topology.algebra.order.monotone_convergence ⟷ Mathlib.Topology.Algebra.Order.MonotoneConvergence

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

@@ -222,7 +222,7 @@ instance [Preorder α] [Preorder β] [TopologicalSpace α] [TopologicalSpace β]
   by
   constructor
   rintro ⟨a, b⟩ s h
-  rw [isLUB_prod, ← range_restrict, ← range_restrict] at h 
+  rw [isLUB_prod, ← range_restrict, ← range_restrict] at h
   have A : tendsto (fun x : s => (x : α × β).1) at_top (𝓝 a) :=
     tendsto_atTop_isLUB (monotone_fst.restrict s) h.1
   have B : tendsto (fun x : s => (x : α × β).2) at_top (𝓝 b) :=
@@ -238,7 +238,7 @@ instance {ι : Type _} {α : ι → Type _} [∀ i, Preorder (α i)] [∀ i, Top
     [∀ i, SupConvergenceClass (α i)] : SupConvergenceClass (∀ i, α i) :=
   by
   refine' ⟨fun f s h => _⟩
-  simp only [isLUB_pi, ← range_restrict] at h 
+  simp only [isLUB_pi, ← range_restrict] at h
   exact tendsto_pi_nhds.2 fun i => tendsto_atTop_isLUB ((monotone_eval _).restrict _) (h i)
 
 instance {ι : Type _} {α : ι → Type _} [∀ i, Preorder (α i)] [∀ i, TopologicalSpace (α i)]

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth, Yury Kudryashov
 -/
-import Mathbin.Topology.Order.Basic
+import Topology.Order.Basic
 
 #align_import topology.algebra.order.monotone_convergence from "leanprover-community/mathlib"@"50832daea47b195a48b5b33b1c8b2162c48c3afc"
 

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

@@ -245,18 +245,18 @@ instance {ι : Type _} {α : ι → Type _} [∀ i, Preorder (α i)] [∀ i, Top
     [∀ i, InfConvergenceClass (α i)] : InfConvergenceClass (∀ i, α i) :=
   show InfConvergenceClass (∀ i, (α i)ᵒᵈ)ᵒᵈ from OrderDual.infConvergenceClass
 
-#print Pi.Sup_convergence_class' /-
-instance Pi.Sup_convergence_class' {ι : Type _} [Preorder α] [TopologicalSpace α]
+#print Pi.supConvergenceClass' /-
+instance Pi.supConvergenceClass' {ι : Type _} [Preorder α] [TopologicalSpace α]
     [SupConvergenceClass α] : SupConvergenceClass (ι → α) :=
   Pi.supConvergenceClass
-#align pi.Sup_convergence_class' Pi.Sup_convergence_class'
+#align pi.Sup_convergence_class' Pi.supConvergenceClass'
 -/
 
-#print Pi.Inf_convergence_class' /-
-instance Pi.Inf_convergence_class' {ι : Type _} [Preorder α] [TopologicalSpace α]
+#print Pi.infConvergenceClass' /-
+instance Pi.infConvergenceClass' {ι : Type _} [Preorder α] [TopologicalSpace α]
     [InfConvergenceClass α] : InfConvergenceClass (ι → α) :=
   Pi.infConvergenceClass
-#align pi.Inf_convergence_class' Pi.Inf_convergence_class'
+#align pi.Inf_convergence_class' Pi.infConvergenceClass'
 -/
 
 #print tendsto_of_monotone /-

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth, Yury Kudryashov
-
-! This file was ported from Lean 3 source module topology.algebra.order.monotone_convergence
-! leanprover-community/mathlib commit 50832daea47b195a48b5b33b1c8b2162c48c3afc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Order.Basic
 
+#align_import topology.algebra.order.monotone_convergence from "leanprover-community/mathlib"@"50832daea47b195a48b5b33b1c8b2162c48c3afc"
+
 /-!
 # Bounded monotone sequences converge
 

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

@@ -147,16 +147,20 @@ section Csupr
 
 variable [ConditionallyCompleteLattice α] [SupConvergenceClass α] {f : ι → α} {a : α}
 
+#print tendsto_atTop_ciSup /-
 theorem tendsto_atTop_ciSup (h_mono : Monotone f) (hbdd : BddAbove <| range f) :
     Tendsto f atTop (𝓝 (⨆ i, f i)) :=
   by
   cases isEmpty_or_nonempty ι
   exacts [tendsto_of_is_empty, tendsto_atTop_isLUB h_mono (isLUB_ciSup hbdd)]
 #align tendsto_at_top_csupr tendsto_atTop_ciSup
+-/
 
+#print tendsto_atBot_ciSup /-
 theorem tendsto_atBot_ciSup (h_anti : Antitone f) (hbdd : BddAbove <| range f) :
     Tendsto f atBot (𝓝 (⨆ i, f i)) := by convert tendsto_atTop_ciSup h_anti.dual hbdd.dual
 #align tendsto_at_bot_csupr tendsto_atBot_ciSup
+-/
 
 end Csupr
 
@@ -164,13 +168,17 @@ section Cinfi
 
 variable [ConditionallyCompleteLattice α] [InfConvergenceClass α] {f : ι → α} {a : α}
 
+#print tendsto_atBot_ciInf /-
 theorem tendsto_atBot_ciInf (h_mono : Monotone f) (hbdd : BddBelow <| range f) :
     Tendsto f atBot (𝓝 (⨅ i, f i)) := by convert tendsto_atTop_ciSup h_mono.dual hbdd.dual
 #align tendsto_at_bot_cinfi tendsto_atBot_ciInf
+-/
 
+#print tendsto_atTop_ciInf /-
 theorem tendsto_atTop_ciInf (h_anti : Antitone f) (hbdd : BddBelow <| range f) :
     Tendsto f atTop (𝓝 (⨅ i, f i)) := by convert tendsto_atBot_ciSup h_anti.dual hbdd.dual
 #align tendsto_at_top_cinfi tendsto_atTop_ciInf
+-/
 
 end Cinfi
 
@@ -178,13 +186,17 @@ section iSup
 
 variable [CompleteLattice α] [SupConvergenceClass α] {f : ι → α} {a : α}
 
+#print tendsto_atTop_iSup /-
 theorem tendsto_atTop_iSup (h_mono : Monotone f) : Tendsto f atTop (𝓝 (⨆ i, f i)) :=
   tendsto_atTop_ciSup h_mono (OrderTop.bddAbove _)
 #align tendsto_at_top_supr tendsto_atTop_iSup
+-/
 
+#print tendsto_atBot_iSup /-
 theorem tendsto_atBot_iSup (h_anti : Antitone f) : Tendsto f atBot (𝓝 (⨆ i, f i)) :=
   tendsto_atBot_ciSup h_anti (OrderTop.bddAbove _)
 #align tendsto_at_bot_supr tendsto_atBot_iSup
+-/
 
 end iSup
 
@@ -192,13 +204,17 @@ section iInf
 
 variable [CompleteLattice α] [InfConvergenceClass α] {f : ι → α} {a : α}
 
+#print tendsto_atBot_iInf /-
 theorem tendsto_atBot_iInf (h_mono : Monotone f) : Tendsto f atBot (𝓝 (⨅ i, f i)) :=
   tendsto_atBot_ciInf h_mono (OrderBot.bddBelow _)
 #align tendsto_at_bot_infi tendsto_atBot_iInf
+-/
 
+#print tendsto_atTop_iInf /-
 theorem tendsto_atTop_iInf (h_anti : Antitone f) : Tendsto f atTop (𝓝 (⨅ i, f i)) :=
   tendsto_atTop_ciInf h_anti (OrderBot.bddBelow _)
 #align tendsto_at_top_infi tendsto_atTop_iInf
+-/
 
 end iInf
 
@@ -246,13 +262,16 @@ instance Pi.Inf_convergence_class' {ι : Type _} [Preorder α] [TopologicalSpace
 #align pi.Inf_convergence_class' Pi.Inf_convergence_class'
 -/
 
+#print tendsto_of_monotone /-
 theorem tendsto_of_monotone {ι α : Type _} [Preorder ι] [TopologicalSpace α]
     [ConditionallyCompleteLinearOrder α] [OrderTopology α] {f : ι → α} (h_mono : Monotone f) :
     Tendsto f atTop atTop ∨ ∃ l, Tendsto f atTop (𝓝 l) :=
   if H : BddAbove (range f) then Or.inr ⟨_, tendsto_atTop_ciSup h_mono H⟩
   else Or.inl <| tendsto_atTop_atTop_of_monotone' h_mono H
 #align tendsto_of_monotone tendsto_of_monotone
+-/
 
+#print tendsto_iff_tendsto_subseq_of_monotone /-
 theorem tendsto_iff_tendsto_subseq_of_monotone {ι₁ ι₂ α : Type _} [SemilatticeSup ι₁] [Preorder ι₂]
     [Nonempty ι₁] [TopologicalSpace α] [ConditionallyCompleteLinearOrder α] [OrderTopology α]
     [NoMaxOrder α] {f : ι₂ → α} {φ : ι₁ → ι₂} {l : α} (hf : Monotone f)
@@ -264,6 +283,7 @@ theorem tendsto_iff_tendsto_subseq_of_monotone {ι₁ ι₂ α : Type _} [Semila
     · exact (not_tendsto_atTop_of_tendsto_nhds h (h'.comp hg)).elim
     · rwa [tendsto_nhds_unique h (hl'.comp hg)]
 #align tendsto_iff_tendsto_subseq_of_monotone tendsto_iff_tendsto_subseq_of_monotone
+-/
 
 /-! The next family of results, such as `is_lub_of_tendsto_at_top` and `supr_eq_of_tendsto`, are
 converses to the standard fact that bounded monotone functions converge. They state, that if a
@@ -274,31 +294,40 @@ Related theorems above (`is_lub.is_lub_of_tendsto`, `is_glb.is_glb_of_tendsto` e
 when `f x` tends to `a` as `x` tends to some point `b` in the domain. -/
 
 
+#print Monotone.ge_of_tendsto /-
 theorem Monotone.ge_of_tendsto [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [SemilatticeSup β] {f : β → α} {a : α} (hf : Monotone f) (ha : Tendsto f atTop (𝓝 a)) (b : β) :
     f b ≤ a :=
   haveI : Nonempty β := Nonempty.intro b
   ge_of_tendsto ha ((eventually_ge_at_top b).mono fun _ hxy => hf hxy)
 #align monotone.ge_of_tendsto Monotone.ge_of_tendsto
+-/
 
+#print Monotone.le_of_tendsto /-
 theorem Monotone.le_of_tendsto [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [SemilatticeInf β] {f : β → α} {a : α} (hf : Monotone f) (ha : Tendsto f atBot (𝓝 a)) (b : β) :
     a ≤ f b :=
   hf.dual.ge_of_tendsto ha b
 #align monotone.le_of_tendsto Monotone.le_of_tendsto
+-/
 
+#print Antitone.le_of_tendsto /-
 theorem Antitone.le_of_tendsto [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [SemilatticeSup β] {f : β → α} {a : α} (hf : Antitone f) (ha : Tendsto f atTop (𝓝 a)) (b : β) :
     a ≤ f b :=
   hf.dual_right.ge_of_tendsto ha b
 #align antitone.le_of_tendsto Antitone.le_of_tendsto
+-/
 
