topology.algebra.order.left_right_lim ⟷ Mathlib.Topology.Algebra.Order.LeftRightLim

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
 import Topology.Order.Basic
-import Topology.Algebra.Order.LeftRight
+import Topology.Order.LeftRight
 
 #align_import topology.algebra.order.left_right_lim from "leanprover-community/mathlib"@"ac34df03f74e6f797efd6991df2e3b7f7d8d33e0"
 

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

@@ -74,7 +74,7 @@ theorem leftLim_eq_of_tendsto [hα : TopologicalSpace α] [h'α : OrderTopology
     {f : α → β} {a : α} {y : β} (h : 𝓝[<] a ≠ ⊥) (h' : Tendsto f (𝓝[<] a) (𝓝 y)) :
     leftLim f a = y := by
   have h'' : ∃ y, tendsto f (𝓝[<] a) (𝓝 y) := ⟨y, h'⟩
-  rw [h'α.topology_eq_generate_intervals] at h h' h'' 
+  rw [h'α.topology_eq_generate_intervals] at h h' h''
   simp only [left_lim, h, h'', not_true, or_self_iff, if_false]
   haveI := ne_bot_iff.2 h
   exact h'.lim_eq
@@ -85,7 +85,7 @@ theorem leftLim_eq_of_tendsto [hα : TopologicalSpace α] [h'α : OrderTopology
 theorem leftLim_eq_of_eq_bot [hα : TopologicalSpace α] [h'α : OrderTopology α] (f : α → β) {a : α}
     (h : 𝓝[<] a = ⊥) : leftLim f a = f a :=
   by
-  rw [h'α.topology_eq_generate_intervals] at h 
+  rw [h'α.topology_eq_generate_intervals] at h
   simp [left_lim, ite_eq_left_iff, h]
 #align left_lim_eq_of_eq_bot leftLim_eq_of_eq_bot
 -/
@@ -235,7 +235,7 @@ theorem continuousWithinAt_Iio_iff_leftLim_eq :
   haveI : (𝓝[Iio x] x).ne_bot := ne_bot_iff.2 h'
   refine' ⟨fun h => tendsto_nhds_unique (hf.tendsto_left_lim x) h.Tendsto, fun h => _⟩
   have := hf.tendsto_left_lim x
-  rwa [h] at this 
+  rwa [h] at this
 #align monotone.continuous_within_at_Iio_iff_left_lim_eq Monotone.continuousWithinAt_Iio_iff_leftLim_eq
 -/
 
@@ -266,7 +266,7 @@ theorem continuousAt_iff_leftLim_eq_rightLim : ContinuousAt f x ↔ leftLim f x
       exact le_right_lim hf (le_refl _)
     refine' continuousAt_iff_continuous_left'_right'.2 ⟨_, _⟩
     · exact hf.continuous_within_at_Iio_iff_left_lim_eq.2 h'
-    · rw [h] at h' 
+    · rw [h] at h'
       exact hf.continuous_within_at_Ioi_iff_right_lim_eq.2 h'
 #align monotone.continuous_at_iff_left_lim_eq_right_lim Monotone.continuousAt_iff_leftLim_eq_rightLim
 -/
@@ -313,7 +313,7 @@ theorem countable_not_continuousWithinAt_Ioi [SecondCountableTopology β] :
       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.left_inv_on_inv_fun_on us, I.left_inv_on_inv_fun_on vs] at ha hb 
+      simp only [I.left_inv_on_inv_fun_on us, I.left_inv_on_inv_fun_on 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⟩

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

@@ -49,7 +49,11 @@ variable {α β : Type _} [LinearOrder α] [TopologicalSpace β]
 let `a : α`. The limit strictly to the left of `f` at `a`, denoted with `left_lim f a`, is defined
 by using the order topology on `α`. If `a` is isolated to its left or the function has no left
 limit, we use `f a` instead to guarantee a good behavior in most cases. -/
-noncomputable irreducible_def Function.leftLim (f : α → β) (a : α) : β := by classical
+noncomputable irreducible_def Function.leftLim (f : α → β) (a : α) : β := by
+  classical
+  haveI : Nonempty β := ⟨f a⟩
+  letI : TopologicalSpace α := Preorder.topology α
+  exact if 𝓝[<] a = ⊥ ∨ ¬∃ y, tendsto f (𝓝[<] a) (𝓝 y) then f a else limUnder (𝓝[<] a) f
 #align function.left_lim Function.leftLim
 -/
 

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

@@ -49,11 +49,7 @@ variable {α β : Type _} [LinearOrder α] [TopologicalSpace β]
 let `a : α`. The limit strictly to the left of `f` at `a`, denoted with `left_lim f a`, is defined
 by using the order topology on `α`. If `a` is isolated to its left or the function has no left
 limit, we use `f a` instead to guarantee a good behavior in most cases. -/
-noncomputable irreducible_def Function.leftLim (f : α → β) (a : α) : β := by
-  classical
-  haveI : Nonempty β := ⟨f a⟩
-  letI : TopologicalSpace α := Preorder.topology α
-  exact if 𝓝[<] a = ⊥ ∨ ¬∃ y, tendsto f (𝓝[<] a) (𝓝 y) then f a else limUnder (𝓝[<] a) f
+noncomputable irreducible_def Function.leftLim (f : α → β) (a : α) : β := by classical
 #align function.left_lim Function.leftLim
 -/
 

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

@@ -275,7 +275,7 @@ theorem continuousAt_iff_leftLim_eq_rightLim : ContinuousAt f x ↔ leftLim f x
 /-- In a second countable space, the set of points where a monotone function is not right-continuous
 is at most countable. Superseded by `countable_not_continuous_at` which gives the two-sided
 version. -/
-theorem countable_not_continuousWithinAt_Ioi [TopologicalSpace.SecondCountableTopology β] :
+theorem countable_not_continuousWithinAt_Ioi [SecondCountableTopology β] :
     Set.Countable {x | ¬ContinuousWithinAt f (Ioi x) x} :=
   by
   /- If `f` is not continuous on the right at `x`, there is an interval `(f x, z x)` which is not
@@ -326,7 +326,7 @@ theorem countable_not_continuousWithinAt_Ioi [TopologicalSpace.SecondCountableTo
 /-- In a second countable space, the set of points where a monotone function is not left-continuous
 is at most countable. Superseded by `countable_not_continuous_at` which gives the two-sided
 version. -/
-theorem countable_not_continuousWithinAt_Iio [TopologicalSpace.SecondCountableTopology β] :
+theorem countable_not_continuousWithinAt_Iio [SecondCountableTopology β] :
     Set.Countable {x | ¬ContinuousWithinAt f (Iio x) x} :=
   hf.dual.countable_not_continuousWithinAt_Ioi
 #align monotone.countable_not_continuous_within_at_Iio Monotone.countable_not_continuousWithinAt_Iio
@@ -335,7 +335,7 @@ theorem countable_not_continuousWithinAt_Iio [TopologicalSpace.SecondCountableTo
 #print Monotone.countable_not_continuousAt /-
 /-- In a second countable space, the set of points where a monotone function is not continuous
 is at most countable. -/
-theorem countable_not_continuousAt [TopologicalSpace.SecondCountableTopology β] :
+theorem countable_not_continuousAt [SecondCountableTopology β] :
     Set.Countable {x | ¬ContinuousAt f x} :=
   by
   apply
@@ -461,7 +461,7 @@ theorem continuousAt_iff_leftLim_eq_rightLim : ContinuousAt f x ↔ leftLim f x
 #print Antitone.countable_not_continuousAt /-
 /-- In a second countable space, the set of points where an antitone function is not continuous
 is at most countable. -/
-theorem countable_not_continuousAt [TopologicalSpace.SecondCountableTopology β] :
+theorem countable_not_continuousAt [SecondCountableTopology β] :
     Set.Countable {x | ¬ContinuousAt f x} :=
   hf.dual_right.countable_not_continuousAt
 #align antitone.countable_not_continuous_at Antitone.countable_not_continuousAt

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathbin.Topology.Order.Basic
-import Mathbin.Topology.Algebra.Order.LeftRight
+import Topology.Order.Basic
+import Topology.Algebra.Order.LeftRight
 
 #align_import topology.algebra.order.left_right_lim from "leanprover-community/mathlib"@"ac34df03f74e6f797efd6991df2e3b7f7d8d33e0"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module topology.algebra.order.left_right_lim
-! leanprover-community/mathlib commit ac34df03f74e6f797efd6991df2e3b7f7d8d33e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Order.Basic
 import Mathbin.Topology.Algebra.Order.LeftRight
 
+#align_import topology.algebra.order.left_right_lim from "leanprover-community/mathlib"@"ac34df03f74e6f797efd6991df2e3b7f7d8d33e0"
+
 /-!
 # Left and right limits
 

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

@@ -72,6 +72,7 @@ noncomputable def Function.rightLim (f : α → β) (a : α) : β :=
 
 open Function
 
+#print leftLim_eq_of_tendsto /-
 theorem leftLim_eq_of_tendsto [hα : TopologicalSpace α] [h'α : OrderTopology α] [T2Space β]
     {f : α → β} {a : α} {y : β} (h : 𝓝[<] a ≠ ⊥) (h' : Tendsto f (𝓝[<] a) (𝓝 y)) :
     leftLim f a = y := by
@@ -81,13 +82,16 @@ theorem leftLim_eq_of_tendsto [hα : TopologicalSpace α] [h'α : OrderTopology
   haveI := ne_bot_iff.2 h
   exact h'.lim_eq
 #align left_lim_eq_of_tendsto leftLim_eq_of_tendsto
+-/
 
+#print leftLim_eq_of_eq_bot /-
 theorem leftLim_eq_of_eq_bot [hα : TopologicalSpace α] [h'α : OrderTopology α] (f : α → β) {a : α}
     (h : 𝓝[<] a = ⊥) : leftLim f a = f a :=
   by
   rw [h'α.topology_eq_generate_intervals] at h 
   simp [left_lim, ite_eq_left_iff, h]
 #align left_lim_eq_of_eq_bot leftLim_eq_of_eq_bot
+-/
 
 end
 
@@ -98,13 +102,14 @@ namespace Monotone
 variable {α β : Type _} [LinearOrder α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β]
   [OrderTopology β] {f : α → β} (hf : Monotone f) {x y : α}
 
