds (a : α) : TendstoIxxClass Icc (𝓝 a) (𝓝 a) := by
-  simp only [nhds_eq_order, infᵢ_subtype']
+  simp only [nhds_eq_order, iInf_subtype']
   refine
-    ((hasBasis_infᵢ_principal_finite _).inf (hasBasis_infᵢ_principal_finite _)).tendstoIxxClass
+    ((hasBasis_iInf_principal_finite _).inf (hasBasis_iInf_principal_finite _)).tendstoIxxClass
       fun s _ => ?_
-  refine' ((ordConnected_binterᵢ _).inter (ordConnected_binterᵢ _)).out <;> intro _ _
+  refine' ((ordConnected_biInter _).inter (ordConnected_biInter _)).out <;> intro _ _
   exacts [ordConnected_Ioi, ordConnected_Iio]
 #align tendsto_Icc_class_nhds tendstoIccClassNhds
 
@@ -974,13 +974,13 @@ theorem tendsto_of_tendsto_of_tendsto_of_le_of_le {f g h : β → α} {b : Filte
 
 theorem nhds_order_unbounded {a : α} (hu : ∃ u, a < u) (hl : ∃ l, l < a) :
     𝓝 a = ⨅ (l) (_h₂ : l < a) (u) (_h₂ : a < u), 𝓟 (Ioo l u) := by
-  simp only [nhds_eq_order, ← inf_binfᵢ, ← binfᵢ_inf, *, ← inf_principal, ← Ioi_inter_Iio]; rfl
+  simp only [nhds_eq_order, ← inf_biInf, ← biInf_inf, *, ← inf_principal, ← Ioi_inter_Iio]; rfl
 #align nhds_order_unbounded nhds_order_unbounded
 
 theorem tendsto_order_unbounded {f : β → α} {a : α} {x : Filter β} (hu : ∃ u, a < u)
     (hl : ∃ l, l < a) (h : ∀ l u, l < a → a < u → ∀ᶠ b in x, l < f b ∧ f b < u) :
     Tendsto f x (𝓝 a) := by
-  simp only [nhds_order_unbounded hu hl, tendsto_infᵢ, tendsto_principal]
+  simp only [nhds_order_unbounded hu hl, tendsto_iInf, tendsto_principal]
   exact fun l hl u => h l u hl
 #align tendsto_order_unbounded tendsto_order_unbounded
 
@@ -997,7 +997,7 @@ instance tendstoIccClassNhdsPi {ι : Type _} {α : ι → Type _} [∀ i, Preord
     TendstoIxxClass Icc (𝓝 f) (𝓝 f) := by
   constructor
   conv in (𝓝 f).smallSets => rw [nhds_pi, Filter.pi]
-  simp only [smallSets_infᵢ, smallSets_comap, tendsto_infᵢ, tendsto_lift', (· ∘ ·),
+  simp only [smallSets_iInf, smallSets_comap, tendsto_iInf, tendsto_lift', (· ∘ ·),
     mem_powerset_iff]
   intro i s hs
   have : Tendsto (fun g : ∀ i, α i => g i) (𝓝 f) (𝓝 (f i)) := (continuous_apply i).tendsto f
@@ -1011,9 +1011,9 @@ theorem induced_topology_le_preorder [Preorder α] [Preorder β] [TopologicalSpa
     induced f ‹TopologicalSpace β› ≤ Preorder.topology α := by
   let _ := Preorder.topology α; have : OrderTopology α := ⟨rfl⟩
   refine le_of_nhds_le_nhds fun x => ?_
-  simp only [nhds_eq_order, nhds_induced, comap_inf, comap_infᵢ, comap_principal, Ioi, Iio, ← hf]
-  refine inf_le_inf (le_infᵢ₂ fun a ha => ?_) (le_infᵢ₂ fun a ha => ?_)
-  exacts [infᵢ₂_le (f a) ha, infᵢ₂_le (f a) ha]
+  simp only [nhds_eq_order, nhds_induced, comap_inf, comap_iInf, comap_principal, Ioi, Iio, ← hf]
+  refine inf_le_inf (le_iInf₂ fun a ha => ?_) (le_iInf₂ fun a ha => ?_)
+  exacts [iInf₂_le (f a) ha, iInf₂_le (f a) ha]
 
 -- porting note: new lemma
 theorem induced_topology_eq_preorder [Preorder α] [Preorder β] [TopologicalSpace β]
@@ -1024,16 +1024,16 @@ theorem induced_topology_eq_preorder [Preorder α] [Preorder β] [TopologicalSpa
   let _ := Preorder.topology α; have : OrderTopology α := ⟨rfl⟩
   refine le_antisymm (induced_topology_le_preorder hf) ?_
   refine le_of_nhds_le_nhds fun a => ?_
-  simp only [nhds_eq_order, nhds_induced, comap_inf, comap_infᵢ, comap_principal]
-  refine inf_le_inf (le_infᵢ₂ fun b hb => ?_) (le_infᵢ₂ fun b hb => ?_)
+  simp only [nhds_eq_order, nhds_induced, comap_inf, comap_iInf, comap_principal]
+  refine inf_le_inf (le_iInf₂ fun b hb => ?_) (le_iInf₂ fun b hb => ?_)
   · rcases em (∃ x, ¬(b < f x)) with (⟨x, hx⟩ | hb)
     · rcases H₁ hb hx with ⟨y, hya, hyb⟩
-      exact infᵢ₂_le_of_le y hya (principal_mono.2 fun z hz => hyb.trans_lt (hf.2 hz))
+      exact iInf₂_le_of_le y hya (principal_mono.2 fun z hz => hyb.trans_lt (hf.2 hz))
     · push_neg at hb
       exact le_principal_iff.2 (univ_mem' hb)
   · rcases em (∃ x, ¬(f x < b)) with (⟨x, hx⟩ | hb)
     · rcases H₂ hb hx with ⟨y, hya, hyb⟩
-      exact infᵢ₂_le_of_le y hya (principal_mono.2 fun z hz => (hf.2 hz).trans_le hyb)
+      exact iInf₂_le_of_le y hya (principal_mono.2 fun z hz => (hf.2 hz).trans_le hyb)
     · push_neg at hb
       exact le_principal_iff.2 (univ_mem' hb)
 
@@ -1083,7 +1083,7 @@ theorem nhdsWithin_Ici_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology 
     𝓝[≥] a = (⨅ (u) (_hu : a < u), 𝓟 (Iio u)) ⊓ 𝓟 (Ici a) := by
   rw [nhdsWithin, nhds_eq_order]
   refine' le_antisymm (inf_le_inf_right _ inf_le_right) (le_inf (le_inf _ inf_le_left) inf_le_right)
-  exact inf_le_right.trans (le_infᵢ₂ fun l hl => principal_mono.2 <| Ici_subset_Ioi.2 hl)
+  exact inf_le_right.trans (le_iInf₂ fun l hl => principal_mono.2 <| Ici_subset_Ioi.2 hl)
 #align nhds_within_Ici_eq'' nhdsWithin_Ici_eq''
 
 theorem nhdsWithin_Iic_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology α] (a : α) :
@@ -1093,18 +1093,18 @@ theorem nhdsWithin_Iic_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology 
 
 theorem nhdsWithin_Ici_eq' [TopologicalSpace α] [Preorder α] [OrderTopology α] {a : α}
     (ha : ∃ u, a < u) : 𝓝[≥] a = ⨅ (u) (_hu : a < u), 𝓟 (Ico a u) := by
-  simp only [nhdsWithin_Ici_eq'', binfᵢ_inf ha, inf_principal, Iio_inter_Ici]
+  simp only [nhdsWithin_Ici_eq'', biInf_inf ha, inf_principal, Iio_inter_Ici]
 #align nhds_within_Ici_eq' nhdsWithin_Ici_eq'
 
 theorem nhdsWithin_Iic_eq' [TopologicalSpace α] [Preorder α] [OrderTopology α] {a : α}
     (ha : ∃ l, l < a) : 𝓝[≤] a = ⨅ l < a, 𝓟 (Ioc l a) := by
-  simp only [nhdsWithin_Iic_eq'', binfᵢ_inf ha, inf_principal, Ioi_inter_Iic]
+  simp only [nhdsWithin_Iic_eq'', biInf_inf ha, inf_principal, Ioi_inter_Iic]
 #align nhds_within_Iic_eq' nhdsWithin_Iic_eq'
 
 theorem nhdsWithin_Ici_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopology α] {a : α}
     (ha : ∃ u, a < u) : (𝓝[≥] a).HasBasis (fun u => a < u) fun u => Ico a u :=
   (nhdsWithin_Ici_eq' ha).symm ▸
-    hasBasis_binfᵢ_principal
+    hasBasis_biInf_principal
       (fun b hb c hc => ⟨min b c, lt_min hb hc, Ico_subset_Ico_right (min_le_left _ _),
         Ico_subset_Ico_right (min_le_right _ _)⟩)
       ha
@@ -1159,7 +1159,7 @@ theorem nhds_bot_basis_Iic [TopologicalSpace α] [LinearOrder α] [OrderBot α]
 
 theorem tendsto_nhds_top_mono [TopologicalSpace β] [Preorder β] [OrderTop β] [OrderTopology β]
     {l : Filter α} {f g : α → β} (hf : Tendsto f l (𝓝 ⊤)) (hg : f ≤ᶠ[l] g) : Tendsto g l (𝓝 ⊤) := by
-  simp only [nhds_top_order, tendsto_infᵢ, tendsto_principal] at hf ⊢
+  simp only [nhds_top_order, tendsto_iInf, tendsto_principal] at hf ⊢
   intro x hx
   filter_upwards [hf x hx, hg] with _ using lt_of_lt_of_le
 #align tendsto_nhds_top_mono tendsto_nhds_top_mono
@@ -1346,12 +1346,12 @@ theorem Dense.topology_eq_generateFrom [DenselyOrdered α] {s : Set α} (hs : De
   · simp only [union_subset_iff, image_subset_iff]
     exact ⟨fun a _ ↦ ⟨a, .inl rfl⟩, fun a _ ↦ ⟨a, .inr rfl⟩⟩
   · rintro _ ⟨a, rfl | rfl⟩
-    · rw [hs.Ioi_eq_bunionᵢ]
+    · rw [hs.Ioi_eq_biUnion]
       let _ := generateFrom (Ioi '' s ∪ Iio '' s)
-      exact isOpen_unionᵢ fun x ↦ isOpen_unionᵢ fun h ↦ .basic _ <| .inl <| mem_image_of_mem _ h.1
-    · rw [hs.Iio_eq_bunionᵢ]
+      exact isOpen_iUnion fun x ↦ isOpen_iUnion fun h ↦ .basic _ <| .inl <| mem_image_of_mem _ h.1
+    · rw [hs.Iio_eq_biUnion]
       let _ := generateFrom (Ioi '' s ∪ Iio '' s)
-      exact isOpen_unionᵢ fun x ↦ isOpen_unionᵢ fun h ↦ .basic _ <| .inr <| mem_image_of_mem _ h.1
+      exact isOpen_iUnion fun x ↦ isOpen_iUnion fun h ↦ .basic _ <| .inr <| mem_image_of_mem _ h.1
 
 variable (α)
 