+#print Antitone.ge_of_tendsto /-
 theorem Antitone.ge_of_tendsto [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [SemilatticeInf β] {f : β → α} {a : α} (hf : Antitone f) (ha : Tendsto f atBot (𝓝 a)) (b : β) :
     f b ≤ a :=
   hf.dual_right.le_of_tendsto ha b
 #align antitone.ge_of_tendsto Antitone.ge_of_tendsto
+-/
 
+#print isLUB_of_tendsto_atTop /-
 theorem isLUB_of_tendsto_atTop [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [Nonempty β] [SemilatticeSup β] {f : β → α} {a : α} (hf : Monotone f)
     (ha : Tendsto f atTop (𝓝 a)) : IsLUB (Set.range f) a :=
@@ -308,37 +337,49 @@ theorem isLUB_of_tendsto_atTop [TopologicalSpace α] [Preorder α] [OrderClosedT
     exact hf.ge_of_tendsto ha b
   · exact fun _ hb => le_of_tendsto' ha fun x => hb (Set.mem_range_self x)
 #align is_lub_of_tendsto_at_top isLUB_of_tendsto_atTop
+-/
 
+#print isGLB_of_tendsto_atBot /-
 theorem isGLB_of_tendsto_atBot [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [Nonempty β] [SemilatticeInf β] {f : β → α} {a : α} (hf : Monotone f)
     (ha : Tendsto f atBot (𝓝 a)) : IsGLB (Set.range f) a :=
   @isLUB_of_tendsto_atTop αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ hf.dual ha
 #align is_glb_of_tendsto_at_bot isGLB_of_tendsto_atBot
+-/
 
+#print isLUB_of_tendsto_atBot /-
 theorem isLUB_of_tendsto_atBot [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [Nonempty β] [SemilatticeInf β] {f : β → α} {a : α} (hf : Antitone f)
     (ha : Tendsto f atBot (𝓝 a)) : IsLUB (Set.range f) a :=
   @isLUB_of_tendsto_atTop α βᵒᵈ _ _ _ _ _ _ _ hf.dual_left ha
 #align is_lub_of_tendsto_at_bot isLUB_of_tendsto_atBot
+-/
 
+#print isGLB_of_tendsto_atTop /-
 theorem isGLB_of_tendsto_atTop [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [Nonempty β] [SemilatticeSup β] {f : β → α} {a : α} (hf : Antitone f)
     (ha : Tendsto f atTop (𝓝 a)) : IsGLB (Set.range f) a :=
   @isGLB_of_tendsto_atBot α βᵒᵈ _ _ _ _ _ _ _ hf.dual_left ha
 #align is_glb_of_tendsto_at_top isGLB_of_tendsto_atTop
+-/
 
+#print iSup_eq_of_tendsto /-
 theorem iSup_eq_of_tendsto {α β} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
     [Nonempty β] [SemilatticeSup β] {f : β → α} {a : α} (hf : Monotone f) :
     Tendsto f atTop (𝓝 a) → iSup f = a :=
   tendsto_nhds_unique (tendsto_atTop_iSup hf)
 #align supr_eq_of_tendsto iSup_eq_of_tendsto
+-/
 
+#print iInf_eq_of_tendsto /-
 theorem iInf_eq_of_tendsto {α} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
     [Nonempty β] [SemilatticeSup β] {f : β → α} {a : α} (hf : Antitone f) :
     Tendsto f atTop (𝓝 a) → iInf f = a :=
   tendsto_nhds_unique (tendsto_atTop_iInf hf)
 #align infi_eq_of_tendsto iInf_eq_of_tendsto
+-/
 
+#print iSup_eq_iSup_subseq_of_monotone /-
 theorem iSup_eq_iSup_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι₂] [CompleteLattice α]
     {l : Filter ι₁} [l.ne_bot] {f : ι₂ → α} {φ : ι₁ → ι₂} (hf : Monotone f)
     (hφ : Tendsto φ l atTop) : (⨆ i, f i) = ⨆ i, f (φ i) :=
@@ -347,10 +388,13 @@ theorem iSup_eq_iSup_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι
       Exists.imp (fun j (hj : i ≤ φ j) => hf hj) (hφ.Eventually <| eventually_ge_atTop i).exists)
     (iSup_mono' fun i => ⟨φ i, le_rfl⟩)
 #align supr_eq_supr_subseq_of_monotone iSup_eq_iSup_subseq_of_monotone
+-/
 
+#print iInf_eq_iInf_subseq_of_monotone /-
 theorem iInf_eq_iInf_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι₂] [CompleteLattice α]
     {l : Filter ι₁} [l.ne_bot] {f : ι₂ → α} {φ : ι₁ → ι₂} (hf : Monotone f)
     (hφ : Tendsto φ l atBot) : (⨅ i, f i) = ⨅ i, f (φ i) :=
   iSup_eq_iSup_subseq_of_monotone hf.dual hφ
 #align infi_eq_infi_subseq_of_monotone iInf_eq_iInf_subseq_of_monotone
+-/
 

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

@@ -151,7 +151,7 @@ theorem tendsto_atTop_ciSup (h_mono : Monotone f) (hbdd : BddAbove <| range f) :
     Tendsto f atTop (𝓝 (⨆ i, f i)) :=
   by
   cases isEmpty_or_nonempty ι
-  exacts[tendsto_of_is_empty, tendsto_atTop_isLUB h_mono (isLUB_ciSup hbdd)]
+  exacts [tendsto_of_is_empty, tendsto_atTop_isLUB h_mono (isLUB_ciSup hbdd)]
 #align tendsto_at_top_csupr tendsto_atTop_ciSup
 
 theorem tendsto_atBot_ciSup (h_anti : Antitone f) (hbdd : BddAbove <| range f) :
@@ -209,7 +209,7 @@ instance [Preorder α] [Preorder β] [TopologicalSpace α] [TopologicalSpace β]
   by
   constructor
   rintro ⟨a, b⟩ s h
-  rw [isLUB_prod, ← range_restrict, ← range_restrict] at h
+  rw [isLUB_prod, ← range_restrict, ← range_restrict] at h 
   have A : tendsto (fun x : s => (x : α × β).1) at_top (𝓝 a) :=
     tendsto_atTop_isLUB (monotone_fst.restrict s) h.1
   have B : tendsto (fun x : s => (x : α × β).2) at_top (𝓝 b) :=
@@ -225,7 +225,7 @@ instance {ι : Type _} {α : ι → Type _} [∀ i, Preorder (α i)] [∀ i, Top
     [∀ i, SupConvergenceClass (α i)] : SupConvergenceClass (∀ i, α i) :=
   by
   refine' ⟨fun f s h => _⟩
-  simp only [isLUB_pi, ← range_restrict] at h
+  simp only [isLUB_pi, ← range_restrict] at h 
   exact tendsto_pi_nhds.2 fun i => tendsto_atTop_isLUB ((monotone_eval _).restrict _) (h i)
 
 instance {ι : Type _} {α : ι → Type _} [∀ i, Preorder (α i)] [∀ i, TopologicalSpace (α i)]

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

@@ -36,7 +36,7 @@ monotone convergence
 
 open Filter Set Function
 
-open Filter Topology Classical
+open scoped Filter Topology Classical
 
 variable {α β : Type _}
 

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

@@ -147,12 +147,6 @@ section Csupr
 
 variable [ConditionallyCompleteLattice α] [SupConvergenceClass α] {f : ι → α} {a : α}
 
-/- warning: tendsto_at_top_csupr -> tendsto_atTop_ciSup is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_3) ι (fun (i : ι) => f i))))
-but is expected to have type
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_3) ι (fun (i : ι) => f i))))
-Case conversion may be inaccurate. Consider using '#align tendsto_at_top_csupr tendsto_atTop_ciSupₓ'. -/
 theorem tendsto_atTop_ciSup (h_mono : Monotone f) (hbdd : BddAbove <| range f) :
     Tendsto f atTop (𝓝 (⨆ i, f i)) :=
   by
@@ -160,12 +154,6 @@ theorem tendsto_atTop_ciSup (h_mono : Monotone f) (hbdd : BddAbove <| range f) :
   exacts[tendsto_of_is_empty, tendsto_atTop_isLUB h_mono (isLUB_ciSup hbdd)]
 #align tendsto_at_top_csupr tendsto_atTop_ciSup
 
-/- warning: tendsto_at_bot_csupr -> tendsto_atBot_ciSup is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_3) ι (fun (i : ι) => f i))))
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-Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_csupr tendsto_atBot_ciSupₓ'. -/
 theorem tendsto_atBot_ciSup (h_anti : Antitone f) (hbdd : BddAbove <| range f) :
     Tendsto f atBot (𝓝 (⨆ i, f i)) := by convert tendsto_atTop_ciSup h_anti.dual hbdd.dual
 #align tendsto_at_bot_csupr tendsto_atBot_ciSup
@@ -176,22 +164,10 @@ section Cinfi
 
 variable [ConditionallyCompleteLattice α] [InfConvergenceClass α] {f : ι → α} {a : α}
 
-/- warning: tendsto_at_bot_cinfi -> tendsto_atBot_ciInf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_cinfi tendsto_atBot_ciInfₓ'. -/
 theorem tendsto_atBot_ciInf (h_mono : Monotone f) (hbdd : BddBelow <| range f) :
     Tendsto f atBot (𝓝 (⨅ i, f i)) := by convert tendsto_atTop_ciSup h_mono.dual hbdd.dual
 #align tendsto_at_bot_cinfi tendsto_atBot_ciInf
 
-/- warning: tendsto_at_top_cinfi -> tendsto_atTop_ciInf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align tendsto_at_top_cinfi tendsto_atTop_ciInfₓ'. -/
 theorem tendsto_atTop_ciInf (h_anti : Antitone f) (hbdd : BddBelow <| range f) :
     Tendsto f atTop (𝓝 (⨅ i, f i)) := by convert tendsto_atBot_ciSup h_anti.dual hbdd.dual
 #align tendsto_at_top_cinfi tendsto_atTop_ciInf
@@ -202,22 +178,10 @@ section iSup
 
 variable [CompleteLattice α] [SupConvergenceClass α] {f : ι → α} {a : α}
 
-/- warning: tendsto_at_top_supr -> tendsto_atTop_iSup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align tendsto_at_top_supr tendsto_atTop_iSupₓ'. -/
 theorem tendsto_atTop_iSup (h_mono : Monotone f) : Tendsto f atTop (𝓝 (⨆ i, f i)) :=
   tendsto_atTop_ciSup h_mono (OrderTop.bddAbove _)
 #align tendsto_at_top_supr tendsto_atTop_iSup
 
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-Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_supr tendsto_atBot_iSupₓ'. -/
 theorem tendsto_atBot_iSup (h_anti : Antitone f) : Tendsto f atBot (𝓝 (⨆ i, f i)) :=
   tendsto_atBot_ciSup h_anti (OrderTop.bddAbove _)
 #align tendsto_at_bot_supr tendsto_atBot_iSup
@@ -228,22 +192,10 @@ section iInf
 
 variable [CompleteLattice α] [InfConvergenceClass α] {f : ι → α} {a : α}
 
-/- warning: tendsto_at_bot_infi -> tendsto_atBot_iInf is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_infi tendsto_atBot_iInfₓ'. -/
 theorem tendsto_atBot_iInf (h_mono : Monotone f) : Tendsto f atBot (𝓝 (⨅ i, f i)) :=
   tendsto_atBot_ciInf h_mono (OrderBot.bddBelow _)
 #align tendsto_at_bot_infi tendsto_atBot_iInf
 