-include hf
-
+#print Monotone.leftLim_eq_sSup /-
 theorem leftLim_eq_sSup [TopologicalSpace α] [OrderTopology α] (h : 𝓝[<] x ≠ ⊥) :
     leftLim f x = sSup (f '' Iio x) :=
   leftLim_eq_of_tendsto h (hf.tendsto_nhdsWithin_Iio x)
 #align monotone.left_lim_eq_Sup Monotone.leftLim_eq_sSup
+-/
 
+#print Monotone.leftLim_le /-
 theorem leftLim_le (h : x ≤ y) : leftLim f x ≤ f y :=
   by
   letI : TopologicalSpace α := Preorder.topology α
@@ -120,7 +125,9 @@ theorem leftLim_le (h : x ≤ y) : leftLim f x ≤ f y :=
     intro z hz
     exact hf (hz.le.trans h)
 #align monotone.left_lim_le Monotone.leftLim_le
+-/
 
+#print Monotone.le_leftLim /-
 theorem le_leftLim (h : x < y) : f x ≤ leftLim f y :=
   by
   letI : TopologicalSpace α := Preorder.topology α
@@ -134,7 +141,9 @@ theorem le_leftLim (h : x < y) : f x ≤ leftLim f y :=
   intro z hz
   exact hf hz.le
 #align monotone.le_left_lim Monotone.le_leftLim
+-/
 
+#print Monotone.leftLim /-
 @[mono]
 protected theorem leftLim : Monotone (leftLim f) :=
   by
@@ -143,23 +152,33 @@ protected theorem leftLim : Monotone (leftLim f) :=
   · exact le_rfl
   · exact (hf.left_lim_le le_rfl).trans (hf.le_left_lim hxy)
 #align monotone.left_lim Monotone.leftLim
+-/
 
+#print Monotone.le_rightLim /-
 theorem le_rightLim (h : x ≤ y) : f x ≤ rightLim f y :=
   hf.dual.leftLim_le h
 #align monotone.le_right_lim Monotone.le_rightLim
+-/
 
+#print Monotone.rightLim_le /-
 theorem rightLim_le (h : x < y) : rightLim f x ≤ f y :=
   hf.dual.le_leftLim h
 #align monotone.right_lim_le Monotone.rightLim_le
+-/
 
+#print Monotone.rightLim /-
 @[mono]
 protected theorem rightLim : Monotone (rightLim f) := fun x y h => hf.dual.leftLim h
 #align monotone.right_lim Monotone.rightLim
+-/
 
+#print Monotone.leftLim_le_rightLim /-
 theorem leftLim_le_rightLim (h : x ≤ y) : leftLim f x ≤ rightLim f y :=
   (hf.leftLim_le le_rfl).trans (hf.le_rightLim h)
 #align monotone.left_lim_le_right_lim Monotone.leftLim_le_rightLim
+-/
 
+#print Monotone.rightLim_le_leftLim /-
 theorem rightLim_le_leftLim (h : x < y) : rightLim f x ≤ leftLim f y :=
   by
   letI : TopologicalSpace α := Preorder.topology α
@@ -174,9 +193,11 @@ theorem rightLim_le_leftLim (h : x < y) : rightLim f x ≤ leftLim f y :=
     right_lim f x ≤ f a := hf.right_lim_le xa
     _ ≤ left_lim f y := hf.le_left_lim ay
 #align monotone.right_lim_le_left_lim Monotone.rightLim_le_leftLim
+-/
 
 variable [TopologicalSpace α] [OrderTopology α]
 
+#print Monotone.tendsto_leftLim /-
 theorem tendsto_leftLim (x : α) : Tendsto f (𝓝[<] x) (𝓝 (leftLim f x)) :=
   by
   rcases eq_or_ne (𝓝[<] x) ⊥ with (h' | h')
@@ -184,21 +205,29 @@ theorem tendsto_leftLim (x : α) : Tendsto f (𝓝[<] x) (𝓝 (leftLim f x)) :=
   rw [left_lim_eq_Sup hf h']
   exact hf.tendsto_nhds_within_Iio x
 #align monotone.tendsto_left_lim Monotone.tendsto_leftLim
+-/
 
+#print Monotone.tendsto_leftLim_within /-
 theorem tendsto_leftLim_within (x : α) : Tendsto f (𝓝[<] x) (𝓝[≤] leftLim f x) :=
   by
   apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within f (hf.tendsto_left_lim x)
   filter_upwards [self_mem_nhdsWithin] with y hy using hf.le_left_lim hy
 #align monotone.tendsto_left_lim_within Monotone.tendsto_leftLim_within
+-/
 
+#print Monotone.tendsto_rightLim /-
 theorem tendsto_rightLim (x : α) : Tendsto f (𝓝[>] x) (𝓝 (rightLim f x)) :=
   hf.dual.tendsto_leftLim x
 #align monotone.tendsto_right_lim Monotone.tendsto_rightLim
+-/
 
+#print Monotone.tendsto_rightLim_within /-
 theorem tendsto_rightLim_within (x : α) : Tendsto f (𝓝[>] x) (𝓝[≥] rightLim f x) :=
   hf.dual.tendsto_leftLim_within x
 #align monotone.tendsto_right_lim_within Monotone.tendsto_rightLim_within
+-/
 
+#print Monotone.continuousWithinAt_Iio_iff_leftLim_eq /-
 /-- A monotone function is continuous to the left at a point if and only if its left limit
 coincides with the value of the function. -/
 theorem continuousWithinAt_Iio_iff_leftLim_eq :
@@ -211,14 +240,18 @@ theorem continuousWithinAt_Iio_iff_leftLim_eq :
   have := hf.tendsto_left_lim x
   rwa [h] at this 
 #align monotone.continuous_within_at_Iio_iff_left_lim_eq Monotone.continuousWithinAt_Iio_iff_leftLim_eq
+-/
 
+#print Monotone.continuousWithinAt_Ioi_iff_rightLim_eq /-
 /-- A monotone function is continuous to the right at a point if and only if its right limit
 coincides with the value of the function. -/
 theorem continuousWithinAt_Ioi_iff_rightLim_eq :
     ContinuousWithinAt f (Ioi x) x ↔ rightLim f x = f x :=
   hf.dual.continuousWithinAt_Iio_iff_leftLim_eq
 #align monotone.continuous_within_at_Ioi_iff_right_lim_eq Monotone.continuousWithinAt_Ioi_iff_rightLim_eq
+-/
 
+#print Monotone.continuousAt_iff_leftLim_eq_rightLim /-
 /-- A monotone function is continuous at a point if and only if its left and right limits
 coincide. -/
 theorem continuousAt_iff_leftLim_eq_rightLim : ContinuousAt f x ↔ leftLim f x = rightLim f x :=
@@ -239,6 +272,7 @@ theorem continuousAt_iff_leftLim_eq_rightLim : ContinuousAt f x ↔ leftLim f x
     · rw [h] at h' 
       exact hf.continuous_within_at_Ioi_iff_right_lim_eq.2 h'
 #align monotone.continuous_at_iff_left_lim_eq_right_lim Monotone.continuousAt_iff_leftLim_eq_rightLim
+-/
 
 #print Monotone.countable_not_continuousWithinAt_Ioi /-
 /-- In a second countable space, the set of points where a monotone function is not right-continuous
@@ -325,79 +359,107 @@ namespace Antitone
 variable {α β : Type _} [LinearOrder α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β]
   [OrderTopology β] {f : α → β} (hf : Antitone f) {x y : α}
 
-include hf
-
+#print Antitone.le_leftLim /-
 theorem le_leftLim (h : x ≤ y) : f y ≤ leftLim f x :=
   hf.dual_right.leftLim_le h
 #align antitone.le_left_lim Antitone.le_leftLim
+-/
 
+#print Antitone.leftLim_le /-
 theorem leftLim_le (h : x < y) : leftLim f y ≤ f x :=
   hf.dual_right.le_leftLim h
 #align antitone.left_lim_le Antitone.leftLim_le
+-/
 
+#print Antitone.leftLim /-
 @[mono]
 protected theorem leftLim : Antitone (leftLim f) :=
   hf.dual_right.leftLim
 #align antitone.left_lim Antitone.leftLim
+-/
 
+#print Antitone.rightLim_le /-
 theorem rightLim_le (h : x ≤ y) : rightLim f y ≤ f x :=
   hf.dual_right.le_rightLim h
 #align antitone.right_lim_le Antitone.rightLim_le
+-/
 
+#print Antitone.le_rightLim /-
 theorem le_rightLim (h : x < y) : f y ≤ rightLim f x :=
   hf.dual_right.rightLim_le h
 #align antitone.le_right_lim Antitone.le_rightLim
+-/
 
+#print Antitone.rightLim /-
 @[mono]
 protected theorem rightLim : Antitone (rightLim f) :=
   hf.dual_right.rightLim
 #align antitone.right_lim Antitone.rightLim
+-/
 
+#print Antitone.rightLim_le_leftLim /-
 theorem rightLim_le_leftLim (h : x ≤ y) : rightLim f y ≤ leftLim f x :=
   hf.dual_right.leftLim_le_rightLim h
 #align antitone.right_lim_le_left_lim Antitone.rightLim_le_leftLim
+-/
 
+#print Antitone.leftLim_le_rightLim /-
 theorem leftLim_le_rightLim (h : x < y) : leftLim f y ≤ rightLim f x :=
   hf.dual_right.rightLim_le_leftLim h
 #align antitone.left_lim_le_right_lim Antitone.leftLim_le_rightLim
+-/
 
 variable [TopologicalSpace α] [OrderTopology α]
 
+#print Antitone.tendsto_leftLim /-
 theorem tendsto_leftLim (x : α) : Tendsto f (𝓝[<] x) (𝓝 (leftLim f x)) :=
   hf.dual_right.tendsto_leftLim x
 #align antitone.tendsto_left_lim Antitone.tendsto_leftLim
+-/
 
+#print Antitone.tendsto_leftLim_within /-
 theorem tendsto_leftLim_within (x : α) : Tendsto f (𝓝[<] x) (𝓝[≥] leftLim f x) :=
   hf.dual_right.tendsto_leftLim_within x
 #align antitone.tendsto_left_lim_within Antitone.tendsto_leftLim_within
+-/
 
+#print Antitone.tendsto_rightLim /-
 theorem tendsto_rightLim (x : α) : Tendsto f (𝓝[>] x) (𝓝 (rightLim f x)) :=
   hf.dual_right.tendsto_rightLim x
 #align antitone.tendsto_right_lim Antitone.tendsto_rightLim
+-/
 