@@ -1379,9 +1379,9 @@ theorem countable_setOf_covby_right [SecondCountableTopology α] :
   suffices H : ∀ a : Set α, IsOpen a → Set.Countable { x | x ∈ s ∧ x ∈ a ∧ y x ∉ a }
   · have : s ⊆ ⋃ a ∈ countableBasis α, { x | x ∈ s ∧ x ∈ a ∧ y x ∉ a } := fun x hx => by
       rcases (isBasis_countableBasis α).exists_mem_of_ne (hy x hx).ne with ⟨a, ab, xa, ya⟩
-      exact mem_unionᵢ₂.2 ⟨a, ab, hx, xa, ya⟩
+      exact mem_iUnion₂.2 ⟨a, ab, hx, xa, ya⟩
     refine Set.Countable.mono this ?_
-    refine' Countable.bunionᵢ (countable_countableBasis α) fun a ha => H _ _
+    refine' Countable.biUnion (countable_countableBasis α) fun a ha => H _ _
     exact isOpen_of_mem_countableBasis ha
   intro a ha
   suffices H : Set.Countable { x | (x ∈ s ∧ x ∈ a ∧ y x ∉ a) ∧ ¬IsBot x }
@@ -1835,29 +1835,29 @@ variable [TopologicalSpace α] [LinearOrderedAddCommGroup α] [OrderTopology α]
 
 variable {l : Filter β} {f g : β → α}
 
-theorem nhds_eq_infᵢ_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r } := by
-  simp only [nhds_eq_order, abs_lt, setOf_and, ← inf_principal, infᵢ_inf_eq]
+theorem nhds_eq_iInf_abs_sub (a : α) : 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r } := by
+  simp only [nhds_eq_order, abs_lt, setOf_and, ← inf_principal, iInf_inf_eq]
   refine (congr_arg₂ _ ?_ ?_).trans inf_comm
-  · refine (Equiv.subLeft a).infᵢ_congr fun x => ?_; simp [Ioi]
-  · refine (Equiv.subRight a).infᵢ_congr fun x => ?_; simp [Iio]
-#align nhds_eq_infi_abs_sub nhds_eq_infᵢ_abs_sub
+  · refine (Equiv.subLeft a).iInf_congr fun x => ?_; simp [Ioi]
+  · refine (Equiv.subRight a).iInf_congr fun x => ?_; simp [Iio]
+#align nhds_eq_infi_abs_sub nhds_eq_iInf_abs_sub
 
 theorem orderTopology_of_nhds_abs {α : Type _} [TopologicalSpace α] [LinearOrderedAddCommGroup α]
     (h_nhds : ∀ a : α, 𝓝 a = ⨅ r > 0, 𝓟 { b | |a - b| < r }) : OrderTopology α := by
   refine' ⟨eq_of_nhds_eq_nhds fun a => _⟩
   rw [h_nhds]
   letI := Preorder.topology α; letI : OrderTopology α := ⟨rfl⟩
-  exact (nhds_eq_infᵢ_abs_sub a).symm
+  exact (nhds_eq_iInf_abs_sub a).symm
 #align order_topology_of_nhds_abs orderTopology_of_nhds_abs
 
 theorem LinearOrderedAddCommGroup.tendsto_nhds {x : Filter β} {a : α} :
     Tendsto f x (𝓝 a) ↔ ∀ ε > (0 : α), ∀ᶠ b in x, |f b - a| < ε := by
-  simp [nhds_eq_infᵢ_abs_sub, abs_sub_comm a]
+  simp [nhds_eq_iInf_abs_sub, abs_sub_comm a]
 #align linear_ordered_add_comm_group.tendsto_nhds LinearOrderedAddCommGroup.tendsto_nhds
 
 theorem eventually_abs_sub_lt (a : α) {ε : α} (hε : 0 < ε) : ∀ᶠ x in 𝓝 a, |x - a| < ε :=
-  (nhds_eq_infᵢ_abs_sub a).symm ▸
-    mem_infᵢ_of_mem ε (mem_infᵢ_of_mem hε <| by simp only [abs_sub_comm, mem_principal_self])
+  (nhds_eq_iInf_abs_sub a).symm ▸
+    mem_iInf_of_mem ε (mem_iInf_of_mem hε <| by simp only [abs_sub_comm, mem_principal_self])
 #align eventually_abs_sub_lt eventually_abs_sub_lt
 
 /-- In a linearly ordered additive commutative group with the order topology, if `f` tends to `C`
@@ -1895,8 +1895,8 @@ theorem Filter.Tendsto.atBot_add {C : α} (hf : Tendsto f l atBot) (hg : Tendsto
 
 theorem nhds_basis_abs_sub_lt [NoMaxOrder α] (a : α) :
     (𝓝 a).HasBasis (fun ε : α => (0 : α) < ε) fun ε => { b | |b - a| < ε } := by
-  simp only [nhds_eq_infᵢ_abs_sub, abs_sub_comm (a := a)]
-  refine hasBasis_binfᵢ_principal' (fun x hx y hy => ?_) (exists_gt _)
+  simp only [nhds_eq_iInf_abs_sub, abs_sub_comm (a := a)]
+  refine hasBasis_biInf_principal' (fun x hx y hy => ?_) (exists_gt _)
   exact ⟨min x y, lt_min hx hy, fun _ hz => hz.trans_le (min_le_left _ _),
     fun _ hz => hz.trans_le (min_le_right _ _)⟩
 #align nhds_basis_abs_sub_lt nhds_basis_abs_sub_lt
@@ -2086,7 +2086,7 @@ alias IsGLB.mem_of_isClosed ← IsClosed.isGLB_mem
 #align is_closed.is_glb_mem IsClosed.isGLB_mem
 
 /-!
-### Existence of sequences tending to `infₛ` or `supₛ` of a given set
+### Existence of sequences tending to `sInf` or `sSup` of a given set
 -/
 
 theorem IsLUB.exists_seq_strictMono_tendsto_of_not_mem {t : Set α} {x : α}
@@ -2135,12 +2135,12 @@ theorem exists_seq_strictMono_tendsto_nhdsWithin [DenselyOrdered α] [NoMinOrder
   ⟨u, hu, hx, tendsto_nhdsWithin_mono_right (range_subset_iff.2 hx) <| tendsto_nhdsWithin_range.2 h⟩
 #align exists_seq_strict_mono_tendsto_nhds_within exists_seq_strictMono_tendsto_nhdsWithin
 
-theorem exists_seq_tendsto_supₛ {α : Type _} [ConditionallyCompleteLinearOrder α]
+theorem exists_seq_tendsto_sSup {α : Type _} [ConditionallyCompleteLinearOrder α]
     [TopologicalSpace α] [OrderTopology α] [FirstCountableTopology α] {S : Set α} (hS : S.Nonempty)
-    (hS' : BddAbove S) : ∃ u : ℕ → α, Monotone u ∧ Tendsto u atTop (𝓝 (supₛ S)) ∧ ∀ n, u n ∈ S := by
-  rcases(isLUB_csupₛ hS hS').exists_seq_monotone_tendsto hS with ⟨u, hu⟩
+    (hS' : BddAbove S) : ∃ u : ℕ → α, Monotone u ∧ Tendsto u atTop (𝓝 (sSup S)) ∧ ∀ n, u n ∈ S := by
+  rcases(isLUB_csSup hS hS').exists_seq_monotone_tendsto hS with ⟨u, hu⟩
   exact ⟨u, hu.1, hu.2.2⟩
-#align exists_seq_tendsto_Sup exists_seq_tendsto_supₛ
+#align exists_seq_tendsto_Sup exists_seq_tendsto_sSup
 
 theorem IsGLB.exists_seq_strictAnti_tendsto_of_not_mem {t : Set α} {x : α}
     [IsCountablyGenerated (𝓝 x)] (htx : IsGLB t x) (not_mem : x ∉ t) (ht : t.Nonempty) :
@@ -2182,11 +2182,11 @@ theorem exists_seq_strictAnti_strictMono_tendsto [DenselyOrdered α] [FirstCount
       fun k l => (hu_anti.antitone (zero_le k)).trans_lt (hv_mem l).1, hux, hvy⟩
 #align exists_seq_strict_anti_strict_mono_tendsto exists_seq_strictAnti_strictMono_tendsto
 
-theorem exists_seq_tendsto_infₛ {α : Type _} [ConditionallyCompleteLinearOrder α]
+theorem exists_seq_tendsto_sInf {α : Type _} [ConditionallyCompleteLinearOrder α]
     [TopologicalSpace α] [OrderTopology α] [FirstCountableTopology α] {S : Set α} (hS : S.Nonempty)
-    (hS' : BddBelow S) : ∃ u : ℕ → α, Antitone u ∧ Tendsto u atTop (𝓝 (infₛ S)) ∧ ∀ n, u n ∈ S :=
-  @exists_seq_tendsto_supₛ αᵒᵈ _ _ _ _ S hS hS'
-#align exists_seq_tendsto_Inf exists_seq_tendsto_infₛ
+    (hS' : BddBelow S) : ∃ u : ℕ → α, Antitone u ∧ Tendsto u atTop (𝓝 (sInf S)) ∧ ∀ n, u n ∈ S :=
+  @exists_seq_tendsto_sSup αᵒᵈ _ _ _ _ S hS hS'
+#align exists_seq_tendsto_Inf exists_seq_tendsto_sInf
 
 end OrderTopology
 
@@ -2607,149 +2607,149 @@ section CompleteLinearOrder
 variable [CompleteLinearOrder α] [TopologicalSpace α] [OrderTopology α] [CompleteLinearOrder β]
   [TopologicalSpace β] [OrderClosedTopology β] [Nonempty γ]
 