-/- warning: tendsto_at_top_infi -> tendsto_atTop_iInf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align tendsto_at_top_infi tendsto_atTop_iInfₓ'. -/
 theorem tendsto_atTop_iInf (h_anti : Antitone f) : Tendsto f atTop (𝓝 (⨅ i, f i)) :=
   tendsto_atTop_ciInf h_anti (OrderBot.bddBelow _)
 #align tendsto_at_top_infi tendsto_atTop_iInf
@@ -294,12 +246,6 @@ instance Pi.Inf_convergence_class' {ι : Type _} [Preorder α] [TopologicalSpace
 #align pi.Inf_convergence_class' Pi.Inf_convergence_class'
 -/
 
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-Case conversion may be inaccurate. Consider using '#align tendsto_of_monotone tendsto_of_monotoneₓ'. -/
 theorem tendsto_of_monotone {ι α : Type _} [Preorder ι] [TopologicalSpace α]
     [ConditionallyCompleteLinearOrder α] [OrderTopology α] {f : ι → α} (h_mono : Monotone f) :
     Tendsto f atTop atTop ∨ ∃ l, Tendsto f atTop (𝓝 l) :=
@@ -307,12 +253,6 @@ theorem tendsto_of_monotone {ι α : Type _} [Preorder ι] [TopologicalSpace α]
   else Or.inl <| tendsto_atTop_atTop_of_monotone' h_mono H
 #align tendsto_of_monotone tendsto_of_monotone
 
-/- warning: tendsto_iff_tendsto_subseq_of_monotone -> tendsto_iff_tendsto_subseq_of_monotone is a dubious translation:
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-  forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {α : Type.{u3}} [_inst_1 : SemilatticeSup.{u1} ι₁] [_inst_2 : Preorder.{u2} ι₂] [_inst_3 : Nonempty.{succ u1} ι₁] [_inst_4 : TopologicalSpace.{u3} α] [_inst_5 : ConditionallyCompleteLinearOrder.{u3} α] [_inst_6 : OrderTopology.{u3} α _inst_4 (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} α _inst_5)))))] [_inst_7 : NoMaxOrder.{u3} α (Preorder.toHasLt.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} α _inst_5))))))] {f : ι₂ -> α} {φ : ι₁ -> ι₂} {l : α}, (Monotone.{u2, u3} ι₂ α _inst_2 (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} α _inst_5))))) f) -> (Filter.Tendsto.{u1, u2} ι₁ ι₂ φ (Filter.atTop.{u1} ι₁ (PartialOrder.toPreorder.{u1} ι₁ (SemilatticeSup.toPartialOrder.{u1} ι₁ _inst_1))) (Filter.atTop.{u2} ι₂ _inst_2)) -> (Iff (Filter.Tendsto.{u2, u3} ι₂ α f (Filter.atTop.{u2} ι₂ _inst_2) (nhds.{u3} α _inst_4 l)) (Filter.Tendsto.{u1, u3} ι₁ α (Function.comp.{succ u1, succ u2, succ u3} ι₁ ι₂ α f φ) (Filter.atTop.{u1} ι₁ (PartialOrder.toPreorder.{u1} ι₁ (SemilatticeSup.toPartialOrder.{u1} ι₁ _inst_1))) (nhds.{u3} α _inst_4 l)))
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-Case conversion may be inaccurate. Consider using '#align tendsto_iff_tendsto_subseq_of_monotone tendsto_iff_tendsto_subseq_of_monotoneₓ'. -/
 theorem tendsto_iff_tendsto_subseq_of_monotone {ι₁ ι₂ α : Type _} [SemilatticeSup ι₁] [Preorder ι₂]
     [Nonempty ι₁] [TopologicalSpace α] [ConditionallyCompleteLinearOrder α] [OrderTopology α]
     [NoMaxOrder α] {f : ι₂ → α} {φ : ι₁ → ι₂} {l : α} (hf : Monotone f)
@@ -334,12 +274,6 @@ Related theorems above (`is_lub.is_lub_of_tendsto`, `is_glb.is_glb_of_tendsto` e
 when `f x` tends to `a` as `x` tends to some point `b` in the domain. -/
 
 
-/- warning: monotone.ge_of_tendsto -> Monotone.ge_of_tendsto is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align monotone.ge_of_tendsto Monotone.ge_of_tendstoₓ'. -/
 theorem Monotone.ge_of_tendsto [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [SemilatticeSup β] {f : β → α} {a : α} (hf : Monotone f) (ha : Tendsto f atTop (𝓝 a)) (b : β) :
     f b ≤ a :=
@@ -347,48 +281,24 @@ theorem Monotone.ge_of_tendsto [TopologicalSpace α] [Preorder α] [OrderClosedT
   ge_of_tendsto ha ((eventually_ge_at_top b).mono fun _ hxy => hf hxy)
 #align monotone.ge_of_tendsto Monotone.ge_of_tendsto
 
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-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : OrderClosedTopology.{u2} α _inst_1 _inst_2] [_inst_4 : SemilatticeInf.{u1} β] {f : β -> α} {a : α}, (Monotone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_4)) _inst_2 f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atBot.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_4))) (nhds.{u2} α _inst_1 a)) -> (forall (b : β), LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) a (f b))
-Case conversion may be inaccurate. Consider using '#align monotone.le_of_tendsto Monotone.le_of_tendstoₓ'. -/
 theorem Monotone.le_of_tendsto [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [SemilatticeInf β] {f : β → α} {a : α} (hf : Monotone f) (ha : Tendsto f atBot (𝓝 a)) (b : β) :
     a ≤ f b :=
   hf.dual.ge_of_tendsto ha b
 #align monotone.le_of_tendsto Monotone.le_of_tendsto
 
-/- warning: antitone.le_of_tendsto -> Antitone.le_of_tendsto is a dubious translation:
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-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : OrderClosedTopology.{u2} α _inst_1 _inst_2] [_inst_4 : SemilatticeSup.{u1} β] {f : β -> α} {a : α}, (Antitone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_4)) _inst_2 f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_4))) (nhds.{u2} α _inst_1 a)) -> (forall (b : β), LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) a (f b))
-Case conversion may be inaccurate. Consider using '#align antitone.le_of_tendsto Antitone.le_of_tendstoₓ'. -/
 theorem Antitone.le_of_tendsto [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [SemilatticeSup β] {f : β → α} {a : α} (hf : Antitone f) (ha : Tendsto f atTop (𝓝 a)) (b : β) :
     a ≤ f b :=
   hf.dual_right.ge_of_tendsto ha b
 #align antitone.le_of_tendsto Antitone.le_of_tendsto
 
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-lean 3 declaration is
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-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : OrderClosedTopology.{u2} α _inst_1 _inst_2] [_inst_4 : SemilatticeInf.{u1} β] {f : β -> α} {a : α}, (Antitone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_4)) _inst_2 f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atBot.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_4))) (nhds.{u2} α _inst_1 a)) -> (forall (b : β), LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) (f b) a)
-Case conversion may be inaccurate. Consider using '#align antitone.ge_of_tendsto Antitone.ge_of_tendstoₓ'. -/
 theorem Antitone.ge_of_tendsto [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [SemilatticeInf β] {f : β → α} {a : α} (hf : Antitone f) (ha : Tendsto f atBot (𝓝 a)) (b : β) :
     f b ≤ a :=
   hf.dual_right.le_of_tendsto ha b
 #align antitone.ge_of_tendsto Antitone.ge_of_tendsto
 
-/- warning: is_lub_of_tendsto_at_top -> isLUB_of_tendsto_atTop is a dubious translation:
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-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : OrderClosedTopology.{u2} α _inst_1 _inst_2] [_inst_4 : Nonempty.{succ u1} β] [_inst_5 : SemilatticeSup.{u1} β] {f : β -> α} {a : α}, (Monotone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5)) _inst_2 f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5))) (nhds.{u2} α _inst_1 a)) -> (IsLUB.{u2} α _inst_2 (Set.range.{u2, succ u1} α β f) a)
-Case conversion may be inaccurate. Consider using '#align is_lub_of_tendsto_at_top isLUB_of_tendsto_atTopₓ'. -/
 theorem isLUB_of_tendsto_atTop [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [Nonempty β] [SemilatticeSup β] {f : β → α} {a : α} (hf : Monotone f)
     (ha : Tendsto f atTop (𝓝 a)) : IsLUB (Set.range f) a :=
@@ -399,72 +309,36 @@ theorem isLUB_of_tendsto_atTop [TopologicalSpace α] [Preorder α] [OrderClosedT
   · exact fun _ hb => le_of_tendsto' ha fun x => hb (Set.mem_range_self x)
 #align is_lub_of_tendsto_at_top isLUB_of_tendsto_atTop
 
-/- warning: is_glb_of_tendsto_at_bot -> isGLB_of_tendsto_atBot is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_glb_of_tendsto_at_bot isGLB_of_tendsto_atBotₓ'. -/
 theorem isGLB_of_tendsto_atBot [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [Nonempty β] [SemilatticeInf β] {f : β → α} {a : α} (hf : Monotone f)
     (ha : Tendsto f atBot (𝓝 a)) : IsGLB (Set.range f) a :=
   @isLUB_of_tendsto_atTop αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ hf.dual ha
 #align is_glb_of_tendsto_at_bot isGLB_of_tendsto_atBot
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_lub_of_tendsto_at_bot isLUB_of_tendsto_atBotₓ'. -/
 theorem isLUB_of_tendsto_atBot [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [Nonempty β] [SemilatticeInf β] {f : β → α} {a : α} (hf : Antitone f)
     (ha : Tendsto f atBot (𝓝 a)) : IsLUB (Set.range f) a :=
   @isLUB_of_tendsto_atTop α βᵒᵈ _ _ _ _ _ _ _ hf.dual_left ha
 #align is_lub_of_tendsto_at_bot isLUB_of_tendsto_atBot
 
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-Case conversion may be inaccurate. Consider using '#align is_glb_of_tendsto_at_top isGLB_of_tendsto_atTopₓ'. -/
 theorem isGLB_of_tendsto_atTop [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [Nonempty β] [SemilatticeSup β] {f : β → α} {a : α} (hf : Antitone f)
     (ha : Tendsto f atTop (𝓝 a)) : IsGLB (Set.range f) a :=
   @isGLB_of_tendsto_atBot α βᵒᵈ _ _ _ _ _ _ _ hf.dual_left ha
 #align is_glb_of_tendsto_at_top isGLB_of_tendsto_atTop
 
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompleteLinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_2))))] [_inst_4 : Nonempty.{succ u2} β] [_inst_5 : SemilatticeSup.{u2} β] {f : β -> α} {a : α}, (Monotone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_5)) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_2)))) f) -> (Filter.Tendsto.{u2, u1} β α f (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_5))) (nhds.{u1} α _inst_1 a)) -> (Eq.{succ u1} α (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_2))) β f) a)
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-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompleteLinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2))))] [_inst_4 : Nonempty.{succ u1} β] [_inst_5 : SemilatticeSup.{u1} β] {f : β -> α} {a : α}, (Monotone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5)) (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2)))) f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5))) (nhds.{u2} α _inst_1 a)) -> (Eq.{succ u2} α (iSup.{u2, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_2)))) β f) a)
-Case conversion may be inaccurate. Consider using '#align supr_eq_of_tendsto iSup_eq_of_tendstoₓ'. -/
 theorem iSup_eq_of_tendsto {α β} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
     [Nonempty β] [SemilatticeSup β] {f : β → α} {a : α} (hf : Monotone f) :
     Tendsto f atTop (𝓝 a) → iSup f = a :=
   tendsto_nhds_unique (tendsto_atTop_iSup hf)
 #align supr_eq_of_tendsto iSup_eq_of_tendsto
 