+#print Antitone.tendsto_rightLim_within /-
 theorem tendsto_rightLim_within (x : α) : Tendsto f (𝓝[>] x) (𝓝[≤] rightLim f x) :=
   hf.dual_right.tendsto_rightLim_within x
 #align antitone.tendsto_right_lim_within Antitone.tendsto_rightLim_within
+-/
 
+#print Antitone.continuousWithinAt_Iio_iff_leftLim_eq /-
 /-- An antitone function is continuous to the left at a point if and only if its left limit
 coincides with the value of the function. -/
 theorem continuousWithinAt_Iio_iff_leftLim_eq :
     ContinuousWithinAt f (Iio x) x ↔ leftLim f x = f x :=
   hf.dual_right.continuousWithinAt_Iio_iff_leftLim_eq
 #align antitone.continuous_within_at_Iio_iff_left_lim_eq Antitone.continuousWithinAt_Iio_iff_leftLim_eq
+-/
 
+#print Antitone.continuousWithinAt_Ioi_iff_rightLim_eq /-
 /-- An antitone function is continuous to the right at a point if and only if its right limit
 coincides with the value of the function. -/
 theorem continuousWithinAt_Ioi_iff_rightLim_eq :
     ContinuousWithinAt f (Ioi x) x ↔ rightLim f x = f x :=
   hf.dual_right.continuousWithinAt_Ioi_iff_rightLim_eq
 #align antitone.continuous_within_at_Ioi_iff_right_lim_eq Antitone.continuousWithinAt_Ioi_iff_rightLim_eq
+-/
 
+#print Antitone.continuousAt_iff_leftLim_eq_rightLim /-
 /-- An antitone function is continuous at a point if and only if its left and right limits
 coincide. -/
 theorem continuousAt_iff_leftLim_eq_rightLim : ContinuousAt f x ↔ leftLim f x = rightLim f x :=
   hf.dual_right.continuousAt_iff_leftLim_eq_rightLim
 #align antitone.continuous_at_iff_left_lim_eq_right_lim Antitone.continuousAt_iff_leftLim_eq_rightLim
+-/
 
 #print Antitone.countable_not_continuousAt /-
 /-- In a second countable space, the set of points where an antitone function is not continuous

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

@@ -173,7 +173,6 @@ theorem rightLim_le_leftLim (h : x < y) : rightLim f x ≤ leftLim f y :=
   calc
     right_lim f x ≤ f a := hf.right_lim_le xa
     _ ≤ left_lim f y := hf.le_left_lim ay
-    
 #align monotone.right_lim_le_left_lim Monotone.rightLim_le_leftLim
 
 variable [TopologicalSpace α] [OrderTopology α]
@@ -271,7 +270,6 @@ theorem countable_not_continuousWithinAt_Ioi [TopologicalSpace.SecondCountableTo
     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 :=

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

@@ -54,9 +54,9 @@ by using the order topology on `α`. If `a` is isolated to its left or the funct
 limit, we use `f a` instead to guarantee a good behavior in most cases. -/
 noncomputable irreducible_def Function.leftLim (f : α → β) (a : α) : β := by
   classical
-    haveI : Nonempty β := ⟨f a⟩
-    letI : TopologicalSpace α := Preorder.topology α
-    exact if 𝓝[<] a = ⊥ ∨ ¬∃ y, tendsto f (𝓝[<] a) (𝓝 y) then f a else limUnder (𝓝[<] a) f
+  haveI : Nonempty β := ⟨f a⟩
+  letI : TopologicalSpace α := Preorder.topology α
+  exact if 𝓝[<] a = ⊥ ∨ ¬∃ y, tendsto f (𝓝[<] a) (𝓝 y) then f a else limUnder (𝓝[<] a) f
 #align function.left_lim Function.leftLim
 -/
 
@@ -189,7 +189,7 @@ theorem tendsto_leftLim (x : α) : Tendsto f (𝓝[<] x) (𝓝 (leftLim f x)) :=
 theorem tendsto_leftLim_within (x : α) : Tendsto f (𝓝[<] x) (𝓝[≤] leftLim f x) :=
   by
   apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within f (hf.tendsto_left_lim x)
-  filter_upwards [self_mem_nhdsWithin]with y hy using hf.le_left_lim hy
+  filter_upwards [self_mem_nhdsWithin] with y hy using hf.le_left_lim hy
 #align monotone.tendsto_left_lim_within Monotone.tendsto_leftLim_within
 
 theorem tendsto_rightLim (x : α) : Tendsto f (𝓝[>] x) (𝓝 (rightLim f x)) :=
@@ -246,22 +246,22 @@ theorem continuousAt_iff_leftLim_eq_rightLim : ContinuousAt f x ↔ leftLim f x
 is at most countable. Superseded by `countable_not_continuous_at` which gives the two-sided
 version. -/
 theorem countable_not_continuousWithinAt_Ioi [TopologicalSpace.SecondCountableTopology β] :
-    Set.Countable { x | ¬ContinuousWithinAt f (Ioi x) x } :=
+    Set.Countable {x | ¬ContinuousWithinAt f (Ioi x) x} :=
   by
   /- If `f` is not continuous on the right at `x`, there is an interval `(f x, z x)` which is not
     reached by `f`. This gives a family of disjoint open intervals in `β`. Such a family can only
     be countable as `β` is second-countable. -/
   nontriviality α
-  let s := { x | ¬ContinuousWithinAt f (Ioi x) x }
+  let s := {x | ¬ContinuousWithinAt f (Ioi x) x}
   have : ∀ x, x ∈ s → ∃ z, f x < z ∧ ∀ y, x < y → z ≤ f y :=
     by
     rintro x (hx : ¬ContinuousWithinAt f (Ioi x) x)
     contrapose! hx
     refine' tendsto_order.2 ⟨fun m hm => _, fun u hu => _⟩
-    · filter_upwards [self_mem_nhdsWithin]with y hy using hm.trans_le (hf (le_of_lt hy))
+    · filter_upwards [self_mem_nhdsWithin] with y hy using hm.trans_le (hf (le_of_lt hy))
     rcases hx u hu with ⟨v, xv, fvu⟩
     have : Ioo x v ∈ 𝓝[>] x := Ioo_mem_nhdsWithin_Ioi ⟨le_refl _, xv⟩
-    filter_upwards [this]with y hy
+    filter_upwards [this] with y hy
     apply (hf hy.2.le).trans_lt fvu
   -- choose `z x` such that `f` does not take the values in `(f x, z x)`.
   choose! z hz using this
@@ -298,7 +298,7 @@ theorem countable_not_continuousWithinAt_Ioi [TopologicalSpace.SecondCountableTo
 is at most countable. Superseded by `countable_not_continuous_at` which gives the two-sided
 version. -/
 theorem countable_not_continuousWithinAt_Iio [TopologicalSpace.SecondCountableTopology β] :
-    Set.Countable { x | ¬ContinuousWithinAt f (Iio x) x } :=
+    Set.Countable {x | ¬ContinuousWithinAt f (Iio x) x} :=
   hf.dual.countable_not_continuousWithinAt_Ioi
 #align monotone.countable_not_continuous_within_at_Iio Monotone.countable_not_continuousWithinAt_Iio
 -/
@@ -307,7 +307,7 @@ theorem countable_not_continuousWithinAt_Iio [TopologicalSpace.SecondCountableTo
 /-- In a second countable space, the set of points where a monotone function is not continuous
 is at most countable. -/
 theorem countable_not_continuousAt [TopologicalSpace.SecondCountableTopology β] :
-    Set.Countable { x | ¬ContinuousAt f x } :=
+    Set.Countable {x | ¬ContinuousAt f x} :=
   by
   apply
     (hf.countable_not_continuous_within_at_Ioi.union hf.countable_not_continuous_within_at_Iio).mono
@@ -405,7 +405,7 @@ theorem continuousAt_iff_leftLim_eq_rightLim : ContinuousAt f x ↔ leftLim f x
 /-- In a second countable space, the set of points where an antitone function is not continuous
 is at most countable. -/
 theorem countable_not_continuousAt [TopologicalSpace.SecondCountableTopology β] :
-    Set.Countable { x | ¬ContinuousAt f x } :=
+    Set.Countable {x | ¬ContinuousAt f x} :=
   hf.dual_right.countable_not_continuousAt
 #align antitone.countable_not_continuous_at Antitone.countable_not_continuousAt
 -/

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

@@ -76,7 +76,7 @@ theorem leftLim_eq_of_tendsto [hα : TopologicalSpace α] [h'α : OrderTopology
     {f : α → β} {a : α} {y : β} (h : 𝓝[<] a ≠ ⊥) (h' : Tendsto f (𝓝[<] a) (𝓝 y)) :
     leftLim f a = y := by
   have h'' : ∃ y, tendsto f (𝓝[<] a) (𝓝 y) := ⟨y, h'⟩
-  rw [h'α.topology_eq_generate_intervals] at h h' h''
+  rw [h'α.topology_eq_generate_intervals] at h h' h'' 
   simp only [left_lim, h, h'', not_true, or_self_iff, if_false]
   haveI := ne_bot_iff.2 h
   exact h'.lim_eq
@@ -85,7 +85,7 @@ theorem leftLim_eq_of_tendsto [hα : TopologicalSpace α] [h'α : OrderTopology
 theorem leftLim_eq_of_eq_bot [hα : TopologicalSpace α] [h'α : OrderTopology α] (f : α → β) {a : α}
     (h : 𝓝[<] a = ⊥) : leftLim f a = f a :=
   by
-  rw [h'α.topology_eq_generate_intervals] at h
+  rw [h'α.topology_eq_generate_intervals] at h 
   simp [left_lim, ite_eq_left_iff, h]
 #align left_lim_eq_of_eq_bot leftLim_eq_of_eq_bot
 
@@ -210,7 +210,7 @@ theorem continuousWithinAt_Iio_iff_leftLim_eq :
   haveI : (𝓝[Iio x] x).ne_bot := ne_bot_iff.2 h'
   refine' ⟨fun h => tendsto_nhds_unique (hf.tendsto_left_lim x) h.Tendsto, fun h => _⟩
   have := hf.tendsto_left_lim x
-  rwa [h] at this
+  rwa [h] at this 
 #align monotone.continuous_within_at_Iio_iff_left_lim_eq Monotone.continuousWithinAt_Iio_iff_leftLim_eq
 