-theorem supₛ_mem_closure {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
-    {s : Set α} (hs : s.Nonempty) : supₛ s ∈ closure s :=
-  (isLUB_supₛ s).mem_closure hs
-#align Sup_mem_closure supₛ_mem_closure
+theorem sSup_mem_closure {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
+    {s : Set α} (hs : s.Nonempty) : sSup s ∈ closure s :=
+  (isLUB_sSup s).mem_closure hs
+#align Sup_mem_closure sSup_mem_closure
 
-theorem infₛ_mem_closure {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
-    {s : Set α} (hs : s.Nonempty) : infₛ s ∈ closure s :=
-  (isGLB_infₛ s).mem_closure hs
-#align Inf_mem_closure infₛ_mem_closure
+theorem sInf_mem_closure {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
+    {s : Set α} (hs : s.Nonempty) : sInf s ∈ closure s :=
+  (isGLB_sInf s).mem_closure hs
+#align Inf_mem_closure sInf_mem_closure
 
-theorem IsClosed.supₛ_mem {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α]
-    [OrderTopology α] {s : Set α} (hs : s.Nonempty) (hc : IsClosed s) : supₛ s ∈ s :=
-  (isLUB_supₛ s).mem_of_isClosed hs hc
-#align is_closed.Sup_mem IsClosed.supₛ_mem
+theorem IsClosed.sSup_mem {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α]
+    [OrderTopology α] {s : Set α} (hs : s.Nonempty) (hc : IsClosed s) : sSup s ∈ s :=
+  (isLUB_sSup s).mem_of_isClosed hs hc
+#align is_closed.Sup_mem IsClosed.sSup_mem
 
-theorem IsClosed.infₛ_mem {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α]
-    [OrderTopology α] {s : Set α} (hs : s.Nonempty) (hc : IsClosed s) : infₛ s ∈ s :=
-  (isGLB_infₛ s).mem_of_isClosed hs hc
-#align is_closed.Inf_mem IsClosed.infₛ_mem
+theorem IsClosed.sInf_mem {α : Type u} [TopologicalSpace α] [CompleteLinearOrder α]
+    [OrderTopology α] {s : Set α} (hs : s.Nonempty) (hc : IsClosed s) : sInf s ∈ s :=
+  (isGLB_sInf s).mem_of_isClosed hs hc
+#align is_closed.Inf_mem IsClosed.sInf_mem
 
 /-- A monotone function continuous at the supremum of a nonempty set sends this supremum to
 the supremum of the image of this set. -/
-theorem Monotone.map_supₛ_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (supₛ s))
-    (Mf : Monotone f) (hs : s.Nonempty) : f (supₛ s) = supₛ (f '' s) :=
+theorem Monotone.map_sSup_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
+    (Mf : Monotone f) (hs : s.Nonempty) : f (sSup s) = sSup (f '' s) :=
   --This is a particular case of the more general `IsLUB.isLUB_of_tendsto`
-  ((isLUB_supₛ _).isLUB_of_tendsto (fun _ _ _ _ xy => Mf xy) hs <|
-    Cf.mono_left inf_le_left).supₛ_eq.symm
-#align monotone.map_Sup_of_continuous_at' Monotone.map_supₛ_of_continuousAt'
+  ((isLUB_sSup _).isLUB_of_tendsto (fun _ _ _ _ xy => Mf xy) hs <|
+    Cf.mono_left inf_le_left).sSup_eq.symm
+#align monotone.map_Sup_of_continuous_at' Monotone.map_sSup_of_continuousAt'
 
 /-- A monotone function `f` sending `bot` to `bot` and continuous at the supremum of a set sends
 this supremum to the supremum of the image of this set. -/
-theorem Monotone.map_supₛ_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (supₛ s))
-    (Mf : Monotone f) (fbot : f ⊥ = ⊥) : f (supₛ s) = supₛ (f '' s) := by
+theorem Monotone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
+    (Mf : Monotone f) (fbot : f ⊥ = ⊥) : f (sSup s) = sSup (f '' s) := by
   cases' s.eq_empty_or_nonempty with h h
   · simp [h, fbot]
-  · exact Mf.map_supₛ_of_continuousAt' Cf h
-#align monotone.map_Sup_of_continuous_at Monotone.map_supₛ_of_continuousAt
+  · exact Mf.map_sSup_of_continuousAt' Cf h
+#align monotone.map_Sup_of_continuous_at Monotone.map_sSup_of_continuousAt
 
 /-- A monotone function continuous at the indexed supremum over a nonempty `Sort` sends this indexed
 supremum to the indexed supremum of the composition. -/
-theorem Monotone.map_supᵢ_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (supᵢ g)) (Mf : Monotone f) : f (⨆ i, g i) = ⨆ i, f (g i) := by
-  rw [supᵢ, Mf.map_supₛ_of_continuousAt' Cf (range_nonempty g), ← range_comp, supᵢ]; rfl
-#align monotone.map_supr_of_continuous_at' Monotone.map_supᵢ_of_continuousAt'
+theorem Monotone.map_iSup_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iSup g)) (Mf : Monotone f) : f (⨆ i, g i) = ⨆ i, f (g i) := by
+  rw [iSup, Mf.map_sSup_of_continuousAt' Cf (range_nonempty g), ← range_comp, iSup]; rfl
+#align monotone.map_supr_of_continuous_at' Monotone.map_iSup_of_continuousAt'
 
 /-- If a monotone function sending `bot` to `bot` is continuous at the indexed supremum over
 a `Sort`, then it sends this indexed supremum to the indexed supremum of the composition. -/
-theorem Monotone.map_supᵢ_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (supᵢ g)) (Mf : Monotone f) (fbot : f ⊥ = ⊥) :
+theorem Monotone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iSup g)) (Mf : Monotone f) (fbot : f ⊥ = ⊥) :
     f (⨆ i, g i) = ⨆ i, f (g i) := by
-  rw [supᵢ, Mf.map_supₛ_of_continuousAt Cf fbot, ← range_comp, supᵢ]; rfl
-#align monotone.map_supr_of_continuous_at Monotone.map_supᵢ_of_continuousAt
+  rw [iSup, Mf.map_sSup_of_continuousAt Cf fbot, ← range_comp, iSup]; rfl
+#align monotone.map_supr_of_continuous_at Monotone.map_iSup_of_continuousAt
 
 /-- A monotone function continuous at the infimum of a nonempty set sends this infimum to
 the infimum of the image of this set. -/
-theorem Monotone.map_infₛ_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (infₛ s))
-    (Mf : Monotone f) (hs : s.Nonempty) : f (infₛ s) = infₛ (f '' s) :=
-  @Monotone.map_supₛ_of_continuousAt' αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual hs
-#align monotone.map_Inf_of_continuous_at' Monotone.map_infₛ_of_continuousAt'
+theorem Monotone.map_sInf_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
+    (Mf : Monotone f) (hs : s.Nonempty) : f (sInf s) = sInf (f '' s) :=
+  @Monotone.map_sSup_of_continuousAt' αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual hs
+#align monotone.map_Inf_of_continuous_at' Monotone.map_sInf_of_continuousAt'
 
 /-- A monotone function `f` sending `top` to `top` and continuous at the infimum of a set sends
 this infimum to the infimum of the image of this set. -/
-theorem Monotone.map_infₛ_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (infₛ s))
-    (Mf : Monotone f) (ftop : f ⊤ = ⊤) : f (infₛ s) = infₛ (f '' s) :=
-  @Monotone.map_supₛ_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual ftop
-#align monotone.map_Inf_of_continuous_at Monotone.map_infₛ_of_continuousAt
+theorem Monotone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
+    (Mf : Monotone f) (ftop : f ⊤ = ⊤) : f (sInf s) = sInf (f '' s) :=
+  @Monotone.map_sSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual ftop
+#align monotone.map_Inf_of_continuous_at Monotone.map_sInf_of_continuousAt
 
 /-- A monotone function continuous at the indexed infimum over a nonempty `Sort` sends this indexed
 infimum to the indexed infimum of the composition. -/
-theorem Monotone.map_infᵢ_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (infᵢ g)) (Mf : Monotone f) : f (⨅ i, g i) = ⨅ i, f (g i) :=
-  @Monotone.map_supᵢ_of_continuousAt' αᵒᵈ βᵒᵈ _ _ _ _ _ _ ι _ f g Cf Mf.dual
-#align monotone.map_infi_of_continuous_at' Monotone.map_infᵢ_of_continuousAt'
+theorem Monotone.map_iInf_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iInf g)) (Mf : Monotone f) : f (⨅ i, g i) = ⨅ i, f (g i) :=
+  @Monotone.map_iSup_of_continuousAt' αᵒᵈ βᵒᵈ _ _ _ _ _ _ ι _ f g Cf Mf.dual
+#align monotone.map_infi_of_continuous_at' Monotone.map_iInf_of_continuousAt'
 
 /-- If a monotone function sending `top` to `top` is continuous at the indexed infimum over
 a `Sort`, then it sends this indexed infimum to the indexed infimum of the composition. -/
-theorem Monotone.map_infᵢ_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (infᵢ g)) (Mf : Monotone f) (ftop : f ⊤ = ⊤) : f (infᵢ g) = infᵢ (f ∘ g) :=
-  @Monotone.map_supᵢ_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ ι f g Cf Mf.dual ftop
-#align monotone.map_infi_of_continuous_at Monotone.map_infᵢ_of_continuousAt
+theorem Monotone.map_iInf_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iInf g)) (Mf : Monotone f) (ftop : f ⊤ = ⊤) : f (iInf g) = iInf (f ∘ g) :=
+  @Monotone.map_iSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ ι f g Cf Mf.dual ftop
+#align monotone.map_infi_of_continuous_at Monotone.map_iInf_of_continuousAt
 
 /-- An antitone function continuous at the supremum of a nonempty set sends this supremum to
 the infimum of the image of this set. -/
-theorem Antitone.map_supₛ_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (supₛ s))
-    (Af : Antitone f) (hs : s.Nonempty) : f (supₛ s) = infₛ (f '' s) :=
-  Monotone.map_supₛ_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (supₛ s) from Cf) Af
+theorem Antitone.map_sSup_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
+    (Af : Antitone f) (hs : s.Nonempty) : f (sSup s) = sInf (f '' s) :=
+  Monotone.map_sSup_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (sSup s) from Cf) Af
     hs
-#align antitone.map_Sup_of_continuous_at' Antitone.map_supₛ_of_continuousAt'
+#align antitone.map_Sup_of_continuous_at' Antitone.map_sSup_of_continuousAt'
 