-/- warning: infi_eq_of_tendsto -> iInf_eq_of_tendsto is a dubious translation:
-lean 3 declaration is
-  forall {β : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompleteLinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2))))] [_inst_4 : Nonempty.{succ u1} β] [_inst_5 : SemilatticeSup.{u1} β] {f : β -> α} {a : α}, (Antitone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5)) (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2)))) f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5))) (nhds.{u2} α _inst_1 a)) -> (Eq.{succ u2} α (iInf.{u2, succ u1} α (ConditionallyCompleteLattice.toHasInf.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2))) β f) a)
-but is expected to have type
-  forall {β : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompleteLinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2))))] [_inst_4 : Nonempty.{succ u1} β] [_inst_5 : SemilatticeSup.{u1} β] {f : β -> α} {a : α}, (Antitone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5)) (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2)))) f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5))) (nhds.{u2} α _inst_1 a)) -> (Eq.{succ u2} α (iInf.{u2, succ u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_2)))) β f) a)
-Case conversion may be inaccurate. Consider using '#align infi_eq_of_tendsto iInf_eq_of_tendstoₓ'. -/
 theorem iInf_eq_of_tendsto {α} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
     [Nonempty β] [SemilatticeSup β] {f : β → α} {a : α} (hf : Antitone f) :
     Tendsto f atTop (𝓝 a) → iInf f = a :=
   tendsto_nhds_unique (tendsto_atTop_iInf hf)
 #align infi_eq_of_tendsto iInf_eq_of_tendsto
 
-/- warning: supr_eq_supr_subseq_of_monotone -> iSup_eq_iSup_subseq_of_monotone is a dubious translation:
-lean 3 declaration is
-  forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {α : Type.{u3}} [_inst_1 : Preorder.{u2} ι₂] [_inst_2 : CompleteLattice.{u3} α] {l : Filter.{u1} ι₁} [_inst_3 : Filter.NeBot.{u1} ι₁ l] {f : ι₂ -> α} {φ : ι₁ -> ι₂}, (Monotone.{u2, u3} ι₂ α _inst_1 (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_2))) f) -> (Filter.Tendsto.{u1, u2} ι₁ ι₂ φ l (Filter.atTop.{u2} ι₂ _inst_1)) -> (Eq.{succ u3} α (iSup.{u3, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u3} α (CompleteLattice.toConditionallyCompleteLattice.{u3} α _inst_2)) ι₂ (fun (i : ι₂) => f i)) (iSup.{u3, succ u1} α (ConditionallyCompleteLattice.toHasSup.{u3} α (CompleteLattice.toConditionallyCompleteLattice.{u3} α _inst_2)) ι₁ (fun (i : ι₁) => f (φ i))))
-but is expected to have type
-  forall {ι₁ : Type.{u3}} {ι₂ : Type.{u2}} {α : Type.{u1}} [_inst_1 : Preorder.{u2} ι₂] [_inst_2 : CompleteLattice.{u1} α] {l : Filter.{u3} ι₁} [_inst_3 : Filter.NeBot.{u3} ι₁ l] {f : ι₂ -> α} {φ : ι₁ -> ι₂}, (Monotone.{u2, u1} ι₂ α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_2))) f) -> (Filter.Tendsto.{u3, u2} ι₁ ι₂ φ l (Filter.atTop.{u2} ι₂ _inst_1)) -> (Eq.{succ u1} α (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_2)) ι₂ (fun (i : ι₂) => f i)) (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_2)) ι₁ (fun (i : ι₁) => f (φ i))))
-Case conversion may be inaccurate. Consider using '#align supr_eq_supr_subseq_of_monotone iSup_eq_iSup_subseq_of_monotoneₓ'. -/
 theorem iSup_eq_iSup_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι₂] [CompleteLattice α]
     {l : Filter ι₁} [l.ne_bot] {f : ι₂ → α} {φ : ι₁ → ι₂} (hf : Monotone f)
     (hφ : Tendsto φ l atTop) : (⨆ i, f i) = ⨆ i, f (φ i) :=
@@ -474,12 +348,6 @@ theorem iSup_eq_iSup_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι
     (iSup_mono' fun i => ⟨φ i, le_rfl⟩)
 #align supr_eq_supr_subseq_of_monotone iSup_eq_iSup_subseq_of_monotone
 
-/- warning: infi_eq_infi_subseq_of_monotone -> iInf_eq_iInf_subseq_of_monotone is a dubious translation:
-lean 3 declaration is
-  forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {α : Type.{u3}} [_inst_1 : Preorder.{u2} ι₂] [_inst_2 : CompleteLattice.{u3} α] {l : Filter.{u1} ι₁} [_inst_3 : Filter.NeBot.{u1} ι₁ l] {f : ι₂ -> α} {φ : ι₁ -> ι₂}, (Monotone.{u2, u3} ι₂ α _inst_1 (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_2))) f) -> (Filter.Tendsto.{u1, u2} ι₁ ι₂ φ l (Filter.atBot.{u2} ι₂ _inst_1)) -> (Eq.{succ u3} α (iInf.{u3, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u3} α (CompleteLattice.toConditionallyCompleteLattice.{u3} α _inst_2)) ι₂ (fun (i : ι₂) => f i)) (iInf.{u3, succ u1} α (ConditionallyCompleteLattice.toHasInf.{u3} α (CompleteLattice.toConditionallyCompleteLattice.{u3} α _inst_2)) ι₁ (fun (i : ι₁) => f (φ i))))
-but is expected to have type
-  forall {ι₁ : Type.{u3}} {ι₂ : Type.{u2}} {α : Type.{u1}} [_inst_1 : Preorder.{u2} ι₂] [_inst_2 : CompleteLattice.{u1} α] {l : Filter.{u3} ι₁} [_inst_3 : Filter.NeBot.{u3} ι₁ l] {f : ι₂ -> α} {φ : ι₁ -> ι₂}, (Monotone.{u2, u1} ι₂ α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_2))) f) -> (Filter.Tendsto.{u3, u2} ι₁ ι₂ φ l (Filter.atBot.{u2} ι₂ _inst_1)) -> (Eq.{succ u1} α (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_2)) ι₂ (fun (i : ι₂) => f i)) (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_2)) ι₁ (fun (i : ι₁) => f (φ i))))
-Case conversion may be inaccurate. Consider using '#align infi_eq_infi_subseq_of_monotone iInf_eq_iInf_subseq_of_monotoneₓ'. -/
 theorem iInf_eq_iInf_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι₂] [CompleteLattice α]
     {l : Filter ι₁} [l.ne_bot] {f : ι₂ → α} {φ : ι₁ → ι₂} (hf : Monotone f)
     (hφ : Tendsto φ l atBot) : (⨅ i, f i) = ⨅ i, f (φ i) :=

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

@@ -263,8 +263,7 @@ instance [Preorder α] [Preorder β] [TopologicalSpace α] [TopologicalSpace β]
   have B : tendsto (fun x : s => (x : α × β).2) at_top (𝓝 b) :=
     tendsto_atTop_isLUB (monotone_snd.restrict s) h.2
   convert A.prod_mk_nhds B
-  ext1 ⟨⟨x, y⟩, h⟩
-  rfl
+  ext1 ⟨⟨x, y⟩, h⟩; rfl
 
 instance [Preorder α] [Preorder β] [TopologicalSpace α] [TopologicalSpace β] [InfConvergenceClass α]
     [InfConvergenceClass β] : InfConvergenceClass (α × β) :=

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

@@ -310,7 +310,7 @@ theorem tendsto_of_monotone {ι α : Type _} [Preorder ι] [TopologicalSpace α]
 
 /- warning: tendsto_iff_tendsto_subseq_of_monotone -> tendsto_iff_tendsto_subseq_of_monotone is a dubious translation:
 lean 3 declaration is
-  forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {α : Type.{u3}} [_inst_1 : SemilatticeSup.{u1} ι₁] [_inst_2 : Preorder.{u2} ι₂] [_inst_3 : Nonempty.{succ u1} ι₁] [_inst_4 : TopologicalSpace.{u3} α] [_inst_5 : ConditionallyCompleteLinearOrder.{u3} α] [_inst_6 : OrderTopology.{u3} α _inst_4 (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} α _inst_5)))))] [_inst_7 : NoMaxOrder.{u3} α (Preorder.toLT.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} α _inst_5))))))] {f : ι₂ -> α} {φ : ι₁ -> ι₂} {l : α}, (Monotone.{u2, u3} ι₂ α _inst_2 (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} α _inst_5))))) f) -> (Filter.Tendsto.{u1, u2} ι₁ ι₂ φ (Filter.atTop.{u1} ι₁ (PartialOrder.toPreorder.{u1} ι₁ (SemilatticeSup.toPartialOrder.{u1} ι₁ _inst_1))) (Filter.atTop.{u2} ι₂ _inst_2)) -> (Iff (Filter.Tendsto.{u2, u3} ι₂ α f (Filter.atTop.{u2} ι₂ _inst_2) (nhds.{u3} α _inst_4 l)) (Filter.Tendsto.{u1, u3} ι₁ α (Function.comp.{succ u1, succ u2, succ u3} ι₁ ι₂ α f φ) (Filter.atTop.{u1} ι₁ (PartialOrder.toPreorder.{u1} ι₁ (SemilatticeSup.toPartialOrder.{u1} ι₁ _inst_1))) (nhds.{u3} α _inst_4 l)))
+  forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {α : Type.{u3}} [_inst_1 : SemilatticeSup.{u1} ι₁] [_inst_2 : Preorder.{u2} ι₂] [_inst_3 : Nonempty.{succ u1} ι₁] [_inst_4 : TopologicalSpace.{u3} α] [_inst_5 : ConditionallyCompleteLinearOrder.{u3} α] [_inst_6 : OrderTopology.{u3} α _inst_4 (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} α _inst_5)))))] [_inst_7 : NoMaxOrder.{u3} α (Preorder.toHasLt.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} α _inst_5))))))] {f : ι₂ -> α} {φ : ι₁ -> ι₂} {l : α}, (Monotone.{u2, u3} ι₂ α _inst_2 (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} α _inst_5))))) f) -> (Filter.Tendsto.{u1, u2} ι₁ ι₂ φ (Filter.atTop.{u1} ι₁ (PartialOrder.toPreorder.{u1} ι₁ (SemilatticeSup.toPartialOrder.{u1} ι₁ _inst_1))) (Filter.atTop.{u2} ι₂ _inst_2)) -> (Iff (Filter.Tendsto.{u2, u3} ι₂ α f (Filter.atTop.{u2} ι₂ _inst_2) (nhds.{u3} α _inst_4 l)) (Filter.Tendsto.{u1, u3} ι₁ α (Function.comp.{succ u1, succ u2, succ u3} ι₁ ι₂ α f φ) (Filter.atTop.{u1} ι₁ (PartialOrder.toPreorder.{u1} ι₁ (SemilatticeSup.toPartialOrder.{u1} ι₁ _inst_1))) (nhds.{u3} α _inst_4 l)))
 but is expected to have type
   forall {ι₁ : Type.{u3}} {ι₂ : Type.{u2}} {α : Type.{u1}} [_inst_1 : SemilatticeSup.{u3} ι₁] [_inst_2 : Preorder.{u2} ι₂] [_inst_3 : Nonempty.{succ u3} ι₁] [_inst_4 : TopologicalSpace.{u1} α] [_inst_5 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_6 : OrderTopology.{u1} α _inst_4 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_5)))))] [_inst_7 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_5))))))] {f : ι₂ -> α} {φ : ι₁ -> ι₂} {l : α}, (Monotone.{u2, u1} ι₂ α _inst_2 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_5))))) f) -> (Filter.Tendsto.{u3, u2} ι₁ ι₂ φ (Filter.atTop.{u3} ι₁ (PartialOrder.toPreorder.{u3} ι₁ (SemilatticeSup.toPartialOrder.{u3} ι₁ _inst_1))) (Filter.atTop.{u2} ι₂ _inst_2)) -> (Iff (Filter.Tendsto.{u2, u1} ι₂ α f (Filter.atTop.{u2} ι₂ _inst_2) (nhds.{u1} α _inst_4 l)) (Filter.Tendsto.{u3, u1} ι₁ α (Function.comp.{succ u3, succ u2, succ u1} ι₁ ι₂ α f φ) (Filter.atTop.{u3} ι₁ (PartialOrder.toPreorder.{u3} ι₁ (SemilatticeSup.toPartialOrder.{u3} ι₁ _inst_1))) (nhds.{u1} α _inst_4 l)))
 Case conversion may be inaccurate. Consider using '#align tendsto_iff_tendsto_subseq_of_monotone tendsto_iff_tendsto_subseq_of_monotoneₓ'. -/
@@ -337,7 +337,7 @@ when `f x` tends to `a` as `x` tends to some point `b` in the domain. -/
 