 /-- A monotone function is continuous to the right at a point if and only if its right limit
@@ -237,7 +237,7 @@ theorem continuousAt_iff_leftLim_eq_rightLim : ContinuousAt f x ↔ leftLim f x
       exact le_right_lim hf (le_refl _)
     refine' continuousAt_iff_continuous_left'_right'.2 ⟨_, _⟩
     · exact hf.continuous_within_at_Iio_iff_left_lim_eq.2 h'
-    · rw [h] at h'
+    · rw [h] at h' 
       exact hf.continuous_within_at_Ioi_iff_right_lim_eq.2 h'
 #align monotone.continuous_at_iff_left_lim_eq_right_lim Monotone.continuousAt_iff_leftLim_eq_rightLim
 
@@ -284,7 +284,7 @@ theorem countable_not_continuousWithinAt_Ioi [TopologicalSpace.SecondCountableTo
       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.left_inv_on_inv_fun_on us, I.left_inv_on_inv_fun_on vs] at ha hb
+      simp only [I.left_inv_on_inv_fun_on us, I.left_inv_on_inv_fun_on 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⟩
@@ -315,7 +315,7 @@ theorem countable_not_continuousAt [TopologicalSpace.SecondCountableTopology β]
   refine' compl_subset_compl.1 _
   simp only [compl_union]
   rintro x ⟨hx, h'x⟩
-  simp only [mem_set_of_eq, Classical.not_not, mem_compl_iff] at hx h'x⊢
+  simp only [mem_set_of_eq, Classical.not_not, mem_compl_iff] at hx h'x ⊢
   exact continuousAt_iff_continuous_left'_right'.2 ⟨h'x, hx⟩
 #align monotone.countable_not_continuous_at Monotone.countable_not_continuousAt
 -/

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

@@ -41,7 +41,7 @@ Prove corresponding stronger results for strict_mono and strict_anti functions.
 
 open Set Filter
 
-open Topology
+open scoped Topology
 
 section
 

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

@@ -72,12 +72,6 @@ noncomputable def Function.rightLim (f : α → β) (a : α) : β :=
 
 open Function
 
-/- warning: left_lim_eq_of_tendsto -> leftLim_eq_of_tendsto is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align left_lim_eq_of_tendsto leftLim_eq_of_tendstoₓ'. -/
 theorem leftLim_eq_of_tendsto [hα : TopologicalSpace α] [h'α : OrderTopology α] [T2Space β]
     {f : α → β} {a : α} {y : β} (h : 𝓝[<] a ≠ ⊥) (h' : Tendsto f (𝓝[<] a) (𝓝 y)) :
     leftLim f a = y := by
@@ -88,12 +82,6 @@ theorem leftLim_eq_of_tendsto [hα : TopologicalSpace α] [h'α : OrderTopology
   exact h'.lim_eq
 #align left_lim_eq_of_tendsto leftLim_eq_of_tendsto
 
-/- warning: left_lim_eq_of_eq_bot -> leftLim_eq_of_eq_bot is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align left_lim_eq_of_eq_bot leftLim_eq_of_eq_botₓ'. -/
 theorem leftLim_eq_of_eq_bot [hα : TopologicalSpace α] [h'α : OrderTopology α] (f : α → β) {a : α}
     (h : 𝓝[<] a = ⊥) : leftLim f a = f a :=
   by
@@ -112,23 +100,11 @@ variable {α β : Type _} [LinearOrder α] [ConditionallyCompleteLinearOrder β]
 
 include hf
 
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-Case conversion may be inaccurate. Consider using '#align monotone.left_lim_eq_Sup Monotone.leftLim_eq_sSupₓ'. -/
 theorem leftLim_eq_sSup [TopologicalSpace α] [OrderTopology α] (h : 𝓝[<] x ≠ ⊥) :
     leftLim f x = sSup (f '' Iio x) :=
   leftLim_eq_of_tendsto h (hf.tendsto_nhdsWithin_Iio x)
 #align monotone.left_lim_eq_Sup Monotone.leftLim_eq_sSup
 
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-Case conversion may be inaccurate. Consider using '#align monotone.left_lim_le Monotone.leftLim_leₓ'. -/
 theorem leftLim_le (h : x ≤ y) : leftLim f x ≤ f y :=
   by
   letI : TopologicalSpace α := Preorder.topology α
@@ -145,12 +121,6 @@ theorem leftLim_le (h : x ≤ y) : leftLim f x ≤ f y :=
     exact hf (hz.le.trans h)
 #align monotone.left_lim_le Monotone.leftLim_le
 
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-Case conversion may be inaccurate. Consider using '#align monotone.le_left_lim Monotone.le_leftLimₓ'. -/
 theorem le_leftLim (h : x < y) : f x ≤ leftLim f y :=
   by
   letI : TopologicalSpace α := Preorder.topology α
@@ -165,12 +135,6 @@ theorem le_leftLim (h : x < y) : f x ≤ leftLim f y :=
   exact hf hz.le
 #align monotone.le_left_lim Monotone.le_leftLim
 
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-Case conversion may be inaccurate. Consider using '#align monotone.left_lim Monotone.leftLimₓ'. -/
 @[mono]
 protected theorem leftLim : Monotone (leftLim f) :=
   by
@@ -180,52 +144,22 @@ protected theorem leftLim : Monotone (leftLim f) :=
   · exact (hf.left_lim_le le_rfl).trans (hf.le_left_lim hxy)
 #align monotone.left_lim Monotone.leftLim
 
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 theorem le_rightLim (h : x ≤ y) : f x ≤ rightLim f y :=
   hf.dual.leftLim_le h
 #align monotone.le_right_lim Monotone.le_rightLim
 
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 theorem rightLim_le (h : x < y) : rightLim f x ≤ f y :=
   hf.dual.le_leftLim h
 #align monotone.right_lim_le Monotone.rightLim_le
 
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 @[mono]
 protected theorem rightLim : Monotone (rightLim f) := fun x y h => hf.dual.leftLim h
 #align monotone.right_lim Monotone.rightLim
 
-/- warning: monotone.left_lim_le_right_lim -> Monotone.leftLim_le_rightLim is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align monotone.left_lim_le_right_lim Monotone.leftLim_le_rightLimₓ'. -/
 theorem leftLim_le_rightLim (h : x ≤ y) : leftLim f x ≤ rightLim f y :=
   (hf.leftLim_le le_rfl).trans (hf.le_rightLim h)
 #align monotone.left_lim_le_right_lim Monotone.leftLim_le_rightLim
 
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-Case conversion may be inaccurate. Consider using '#align monotone.right_lim_le_left_lim Monotone.rightLim_le_leftLimₓ'. -/
 theorem rightLim_le_leftLim (h : x < y) : rightLim f x ≤ leftLim f y :=
   by
   letI : TopologicalSpace α := Preorder.topology α
@@ -244,12 +178,6 @@ theorem rightLim_le_leftLim (h : x < y) : rightLim f x ≤ leftLim f y :=
 
 variable [TopologicalSpace α] [OrderTopology α]
 
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-Case conversion may be inaccurate. Consider using '#align monotone.tendsto_left_lim Monotone.tendsto_leftLimₓ'. -/
 theorem tendsto_leftLim (x : α) : Tendsto f (𝓝[<] x) (𝓝 (leftLim f x)) :=
   by
   rcases eq_or_ne (𝓝[<] x) ⊥ with (h' | h')
@@ -258,44 +186,20 @@ theorem tendsto_leftLim (x : α) : Tendsto f (𝓝[<] x) (𝓝 (leftLim f x)) :=
   exact hf.tendsto_nhds_within_Iio x
 #align monotone.tendsto_left_lim Monotone.tendsto_leftLim
 
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-Case conversion may be inaccurate. Consider using '#align monotone.tendsto_left_lim_within Monotone.tendsto_leftLim_withinₓ'. -/
 theorem tendsto_leftLim_within (x : α) : Tendsto f (𝓝[<] x) (𝓝[≤] leftLim f x) :=
   by
   apply tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within f (hf.tendsto_left_lim x)
   filter_upwards [self_mem_nhdsWithin]with y hy using hf.le_left_lim hy
 #align monotone.tendsto_left_lim_within Monotone.tendsto_leftLim_within
 
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-Case conversion may be inaccurate. Consider using '#align monotone.tendsto_right_lim Monotone.tendsto_rightLimₓ'. -/
 theorem tendsto_rightLim (x : α) : Tendsto f (𝓝[>] x) (𝓝 (rightLim f x)) :=
   hf.dual.tendsto_leftLim x
 #align monotone.tendsto_right_lim Monotone.tendsto_rightLim
 
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-Case conversion may be inaccurate. Consider using '#align monotone.tendsto_right_lim_within Monotone.tendsto_rightLim_withinₓ'. -/
 theorem tendsto_rightLim_within (x : α) : Tendsto f (𝓝[>] x) (𝓝[≥] rightLim f x) :=
   hf.dual.tendsto_leftLim_within x
 #align monotone.tendsto_right_lim_within Monotone.tendsto_rightLim_within
 
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-Case conversion may be inaccurate. Consider using '#align monotone.continuous_within_at_Iio_iff_left_lim_eq Monotone.continuousWithinAt_Iio_iff_leftLim_eqₓ'. -/
 /-- A monotone function is continuous to the left at a point if and only if its left limit
 coincides with the value of the function. -/
 theorem continuousWithinAt_Iio_iff_leftLim_eq :
@@ -309,12 +213,6 @@ theorem continuousWithinAt_Iio_iff_leftLim_eq :
   rwa [h] at this
 #align monotone.continuous_within_at_Iio_iff_left_lim_eq Monotone.continuousWithinAt_Iio_iff_leftLim_eq
 
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-Case conversion may be inaccurate. Consider using '#align monotone.continuous_within_at_Ioi_iff_right_lim_eq Monotone.continuousWithinAt_Ioi_iff_rightLim_eqₓ'. -/
 /-- A monotone function is continuous to the right at a point if and only if its right limit
 coincides with the value of the function. -/
 theorem continuousWithinAt_Ioi_iff_rightLim_eq :
@@ -322,12 +220,6 @@ theorem continuousWithinAt_Ioi_iff_rightLim_eq :
   hf.dual.continuousWithinAt_Iio_iff_leftLim_eq
 #align monotone.continuous_within_at_Ioi_iff_right_lim_eq Monotone.continuousWithinAt_Ioi_iff_rightLim_eq
 