 /-- An antitone function `f` sending `bot` to `top` and continuous at the supremum of a set sends
 this supremum to the infimum of the image of this set. -/
-theorem Antitone.map_supₛ_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (supₛ s))
-    (Af : Antitone f) (fbot : f ⊥ = ⊤) : f (supₛ s) = infₛ (f '' s) :=
-  Monotone.map_supₛ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (supₛ s) from Cf) Af
+theorem Antitone.map_sSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
+    (Af : Antitone f) (fbot : f ⊥ = ⊤) : f (sSup s) = sInf (f '' s) :=
+  Monotone.map_sSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (sSup s) from Cf) Af
     fbot
-#align antitone.map_Sup_of_continuous_at Antitone.map_supₛ_of_continuousAt
+#align antitone.map_Sup_of_continuous_at Antitone.map_sSup_of_continuousAt
 
 /-- An antitone function continuous at the indexed supremum over a nonempty `Sort` sends this
 indexed supremum to the indexed infimum of the composition. -/
-theorem Antitone.map_supᵢ_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (supᵢ g)) (Af : Antitone f) : f (⨆ i, g i) = ⨅ i, f (g i) :=
-  Monotone.map_supᵢ_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (supᵢ g) from Cf) Af
-#align antitone.map_supr_of_continuous_at' Antitone.map_supᵢ_of_continuousAt'
+theorem Antitone.map_iSup_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iSup g)) (Af : Antitone f) : f (⨆ i, g i) = ⨅ i, f (g i) :=
+  Monotone.map_iSup_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (iSup g) from Cf) Af
+#align antitone.map_supr_of_continuous_at' Antitone.map_iSup_of_continuousAt'
 
 /-- An antitone function sending `bot` to `top` is continuous at the indexed supremum over
 a `Sort`, then it sends this indexed supremum to the indexed supremum of the composition. -/
-theorem Antitone.map_supᵢ_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (supᵢ g)) (Af : Antitone f) (fbot : f ⊥ = ⊤) :
+theorem Antitone.map_iSup_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iSup g)) (Af : Antitone f) (fbot : f ⊥ = ⊤) :
     f (⨆ i, g i) = ⨅ i, f (g i) :=
-  Monotone.map_supᵢ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (supᵢ g) from Cf) Af
+  Monotone.map_iSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (iSup g) from Cf) Af
     fbot
-#align antitone.map_supr_of_continuous_at Antitone.map_supᵢ_of_continuousAt
+#align antitone.map_supr_of_continuous_at Antitone.map_iSup_of_continuousAt
 
 /-- An antitone function continuous at the infimum of a nonempty set sends this infimum to
 the supremum of the image of this set. -/
-theorem Antitone.map_infₛ_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (infₛ s))
-    (Af : Antitone f) (hs : s.Nonempty) : f (infₛ s) = supₛ (f '' s) :=
-  Monotone.map_infₛ_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (infₛ s) from Cf) Af
+theorem Antitone.map_sInf_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
+    (Af : Antitone f) (hs : s.Nonempty) : f (sInf s) = sSup (f '' s) :=
+  Monotone.map_sInf_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (sInf s) from Cf) Af
     hs
-#align antitone.map_Inf_of_continuous_at' Antitone.map_infₛ_of_continuousAt'
+#align antitone.map_Inf_of_continuous_at' Antitone.map_sInf_of_continuousAt'
 
 /-- An antitone function `f` sending `top` to `bot` and continuous at the infimum of a set sends
 this infimum to the supremum of the image of this set. -/
-theorem Antitone.map_infₛ_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (infₛ s))
-    (Af : Antitone f) (ftop : f ⊤ = ⊥) : f (infₛ s) = supₛ (f '' s) :=
-  Monotone.map_infₛ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (infₛ s) from Cf) Af
+theorem Antitone.map_sInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
+    (Af : Antitone f) (ftop : f ⊤ = ⊥) : f (sInf s) = sSup (f '' s) :=
+  Monotone.map_sInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (sInf s) from Cf) Af
     ftop
-#align antitone.map_Inf_of_continuous_at Antitone.map_infₛ_of_continuousAt
+#align antitone.map_Inf_of_continuous_at Antitone.map_sInf_of_continuousAt
 
 /-- An antitone function continuous at the indexed infimum over a nonempty `Sort` sends this indexed
 infimum to the indexed supremum of the composition. -/
-theorem Antitone.map_infᵢ_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (infᵢ g)) (Af : Antitone f) : f (⨅ i, g i) = ⨆ i, f (g i) :=
-  Monotone.map_infᵢ_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (infᵢ g) from Cf) Af
-#align antitone.map_infi_of_continuous_at' Antitone.map_infᵢ_of_continuousAt'
+theorem Antitone.map_iInf_of_continuousAt' {ι : Sort _} [Nonempty ι] {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iInf g)) (Af : Antitone f) : f (⨅ i, g i) = ⨆ i, f (g i) :=
+  Monotone.map_iInf_of_continuousAt' (show ContinuousAt (OrderDual.toDual ∘ f) (iInf g) from Cf) Af
+#align antitone.map_infi_of_continuous_at' Antitone.map_iInf_of_continuousAt'
 
 /-- If an antitone function sending `top` to `bot` is continuous at the indexed infimum over
 a `Sort`, then it sends this indexed infimum to the indexed supremum of the composition. -/
-theorem Antitone.map_infᵢ_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
-    (Cf : ContinuousAt f (infᵢ g)) (Af : Antitone f) (ftop : f ⊤ = ⊥) : f (infᵢ g) = supᵢ (f ∘ g) :=
-  Monotone.map_infᵢ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (infᵢ g) from Cf) Af
+theorem Antitone.map_iInf_of_continuousAt {ι : Sort _} {f : α → β} {g : ι → α}
+    (Cf : ContinuousAt f (iInf g)) (Af : Antitone f) (ftop : f ⊤ = ⊥) : f (iInf g) = iSup (f ∘ g) :=
+  Monotone.map_iInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (iInf g) from Cf) Af
     ftop
-#align antitone.map_infi_of_continuous_at Antitone.map_infᵢ_of_continuousAt
+#align antitone.map_infi_of_continuous_at Antitone.map_iInf_of_continuousAt
 
 end CompleteLinearOrder
 
@@ -2758,104 +2758,104 @@ section ConditionallyCompleteLinearOrder
 variable [ConditionallyCompleteLinearOrder α] [TopologicalSpace α] [OrderTopology α]
   [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderClosedTopology β] [Nonempty γ]
 
-theorem csupₛ_mem_closure {s : Set α} (hs : s.Nonempty) (B : BddAbove s) : supₛ s ∈ closure s :=
-  (isLUB_csupₛ hs B).mem_closure hs
-#align cSup_mem_closure csupₛ_mem_closure
+theorem csSup_mem_closure {s : Set α} (hs : s.Nonempty) (B : BddAbove s) : sSup s ∈ closure s :=
+  (isLUB_csSup hs B).mem_closure hs
+#align cSup_mem_closure csSup_mem_closure
 
-theorem cinfₛ_mem_closure {s : Set α} (hs : s.Nonempty) (B : BddBelow s) : infₛ s ∈ closure s :=
-  (isGLB_cinfₛ hs B).mem_closure hs
-#align cInf_mem_closure cinfₛ_mem_closure
+theorem csInf_mem_closure {s : Set α} (hs : s.Nonempty) (B : BddBelow s) : sInf s ∈ closure s :=
+  (isGLB_csInf hs B).mem_closure hs
+#align cInf_mem_closure csInf_mem_closure
 
-theorem IsClosed.csupₛ_mem {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddAbove s) :
-    supₛ s ∈ s :=
-  (isLUB_csupₛ hs B).mem_of_isClosed hs hc
-#align is_closed.cSup_mem IsClosed.csupₛ_mem
+theorem IsClosed.csSup_mem {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddAbove s) :
+    sSup s ∈ s :=
+  (isLUB_csSup hs B).mem_of_isClosed hs hc
+#align is_closed.cSup_mem IsClosed.csSup_mem
 
-theorem IsClosed.cinfₛ_mem {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddBelow s) :
-    infₛ s ∈ s :=
-  (isGLB_cinfₛ hs B).mem_of_isClosed hs hc
-#align is_closed.cInf_mem IsClosed.cinfₛ_mem
+theorem IsClosed.csInf_mem {s : Set α} (hc : IsClosed s) (hs : s.Nonempty) (B : BddBelow s) :
+    sInf s ∈ s :=
+  (isGLB_csInf hs B).mem_of_isClosed hs hc
+#align is_closed.cInf_mem IsClosed.csInf_mem
 
 /-- If a monotone function is continuous at the supremum of a nonempty bounded above set `s`,
 then it sends this supremum to the supremum of the image of `s`. -/
-theorem Monotone.map_csupₛ_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (supₛ s))
-    (Mf : Monotone f) (ne : s.Nonempty) (H : BddAbove s) : f (supₛ s) = supₛ (f '' s) := by
-  refine' ((isLUB_csupₛ (ne.image f) (Mf.map_bddAbove H)).unique _).symm
-  refine' (isLUB_csupₛ ne H).isLUB_of_tendsto (fun x _ y _ xy => Mf xy) ne _
+theorem Monotone.map_csSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
+    (Mf : Monotone f) (ne : s.Nonempty) (H : BddAbove s) : f (sSup s) = sSup (f '' s) := by
+  refine' ((isLUB_csSup (ne.image f) (Mf.map_bddAbove H)).unique _).symm
+  refine' (isLUB_csSup ne H).isLUB_of_tendsto (fun x _ y _ xy => Mf xy) ne _
   exact Cf.mono_left inf_le_left
-#align monotone.map_cSup_of_continuous_at Monotone.map_csupₛ_of_continuousAt
+#align monotone.map_cSup_of_continuous_at Monotone.map_csSup_of_continuousAt
 