 /- warning: monotone.ge_of_tendsto -> Monotone.ge_of_tendsto is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_4 : SemilatticeSup.{u2} β] {f : β -> α} {a : α}, (Monotone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_4)) _inst_2 f) -> (Filter.Tendsto.{u2, u1} β α f (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_4))) (nhds.{u1} α _inst_1 a)) -> (forall (b : β), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f b) a)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_4 : SemilatticeSup.{u2} β] {f : β -> α} {a : α}, (Monotone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_4)) _inst_2 f) -> (Filter.Tendsto.{u2, u1} β α f (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_4))) (nhds.{u1} α _inst_1 a)) -> (forall (b : β), LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (f b) a)
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : OrderClosedTopology.{u2} α _inst_1 _inst_2] [_inst_4 : SemilatticeSup.{u1} β] {f : β -> α} {a : α}, (Monotone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_4)) _inst_2 f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_4))) (nhds.{u2} α _inst_1 a)) -> (forall (b : β), LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) (f b) a)
 Case conversion may be inaccurate. Consider using '#align monotone.ge_of_tendsto Monotone.ge_of_tendstoₓ'. -/
@@ -350,7 +350,7 @@ theorem Monotone.ge_of_tendsto [TopologicalSpace α] [Preorder α] [OrderClosedT
 
 /- warning: monotone.le_of_tendsto -> Monotone.le_of_tendsto is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_4 : SemilatticeInf.{u2} β] {f : β -> α} {a : α}, (Monotone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_4)) _inst_2 f) -> (Filter.Tendsto.{u2, u1} β α f (Filter.atBot.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_4))) (nhds.{u1} α _inst_1 a)) -> (forall (b : β), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (f b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_4 : SemilatticeInf.{u2} β] {f : β -> α} {a : α}, (Monotone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_4)) _inst_2 f) -> (Filter.Tendsto.{u2, u1} β α f (Filter.atBot.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_4))) (nhds.{u1} α _inst_1 a)) -> (forall (b : β), LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (f b))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : OrderClosedTopology.{u2} α _inst_1 _inst_2] [_inst_4 : SemilatticeInf.{u1} β] {f : β -> α} {a : α}, (Monotone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_4)) _inst_2 f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atBot.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_4))) (nhds.{u2} α _inst_1 a)) -> (forall (b : β), LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) a (f b))
 Case conversion may be inaccurate. Consider using '#align monotone.le_of_tendsto Monotone.le_of_tendstoₓ'. -/
@@ -362,7 +362,7 @@ theorem Monotone.le_of_tendsto [TopologicalSpace α] [Preorder α] [OrderClosedT
 
 /- warning: antitone.le_of_tendsto -> Antitone.le_of_tendsto is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_4 : SemilatticeSup.{u2} β] {f : β -> α} {a : α}, (Antitone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_4)) _inst_2 f) -> (Filter.Tendsto.{u2, u1} β α f (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_4))) (nhds.{u1} α _inst_1 a)) -> (forall (b : β), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) a (f b))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_4 : SemilatticeSup.{u2} β] {f : β -> α} {a : α}, (Antitone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_4)) _inst_2 f) -> (Filter.Tendsto.{u2, u1} β α f (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_4))) (nhds.{u1} α _inst_1 a)) -> (forall (b : β), LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) a (f b))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : OrderClosedTopology.{u2} α _inst_1 _inst_2] [_inst_4 : SemilatticeSup.{u1} β] {f : β -> α} {a : α}, (Antitone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_4)) _inst_2 f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_4))) (nhds.{u2} α _inst_1 a)) -> (forall (b : β), LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) a (f b))
 Case conversion may be inaccurate. Consider using '#align antitone.le_of_tendsto Antitone.le_of_tendstoₓ'. -/
@@ -374,7 +374,7 @@ theorem Antitone.le_of_tendsto [TopologicalSpace α] [Preorder α] [OrderClosedT
 
 /- warning: antitone.ge_of_tendsto -> Antitone.ge_of_tendsto is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_4 : SemilatticeInf.{u2} β] {f : β -> α} {a : α}, (Antitone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_4)) _inst_2 f) -> (Filter.Tendsto.{u2, u1} β α f (Filter.atBot.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_4))) (nhds.{u1} α _inst_1 a)) -> (forall (b : β), LE.le.{u1} α (Preorder.toLE.{u1} α _inst_2) (f b) a)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : Preorder.{u1} α] [_inst_3 : OrderClosedTopology.{u1} α _inst_1 _inst_2] [_inst_4 : SemilatticeInf.{u2} β] {f : β -> α} {a : α}, (Antitone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_4)) _inst_2 f) -> (Filter.Tendsto.{u2, u1} β α f (Filter.atBot.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β _inst_4))) (nhds.{u1} α _inst_1 a)) -> (forall (b : β), LE.le.{u1} α (Preorder.toHasLe.{u1} α _inst_2) (f b) a)
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : Preorder.{u2} α] [_inst_3 : OrderClosedTopology.{u2} α _inst_1 _inst_2] [_inst_4 : SemilatticeInf.{u1} β] {f : β -> α} {a : α}, (Antitone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_4)) _inst_2 f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atBot.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β _inst_4))) (nhds.{u2} α _inst_1 a)) -> (forall (b : β), LE.le.{u2} α (Preorder.toLE.{u2} α _inst_2) (f b) a)
 Case conversion may be inaccurate. Consider using '#align antitone.ge_of_tendsto Antitone.ge_of_tendstoₓ'. -/

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

@@ -147,28 +147,28 @@ section Csupr
 
 variable [ConditionallyCompleteLattice α] [SupConvergenceClass α] {f : ι → α} {a : α}
 
-/- warning: tendsto_at_top_csupr -> tendsto_atTop_csupᵢ is a dubious translation:
+/- warning: tendsto_at_top_csupr -> tendsto_atTop_ciSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_3) ι (fun (i : ι) => f i))))
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_3) ι (fun (i : ι) => f i))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_3) ι (fun (i : ι) => f i))))
-Case conversion may be inaccurate. Consider using '#align tendsto_at_top_csupr tendsto_atTop_csupᵢₓ'. -/
-theorem tendsto_atTop_csupᵢ (h_mono : Monotone f) (hbdd : BddAbove <| range f) :
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_3) ι (fun (i : ι) => f i))))
+Case conversion may be inaccurate. Consider using '#align tendsto_at_top_csupr tendsto_atTop_ciSupₓ'. -/
+theorem tendsto_atTop_ciSup (h_mono : Monotone f) (hbdd : BddAbove <| range f) :
     Tendsto f atTop (𝓝 (⨆ i, f i)) :=
   by
   cases isEmpty_or_nonempty ι
-  exacts[tendsto_of_is_empty, tendsto_atTop_isLUB h_mono (isLUB_csupᵢ hbdd)]
-#align tendsto_at_top_csupr tendsto_atTop_csupᵢ
+  exacts[tendsto_of_is_empty, tendsto_atTop_isLUB h_mono (isLUB_ciSup hbdd)]
+#align tendsto_at_top_csupr tendsto_atTop_ciSup
 
-/- warning: tendsto_at_bot_csupr -> tendsto_atBot_csupᵢ is a dubious translation:
+/- warning: tendsto_at_bot_csupr -> tendsto_atBot_ciSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_3) ι (fun (i : ι) => f i))))
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_3) ι (fun (i : ι) => f i))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_3) ι (fun (i : ι) => f i))))
-Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_csupr tendsto_atBot_csupᵢₓ'. -/
-theorem tendsto_atBot_csupᵢ (h_anti : Antitone f) (hbdd : BddAbove <| range f) :
-    Tendsto f atBot (𝓝 (⨆ i, f i)) := by convert tendsto_atTop_csupᵢ h_anti.dual hbdd.dual
-#align tendsto_at_bot_csupr tendsto_atBot_csupᵢ
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_3) ι (fun (i : ι) => f i))))
+Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_csupr tendsto_atBot_ciSupₓ'. -/
+theorem tendsto_atBot_ciSup (h_anti : Antitone f) (hbdd : BddAbove <| range f) :
+    Tendsto f atBot (𝓝 (⨆ i, f i)) := by convert tendsto_atTop_ciSup h_anti.dual hbdd.dual
+#align tendsto_at_bot_csupr tendsto_atBot_ciSup
 
 end Csupr
 
@@ -176,79 +176,79 @@ section Cinfi
 
 variable [ConditionallyCompleteLattice α] [InfConvergenceClass α] {f : ι → α} {a : α}
 
-/- warning: tendsto_at_bot_cinfi -> tendsto_atBot_cinfᵢ is a dubious translation:
+/- warning: tendsto_at_bot_cinfi -> tendsto_atBot_ciInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_3) ι (fun (i : ι) => f i))))
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_3) ι (fun (i : ι) => f i))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_3) ι (fun (i : ι) => f i))))
-Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_cinfi tendsto_atBot_cinfᵢₓ'. -/
-theorem tendsto_atBot_cinfᵢ (h_mono : Monotone f) (hbdd : BddBelow <| range f) :
-    Tendsto f atBot (𝓝 (⨅ i, f i)) := by convert tendsto_atTop_csupᵢ h_mono.dual hbdd.dual
-#align tendsto_at_bot_cinfi tendsto_atBot_cinfᵢ
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_3) ι (fun (i : ι) => f i))))
+Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_cinfi tendsto_atBot_ciInfₓ'. -/
+theorem tendsto_atBot_ciInf (h_mono : Monotone f) (hbdd : BddBelow <| range f) :
+    Tendsto f atBot (𝓝 (⨅ i, f i)) := by convert tendsto_atTop_ciSup h_mono.dual hbdd.dual
+#align tendsto_at_bot_cinfi tendsto_atBot_ciInf
 