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 /-- A monotone function is continuous at a point if and only if its left and right limits
 coincide. -/
 theorem continuousAt_iff_leftLim_eq_rightLim : ContinuousAt f x ↔ leftLim f x = rightLim f x :=
@@ -437,136 +329,58 @@ variable {α β : Type _} [LinearOrder α] [ConditionallyCompleteLinearOrder β]
 
 include hf
 
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-Case conversion may be inaccurate. Consider using '#align antitone.le_left_lim Antitone.le_leftLimₓ'. -/
 theorem le_leftLim (h : x ≤ y) : f y ≤ leftLim f x :=
   hf.dual_right.leftLim_le h
 #align antitone.le_left_lim Antitone.le_leftLim
 
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 theorem leftLim_le (h : x < y) : leftLim f y ≤ f x :=
   hf.dual_right.le_leftLim h
 #align antitone.left_lim_le Antitone.leftLim_le
 
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 @[mono]
 protected theorem leftLim : Antitone (leftLim f) :=
   hf.dual_right.leftLim
 #align antitone.left_lim Antitone.leftLim
 
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-Case conversion may be inaccurate. Consider using '#align antitone.right_lim_le Antitone.rightLim_leₓ'. -/
 theorem rightLim_le (h : x ≤ y) : rightLim f y ≤ f x :=
   hf.dual_right.le_rightLim h
 #align antitone.right_lim_le Antitone.rightLim_le
 
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 theorem le_rightLim (h : x < y) : f y ≤ rightLim f x :=
   hf.dual_right.rightLim_le h
 #align antitone.le_right_lim Antitone.le_rightLim
 
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 @[mono]
 protected theorem rightLim : Antitone (rightLim f) :=
   hf.dual_right.rightLim
 #align antitone.right_lim Antitone.rightLim
 
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 theorem rightLim_le_leftLim (h : x ≤ y) : rightLim f y ≤ leftLim f x :=
   hf.dual_right.leftLim_le_rightLim h
 #align antitone.right_lim_le_left_lim Antitone.rightLim_le_leftLim
 
-/- warning: antitone.left_lim_le_right_lim -> Antitone.leftLim_le_rightLim is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align antitone.left_lim_le_right_lim Antitone.leftLim_le_rightLimₓ'. -/
 theorem leftLim_le_rightLim (h : x < y) : leftLim f y ≤ rightLim f x :=
   hf.dual_right.rightLim_le_leftLim h
 #align antitone.left_lim_le_right_lim Antitone.leftLim_le_rightLim
 
 variable [TopologicalSpace α] [OrderTopology α]
 
-/- warning: antitone.tendsto_left_lim -> Antitone.tendsto_leftLim is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align antitone.tendsto_left_lim Antitone.tendsto_leftLimₓ'. -/
 theorem tendsto_leftLim (x : α) : Tendsto f (𝓝[<] x) (𝓝 (leftLim f x)) :=
   hf.dual_right.tendsto_leftLim x
 #align antitone.tendsto_left_lim Antitone.tendsto_leftLim
 
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-Case conversion may be inaccurate. Consider using '#align antitone.tendsto_left_lim_within Antitone.tendsto_leftLim_withinₓ'. -/
 theorem tendsto_leftLim_within (x : α) : Tendsto f (𝓝[<] x) (𝓝[≥] leftLim f x) :=
   hf.dual_right.tendsto_leftLim_within x
 #align antitone.tendsto_left_lim_within Antitone.tendsto_leftLim_within
 
-/- warning: antitone.tendsto_right_lim -> Antitone.tendsto_rightLim is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{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_2))))) f) -> (forall [_inst_5 : TopologicalSpace.{u1} α] [_inst_6 : OrderTopology.{u1} α _inst_5 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))] (x : α), Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α _inst_5 x (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) x)) (nhds.{u2} β _inst_3 (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f x)))
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-Case conversion may be inaccurate. Consider using '#align antitone.tendsto_right_lim Antitone.tendsto_rightLimₓ'. -/
 theorem tendsto_rightLim (x : α) : Tendsto f (𝓝[>] x) (𝓝 (rightLim f x)) :=
   hf.dual_right.tendsto_rightLim x
 #align antitone.tendsto_right_lim Antitone.tendsto_rightLim
 
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align antitone.tendsto_right_lim_within Antitone.tendsto_rightLim_withinₓ'. -/
 theorem tendsto_rightLim_within (x : α) : Tendsto f (𝓝[>] x) (𝓝[≤] rightLim f x) :=
   hf.dual_right.tendsto_rightLim_within x
 #align antitone.tendsto_right_lim_within Antitone.tendsto_rightLim_within
 
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{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_2))))) f) -> (forall {x : α} [_inst_5 : TopologicalSpace.{u1} α] [_inst_6 : OrderTopology.{u1} α _inst_5 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))], Iff (ContinuousWithinAt.{u1, u2} α β _inst_5 _inst_3 f (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) x) x) (Eq.{succ u2} β (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f x) (f x)))
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-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {f : α -> β}, (Antitone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} [_inst_5 : TopologicalSpace.{u2} α] [_inst_6 : OrderTopology.{u2} α _inst_5 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))], Iff (ContinuousWithinAt.{u2, u1} α β _inst_5 _inst_3 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_1))))) x) x) (Eq.{succ u1} β (Function.leftLim.{u2, u1} α β _inst_1 _inst_3 f x) (f x)))
-Case conversion may be inaccurate. Consider using '#align antitone.continuous_within_at_Iio_iff_left_lim_eq Antitone.continuousWithinAt_Iio_iff_leftLim_eqₓ'. -/
 /-- An antitone function is continuous to the left at a point if and only if its left limit
 coincides with the value of the function. -/
 theorem continuousWithinAt_Iio_iff_leftLim_eq :
@@ -574,12 +388,6 @@ theorem continuousWithinAt_Iio_iff_leftLim_eq :
   hf.dual_right.continuousWithinAt_Iio_iff_leftLim_eq
 #align antitone.continuous_within_at_Iio_iff_left_lim_eq Antitone.continuousWithinAt_Iio_iff_leftLim_eq
 
-/- warning: antitone.continuous_within_at_Ioi_iff_right_lim_eq -> Antitone.continuousWithinAt_Ioi_iff_rightLim_eq is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{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_2))))) f) -> (forall {x : α} [_inst_5 : TopologicalSpace.{u1} α] [_inst_6 : OrderTopology.{u1} α _inst_5 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))], Iff (ContinuousWithinAt.{u1, u2} α β _inst_5 _inst_3 f (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) x) x) (Eq.{succ u2} β (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f x) (f x)))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {f : α -> β}, (Antitone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} [_inst_5 : TopologicalSpace.{u2} α] [_inst_6 : OrderTopology.{u2} α _inst_5 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))], Iff (ContinuousWithinAt.{u2, u1} α β _inst_5 _inst_3 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_1))))) x) x) (Eq.{succ u1} β (Function.rightLim.{u2, u1} α β _inst_1 _inst_3 f x) (f x)))
-Case conversion may be inaccurate. Consider using '#align antitone.continuous_within_at_Ioi_iff_right_lim_eq Antitone.continuousWithinAt_Ioi_iff_rightLim_eqₓ'. -/
 /-- An antitone function is continuous to the right at a point if and only if its right limit
 coincides with the value of the function. -/
 theorem continuousWithinAt_Ioi_iff_rightLim_eq :
@@ -587,12 +395,6 @@ theorem continuousWithinAt_Ioi_iff_rightLim_eq :
   hf.dual_right.continuousWithinAt_Ioi_iff_rightLim_eq
 #align antitone.continuous_within_at_Ioi_iff_right_lim_eq Antitone.continuousWithinAt_Ioi_iff_rightLim_eq
 
-/- warning: antitone.continuous_at_iff_left_lim_eq_right_lim -> Antitone.continuousAt_iff_leftLim_eq_rightLim is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{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_2))))) f) -> (forall {x : α} [_inst_5 : TopologicalSpace.{u1} α] [_inst_6 : OrderTopology.{u1} α _inst_5 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))], Iff (ContinuousAt.{u1, u2} α β _inst_5 _inst_3 f x) (Eq.{succ u2} β (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f x) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f x)))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {f : α -> β}, (Antitone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} [_inst_5 : TopologicalSpace.{u2} α] [_inst_6 : OrderTopology.{u2} α _inst_5 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))], Iff (ContinuousAt.{u2, u1} α β _inst_5 _inst_3 f x) (Eq.{succ u1} β (Function.leftLim.{u2, u1} α β _inst_1 _inst_3 f x) (Function.rightLim.{u2, u1} α β _inst_1 _inst_3 f x)))
-Case conversion may be inaccurate. Consider using '#align antitone.continuous_at_iff_left_lim_eq_right_lim Antitone.continuousAt_iff_leftLim_eq_rightLimₓ'. -/
 /-- An antitone function is continuous at a point if and only if its left and right limits
 coincide. -/
 theorem continuousAt_iff_leftLim_eq_rightLim : ContinuousAt f x ↔ leftLim f x = rightLim f x :=

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

@@ -156,8 +156,7 @@ theorem le_leftLim (h : x < y) : f x ≤ leftLim f y :=
   letI : TopologicalSpace α := Preorder.topology α
   haveI : OrderTopology α := ⟨rfl⟩
   rcases eq_or_ne (𝓝[<] y) ⊥ with (h' | h')
-  · rw [leftLim_eq_of_eq_bot _ h']
-    exact hf h.le
+  · rw [leftLim_eq_of_eq_bot _ h']; exact hf h.le
   rw [left_lim_eq_Sup hf h']
   refine' le_csSup ⟨f y, _⟩ (mem_image_of_mem _ h)
   simp only [upperBounds, mem_image, mem_Iio, forall_exists_index, and_imp,

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

@@ -125,7 +125,7 @@ theorem leftLim_eq_sSup [TopologicalSpace α] [OrderTopology α] (h : 𝓝[<] x
 
 /- warning: monotone.left_lim_le -> Monotone.leftLim_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {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_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) f) -> (forall {x : α} {y : 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_1))))) x y) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f x) (f y)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {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_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) f) -> (forall {x : α} {y : 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_1))))) x y) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f x) (f y)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {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_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} {y : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) x y) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))) (Function.leftLim.{u2, u1} α β _inst_1 _inst_3 f x) (f y)))
 Case conversion may be inaccurate. Consider using '#align monotone.left_lim_le Monotone.leftLim_leₓ'. -/
@@ -147,7 +147,7 @@ theorem leftLim_le (h : x ≤ y) : leftLim f x ≤ f y :=
 