 /-- If a monotone function is continuous at the indexed supremum of a bounded function on
 a nonempty `Sort`, then it sends this supremum to the supremum of the composition. -/
-theorem Monotone.map_csupᵢ_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
+theorem Monotone.map_ciSup_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
     (Mf : Monotone f) (H : BddAbove (range g)) : f (⨆ i, g i) = ⨆ i, f (g i) := by
-  rw [supᵢ, Mf.map_csupₛ_of_continuousAt Cf (range_nonempty _) H, ← range_comp, supᵢ]; rfl
-#align monotone.map_csupr_of_continuous_at Monotone.map_csupᵢ_of_continuousAt
+  rw [iSup, Mf.map_csSup_of_continuousAt Cf (range_nonempty _) H, ← range_comp, iSup]; rfl
+#align monotone.map_csupr_of_continuous_at Monotone.map_ciSup_of_continuousAt
 
 /-- If a monotone function is continuous at the infimum of a nonempty bounded below set `s`,
 then it sends this infimum to the infimum of the image of `s`. -/
-theorem Monotone.map_cinfₛ_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (infₛ s))
-    (Mf : Monotone f) (ne : s.Nonempty) (H : BddBelow s) : f (infₛ s) = infₛ (f '' s) :=
-  @Monotone.map_csupₛ_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual ne H
-#align monotone.map_cInf_of_continuous_at Monotone.map_cinfₛ_of_continuousAt
+theorem Monotone.map_csInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
+    (Mf : Monotone f) (ne : s.Nonempty) (H : BddBelow s) : f (sInf s) = sInf (f '' s) :=
+  @Monotone.map_csSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ f s Cf Mf.dual ne H
+#align monotone.map_cInf_of_continuous_at Monotone.map_csInf_of_continuousAt
 
 /-- A continuous monotone function sends indexed infimum to indexed infimum in conditionally
 complete linear order, under a boundedness assumption. -/
-theorem Monotone.map_cinfᵢ_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
+theorem Monotone.map_ciInf_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
     (Mf : Monotone f) (H : BddBelow (range g)) : f (⨅ i, g i) = ⨅ i, f (g i) :=
-  @Monotone.map_csupᵢ_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ _ Cf Mf.dual H
-#align monotone.map_cinfi_of_continuous_at Monotone.map_cinfᵢ_of_continuousAt
+  @Monotone.map_ciSup_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ _ Cf Mf.dual H
+#align monotone.map_cinfi_of_continuous_at Monotone.map_ciInf_of_continuousAt
 
 /-- If an antitone function is continuous at the supremum of a nonempty bounded above set `s`,
 then it sends this supremum to the infimum of the image of `s`. -/
-theorem Antitone.map_csupₛ_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (supₛ s))
-    (Af : Antitone f) (ne : s.Nonempty) (H : BddAbove s) : f (supₛ s) = infₛ (f '' s) :=
-  Monotone.map_csupₛ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (supₛ s) from Cf) Af
+theorem Antitone.map_csSup_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sSup s))
+    (Af : Antitone f) (ne : s.Nonempty) (H : BddAbove s) : f (sSup s) = sInf (f '' s) :=
+  Monotone.map_csSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (sSup s) from Cf) Af
     ne H
-#align antitone.map_cSup_of_continuous_at Antitone.map_csupₛ_of_continuousAt
+#align antitone.map_cSup_of_continuous_at Antitone.map_csSup_of_continuousAt
 
 /-- If an antitone function is continuous at the indexed supremum of a bounded function on
 a nonempty `Sort`, then it sends this supremum to the infimum of the composition. -/
-theorem Antitone.map_csupᵢ_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
+theorem Antitone.map_ciSup_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
     (Af : Antitone f) (H : BddAbove (range g)) : f (⨆ i, g i) = ⨅ i, f (g i) :=
-  Monotone.map_csupᵢ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (⨆ i, g i) from Cf)
+  Monotone.map_ciSup_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (⨆ i, g i) from Cf)
     Af H
-#align antitone.map_csupr_of_continuous_at Antitone.map_csupᵢ_of_continuousAt
+#align antitone.map_csupr_of_continuous_at Antitone.map_ciSup_of_continuousAt
 
 /-- If an antitone function is continuous at the infimum of a nonempty bounded below set `s`,
 then it sends this infimum to the supremum of the image of `s`. -/
-theorem Antitone.map_cinfₛ_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (infₛ s))
-    (Af : Antitone f) (ne : s.Nonempty) (H : BddBelow s) : f (infₛ s) = supₛ (f '' s) :=
-  Monotone.map_cinfₛ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (infₛ s) from Cf) Af
+theorem Antitone.map_csInf_of_continuousAt {f : α → β} {s : Set α} (Cf : ContinuousAt f (sInf s))
+    (Af : Antitone f) (ne : s.Nonempty) (H : BddBelow s) : f (sInf s) = sSup (f '' s) :=
+  Monotone.map_csInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (sInf s) from Cf) Af
     ne H
-#align antitone.map_cInf_of_continuous_at Antitone.map_cinfₛ_of_continuousAt
+#align antitone.map_cInf_of_continuous_at Antitone.map_csInf_of_continuousAt
 
 /-- A continuous antitone function sends indexed infimum to indexed supremum in conditionally
 complete linear order, under a boundedness assumption. -/
-theorem Antitone.map_cinfᵢ_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
+theorem Antitone.map_ciInf_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
     (Af : Antitone f) (H : BddBelow (range g)) : f (⨅ i, g i) = ⨆ i, f (g i) :=
-  Monotone.map_cinfᵢ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (⨅ i, g i) from Cf)
+  Monotone.map_ciInf_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (⨅ i, g i) from Cf)
     Af H
-#align antitone.map_cinfi_of_continuous_at Antitone.map_cinfᵢ_of_continuousAt
+#align antitone.map_cinfi_of_continuous_at Antitone.map_ciInf_of_continuousAt
 
-/-- A monotone map has a limit to the left of any point `x`, equal to `supₛ (f '' (Iio x))`. -/
+/-- A monotone map has a limit to the left of any point `x`, equal to `sSup (f '' (Iio x))`. -/
 theorem Monotone.tendsto_nhdsWithin_Iio {α β : Type _} [LinearOrder α] [TopologicalSpace α]
     [OrderTopology α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderTopology β]
-    {f : α → β} (Mf : Monotone f) (x : α) : Tendsto f (𝓝[<] x) (𝓝 (supₛ (f '' Iio x))) := by
+    {f : α → β} (Mf : Monotone f) (x : α) : Tendsto f (𝓝[<] x) (𝓝 (sSup (f '' Iio x))) := by
   rcases eq_empty_or_nonempty (Iio x) with (h | h); · simp [h]
   refine' tendsto_order.2 ⟨fun l hl => _, fun m hm => _⟩
   · obtain ⟨z, zx, lz⟩ : ∃ a : α, a < x ∧ l < f a := by
       simpa only [mem_image, exists_prop, exists_exists_and_eq_and] using
-        exists_lt_of_lt_csupₛ (nonempty_image_iff.2 h) hl
+        exists_lt_of_lt_csSup (nonempty_image_iff.2 h) hl
     exact mem_of_superset (Ioo_mem_nhdsWithin_Iio' zx) fun y hy => lz.trans_le (Mf hy.1.le)
   · refine mem_of_superset self_mem_nhdsWithin fun _ hy => lt_of_le_of_lt ?_ hm
-    exact le_csupₛ (Mf.map_bddAbove bddAbove_Iio) (mem_image_of_mem _ hy)
+    exact le_csSup (Mf.map_bddAbove bddAbove_Iio) (mem_image_of_mem _ hy)
 #align monotone.tendsto_nhds_within_Iio Monotone.tendsto_nhdsWithin_Iio
 
-/-- A monotone map has a limit to the right of any point `x`, equal to `infₛ (f '' (Ioi x))`. -/
+/-- A monotone map has a limit to the right of any point `x`, equal to `sInf (f '' (Ioi x))`. -/
 theorem Monotone.tendsto_nhdsWithin_Ioi {α β : Type _} [LinearOrder α] [TopologicalSpace α]
     [OrderTopology α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β] [OrderTopology β]
-    {f : α → β} (Mf : Monotone f) (x : α) : Tendsto f (𝓝[>] x) (𝓝 (infₛ (f '' Ioi x))) :=
+    {f : α → β} (Mf : Monotone f) (x : α) : Tendsto f (𝓝[>] x) (𝓝 (sInf (f '' Ioi x))) :=
   @Monotone.tendsto_nhdsWithin_Iio αᵒᵈ βᵒᵈ _ _ _ _ _ _ f Mf.dual x
 #align monotone.tendsto_nhds_within_Ioi Monotone.tendsto_nhdsWithin_Ioi
 

@@ -59,7 +59,7 @@ see their statements.
   (resp., `b ≤ f x`), then `a ≤ b` (resp., `b ≤ a); we also provide primed versions
   that assume the inequalities to hold for all `x`.
 
-### Min, max, `Sup` and `Inf`
+### Min, max, `supₛ` and `infₛ`
 
 * `Continuous.min`, `Continuous.max`: pointwise `min`/`max` of two continuous functions is
   continuous.
@@ -75,7 +75,7 @@ We do _not_ register the order topology as an instance on a preorder (or even on
 Indeed, on many such spaces, a topology has already been constructed in a different way (think
 of the discrete spaces `ℕ` or `ℤ`, or `ℝ` that could inherit a topology as the completion of `ℚ`),
 and is in general not defeq to the one generated by the intervals. We make it available as a
-definition `preorder.topology α` though, that can be registered as an instance when necessary, or
+definition `Preorder.topology α` though, that can be registered as an instance when necessary, or
 for specific types.
 -/
 
@@ -1356,7 +1356,7 @@ theorem Dense.topology_eq_generateFrom [DenselyOrdered α] {s : Set α} (hs : De
 variable (α)
 
 /-- Let `α` be a densely ordered linear order with order topology. If `α` is a separable space, then
-it has second countable topology. Note that the "densely ordered" assumption cannot be droped, see
+it has second countable topology. Note that the "densely ordered" assumption cannot be dropped, see
 [double arrow space](https://topology.pi-base.org/spaces/S000093) for a counterexample. -/
 theorem TopologicalSpace.SecondCountableTopology.of_separableSpace_orderTopology [DenselyOrdered α]
     [SeparableSpace α] : SecondCountableTopology α := by
@@ -2086,7 +2086,7 @@ alias IsGLB.mem_of_isClosed ← IsClosed.isGLB_mem
 #align is_closed.is_glb_mem IsClosed.isGLB_mem
 