-/- warning: tendsto_at_top_cinfi -> tendsto_atTop_cinfᵢ is a dubious translation:
+/- warning: tendsto_at_top_cinfi -> tendsto_atTop_ciInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_3) ι (fun (i : ι) => f i))))
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_3) ι (fun (i : ι) => f i))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_3) ι (fun (i : ι) => f i))))
-Case conversion may be inaccurate. Consider using '#align tendsto_at_top_cinfi tendsto_atTop_cinfᵢₓ'. -/
-theorem tendsto_atTop_cinfᵢ (h_anti : Antitone f) (hbdd : BddBelow <| range f) :
-    Tendsto f atTop (𝓝 (⨅ i, f i)) := by convert tendsto_atBot_csupᵢ h_anti.dual hbdd.dual
-#align tendsto_at_top_cinfi tendsto_atTop_cinfᵢ
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_3) ι (fun (i : ι) => f i))))
+Case conversion may be inaccurate. Consider using '#align tendsto_at_top_cinfi tendsto_atTop_ciInfₓ'. -/
+theorem tendsto_atTop_ciInf (h_anti : Antitone f) (hbdd : BddBelow <| range f) :
+    Tendsto f atTop (𝓝 (⨅ i, f i)) := by convert tendsto_atBot_ciSup h_anti.dual hbdd.dual
+#align tendsto_at_top_cinfi tendsto_atTop_ciInf
 
 end Cinfi
 
-section supᵢ
+section iSup
 
 variable [CompleteLattice α] [SupConvergenceClass α] {f : ι → α} {a : α}
 
-/- warning: tendsto_at_top_supr -> tendsto_atTop_supᵢ is a dubious translation:
+/- warning: tendsto_at_top_supr -> tendsto_atTop_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
-Case conversion may be inaccurate. Consider using '#align tendsto_at_top_supr tendsto_atTop_supᵢₓ'. -/
-theorem tendsto_atTop_supᵢ (h_mono : Monotone f) : Tendsto f atTop (𝓝 (⨆ i, f i)) :=
-  tendsto_atTop_csupᵢ h_mono (OrderTop.bddAbove _)
-#align tendsto_at_top_supr tendsto_atTop_supᵢ
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
+Case conversion may be inaccurate. Consider using '#align tendsto_at_top_supr tendsto_atTop_iSupₓ'. -/
+theorem tendsto_atTop_iSup (h_mono : Monotone f) : Tendsto f atTop (𝓝 (⨆ i, f i)) :=
+  tendsto_atTop_ciSup h_mono (OrderTop.bddAbove _)
+#align tendsto_at_top_supr tendsto_atTop_iSup
 
-/- warning: tendsto_at_bot_supr -> tendsto_atBot_supᵢ is a dubious translation:
+/- warning: tendsto_at_bot_supr -> tendsto_atBot_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
-Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_supr tendsto_atBot_supᵢₓ'. -/
-theorem tendsto_atBot_supᵢ (h_anti : Antitone f) : Tendsto f atBot (𝓝 (⨆ i, f i)) :=
-  tendsto_atBot_csupᵢ h_anti (OrderTop.bddAbove _)
-#align tendsto_at_bot_supr tendsto_atBot_supᵢ
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
+Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_supr tendsto_atBot_iSupₓ'. -/
+theorem tendsto_atBot_iSup (h_anti : Antitone f) : Tendsto f atBot (𝓝 (⨆ i, f i)) :=
+  tendsto_atBot_ciSup h_anti (OrderTop.bddAbove _)
+#align tendsto_at_bot_supr tendsto_atBot_iSup
 
-end supᵢ
+end iSup
 
-section infᵢ
+section iInf
 
 variable [CompleteLattice α] [InfConvergenceClass α] {f : ι → α} {a : α}
 
-/- warning: tendsto_at_bot_infi -> tendsto_atBot_infᵢ is a dubious translation:
+/- warning: tendsto_at_bot_infi -> tendsto_atBot_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
-Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_infi tendsto_atBot_infᵢₓ'. -/
-theorem tendsto_atBot_infᵢ (h_mono : Monotone f) : Tendsto f atBot (𝓝 (⨅ i, f i)) :=
-  tendsto_atBot_cinfᵢ h_mono (OrderBot.bddBelow _)
-#align tendsto_at_bot_infi tendsto_atBot_infᵢ
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
+Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_infi tendsto_atBot_iInfₓ'. -/
+theorem tendsto_atBot_iInf (h_mono : Monotone f) : Tendsto f atBot (𝓝 (⨅ i, f i)) :=
+  tendsto_atBot_ciInf h_mono (OrderBot.bddBelow _)
+#align tendsto_at_bot_infi tendsto_atBot_iInf
 
-/- warning: tendsto_at_top_infi -> tendsto_atTop_infᵢ is a dubious translation:
+/- warning: tendsto_at_top_infi -> tendsto_atTop_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
-Case conversion may be inaccurate. Consider using '#align tendsto_at_top_infi tendsto_atTop_infᵢₓ'. -/
-theorem tendsto_atTop_infᵢ (h_anti : Antitone f) : Tendsto f atTop (𝓝 (⨅ i, f i)) :=
-  tendsto_atTop_cinfᵢ h_anti (OrderBot.bddBelow _)
-#align tendsto_at_top_infi tendsto_atTop_infᵢ
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
+Case conversion may be inaccurate. Consider using '#align tendsto_at_top_infi tendsto_atTop_iInfₓ'. -/
+theorem tendsto_atTop_iInf (h_anti : Antitone f) : Tendsto f atTop (𝓝 (⨅ i, f i)) :=
+  tendsto_atTop_ciInf h_anti (OrderBot.bddBelow _)
+#align tendsto_at_top_infi tendsto_atTop_iInf
 
-end infᵢ
+end iInf
 
 end
 
@@ -304,7 +304,7 @@ Case conversion may be inaccurate. Consider using '#align tendsto_of_monotone te
 theorem tendsto_of_monotone {ι α : Type _} [Preorder ι] [TopologicalSpace α]
     [ConditionallyCompleteLinearOrder α] [OrderTopology α] {f : ι → α} (h_mono : Monotone f) :
     Tendsto f atTop atTop ∨ ∃ l, Tendsto f atTop (𝓝 l) :=
-  if H : BddAbove (range f) then Or.inr ⟨_, tendsto_atTop_csupᵢ h_mono H⟩
+  if H : BddAbove (range f) then Or.inr ⟨_, tendsto_atTop_ciSup h_mono H⟩
   else Or.inl <| tendsto_atTop_atTop_of_monotone' h_mono H
 #align tendsto_of_monotone tendsto_of_monotone
 
@@ -436,54 +436,54 @@ theorem isGLB_of_tendsto_atTop [TopologicalSpace α] [Preorder α] [OrderClosedT
   @isGLB_of_tendsto_atBot α βᵒᵈ _ _ _ _ _ _ _ hf.dual_left ha
 #align is_glb_of_tendsto_at_top isGLB_of_tendsto_atTop
 
-/- warning: supr_eq_of_tendsto -> supᵢ_eq_of_tendsto is a dubious translation:
+/- warning: supr_eq_of_tendsto -> iSup_eq_of_tendsto is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompleteLinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_2))))] [_inst_4 : Nonempty.{succ u2} β] [_inst_5 : SemilatticeSup.{u2} β] {f : β -> α} {a : α}, (Monotone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_5)) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_2)))) f) -> (Filter.Tendsto.{u2, u1} β α f (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_5))) (nhds.{u1} α _inst_1 a)) -> (Eq.{succ u1} α (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_2))) β f) a)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : CompleteLinearOrder.{u1} α] [_inst_3 : OrderTopology.{u1} α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_2))))] [_inst_4 : Nonempty.{succ u2} β] [_inst_5 : SemilatticeSup.{u2} β] {f : β -> α} {a : α}, (Monotone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_5)) (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_2)))) f) -> (Filter.Tendsto.{u2, u1} β α f (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_5))) (nhds.{u1} α _inst_1 a)) -> (Eq.{succ u1} α (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α (CompleteLinearOrder.toCompleteLattice.{u1} α _inst_2))) β f) a)
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompleteLinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2))))] [_inst_4 : Nonempty.{succ u1} β] [_inst_5 : SemilatticeSup.{u1} β] {f : β -> α} {a : α}, (Monotone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5)) (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2)))) f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5))) (nhds.{u2} α _inst_1 a)) -> (Eq.{succ u2} α (supᵢ.{u2, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_2)))) β f) a)
-Case conversion may be inaccurate. Consider using '#align supr_eq_of_tendsto supᵢ_eq_of_tendstoₓ'. -/
-theorem supᵢ_eq_of_tendsto {α β} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompleteLinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2))))] [_inst_4 : Nonempty.{succ u1} β] [_inst_5 : SemilatticeSup.{u1} β] {f : β -> α} {a : α}, (Monotone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5)) (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2)))) f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5))) (nhds.{u2} α _inst_1 a)) -> (Eq.{succ u2} α (iSup.{u2, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_2)))) β f) a)
+Case conversion may be inaccurate. Consider using '#align supr_eq_of_tendsto iSup_eq_of_tendstoₓ'. -/
+theorem iSup_eq_of_tendsto {α β} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
     [Nonempty β] [SemilatticeSup β] {f : β → α} {a : α} (hf : Monotone f) :
-    Tendsto f atTop (𝓝 a) → supᵢ f = a :=
-  tendsto_nhds_unique (tendsto_atTop_supᵢ hf)
-#align supr_eq_of_tendsto supᵢ_eq_of_tendsto
+    Tendsto f atTop (𝓝 a) → iSup f = a :=
+  tendsto_nhds_unique (tendsto_atTop_iSup hf)
+#align supr_eq_of_tendsto iSup_eq_of_tendsto
 
-/- warning: infi_eq_of_tendsto -> infᵢ_eq_of_tendsto is a dubious translation:
+/- warning: infi_eq_of_tendsto -> iInf_eq_of_tendsto is a dubious translation:
 lean 3 declaration is
-  forall {β : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompleteLinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2))))] [_inst_4 : Nonempty.{succ u1} β] [_inst_5 : SemilatticeSup.{u1} β] {f : β -> α} {a : α}, (Antitone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5)) (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2)))) f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5))) (nhds.{u2} α _inst_1 a)) -> (Eq.{succ u2} α (infᵢ.{u2, succ u1} α (ConditionallyCompleteLattice.toHasInf.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2))) β f) a)
+  forall {β : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompleteLinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2))))] [_inst_4 : Nonempty.{succ u1} β] [_inst_5 : SemilatticeSup.{u1} β] {f : β -> α} {a : α}, (Antitone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5)) (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2)))) f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5))) (nhds.{u2} α _inst_1 a)) -> (Eq.{succ u2} α (iInf.{u2, succ u1} α (ConditionallyCompleteLattice.toHasInf.{u2} α (CompleteLattice.toConditionallyCompleteLattice.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2))) β f) a)
 but is expected to have type
-  forall {β : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompleteLinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2))))] [_inst_4 : Nonempty.{succ u1} β] [_inst_5 : SemilatticeSup.{u1} β] {f : β -> α} {a : α}, (Antitone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5)) (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2)))) f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5))) (nhds.{u2} α _inst_1 a)) -> (Eq.{succ u2} α (infᵢ.{u2, succ u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_2)))) β f) a)
-Case conversion may be inaccurate. Consider using '#align infi_eq_of_tendsto infᵢ_eq_of_tendstoₓ'. -/
-theorem infᵢ_eq_of_tendsto {α} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
+  forall {β : Type.{u1}} {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : CompleteLinearOrder.{u2} α] [_inst_3 : OrderTopology.{u2} α _inst_1 (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2))))] [_inst_4 : Nonempty.{succ u1} β] [_inst_5 : SemilatticeSup.{u1} β] {f : β -> α} {a : α}, (Antitone.{u1, u2} β α (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5)) (PartialOrder.toPreorder.{u2} α (CompleteSemilatticeInf.toPartialOrder.{u2} α (CompleteLattice.toCompleteSemilatticeInf.{u2} α (CompleteLinearOrder.toCompleteLattice.{u2} α _inst_2)))) f) -> (Filter.Tendsto.{u1, u2} β α f (Filter.atTop.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_5))) (nhds.{u2} α _inst_1 a)) -> (Eq.{succ u2} α (iInf.{u2, succ u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} α _inst_2)))) β f) a)
+Case conversion may be inaccurate. Consider using '#align infi_eq_of_tendsto iInf_eq_of_tendstoₓ'. -/
+theorem iInf_eq_of_tendsto {α} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
     [Nonempty β] [SemilatticeSup β] {f : β → α} {a : α} (hf : Antitone f) :
-    Tendsto f atTop (𝓝 a) → infᵢ f = a :=
-  tendsto_nhds_unique (tendsto_atTop_infᵢ hf)
-#align infi_eq_of_tendsto infᵢ_eq_of_tendsto
+    Tendsto f atTop (𝓝 a) → iInf f = a :=
+  tendsto_nhds_unique (tendsto_atTop_iInf hf)
+#align infi_eq_of_tendsto iInf_eq_of_tendsto
 