 /- warning: monotone.le_left_lim -> Monotone.le_leftLim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {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_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) f) -> (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_1))))) x y) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (f x) (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f y)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {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_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) f) -> (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_1))))) x y) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (f x) (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f y)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {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_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} {y : α}, (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_1)))))) x y) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))) (f x) (Function.leftLim.{u2, u1} α β _inst_1 _inst_3 f y)))
 Case conversion may be inaccurate. Consider using '#align monotone.le_left_lim Monotone.le_leftLimₓ'. -/
@@ -183,7 +183,7 @@ protected theorem leftLim : Monotone (leftLim f) :=
 
 /- warning: monotone.le_right_lim -> Monotone.le_rightLim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {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_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) f) -> (forall {x : α} {y : 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_1))))) x y) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (f x) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f y)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {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_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) f) -> (forall {x : α} {y : 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_1))))) x y) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (f x) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f y)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {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_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} {y : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) x y) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))) (f x) (Function.rightLim.{u2, u1} α β _inst_1 _inst_3 f y)))
 Case conversion may be inaccurate. Consider using '#align monotone.le_right_lim Monotone.le_rightLimₓ'. -/
@@ -193,7 +193,7 @@ theorem le_rightLim (h : x ≤ y) : f x ≤ rightLim f y :=
 
 /- warning: monotone.right_lim_le -> Monotone.rightLim_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {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_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) f) -> (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_1))))) x y) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f x) (f y)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {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_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) f) -> (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_1))))) x y) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f x) (f y)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {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_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} {y : α}, (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_1)))))) x y) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))) (Function.rightLim.{u2, u1} α β _inst_1 _inst_3 f x) (f y)))
 Case conversion may be inaccurate. Consider using '#align monotone.right_lim_le Monotone.rightLim_leₓ'. -/
@@ -213,7 +213,7 @@ protected theorem rightLim : Monotone (rightLim f) := fun x y h => hf.dual.leftL
 
 /- warning: monotone.left_lim_le_right_lim -> Monotone.leftLim_le_rightLim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {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_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) f) -> (forall {x : α} {y : 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_1))))) x y) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f x) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f y)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {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_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) f) -> (forall {x : α} {y : 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_1))))) x y) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f x) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f y)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {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_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} {y : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) x y) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))) (Function.leftLim.{u2, u1} α β _inst_1 _inst_3 f x) (Function.rightLim.{u2, u1} α β _inst_1 _inst_3 f y)))
 Case conversion may be inaccurate. Consider using '#align monotone.left_lim_le_right_lim Monotone.leftLim_le_rightLimₓ'. -/
@@ -223,7 +223,7 @@ theorem leftLim_le_rightLim (h : x ≤ y) : leftLim f x ≤ rightLim f y :=
 
 /- warning: monotone.right_lim_le_left_lim -> Monotone.rightLim_le_leftLim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {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_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) f) -> (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_1))))) x y) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f x) (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f y)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {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_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) f) -> (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_1))))) x y) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f x) (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f y)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {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_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} {y : α}, (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_1)))))) x y) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))) (Function.rightLim.{u2, u1} α β _inst_1 _inst_3 f x) (Function.leftLim.{u2, u1} α β _inst_1 _inst_3 f y)))
 Case conversion may be inaccurate. Consider using '#align monotone.right_lim_le_left_lim Monotone.rightLim_le_leftLimₓ'. -/
@@ -440,7 +440,7 @@ include hf
 
 /- warning: antitone.le_left_lim -> Antitone.le_leftLim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{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_2))))) f) -> (forall {x : α} {y : 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_1))))) x y) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (f y) (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f x)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{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_2))))) f) -> (forall {x : α} {y : 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_1))))) x y) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (f y) (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f x)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {f : α -> β}, (Antitone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} {y : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) x y) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))) (f y) (Function.leftLim.{u2, u1} α β _inst_1 _inst_3 f x)))
 Case conversion may be inaccurate. Consider using '#align antitone.le_left_lim Antitone.le_leftLimₓ'. -/
@@ -450,7 +450,7 @@ theorem le_leftLim (h : x ≤ y) : f y ≤ leftLim f x :=
 
 /- warning: antitone.left_lim_le -> Antitone.leftLim_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{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_2))))) f) -> (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_1))))) x y) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f y) (f x)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{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_2))))) f) -> (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_1))))) x y) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f y) (f x)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {f : α -> β}, (Antitone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} {y : α}, (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_1)))))) x y) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))) (Function.leftLim.{u2, u1} α β _inst_1 _inst_3 f y) (f x)))
 Case conversion may be inaccurate. Consider using '#align antitone.left_lim_le Antitone.leftLim_leₓ'. -/
@@ -471,7 +471,7 @@ protected theorem leftLim : Antitone (leftLim f) :=
 
 /- warning: antitone.right_lim_le -> Antitone.rightLim_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{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_2))))) f) -> (forall {x : α} {y : 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_1))))) x y) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f y) (f x)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{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_2))))) f) -> (forall {x : α} {y : 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_1))))) x y) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f y) (f x)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {f : α -> β}, (Antitone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} {y : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) x y) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))) (Function.rightLim.{u2, u1} α β _inst_1 _inst_3 f y) (f x)))
 Case conversion may be inaccurate. Consider using '#align antitone.right_lim_le Antitone.rightLim_leₓ'. -/
@@ -481,7 +481,7 @@ theorem rightLim_le (h : x ≤ y) : rightLim f y ≤ f x :=
 
 /- warning: antitone.le_right_lim -> Antitone.le_rightLim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{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_2))))) f) -> (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_1))))) x y) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (f y) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f x)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{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_2))))) f) -> (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_1))))) x y) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (f y) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f x)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {f : α -> β}, (Antitone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} {y : α}, (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_1)))))) x y) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))) (f y) (Function.rightLim.{u2, u1} α β _inst_1 _inst_3 f x)))
 Case conversion may be inaccurate. Consider using '#align antitone.le_right_lim Antitone.le_rightLimₓ'. -/
@@ -502,7 +502,7 @@ protected theorem rightLim : Antitone (rightLim f) :=
 
 /- warning: antitone.right_lim_le_left_lim -> Antitone.rightLim_le_leftLim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{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_2))))) f) -> (forall {x : α} {y : 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_1))))) x y) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f y) (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f x)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{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_2))))) f) -> (forall {x : α} {y : 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_1))))) x y) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f y) (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f x)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {f : α -> β}, (Antitone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} {y : α}, (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))) x y) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))) (Function.rightLim.{u2, u1} α β _inst_1 _inst_3 f y) (Function.leftLim.{u2, u1} α β _inst_1 _inst_3 f x)))
 Case conversion may be inaccurate. Consider using '#align antitone.right_lim_le_left_lim Antitone.rightLim_le_leftLimₓ'. -/
@@ -512,7 +512,7 @@ theorem rightLim_le_leftLim (h : x ≤ y) : rightLim f y ≤ leftLim f x :=
 
 /- warning: antitone.left_lim_le_right_lim -> Antitone.leftLim_le_rightLim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{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_2))))) f) -> (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_1))))) x y) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f y) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f x)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {f : α -> β}, (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{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_2))))) f) -> (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_1))))) x y) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))) (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f y) (Function.rightLim.{u1, u2} α β _inst_1 _inst_3 f x)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {f : α -> β}, (Antitone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} {y : α}, (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_1)))))) x y) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))) (Function.leftLim.{u2, u1} α β _inst_1 _inst_3 f y) (Function.rightLim.{u2, u1} α β _inst_1 _inst_3 f x)))
 Case conversion may be inaccurate. Consider using '#align antitone.left_lim_le_right_lim Antitone.leftLim_le_rightLimₓ'. -/

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

@@ -112,16 +112,16 @@ variable {α β : Type _} [LinearOrder α] [ConditionallyCompleteLinearOrder β]
 
 include hf
 
-/- warning: monotone.left_lim_eq_Sup -> Monotone.leftLim_eq_supₛ is a dubious translation:
+/- warning: monotone.left_lim_eq_Sup -> Monotone.leftLim_eq_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {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_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) f) -> (forall {x : α} [_inst_5 : TopologicalSpace.{u1} α] [_inst_6 : OrderTopology.{u1} α _inst_5 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))], (Ne.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_5 x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) x)) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))) -> (Eq.{succ u2} β (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f x) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)) (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_1)))) x)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] [_inst_3 : TopologicalSpace.{u2} β] [_inst_4 : OrderTopology.{u2} β _inst_3 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)))))] {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_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) f) -> (forall {x : α} [_inst_5 : TopologicalSpace.{u1} α] [_inst_6 : OrderTopology.{u1} α _inst_5 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1))))], (Ne.{succ u1} (Filter.{u1} α) (nhdsWithin.{u1} α _inst_5 x (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) x)) (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))) -> (Eq.{succ u2} β (Function.leftLim.{u1, u2} α β _inst_1 _inst_3 f x) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2)) (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_1)))) x)))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {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_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} [_inst_5 : TopologicalSpace.{u2} α] [_inst_6 : OrderTopology.{u2} α _inst_5 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))], (Ne.{succ u2} (Filter.{u2} α) (nhdsWithin.{u2} α _inst_5 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_1))))) x)) (Bot.bot.{u2} (Filter.{u2} α) (CompleteLattice.toBot.{u2} (Filter.{u2} α) (Filter.instCompleteLatticeFilter.{u2} α)))) -> (Eq.{succ u1} β (Function.leftLim.{u2, u1} α β _inst_1 _inst_3 f x) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)) (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_1))))) x)))))
-Case conversion may be inaccurate. Consider using '#align monotone.left_lim_eq_Sup Monotone.leftLim_eq_supₛₓ'. -/
-theorem leftLim_eq_supₛ [TopologicalSpace α] [OrderTopology α] (h : 𝓝[<] x ≠ ⊥) :
-    leftLim f x = supₛ (f '' Iio x) :=
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] [_inst_3 : TopologicalSpace.{u1} β] [_inst_4 : OrderTopology.{u1} β _inst_3 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)))))] {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_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f) -> (forall {x : α} [_inst_5 : TopologicalSpace.{u2} α] [_inst_6 : OrderTopology.{u2} α _inst_5 (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1)))))], (Ne.{succ u2} (Filter.{u2} α) (nhdsWithin.{u2} α _inst_5 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_1))))) x)) (Bot.bot.{u2} (Filter.{u2} α) (CompleteLattice.toBot.{u2} (Filter.{u2} α) (Filter.instCompleteLatticeFilter.{u2} α)))) -> (Eq.{succ u1} β (Function.leftLim.{u2, u1} α β _inst_1 _inst_3 f x) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2)) (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_1))))) x)))))
+Case conversion may be inaccurate. Consider using '#align monotone.left_lim_eq_Sup Monotone.leftLim_eq_sSupₓ'. -/
+theorem leftLim_eq_sSup [TopologicalSpace α] [OrderTopology α] (h : 𝓝[<] x ≠ ⊥) :
+    leftLim f x = sSup (f '' Iio x) :=
   leftLim_eq_of_tendsto h (hf.tendsto_nhdsWithin_Iio x)
-#align monotone.left_lim_eq_Sup Monotone.leftLim_eq_supₛ
+#align monotone.left_lim_eq_Sup Monotone.leftLim_eq_sSup
 