 /-!
-### Existence of sequences tending to Inf or Sup of a given set
+### Existence of sequences tending to `infₛ` or `supₛ` of a given set
 -/
 
 theorem IsLUB.exists_seq_strictMono_tendsto_of_not_mem {t : Set α} {x : α}
@@ -2631,11 +2631,9 @@ theorem IsClosed.infₛ_mem {α : Type u} [TopologicalSpace α] [CompleteLinearO
 the supremum of the image of this set. -/
 theorem Monotone.map_supₛ_of_continuousAt' {f : α → β} {s : Set α} (Cf : ContinuousAt f (supₛ s))
     (Mf : Monotone f) (hs : s.Nonempty) : f (supₛ s) = supₛ (f '' s) :=
-  ((--This is a particular case of the more general is_lub.is_lub_of_tendsto
-              isLUB_supₛ
-              _).isLUB_of_tendsto
-          (fun _ _ _ _ xy => Mf xy) hs <|
-        Cf.mono_left inf_le_left).supₛ_eq.symm
+  --This is a particular case of the more general `IsLUB.isLUB_of_tendsto`
+  ((isLUB_supₛ _).isLUB_of_tendsto (fun _ _ _ _ xy => Mf xy) hs <|
+    Cf.mono_left inf_le_left).supₛ_eq.symm
 #align monotone.map_Sup_of_continuous_at' Monotone.map_supₛ_of_continuousAt'
 
 /-- A monotone function `f` sending `bot` to `bot` and continuous at the supremum of a set sends
@@ -2789,10 +2787,10 @@ theorem Monotone.map_csupₛ_of_continuousAt {f : α → β} {s : Set α} (Cf :
 
 /-- If a monotone function is continuous at the indexed supremum of a bounded function on
 a nonempty `Sort`, then it sends this supremum to the supremum of the composition. -/
-theorem Monotone.map_csupr_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
+theorem Monotone.map_csupᵢ_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
     (Mf : Monotone f) (H : BddAbove (range g)) : f (⨆ i, g i) = ⨆ i, f (g i) := by
   rw [supᵢ, Mf.map_csupₛ_of_continuousAt Cf (range_nonempty _) H, ← range_comp, supᵢ]; rfl
-#align monotone.map_csupr_of_continuous_at Monotone.map_csupr_of_continuousAt
+#align monotone.map_csupr_of_continuous_at Monotone.map_csupᵢ_of_continuousAt
 
 /-- If a monotone function is continuous at the infimum of a nonempty bounded below set `s`,
 then it sends this infimum to the infimum of the image of `s`. -/
@@ -2805,7 +2803,7 @@ theorem Monotone.map_cinfₛ_of_continuousAt {f : α → β} {s : Set α} (Cf :
 complete linear order, under a boundedness assumption. -/
 theorem Monotone.map_cinfᵢ_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨅ i, g i))
     (Mf : Monotone f) (H : BddBelow (range g)) : f (⨅ i, g i) = ⨅ i, f (g i) :=
-  @Monotone.map_csupr_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ _ Cf Mf.dual H
+  @Monotone.map_csupᵢ_of_continuousAt αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ _ Cf Mf.dual H
 #align monotone.map_cinfi_of_continuous_at Monotone.map_cinfᵢ_of_continuousAt
 
 /-- If an antitone function is continuous at the supremum of a nonempty bounded above set `s`,
@@ -2818,11 +2816,11 @@ theorem Antitone.map_csupₛ_of_continuousAt {f : α → β} {s : Set α} (Cf :
 
 /-- If an antitone function is continuous at the indexed supremum of a bounded function on
 a nonempty `Sort`, then it sends this supremum to the infimum of the composition. -/
-theorem Antitone.map_csupr_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
+theorem Antitone.map_csupᵢ_of_continuousAt {f : α → β} {g : γ → α} (Cf : ContinuousAt f (⨆ i, g i))
     (Af : Antitone f) (H : BddAbove (range g)) : f (⨆ i, g i) = ⨅ i, f (g i) :=
-  Monotone.map_csupr_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (⨆ i, g i) from Cf)
+  Monotone.map_csupᵢ_of_continuousAt (show ContinuousAt (OrderDual.toDual ∘ f) (⨆ i, g i) from Cf)
     Af H
-#align antitone.map_csupr_of_continuous_at Antitone.map_csupr_of_continuousAt
+#align antitone.map_csupr_of_continuous_at Antitone.map_csupᵢ_of_continuousAt
 
 /-- If an antitone function is continuous at the infimum of a nonempty bounded below set `s`,
 then it sends this infimum to the supremum of the image of `s`. -/

Co-authored-by: Eric Rodriguez <37984851+ericrbg@users.noreply.github.com>

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module topology.order.basic
-! leanprover-community/mathlib commit b363547b3113d350d053abdf2884e9850a56b205
+! leanprover-community/mathlib commit c985ae9840e06836a71db38de372f20acb49b790
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -2346,8 +2346,8 @@ theorem frontier_Iio [NoMinOrder α] {a : α} : frontier (Iio a) = {a} :=
 #align frontier_Iio frontier_Iio
 
 @[simp]
-theorem frontier_Icc [NoMinOrder α] [NoMaxOrder α] {a b : α} (h : a < b) :
-    frontier (Icc a b) = {a, b} := by simp [frontier, le_of_lt h, Icc_diff_Ioo_same]
+theorem frontier_Icc [NoMinOrder α] [NoMaxOrder α] {a b : α} (h : a ≤ b) :
+    frontier (Icc a b) = {a, b} := by simp [frontier, h, Icc_diff_Ioo_same]
 #align frontier_Icc frontier_Icc
 
 @[simp]

• There is now configuration for congr!, convert, and convert_to to control parts of the congruence algorithm, in particular transparency settings when applying congruence lemmas.
• congr! now applies congruence lemmas with reducible transparency by default. This prevents it from unfolding definitions when applying congruence lemmas. It also now tries both the LHS-biased and RHS-biased simp congruence lemmas, with a configuration option to set which it should try first.
• There is now a new HEq congruence lemma generator that gives each hypothesis access to the proofs of previous hypotheses. This means that if you have an equality ⊢ ⟨a, x⟩ = ⟨b, y⟩ of sigma types, congr! turns this into goals ⊢ a = b and ⊢ a = b → HEq x y (note that congr! will also auto-introduce a = b for you in the second goal). This congruence lemma generator applies to more cases than the simp congruence lemma generator does.
• congr! (and hence convert) are more careful about applying lemmas that don't force definitions to unfold. There were a number of cases in mathlib where the implementation of congr was being abused to unfold definitions.
• With set_option trace.congr! true you can see what congr! sees when it is deciding on congruence lemmas.
• There is also a bug fix in convert_to to do using 1 when there is no using clause, to match its documentation.

Note that congr! is more capable than congr at finding a way to equate left-hand sides and right-hand sides, so you will frequently need to limit its depth with a using clause. However, there is also a new heuristic to prevent considering unlikely-to-be-provable type equalities (controlled by the typeEqs option), which can help limit the depth automatically.

There is also a predefined configuration that you can invoke with, for example, convert (config := .unfoldSameFun) h, that causes it to behave more like congr, including using default transparency when unfolding.

@@ -891,8 +891,8 @@ variable [TopologicalSpace α] [Preorder α] [t : OrderTopology α]
 
 instance : OrderTopology αᵒᵈ :=
   ⟨by
-    convert @OrderTopology.topology_eq_generate_intervals α _ _ _
-    conv in _ ∨ _ => rw [or_comm]⟩
+    convert @OrderTopology.topology_eq_generate_intervals α _ _ _ using 6
+    apply or_comm⟩
 
 theorem isOpen_iff_generate_intervals {s : Set α} :
     IsOpen s ↔ GenerateOpen { s | ∃ a, s = Ioi a ∨ s = Iio a } s := by
@@ -1112,7 +1112,7 @@ theorem nhdsWithin_Ici_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopol
 
 theorem nhdsWithin_Iic_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopology α] {a : α}
     (ha : ∃ l, l < a) : (𝓝[≤] a).HasBasis (fun l => l < a) fun l => Ioc l a := by
-  convert @nhdsWithin_Ici_basis' αᵒᵈ _ _ _ (toDual a) ha
+  convert @nhdsWithin_Ici_basis' αᵒᵈ _ _ _ (toDual a) ha using 2
   exact (@dual_Ico _ _ _ _).symm
 #align nhds_within_Iic_basis' nhdsWithin_Iic_basis'
 
@@ -1421,8 +1421,8 @@ theorem countable_of_isolated_right' [SecondCountableTopology α] :
 second-countable. -/
 theorem countable_setOf_covby_left [SecondCountableTopology α] :
     Set.Countable { x : α | ∃ y, y ⋖ x } := by
-  convert @countable_setOf_covby_right αᵒᵈ _ _ _ _
-  exact Set.ext fun x => exists_congr fun y => toDual_covby_toDual_iff.symm
+  convert @countable_setOf_covby_right αᵒᵈ _ _ _ _ using 5
+  exact toDual_covby_toDual_iff.symm
 
 /-- The set of points which are isolated on the left is countable when the space is
 second-countable. -/
@@ -1710,7 +1710,8 @@ theorem nhdsWithin_Iio_basis' {a : α} (h : ∃ b, b < a) : (𝓝[<] a).HasBasis
   ⟨fun _ => mem_nhdsWithin_Iio_iff_exists_Ioo_subset' h⟩
 
 theorem nhdsWithin_Iio_eq_bot_iff {a : α} : 𝓝[<] a = ⊥ ↔ IsBot a ∨ ∃ b, b ⋖ a := by
-    convert nhdsWithin_Ioi_eq_bot_iff (a := OrderDual.toDual a) using 4
+    convert (config := {preTransparency := .default})
+      nhdsWithin_Ioi_eq_bot_iff (a := OrderDual.toDual a) using 4
     exact ofDual_covby_ofDual_iff
 
 open List in

API changes

• Add ENNReal.range_coe, ENNReal.range_coe', and ENNReal.coe_strictMono.
• Add instances for DenselyOrdered EReal, T5Space EReal, ContinuousNeg EReal, and CanLift EReal ENNReal _ _.
• Add EReal.range_coe, EReal.range_coe_eq_Ioo, EReal.range_coe_ennreal.
• Add EReal.denseRange_ratCast, EReal.nhds_top_basis, EReal.nhds_bot_basis.
• Deprecate EReal.negHomeo and EReal.continuous_neg.
• Generalize orderTopology_of_ordConnected to StrictMono.induced_topology_eq_preorder and StrictMono.embedding_of_ordConnected, use it to prove that some coercions are embeddings.
• Prove TopologicalSpace.SecondCountableTopology.of_separableSpace_orderTopology and helper lemmas Dense.topology_eq_generateFrom, Dense.Ioi_eq_bunionᵢ, and Dense.Iio_eq_bunionᵢ.