-/- warning: supr_eq_supr_subseq_of_monotone -> supᵢ_eq_supᵢ_subseq_of_monotone is a dubious translation:
+/- warning: supr_eq_supr_subseq_of_monotone -> iSup_eq_iSup_subseq_of_monotone is a dubious translation:
 lean 3 declaration is
-  forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {α : Type.{u3}} [_inst_1 : Preorder.{u2} ι₂] [_inst_2 : CompleteLattice.{u3} α] {l : Filter.{u1} ι₁} [_inst_3 : Filter.NeBot.{u1} ι₁ l] {f : ι₂ -> α} {φ : ι₁ -> ι₂}, (Monotone.{u2, u3} ι₂ α _inst_1 (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_2))) f) -> (Filter.Tendsto.{u1, u2} ι₁ ι₂ φ l (Filter.atTop.{u2} ι₂ _inst_1)) -> (Eq.{succ u3} α (supᵢ.{u3, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u3} α (CompleteLattice.toConditionallyCompleteLattice.{u3} α _inst_2)) ι₂ (fun (i : ι₂) => f i)) (supᵢ.{u3, succ u1} α (ConditionallyCompleteLattice.toHasSup.{u3} α (CompleteLattice.toConditionallyCompleteLattice.{u3} α _inst_2)) ι₁ (fun (i : ι₁) => f (φ i))))
+  forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {α : Type.{u3}} [_inst_1 : Preorder.{u2} ι₂] [_inst_2 : CompleteLattice.{u3} α] {l : Filter.{u1} ι₁} [_inst_3 : Filter.NeBot.{u1} ι₁ l] {f : ι₂ -> α} {φ : ι₁ -> ι₂}, (Monotone.{u2, u3} ι₂ α _inst_1 (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_2))) f) -> (Filter.Tendsto.{u1, u2} ι₁ ι₂ φ l (Filter.atTop.{u2} ι₂ _inst_1)) -> (Eq.{succ u3} α (iSup.{u3, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u3} α (CompleteLattice.toConditionallyCompleteLattice.{u3} α _inst_2)) ι₂ (fun (i : ι₂) => f i)) (iSup.{u3, succ u1} α (ConditionallyCompleteLattice.toHasSup.{u3} α (CompleteLattice.toConditionallyCompleteLattice.{u3} α _inst_2)) ι₁ (fun (i : ι₁) => f (φ i))))
 but is expected to have type
-  forall {ι₁ : Type.{u3}} {ι₂ : Type.{u2}} {α : Type.{u1}} [_inst_1 : Preorder.{u2} ι₂] [_inst_2 : CompleteLattice.{u1} α] {l : Filter.{u3} ι₁} [_inst_3 : Filter.NeBot.{u3} ι₁ l] {f : ι₂ -> α} {φ : ι₁ -> ι₂}, (Monotone.{u2, u1} ι₂ α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_2))) f) -> (Filter.Tendsto.{u3, u2} ι₁ ι₂ φ l (Filter.atTop.{u2} ι₂ _inst_1)) -> (Eq.{succ u1} α (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_2)) ι₂ (fun (i : ι₂) => f i)) (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_2)) ι₁ (fun (i : ι₁) => f (φ i))))
-Case conversion may be inaccurate. Consider using '#align supr_eq_supr_subseq_of_monotone supᵢ_eq_supᵢ_subseq_of_monotoneₓ'. -/
-theorem supᵢ_eq_supᵢ_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι₂] [CompleteLattice α]
+  forall {ι₁ : Type.{u3}} {ι₂ : Type.{u2}} {α : Type.{u1}} [_inst_1 : Preorder.{u2} ι₂] [_inst_2 : CompleteLattice.{u1} α] {l : Filter.{u3} ι₁} [_inst_3 : Filter.NeBot.{u3} ι₁ l] {f : ι₂ -> α} {φ : ι₁ -> ι₂}, (Monotone.{u2, u1} ι₂ α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_2))) f) -> (Filter.Tendsto.{u3, u2} ι₁ ι₂ φ l (Filter.atTop.{u2} ι₂ _inst_1)) -> (Eq.{succ u1} α (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_2)) ι₂ (fun (i : ι₂) => f i)) (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_2)) ι₁ (fun (i : ι₁) => f (φ i))))
+Case conversion may be inaccurate. Consider using '#align supr_eq_supr_subseq_of_monotone iSup_eq_iSup_subseq_of_monotoneₓ'. -/
+theorem iSup_eq_iSup_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι₂] [CompleteLattice α]
     {l : Filter ι₁} [l.ne_bot] {f : ι₂ → α} {φ : ι₁ → ι₂} (hf : Monotone f)
     (hφ : Tendsto φ l atTop) : (⨆ i, f i) = ⨆ i, f (φ i) :=
   le_antisymm
-    (supᵢ_mono' fun i =>
+    (iSup_mono' fun i =>
       Exists.imp (fun j (hj : i ≤ φ j) => hf hj) (hφ.Eventually <| eventually_ge_atTop i).exists)
-    (supᵢ_mono' fun i => ⟨φ i, le_rfl⟩)
-#align supr_eq_supr_subseq_of_monotone supᵢ_eq_supᵢ_subseq_of_monotone
+    (iSup_mono' fun i => ⟨φ i, le_rfl⟩)
+#align supr_eq_supr_subseq_of_monotone iSup_eq_iSup_subseq_of_monotone
 
-/- warning: infi_eq_infi_subseq_of_monotone -> infᵢ_eq_infᵢ_subseq_of_monotone is a dubious translation:
+/- warning: infi_eq_infi_subseq_of_monotone -> iInf_eq_iInf_subseq_of_monotone is a dubious translation:
 lean 3 declaration is
-  forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {α : Type.{u3}} [_inst_1 : Preorder.{u2} ι₂] [_inst_2 : CompleteLattice.{u3} α] {l : Filter.{u1} ι₁} [_inst_3 : Filter.NeBot.{u1} ι₁ l] {f : ι₂ -> α} {φ : ι₁ -> ι₂}, (Monotone.{u2, u3} ι₂ α _inst_1 (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_2))) f) -> (Filter.Tendsto.{u1, u2} ι₁ ι₂ φ l (Filter.atBot.{u2} ι₂ _inst_1)) -> (Eq.{succ u3} α (infᵢ.{u3, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u3} α (CompleteLattice.toConditionallyCompleteLattice.{u3} α _inst_2)) ι₂ (fun (i : ι₂) => f i)) (infᵢ.{u3, succ u1} α (ConditionallyCompleteLattice.toHasInf.{u3} α (CompleteLattice.toConditionallyCompleteLattice.{u3} α _inst_2)) ι₁ (fun (i : ι₁) => f (φ i))))
+  forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {α : Type.{u3}} [_inst_1 : Preorder.{u2} ι₂] [_inst_2 : CompleteLattice.{u3} α] {l : Filter.{u1} ι₁} [_inst_3 : Filter.NeBot.{u1} ι₁ l] {f : ι₂ -> α} {φ : ι₁ -> ι₂}, (Monotone.{u2, u3} ι₂ α _inst_1 (PartialOrder.toPreorder.{u3} α (CompleteSemilatticeInf.toPartialOrder.{u3} α (CompleteLattice.toCompleteSemilatticeInf.{u3} α _inst_2))) f) -> (Filter.Tendsto.{u1, u2} ι₁ ι₂ φ l (Filter.atBot.{u2} ι₂ _inst_1)) -> (Eq.{succ u3} α (iInf.{u3, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u3} α (CompleteLattice.toConditionallyCompleteLattice.{u3} α _inst_2)) ι₂ (fun (i : ι₂) => f i)) (iInf.{u3, succ u1} α (ConditionallyCompleteLattice.toHasInf.{u3} α (CompleteLattice.toConditionallyCompleteLattice.{u3} α _inst_2)) ι₁ (fun (i : ι₁) => f (φ i))))
 but is expected to have type
-  forall {ι₁ : Type.{u3}} {ι₂ : Type.{u2}} {α : Type.{u1}} [_inst_1 : Preorder.{u2} ι₂] [_inst_2 : CompleteLattice.{u1} α] {l : Filter.{u3} ι₁} [_inst_3 : Filter.NeBot.{u3} ι₁ l] {f : ι₂ -> α} {φ : ι₁ -> ι₂}, (Monotone.{u2, u1} ι₂ α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_2))) f) -> (Filter.Tendsto.{u3, u2} ι₁ ι₂ φ l (Filter.atBot.{u2} ι₂ _inst_1)) -> (Eq.{succ u1} α (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_2)) ι₂ (fun (i : ι₂) => f i)) (infᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_2)) ι₁ (fun (i : ι₁) => f (φ i))))
-Case conversion may be inaccurate. Consider using '#align infi_eq_infi_subseq_of_monotone infᵢ_eq_infᵢ_subseq_of_monotoneₓ'. -/
-theorem infᵢ_eq_infᵢ_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι₂] [CompleteLattice α]
+  forall {ι₁ : Type.{u3}} {ι₂ : Type.{u2}} {α : Type.{u1}} [_inst_1 : Preorder.{u2} ι₂] [_inst_2 : CompleteLattice.{u1} α] {l : Filter.{u3} ι₁} [_inst_3 : Filter.NeBot.{u3} ι₁ l] {f : ι₂ -> α} {φ : ι₁ -> ι₂}, (Monotone.{u2, u1} ι₂ α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_2))) f) -> (Filter.Tendsto.{u3, u2} ι₁ ι₂ φ l (Filter.atBot.{u2} ι₂ _inst_1)) -> (Eq.{succ u1} α (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_2)) ι₂ (fun (i : ι₂) => f i)) (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_2)) ι₁ (fun (i : ι₁) => f (φ i))))
+Case conversion may be inaccurate. Consider using '#align infi_eq_infi_subseq_of_monotone iInf_eq_iInf_subseq_of_monotoneₓ'. -/
+theorem iInf_eq_iInf_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι₂] [CompleteLattice α]
     {l : Filter ι₁} [l.ne_bot] {f : ι₂ → α} {φ : ι₁ → ι₂} (hf : Monotone f)
     (hφ : Tendsto φ l atBot) : (⨅ i, f i) = ⨅ i, f (φ i) :=
-  supᵢ_eq_supᵢ_subseq_of_monotone hf.dual hφ
-#align infi_eq_infi_subseq_of_monotone infᵢ_eq_infᵢ_subseq_of_monotone
+  iSup_eq_iSup_subseq_of_monotone hf.dual hφ
+#align infi_eq_infi_subseq_of_monotone iInf_eq_iInf_subseq_of_monotone
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ddec54a71a0dd025c05445d467f1a2b7d586a3ba