 /- warning: monotone.left_lim_le -> Monotone.leftLim_le is a dubious translation:
 lean 3 declaration is
@@ -137,7 +137,7 @@ theorem leftLim_le (h : x ≤ y) : leftLim f x ≤ f y :=
   · simpa [left_lim, h'] using hf h
   haveI A : ne_bot (𝓝[<] x) := ne_bot_iff.2 h'
   rw [left_lim_eq_Sup hf h']
-  refine' csupₛ_le _ _
+  refine' csSup_le _ _
   · simp only [nonempty_image_iff]
     exact (forall_mem_nonempty_iff_ne_bot.2 A) _ self_mem_nhdsWithin
   · simp only [mem_image, mem_Iio, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂]
@@ -159,7 +159,7 @@ theorem le_leftLim (h : x < y) : f x ≤ leftLim f y :=
   · rw [leftLim_eq_of_eq_bot _ h']
     exact hf h.le
   rw [left_lim_eq_Sup hf h']
-  refine' le_csupₛ ⟨f y, _⟩ (mem_image_of_mem _ h)
+  refine' le_csSup ⟨f y, _⟩ (mem_image_of_mem _ h)
   simp only [upperBounds, mem_image, mem_Iio, forall_exists_index, and_imp,
     forall_apply_eq_imp_iff₂, mem_set_of_eq]
   intro z hz

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

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathlib.Topology.Order.Basic
 import Mathlib.Topology.Order.LeftRight
+import Mathlib.Topology.Order.Monotone
 
 #align_import topology.algebra.order.left_right_lim from "leanprover-community/mathlib"@"0a0ec35061ed9960bf0e7ffb0335f44447b58977"
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
 import Mathlib.Topology.Order.Basic
-import Mathlib.Topology.Algebra.Order.LeftRight
+import Mathlib.Topology.Order.LeftRight
 
 #align_import topology.algebra.order.left_right_lim from "leanprover-community/mathlib"@"0a0ec35061ed9960bf0e7ffb0335f44447b58977"
 

• 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).

@@ -115,7 +115,7 @@ theorem leftLim_le (h : x ≤ y) : leftLim f x ≤ f y := by
   haveI A : NeBot (𝓝[<] x) := neBot_iff.2 h'
   rw [leftLim_eq_sSup hf h']
   refine' csSup_le _ _
-  · simp only [nonempty_image_iff]
+  · simp only [image_nonempty]
     exact (forall_mem_nonempty_iff_neBot.2 A) _ self_mem_nhdsWithin
   · simp only [mem_image, mem_Iio, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂]
     intro z hz

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...

@@ -237,7 +237,7 @@ theorem continuousAt_iff_leftLim_eq_rightLim : ContinuousAt f x ↔ leftLim f x
 /-- In a second countable space, the set of points where a monotone function is not right-continuous
 is at most countable. Superseded by `countable_not_continuousAt` which gives the two-sided
 version. -/
-theorem countable_not_continuousWithinAt_Ioi [TopologicalSpace.SecondCountableTopology β] :
+theorem countable_not_continuousWithinAt_Ioi [SecondCountableTopology β] :
     Set.Countable { x | ¬ContinuousWithinAt f (Ioi x) x } := by
   apply (countable_image_lt_image_Ioi f).mono
   rintro x (hx : ¬ContinuousWithinAt f (Ioi x) x)
@@ -255,14 +255,14 @@ theorem countable_not_continuousWithinAt_Ioi [TopologicalSpace.SecondCountableTo
 /-- In a second countable space, the set of points where a monotone function is not left-continuous
 is at most countable. Superseded by `countable_not_continuousAt` which gives the two-sided
 version. -/
-theorem countable_not_continuousWithinAt_Iio [TopologicalSpace.SecondCountableTopology β] :
+theorem countable_not_continuousWithinAt_Iio [SecondCountableTopology β] :
     Set.Countable { x | ¬ContinuousWithinAt f (Iio x) x } :=
   hf.dual.countable_not_continuousWithinAt_Ioi
 #align monotone.countable_not_continuous_within_at_Iio Monotone.countable_not_continuousWithinAt_Iio
 
 /-- In a second countable space, the set of points where a monotone function is not continuous
 is at most countable. -/
-theorem countable_not_continuousAt [TopologicalSpace.SecondCountableTopology β] :
+theorem countable_not_continuousAt [SecondCountableTopology β] :
     Set.Countable { x | ¬ContinuousAt f x } := by
   apply
     (hf.countable_not_continuousWithinAt_Ioi.union hf.countable_not_continuousWithinAt_Iio).mono
@@ -355,7 +355,7 @@ theorem continuousAt_iff_leftLim_eq_rightLim : ContinuousAt f x ↔ leftLim f x
 
 /-- In a second countable space, the set of points where an antitone function is not continuous
 is at most countable. -/
-theorem countable_not_continuousAt [TopologicalSpace.SecondCountableTopology β] :
+theorem countable_not_continuousAt [SecondCountableTopology β] :
     Set.Countable { x | ¬ContinuousAt f x } :=
   hf.dual_right.countable_not_continuousAt
 #align antitone.countable_not_continuous_at Antitone.countable_not_continuousAt

mathport was forgetting a space in filter_upwards [...]with instead of filter_upwards [...] with.

@@ -248,7 +248,7 @@ theorem countable_not_continuousWithinAt_Ioi [TopologicalSpace.SecondCountableTo
       (hf (le_of_lt hy))
   rcases hx u hu with ⟨v, xv, fvu⟩
   have : Ioo x v ∈ 𝓝[>] x := Ioo_mem_nhdsWithin_Ioi ⟨le_refl _, xv⟩
-  filter_upwards [this]with y hy
+  filter_upwards [this] with y hy
   apply (hf hy.2.le).trans_lt fvu
 #align monotone.countable_not_continuous_within_at_Ioi Monotone.countable_not_continuousWithinAt_Ioi
 

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>

@@ -239,46 +239,17 @@ is at most countable. Superseded by `countable_not_continuousAt` which gives the
 version. -/
 theorem countable_not_continuousWithinAt_Ioi [TopologicalSpace.SecondCountableTopology β] :
     Set.Countable { x | ¬ContinuousWithinAt f (Ioi x) x } := by
-  /- If `f` is not continuous on the right at `x`, there is an interval `(f x, z x)` which is not
-    reached by `f`. This gives a family of disjoint open intervals in `β`. Such a family can only
-    be countable as `β` is second-countable. -/
-  nontriviality α
-  let s := { x | ¬ContinuousWithinAt f (Ioi x) x }
-  have : ∀ x, x ∈ s → ∃ z, f x < z ∧ ∀ y, x < y → z ≤ f y := by
-    rintro x (hx : ¬ContinuousWithinAt f (Ioi x) x)
-    contrapose! hx
-    refine' tendsto_order.2 ⟨fun m hm => _, fun u hu => _⟩
-    · filter_upwards [@self_mem_nhdsWithin _ _ x (Ioi x)] with y hy using hm.trans_le
-        (hf (le_of_lt hy))
-    rcases hx u hu with ⟨v, xv, fvu⟩
-    have : Ioo x v ∈ 𝓝[>] x := Ioo_mem_nhdsWithin_Ioi ⟨le_refl _, xv⟩
-    filter_upwards [this]with y hy
-    apply (hf hy.2.le).trans_lt fvu
-  -- 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
+  apply (countable_image_lt_image_Ioi f).mono
+  rintro x (hx : ¬ContinuousWithinAt f (Ioi x) x)
+  dsimp
+  contrapose! hx
+  refine' tendsto_order.2 ⟨fun m hm => _, fun u hu => _⟩
+  · filter_upwards [@self_mem_nhdsWithin _ _ x (Ioi x)] with y hy using hm.trans_le
+      (hf (le_of_lt hy))
+  rcases hx u hu with ⟨v, xv, fvu⟩
+  have : Ioo x v ∈ 𝓝[>] x := Ioo_mem_nhdsWithin_Ioi ⟨le_refl _, xv⟩
+  filter_upwards [this]with y hy
+  apply (hf hy.2.le).trans_lt fvu
 #align monotone.countable_not_continuous_within_at_Ioi Monotone.countable_not_continuousWithinAt_Ioi
 
 /-- In a second countable space, the set of points where a monotone function is not left-continuous

@@ -78,6 +78,16 @@ theorem leftLim_eq_of_eq_bot [hα : TopologicalSpace α] [h'α : OrderTopology 
   simp [leftLim, ite_eq_left_iff, h]
 #align left_lim_eq_of_eq_bot leftLim_eq_of_eq_bot
 
+theorem rightLim_eq_of_tendsto [TopologicalSpace α] [OrderTopology α] [T2Space β]
+    {f : α → β} {a : α} {y : β} (h : 𝓝[>] a ≠ ⊥) (h' : Tendsto f (𝓝[>] a) (𝓝 y)) :
+    Function.rightLim f a = y :=
+  @leftLim_eq_of_tendsto αᵒᵈ _ _ _ _ _ _ f a y h h'
+#align right_lim_eq_of_tendsto rightLim_eq_of_tendsto
+
+theorem rightLim_eq_of_eq_bot [TopologicalSpace α] [OrderTopology α] (f : α → β) {a : α}
+    (h : 𝓝[>] a = ⊥) : rightLim f a = f a :=
+  @leftLim_eq_of_eq_bot αᵒᵈ _ _ _ _ _  f a h
+
 end
 
 open Function
@@ -92,6 +102,11 @@ theorem leftLim_eq_sSup [TopologicalSpace α] [OrderTopology α] (h : 𝓝[<] x
   leftLim_eq_of_tendsto h (hf.tendsto_nhdsWithin_Iio x)
 #align monotone.left_lim_eq_Sup Monotone.leftLim_eq_sSup
 
+theorem rightLim_eq_sInf [TopologicalSpace α] [OrderTopology α] (h : 𝓝[>] x ≠ ⊥) :
+    rightLim f x = sInf (f '' Ioi x) :=
+  rightLim_eq_of_tendsto h (hf.tendsto_nhdsWithin_Ioi x)
+#align right_lim_eq_Inf Monotone.rightLim_eq_sInf
+
 theorem leftLim_le (h : x ≤ y) : leftLim f x ≤ f y := by
   letI : TopologicalSpace α := Preorder.topology α
   haveI : OrderTopology α := ⟨rfl⟩

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

This has nice performance benefits.