@@ -790,6 +790,16 @@ theorem Dense.exists_between [DenselyOrdered α] {s : Set α} (hs : Dense s) {x
   hs.exists_mem_open isOpen_Ioo (nonempty_Ioo.2 h)
 #align dense.exists_between Dense.exists_between
 
+theorem Dense.Ioi_eq_bunionᵢ [DenselyOrdered α] {s : Set α} (hs : Dense s) (x : α) :
+    Ioi x = ⋃ y ∈ s ∩ Ioi x, Ioi y := by
+  refine Subset.antisymm (fun z hz ↦ ?_) (unionᵢ₂_subset fun y hy ↦ Ioi_subset_Ioi (le_of_lt hy.2))
+  rcases hs.exists_between hz with ⟨y, hys, hxy, hyz⟩
+  exact mem_unionᵢ₂.2 ⟨y, ⟨hys, hxy⟩, hyz⟩
+
+theorem Dense.Iio_eq_bunionᵢ [DenselyOrdered α] {s : Set α} (hs : Dense s) (x : α) :
+    Iio x = ⋃ y ∈ s ∩ Iio x, Iio y :=
+  Dense.Ioi_eq_bunionᵢ (α := αᵒᵈ) hs x
+
 variable [Nonempty α] [TopologicalSpace β]
 
 /-- A compact set is bounded below -/
@@ -1043,15 +1053,30 @@ theorem induced_orderTopology {α : Type u} {β : Type v} [Preorder α] [ta : To
     fun ax => let ⟨b, ab, bx⟩ := H ax; ⟨b, hf.1 ab, le_of_lt bx⟩
 #align induced_order_topology induced_orderTopology
 
+/-- The topology induced by a strictly monotone function with order-connected range is the preorder
+topology. -/
+nonrec theorem StrictMono.induced_topology_eq_preorder {α β : Type _} [LinearOrder α]
+    [LinearOrder β] [t : TopologicalSpace β] [OrderTopology β] {f : α → β}
+    (hf : StrictMono f) (hc : OrdConnected (range f)) : t.induced f = Preorder.topology α := by
+  refine induced_topology_eq_preorder hf.lt_iff_lt (fun h₁ h₂ => ?_) fun h₁ h₂ => ?_
+  · rcases hc.out (mem_range_self _) (mem_range_self _) ⟨not_lt.1 h₂, h₁.le⟩ with ⟨y, rfl⟩
+    exact ⟨y, hf.lt_iff_lt.1 h₁, le_rfl⟩
+  · rcases hc.out (mem_range_self _) (mem_range_self _) ⟨h₁.le, not_lt.1 h₂⟩ with ⟨y, rfl⟩
+    exact ⟨y, hf.lt_iff_lt.1 h₁, le_rfl⟩
+
+/-- A strictly monotone function between linear orders with order topology is a topological
+embedding provided that the range of `f` is  order-connected. -/
+theorem StrictMono.embedding_of_ordConnected {α β : Type _} [LinearOrder α] [LinearOrder β]
+    [TopologicalSpace α] [h : OrderTopology α] [TopologicalSpace β] [OrderTopology β] {f : α → β}
+    (hf : StrictMono f) (hc : OrdConnected (range f)) : Embedding f :=
+  ⟨⟨h.1.trans <| Eq.symm <| hf.induced_topology_eq_preorder hc⟩, hf.injective⟩
+
 /-- On an `Set.OrdConnected` subset of a linear order, the order topology for the restriction of the
 order is the same as the restriction to the subset of the order topology. -/
 instance orderTopology_of_ordConnected {α : Type u} [TopologicalSpace α] [LinearOrder α]
-    [OrderTopology α] {t : Set α} [ht : OrdConnected t] : OrderTopology t := by
-  refine ⟨induced_topology_eq_preorder Iff.rfl (fun h₁ h₂ => ?_) (fun h₁ h₂ => ?_)⟩
-  · have := ht.out (Subtype.property _) (Subtype.property _) ⟨not_lt.1 h₂, h₁.le⟩
-    exact ⟨⟨_, this⟩, h₁, le_rfl⟩
-  · have := ht.out (Subtype.property _) (Subtype.property _) ⟨h₁.le, not_lt.1 h₂⟩
-    exact ⟨⟨_, this⟩, h₁, le_rfl⟩
+    [OrderTopology α] {t : Set α} [ht : OrdConnected t] : OrderTopology t :=
+  ⟨(Subtype.strictMono_coe t).induced_topology_eq_preorder $ by
+    rwa [← @Subtype.range_val _ t] at ht⟩
 #align order_topology_of_ord_connected orderTopology_of_ordConnected
 
 theorem nhdsWithin_Ici_eq'' [TopologicalSpace α] [Preorder α] [OrderTopology α] (a : α) :
@@ -1314,6 +1339,33 @@ theorem Filter.Eventually.exists_Ioo_subset [NoMaxOrder α] [NoMinOrder α] {a :
   mem_nhds_iff_exists_Ioo_subset.1 hp
 #align filter.eventually.exists_Ioo_subset Filter.Eventually.exists_Ioo_subset
 
+theorem Dense.topology_eq_generateFrom [DenselyOrdered α] {s : Set α} (hs : Dense s) :
+    ‹TopologicalSpace α› = .generateFrom (Ioi '' s ∪ Iio '' s) := by
+  refine (OrderTopology.topology_eq_generate_intervals (α := α)).trans ?_
+  refine le_antisymm (generateFrom_anti ?_) (le_generateFrom ?_)
+  · simp only [union_subset_iff, image_subset_iff]
+    exact ⟨fun a _ ↦ ⟨a, .inl rfl⟩, fun a _ ↦ ⟨a, .inr rfl⟩⟩
+  · rintro _ ⟨a, rfl | rfl⟩
+    · rw [hs.Ioi_eq_bunionᵢ]
+      let _ := generateFrom (Ioi '' s ∪ Iio '' s)
+      exact isOpen_unionᵢ fun x ↦ isOpen_unionᵢ fun h ↦ .basic _ <| .inl <| mem_image_of_mem _ h.1
+    · rw [hs.Iio_eq_bunionᵢ]
+      let _ := generateFrom (Ioi '' s ∪ Iio '' s)
+      exact isOpen_unionᵢ fun x ↦ isOpen_unionᵢ fun h ↦ .basic _ <| .inr <| mem_image_of_mem _ h.1
+
+variable (α)
+
+/-- Let `α` be a densely ordered linear order with order topology. If `α` is a separable space, then
+it has second countable topology. Note that the "densely ordered" assumption cannot be droped, see
+[double arrow space](https://topology.pi-base.org/spaces/S000093) for a counterexample. -/
+theorem TopologicalSpace.SecondCountableTopology.of_separableSpace_orderTopology [DenselyOrdered α]
+    [SeparableSpace α] : SecondCountableTopology α := by
+  rcases exists_countable_dense α with ⟨s, hc, hd⟩
+  refine ⟨⟨_, ?_, hd.topology_eq_generateFrom⟩⟩
+  exact (hc.image _).union (hc.image _)
+
+variable {α}
+
 -- porting note: new lemma
 /-- The set of points which are isolated on the right is countable when the space is
 second-countable. -/

This introduces a tactic congr! that is an analogue to mathlib 3's congr'. It is a more insistent version of congr that makes use of more congruence lemmas (including user congruence lemmas), propext, funext, and Subsingleton instances. It also has a feature to lift reflexive relations to equalities. Along with funext, the tactic does intros, allowing congr! to get access to function bodies; the introduced variables can be named using rename_i if needed.

This also modifies convert to use congr! rather than congr, which makes it work more like the mathlib3 version of the tactic.

@@ -1088,7 +1088,7 @@ theorem nhdsWithin_Ici_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopol
 theorem nhdsWithin_Iic_basis' [TopologicalSpace α] [LinearOrder α] [OrderTopology α] {a : α}
     (ha : ∃ l, l < a) : (𝓝[≤] a).HasBasis (fun l => l < a) fun l => Ioc l a := by
   convert @nhdsWithin_Ici_basis' αᵒᵈ _ _ _ (toDual a) ha
-  exact funext fun x => (@dual_Ico _ _ _ _).symm
+  exact (@dual_Ico _ _ _ _).symm
 #align nhds_within_Iic_basis' nhdsWithin_Iic_basis'
 
 theorem nhdsWithin_Ici_basis [TopologicalSpace α] [LinearOrder α] [OrderTopology α] [NoMaxOrder α]
@@ -1658,8 +1658,8 @@ theorem nhdsWithin_Iio_basis' {a : α} (h : ∃ b, b < a) : (𝓝[<] a).HasBasis
   ⟨fun _ => mem_nhdsWithin_Iio_iff_exists_Ioo_subset' h⟩
 
 theorem nhdsWithin_Iio_eq_bot_iff {a : α} : 𝓝[<] a = ⊥ ↔ IsBot a ∨ ∃ b, b ⋖ a := by
-    convert nhdsWithin_Ioi_eq_bot_iff (a := OrderDual.toDual a)
-    exact funext <| fun _ => propext ofDual_covby_ofDual_iff
+    convert nhdsWithin_Ioi_eq_bot_iff (a := OrderDual.toDual a) using 4
+    exact ofDual_covby_ofDual_iff
 
 open List in
 /-- The following statements are equivalent:

@@ -174,8 +174,8 @@ theorem le_of_tendsto_of_tendsto {f g : β → α} {b : Filter β} {a₁ a₂ :
   show (a₁, a₂) ∈ { p : α × α | p.1 ≤ p.2 } from t.isClosed_le'.mem_of_tendsto this h
 #align le_of_tendsto_of_tendsto le_of_tendsto_of_tendsto
 
-alias le_of_tendsto_of_tendsto ← tendsto_le_of_eventuallyLe
-#align tendsto_le_of_eventually_le tendsto_le_of_eventuallyLe
+alias le_of_tendsto_of_tendsto ← tendsto_le_of_eventuallyLE
+#align tendsto_le_of_eventually_le tendsto_le_of_eventuallyLE
 
 theorem le_of_tendsto_of_tendsto' {f g : β → α} {b : Filter β} {a₁ a₂ : α} [NeBot b]
     (hf : Tendsto f b (𝓝 a₁)) (hg : Tendsto g b (𝓝 a₂)) (h : ∀ x, f x ≤ g x) : a₁ ≤ a₂ :=