@@ -39,7 +39,7 @@ open Topology
 
 section
 
-variable {α β : Type _} [LinearOrder α] [TopologicalSpace β]
+variable {α β : Type*} [LinearOrder α] [TopologicalSpace β]
 
 /-- Let `f : α → β` be a function from a linear order `α` to a topological space `β`, and
 let `a : α`. The limit strictly to the left of `f` at `a`, denoted with `leftLim f a`, is defined
@@ -84,7 +84,7 @@ open Function
 
 namespace Monotone
 
-variable {α β : Type _} [LinearOrder α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β]
+variable {α β : Type*} [LinearOrder α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β]
   [OrderTopology β] {f : α → β} (hf : Monotone f) {x y : α}
 
 theorem leftLim_eq_sSup [TopologicalSpace α] [OrderTopology α] (h : 𝓝[<] x ≠ ⊥) :
@@ -292,7 +292,7 @@ end Monotone
 
 namespace Antitone
 
-variable {α β : Type _} [LinearOrder α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β]
+variable {α β : Type*} [LinearOrder α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β]
   [OrderTopology β] {f : α → β} (hf : Antitone f) {x y : α}
 
 theorem le_leftLim (h : x ≤ y) : f y ≤ leftLim f x :=

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module topology.algebra.order.left_right_lim
-! leanprover-community/mathlib commit 0a0ec35061ed9960bf0e7ffb0335f44447b58977
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Order.Basic
 import Mathlib.Topology.Algebra.Order.LeftRight
 
+#align_import topology.algebra.order.left_right_lim from "leanprover-community/mathlib"@"0a0ec35061ed9960bf0e7ffb0335f44447b58977"
+
 /-!
 # Left and right limits
 

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -287,7 +287,7 @@ theorem countable_not_continuousAt [TopologicalSpace.SecondCountableTopology β]
   refine' compl_subset_compl.1 _
   simp only [compl_union]
   rintro x ⟨hx, h'x⟩
-  simp only [mem_setOf_eq, Classical.not_not, mem_compl_iff] at hx h'x⊢
+  simp only [mem_setOf_eq, Classical.not_not, mem_compl_iff] at hx h'x ⊢
   exact continuousAt_iff_continuous_left'_right'.2 ⟨h'x, hx⟩
 #align monotone.countable_not_continuous_at Monotone.countable_not_continuousAt
 

This makes a mathlib4 version of mathlib3's tactic.basic, now called Mathlib.Tactic.Common, which imports all tactics which do not have significant theory requirements, and then is imported all across the base of the hierarchy.

This ensures that all common tactics are available nearly everywhere in the library, rather than having to be imported one-by-one as you need them.

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

@@ -8,7 +8,6 @@ Authors: Sébastien Gouëzel
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathlib.Tactic.WLOG
 import Mathlib.Topology.Order.Basic
 import Mathlib.Topology.Algebra.Order.LeftRight
 

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>

@@ -91,10 +91,10 @@ namespace Monotone
 variable {α β : Type _} [LinearOrder α] [ConditionallyCompleteLinearOrder β] [TopologicalSpace β]
   [OrderTopology β] {f : α → β} (hf : Monotone f) {x y : α}
 
-theorem leftLim_eq_supₛ [TopologicalSpace α] [OrderTopology α] (h : 𝓝[<] x ≠ ⊥) :
-    leftLim f x = supₛ (f '' Iio x) :=
+theorem leftLim_eq_sSup [TopologicalSpace α] [OrderTopology α] (h : 𝓝[<] x ≠ ⊥) :
+    leftLim f x = sSup (f '' Iio x) :=
   leftLim_eq_of_tendsto h (hf.tendsto_nhdsWithin_Iio x)
-#align monotone.left_lim_eq_Sup Monotone.leftLim_eq_supₛ
+#align monotone.left_lim_eq_Sup Monotone.leftLim_eq_sSup
 
 theorem leftLim_le (h : x ≤ y) : leftLim f x ≤ f y := by
   letI : TopologicalSpace α := Preorder.topology α
@@ -102,8 +102,8 @@ theorem leftLim_le (h : x ≤ y) : leftLim f x ≤ f y := by
   rcases eq_or_ne (𝓝[<] x) ⊥ with (h' | h')
   · simpa [leftLim, h'] using hf h
   haveI A : NeBot (𝓝[<] x) := neBot_iff.2 h'
-  rw [leftLim_eq_supₛ hf h']
-  refine' csupₛ_le _ _
+  rw [leftLim_eq_sSup hf h']
+  refine' csSup_le _ _
   · simp only [nonempty_image_iff]
     exact (forall_mem_nonempty_iff_neBot.2 A) _ self_mem_nhdsWithin
   · simp only [mem_image, mem_Iio, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂]
@@ -117,8 +117,8 @@ theorem le_leftLim (h : x < y) : f x ≤ leftLim f y := by
   rcases eq_or_ne (𝓝[<] y) ⊥ with (h' | h')
   · rw [leftLim_eq_of_eq_bot _ h']
     exact hf h.le
-  rw [leftLim_eq_supₛ hf h']
-  refine' le_csupₛ ⟨f y, _⟩ (mem_image_of_mem _ h)
+  rw [leftLim_eq_sSup hf h']
+  refine' le_csSup ⟨f y, _⟩ (mem_image_of_mem _ h)
   simp only [upperBounds, mem_image, mem_Iio, forall_exists_index, and_imp,
     forall_apply_eq_imp_iff₂, mem_setOf_eq]
   intro z hz
@@ -168,7 +168,7 @@ variable [TopologicalSpace α] [OrderTopology α]
 theorem tendsto_leftLim (x : α) : Tendsto f (𝓝[<] x) (𝓝 (leftLim f x)) := by
   rcases eq_or_ne (𝓝[<] x) ⊥ with (h' | h')
   · simp [h']
-  rw [leftLim_eq_supₛ hf h']
+  rw [leftLim_eq_sSup hf h']
   exact hf.tendsto_nhdsWithin_Iio x
 #align monotone.tendsto_left_lim Monotone.tendsto_leftLim
 

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

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

@@ -213,8 +213,7 @@ theorem continuousAt_iff_leftLim_eq_rightLim : ContinuousAt f x ↔ leftLim f x
     have B : rightLim f x = f x :=
       hf.continuousWithinAt_Ioi_iff_rightLim_eq.1 h.continuousWithinAt
     exact A.trans B.symm
-  · have h' : leftLim f x = f x :=
-      by
+  · have h' : leftLim f x = f x := by
       apply le_antisymm (leftLim_le hf (le_refl _))
       rw [h]
       exact le_rightLim hf (le_refl _)
@@ -234,8 +233,7 @@ theorem countable_not_continuousWithinAt_Ioi [TopologicalSpace.SecondCountableTo
     be countable as `β` is second-countable. -/
   nontriviality α
   let s := { x | ¬ContinuousWithinAt f (Ioi x) x }
-  have : ∀ x, x ∈ s → ∃ z, f x < z ∧ ∀ y, x < y → z ≤ f y :=
-    by
+  have : ∀ x, x ∈ s → ∃ z, f x < z ∧ ∀ y, x < y → z ≤ f y := by
     rintro x (hx : ¬ContinuousWithinAt f (Ioi x) x)
     contrapose! hx
     refine' tendsto_order.2 ⟨fun m hm => _, fun u hu => _⟩
@@ -256,8 +254,7 @@ theorem countable_not_continuousWithinAt_Ioi [TopologicalSpace.SecondCountableTo
 
   -- 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 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

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -161,7 +161,6 @@ theorem rightLim_le_leftLim (h : x < y) : rightLim f x ≤ leftLim f y := by
   calc
     rightLim f x ≤ f a := hf.rightLim_le xa
     _ ≤ leftLim f y := hf.le_leftLim ay
-
 #align monotone.right_lim_le_left_lim Monotone.rightLim_le_leftLim
 
 variable [TopologicalSpace α] [OrderTopology α]

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

I think I got all of the monos.

@@ -125,7 +125,7 @@ theorem le_leftLim (h : x < y) : f x ≤ leftLim f y := by
   exact hf hz.le
 #align monotone.le_left_lim Monotone.le_leftLim
 
--- @[mono] -- Porting note: restore `mono` attribute
+@[mono]
 protected theorem leftLim : Monotone (leftLim f) := by
   intro x y h
   rcases eq_or_lt_of_le h with (rfl | hxy)
@@ -141,7 +141,7 @@ theorem rightLim_le (h : x < y) : rightLim f x ≤ f y :=
   hf.dual.le_leftLim h
 #align monotone.right_lim_le Monotone.rightLim_le
 
--- @[mono] -- Porting note: restore `mono` attribute
+@[mono]
 protected theorem rightLim : Monotone (rightLim f) := fun _ _ h => hf.dual.leftLim h
 #align monotone.right_lim Monotone.rightLim
 
@@ -311,7 +311,7 @@ theorem leftLim_le (h : x < y) : leftLim f y ≤ f x :=
   hf.dual_right.le_leftLim h
 #align antitone.left_lim_le Antitone.leftLim_le
 
--- @[mono] -- Porting note: restore `mono` attribute
+@[mono]
 protected theorem leftLim : Antitone (leftLim f) :=
   hf.dual_right.leftLim
 #align antitone.left_lim Antitone.leftLim
@@ -324,7 +324,7 @@ theorem le_rightLim (h : x < y) : f y ≤ rightLim f x :=
   hf.dual_right.rightLim_le h
 #align antitone.le_right_lim Antitone.le_rightLim
 
--- @[mono] -- Porting note: restore `mono` attribute
+@[mono]
 protected theorem rightLim : Antitone (rightLim f) :=
   hf.dual_right.rightLim
 #align antitone.right_lim Antitone.rightLim

Co-authored-by: thorimur <68410468+thorimur@users.noreply.github.com> Co-authored-by: Johan Commelin <johan@commelin.net>