@@ -401,6 +401,9 @@ theorem Ioo_mem_nhdsWithin_Ioi {a b c : α} (H : b ∈ Ico a c) : Ioo a c ∈ 
 theorem Ioo_mem_nhdsWithin_Ioi' {a b : α} (H : a < b) : Ioo a b ∈ 𝓝[>] a :=
   Ioo_mem_nhdsWithin_Ioi ⟨le_rfl, H⟩
 
+theorem Covby.nhdsWithin_Ioi {a b : α} (h : a ⋖ b) : 𝓝[>] a = ⊥ :=
+  empty_mem_iff_bot.mp <| h.Ioo_eq ▸ Ioo_mem_nhdsWithin_Ioi' h.1
+
 theorem Ioc_mem_nhdsWithin_Ioi {a b c : α} (H : b ∈ Ico a c) : Ioc a c ∈ 𝓝[>] b :=
   mem_of_superset (Ioo_mem_nhdsWithin_Ioi H) Ioo_subset_Ioc_self
 #align Ioc_mem_nhds_within_Ioi Ioc_mem_nhdsWithin_Ioi
@@ -460,6 +463,9 @@ theorem Ioo_mem_nhdsWithin_Iio {a b c : α} (H : b ∈ Ioc a c) : Ioo a c ∈ 
 theorem Ioo_mem_nhdsWithin_Iio' {a b : α} (H : a < b) : Ioo a b ∈ 𝓝[<] b :=
   Ioo_mem_nhdsWithin_Iio ⟨H, le_rfl⟩
 
+theorem Covby.nhdsWithin_Iio {a b : α} (h : a ⋖ b) : 𝓝[<] b = ⊥ :=
+  empty_mem_iff_bot.mp <| h.Ioo_eq ▸ Ioo_mem_nhdsWithin_Iio' h.1
+
 theorem Ico_mem_nhdsWithin_Iio {a b c : α} (H : b ∈ Ioc a c) : Ico a c ∈ 𝓝[<] b :=
   mem_of_superset (Ioo_mem_nhdsWithin_Iio H) Ioo_subset_Ico_self
 #align Ico_mem_nhds_within_Iio Ico_mem_nhdsWithin_Iio
@@ -1556,6 +1562,17 @@ theorem mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' {a u' : α} {s : Set α} (hu'
   (TFAE_mem_nhdsWithin_Ioi hu' s).out 0 4
 #align mem_nhds_within_Ioi_iff_exists_Ioo_subset' mem_nhdsWithin_Ioi_iff_exists_Ioo_subset'
 
+theorem nhdsWithin_Ioi_basis' {a : α} (h : ∃ b, a < b) : (𝓝[>] a).HasBasis (a < ·) (Ioo a) :=
+  let ⟨_, h⟩ := h
+  ⟨fun _ => mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' h⟩
+
+theorem nhdsWithin_Ioi_eq_bot_iff {a : α} : 𝓝[>] a = ⊥ ↔ IsTop a ∨ ∃ b, a ⋖ b := by
+  by_cases ha : IsTop a
+  · simp [ha, ha.isMax.Ioi_eq]
+  · simp only [ha, false_or]
+    rw [isTop_iff_isMax, not_isMax_iff] at ha
+    simp only [(nhdsWithin_Ioi_basis' ha).eq_bot_iff, covby_iff_Ioo_eq]
+
 /-- A set is a neighborhood of `a` within `(a, +∞)` if and only if it contains an interval `(a, u)`
 with `a < u`. -/
 theorem mem_nhdsWithin_Ioi_iff_exists_Ioo_subset [NoMaxOrder α] {a : α} {s : Set α} :
@@ -1564,6 +1581,19 @@ theorem mem_nhdsWithin_Ioi_iff_exists_Ioo_subset [NoMaxOrder α] {a : α} {s : S
   mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' hu'
 #align mem_nhds_within_Ioi_iff_exists_Ioo_subset mem_nhdsWithin_Ioi_iff_exists_Ioo_subset
 
+/-- The set of points which are isolated on the right is countable when the space is
+second-countable. -/
+theorem countable_setOf_isolated_right [SecondCountableTopology α] :
+    { x : α | 𝓝[>] x = ⊥ }.Countable := by
+  simp only [nhdsWithin_Ioi_eq_bot_iff, setOf_or]
+  exact (subsingleton_isTop α).countable.union countable_setOf_covby_right
+
+/-- The set of points which are isolated on the left is countable when the space is
+second-countable. -/
+theorem countable_setOf_isolated_left [SecondCountableTopology α] :
+    { x : α | 𝓝[<] x = ⊥ }.Countable :=
+  countable_setOf_isolated_right (α := αᵒᵈ)
+
 /-- A set is a neighborhood of `a` within `(a, +∞)` if and only if it contains an interval `(a, u]`
 with `a < u`. -/
 theorem mem_nhdsWithin_Ioi_iff_exists_Ioc_subset [NoMaxOrder α] [DenselyOrdered α] {a : α}
@@ -1623,6 +1653,14 @@ theorem mem_nhdsWithin_Iio_iff_exists_Ico_subset [NoMinOrder α] [DenselyOrdered
   simpa only [OrderDual.exists, exists_prop, dual_Ioc] using this
 #align mem_nhds_within_Iio_iff_exists_Ico_subset mem_nhdsWithin_Iio_iff_exists_Ico_subset
 
+theorem nhdsWithin_Iio_basis' {a : α} (h : ∃ b, b < a) : (𝓝[<] a).HasBasis (· < a) (Ioo · a) :=
+  let ⟨_, h⟩ := h
+  ⟨fun _ => mem_nhdsWithin_Iio_iff_exists_Ioo_subset' h⟩
+
+theorem nhdsWithin_Iio_eq_bot_iff {a : α} : 𝓝[<] a = ⊥ ↔ IsBot a ∨ ∃ b, b ⋖ a := by
+    convert nhdsWithin_Ioi_eq_bot_iff (a := OrderDual.toDual a)
+    exact funext <| fun _ => propext ofDual_covby_ofDual_iff
+
 open List in
 /-- The following statements are equivalent:
 

We implement the continuity tactic using aesop, this makes it more robust and reduces the code to trivial macros.

@@ -668,14 +668,14 @@ nonrec theorem ContinuousAt.eventually_lt {x₀ : β} (hf : ContinuousAt f x₀)
   hf.eventually_lt hg hfg
 #align continuous_at.eventually_lt ContinuousAt.eventually_lt
 
--- porting note: todo: restore @[continuity]
+@[continuity]
 protected theorem Continuous.min (hf : Continuous f) (hg : Continuous g) :
     Continuous fun b => min (f b) (g b) := by
   simp only [min_def]
   exact hf.if_le hg hf hg fun x => id
 #align continuous.min Continuous.min
 
--- porting note: todo: restore @[continuity]
+@[continuity]
 protected theorem Continuous.max (hf : Continuous f) (hg : Continuous g) :
     Continuous fun b => max (f b) (g b) :=
   @Continuous.min αᵒᵈ _ _ _ _ _ _ _ hf hg

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

@@ -2283,9 +2283,9 @@ theorem nhdsWithin_Ioi_neBot [NoMaxOrder α] {a b : α} (H : a ≤ b) : NeBot (
   nhdsWithin_Ioi_neBot' nonempty_Ioi H
 #align nhds_within_Ioi_ne_bot nhdsWithin_Ioi_neBot
 
-theorem nhdsWithin_Ioi_self_ne_bot' {a : α} (H : (Ioi a).Nonempty) : NeBot (𝓝[>] a) :=
+theorem nhdsWithin_Ioi_self_neBot' {a : α} (H : (Ioi a).Nonempty) : NeBot (𝓝[>] a) :=
   nhdsWithin_Ioi_neBot' H (le_refl a)
-#align nhds_within_Ioi_self_ne_bot' nhdsWithin_Ioi_self_ne_bot'
+#align nhds_within_Ioi_self_ne_bot' nhdsWithin_Ioi_self_neBot'
 
 @[instance]
 theorem nhdsWithin_Ioi_self_neBot [NoMaxOrder α] (a : α) : NeBot (𝓝[>] a) :=
@@ -2298,18 +2298,18 @@ theorem Filter.Eventually.exists_gt [NoMaxOrder α] {a : α} {p : α → Prop} (
     ((h.filter_mono (@nhdsWithin_le_nhds _ _ a (Ioi a))).and self_mem_nhdsWithin).exists
 #align filter.eventually.exists_gt Filter.Eventually.exists_gt
 
-theorem nhdsWithin_Iio_ne_bot' {b c : α} (H₁ : (Iio c).Nonempty) (H₂ : b ≤ c) :
+theorem nhdsWithin_Iio_neBot' {b c : α} (H₁ : (Iio c).Nonempty) (H₂ : b ≤ c) :
     NeBot (𝓝[Iio c] b) :=
   mem_closure_iff_nhdsWithin_neBot.1 <| by rwa [closure_Iio' H₁]
-#align nhds_within_Iio_ne_bot' nhdsWithin_Iio_ne_bot'
+#align nhds_within_Iio_ne_bot' nhdsWithin_Iio_neBot'
 
 theorem nhdsWithin_Iio_neBot [NoMinOrder α] {a b : α} (H : a ≤ b) : NeBot (𝓝[Iio b] a) :=
-  nhdsWithin_Iio_ne_bot' nonempty_Iio H
+  nhdsWithin_Iio_neBot' nonempty_Iio H
 #align nhds_within_Iio_ne_bot nhdsWithin_Iio_neBot
 
-theorem nhdsWithin_Iio_self_ne_bot' {b : α} (H : (Iio b).Nonempty) : NeBot (𝓝[<] b) :=
-  nhdsWithin_Iio_ne_bot' H (le_refl b)
-#align nhds_within_Iio_self_ne_bot' nhdsWithin_Iio_self_ne_bot'
+theorem nhdsWithin_Iio_self_neBot' {b : α} (H : (Iio b).Nonempty) : NeBot (𝓝[<] b) :=
+  nhdsWithin_Iio_neBot' H (le_refl b)
+#align nhds_within_Iio_self_ne_bot' nhdsWithin_Iio_self_neBot'
 
 @[instance]
 theorem nhdsWithin_Iio_self_neBot [NoMinOrder α] (a : α) : NeBot (𝓝[<] a) :=