@@ -147,28 +147,28 @@ section Csupr
 
 variable [ConditionallyCompleteLattice α] [SupConvergenceClass α] {f : ι → α} {a : α}
 
-/- warning: tendsto_at_top_csupr -> tendsto_atTop_csupr is a dubious translation:
+/- warning: tendsto_at_top_csupr -> tendsto_atTop_csupᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_3) ι (fun (i : ι) => f i))))
 but is expected to have type
   forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_3) ι (fun (i : ι) => f i))))
-Case conversion may be inaccurate. Consider using '#align tendsto_at_top_csupr tendsto_atTop_csuprₓ'. -/
-theorem tendsto_atTop_csupr (h_mono : Monotone f) (hbdd : BddAbove <| range f) :
+Case conversion may be inaccurate. Consider using '#align tendsto_at_top_csupr tendsto_atTop_csupᵢₓ'. -/
+theorem tendsto_atTop_csupᵢ (h_mono : Monotone f) (hbdd : BddAbove <| range f) :
     Tendsto f atTop (𝓝 (⨆ i, f i)) :=
   by
   cases isEmpty_or_nonempty ι
   exacts[tendsto_of_is_empty, tendsto_atTop_isLUB h_mono (isLUB_csupᵢ hbdd)]
-#align tendsto_at_top_csupr tendsto_atTop_csupr
+#align tendsto_at_top_csupr tendsto_atTop_csupᵢ
 
-/- warning: tendsto_at_bot_csupr -> tendsto_atBot_csupr is a dubious translation:
+/- warning: tendsto_at_bot_csupr -> tendsto_atBot_csupᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_3) ι (fun (i : ι) => f i))))
 but is expected to have type
   forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_3) ι (fun (i : ι) => f i))))
-Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_csupr tendsto_atBot_csuprₓ'. -/
-theorem tendsto_atBot_csupr (h_anti : Antitone f) (hbdd : BddAbove <| range f) :
-    Tendsto f atBot (𝓝 (⨆ i, f i)) := by convert tendsto_atTop_csupr h_anti.dual hbdd.dual
-#align tendsto_at_bot_csupr tendsto_atBot_csupr
+Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_csupr tendsto_atBot_csupᵢₓ'. -/
+theorem tendsto_atBot_csupᵢ (h_anti : Antitone f) (hbdd : BddAbove <| range f) :
+    Tendsto f atBot (𝓝 (⨆ i, f i)) := by convert tendsto_atTop_csupᵢ h_anti.dual hbdd.dual
+#align tendsto_at_bot_csupr tendsto_atBot_csupᵢ
 
 end Csupr
 
@@ -176,25 +176,25 @@ section Cinfi
 
 variable [ConditionallyCompleteLattice α] [InfConvergenceClass α] {f : ι → α} {a : α}
 
-/- warning: tendsto_at_bot_cinfi -> tendsto_atBot_cinfi is a dubious translation:
+/- warning: tendsto_at_bot_cinfi -> tendsto_atBot_cinfᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_3) ι (fun (i : ι) => f i))))
 but is expected to have type
   forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_3) ι (fun (i : ι) => f i))))
-Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_cinfi tendsto_atBot_cinfiₓ'. -/
-theorem tendsto_atBot_cinfi (h_mono : Monotone f) (hbdd : BddBelow <| range f) :
-    Tendsto f atBot (𝓝 (⨅ i, f i)) := by convert tendsto_atTop_csupr h_mono.dual hbdd.dual
-#align tendsto_at_bot_cinfi tendsto_atBot_cinfi
+Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_cinfi tendsto_atBot_cinfᵢₓ'. -/
+theorem tendsto_atBot_cinfᵢ (h_mono : Monotone f) (hbdd : BddBelow <| range f) :
+    Tendsto f atBot (𝓝 (⨅ i, f i)) := by convert tendsto_atTop_csupᵢ h_mono.dual hbdd.dual
+#align tendsto_at_bot_cinfi tendsto_atBot_cinfᵢ
 
-/- warning: tendsto_at_top_cinfi -> tendsto_atTop_cinfi is a dubious translation:
+/- warning: tendsto_at_top_cinfi -> tendsto_atTop_cinfᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_3) ι (fun (i : ι) => f i))))
 but is expected to have type
   forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : ConditionallyCompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) f) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_3)))) (Set.range.{u1, succ u2} α ι f)) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_3) ι (fun (i : ι) => f i))))
-Case conversion may be inaccurate. Consider using '#align tendsto_at_top_cinfi tendsto_atTop_cinfiₓ'. -/
-theorem tendsto_atTop_cinfi (h_anti : Antitone f) (hbdd : BddBelow <| range f) :
-    Tendsto f atTop (𝓝 (⨅ i, f i)) := by convert tendsto_atBot_csupr h_anti.dual hbdd.dual
-#align tendsto_at_top_cinfi tendsto_atTop_cinfi
+Case conversion may be inaccurate. Consider using '#align tendsto_at_top_cinfi tendsto_atTop_cinfᵢₓ'. -/
+theorem tendsto_atTop_cinfᵢ (h_anti : Antitone f) (hbdd : BddBelow <| range f) :
+    Tendsto f atTop (𝓝 (⨅ i, f i)) := by convert tendsto_atBot_csupᵢ h_anti.dual hbdd.dual
+#align tendsto_at_top_cinfi tendsto_atTop_cinfᵢ
 
 end Cinfi
 
@@ -209,7 +209,7 @@ but is expected to have type
   forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
 Case conversion may be inaccurate. Consider using '#align tendsto_at_top_supr tendsto_atTop_supᵢₓ'. -/
 theorem tendsto_atTop_supᵢ (h_mono : Monotone f) : Tendsto f atTop (𝓝 (⨆ i, f i)) :=
-  tendsto_atTop_csupr h_mono (OrderTop.bddAbove _)
+  tendsto_atTop_csupᵢ h_mono (OrderTop.bddAbove _)
 #align tendsto_at_top_supr tendsto_atTop_supᵢ
 
 /- warning: tendsto_at_bot_supr -> tendsto_atBot_supᵢ is a dubious translation:
@@ -219,7 +219,7 @@ but is expected to have type
   forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : SupConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
 Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_supr tendsto_atBot_supᵢₓ'. -/
 theorem tendsto_atBot_supᵢ (h_anti : Antitone f) : Tendsto f atBot (𝓝 (⨆ i, f i)) :=
-  tendsto_atBot_csupr h_anti (OrderTop.bddAbove _)
+  tendsto_atBot_csupᵢ h_anti (OrderTop.bddAbove _)
 #align tendsto_at_bot_supr tendsto_atBot_supᵢ
 
 end supᵢ
@@ -235,7 +235,7 @@ but is expected to have type
   forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Monotone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atBot.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
 Case conversion may be inaccurate. Consider using '#align tendsto_at_bot_infi tendsto_atBot_infᵢₓ'. -/
 theorem tendsto_atBot_infᵢ (h_mono : Monotone f) : Tendsto f atBot (𝓝 (⨅ i, f i)) :=
-  tendsto_atBot_cinfi h_mono (OrderBot.bddBelow _)
+  tendsto_atBot_cinfᵢ h_mono (OrderBot.bddBelow _)
 #align tendsto_at_bot_infi tendsto_atBot_infᵢ
 
 /- warning: tendsto_at_top_infi -> tendsto_atTop_infᵢ is a dubious translation:
@@ -245,7 +245,7 @@ but is expected to have type
   forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : Preorder.{u2} ι] [_inst_2 : TopologicalSpace.{u1} α] [_inst_3 : CompleteLattice.{u1} α] [_inst_4 : InfConvergenceClass.{u1} α (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) _inst_2] {f : ι -> α}, (Antitone.{u2, u1} ι α _inst_1 (PartialOrder.toPreorder.{u1} α (CompleteSemilatticeInf.toPartialOrder.{u1} α (CompleteLattice.toCompleteSemilatticeInf.{u1} α _inst_3))) f) -> (Filter.Tendsto.{u2, u1} ι α f (Filter.atTop.{u2} ι _inst_1) (nhds.{u1} α _inst_2 (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (CompleteLattice.toConditionallyCompleteLattice.{u1} α _inst_3)) ι (fun (i : ι) => f i))))
 Case conversion may be inaccurate. Consider using '#align tendsto_at_top_infi tendsto_atTop_infᵢₓ'. -/
 theorem tendsto_atTop_infᵢ (h_anti : Antitone f) : Tendsto f atTop (𝓝 (⨅ i, f i)) :=
-  tendsto_atTop_cinfi h_anti (OrderBot.bddBelow _)
+  tendsto_atTop_cinfᵢ h_anti (OrderBot.bddBelow _)
 #align tendsto_at_top_infi tendsto_atTop_infᵢ
 
 end infᵢ
@@ -304,7 +304,7 @@ Case conversion may be inaccurate. Consider using '#align tendsto_of_monotone te
 theorem tendsto_of_monotone {ι α : Type _} [Preorder ι] [TopologicalSpace α]
     [ConditionallyCompleteLinearOrder α] [OrderTopology α] {f : ι → α} (h_mono : Monotone f) :
     Tendsto f atTop atTop ∨ ∃ l, Tendsto f atTop (𝓝 l) :=
-  if H : BddAbove (range f) then Or.inr ⟨_, tendsto_atTop_csupr h_mono H⟩
+  if H : BddAbove (range f) then Or.inr ⟨_, tendsto_atTop_csupᵢ h_mono H⟩
   else Or.inl <| tendsto_atTop_atTop_of_monotone' h_mono H
 #align tendsto_of_monotone tendsto_of_monotone
 

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

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

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

@@ -30,7 +30,8 @@ monotone convergence
 
 open Filter Set Function
 
-open Filter Topology Classical
+open scoped Classical
+open Filter Topology
 
 variable {α β : Type*}
 

Add tendsto_iff_tendsto_subseq_of_antitone, next to tendsto_iff_tendsto_subseq_of_monotone.

Co-authored-by: Rémy Degenne <remydegenne@gmail.com>

@@ -244,6 +244,12 @@ theorem tendsto_iff_tendsto_subseq_of_monotone {ι₁ ι₂ α : Type*} [Semilat
     · rwa [tendsto_nhds_unique h (hl'.comp hg)]
 #align tendsto_iff_tendsto_subseq_of_monotone tendsto_iff_tendsto_subseq_of_monotone
 
+theorem tendsto_iff_tendsto_subseq_of_antitone {ι₁ ι₂ α : Type*} [SemilatticeSup ι₁] [Preorder ι₂]
+    [Nonempty ι₁] [TopologicalSpace α] [ConditionallyCompleteLinearOrder α] [OrderTopology α]
+    [NoMinOrder α] {f : ι₂ → α} {φ : ι₁ → ι₂} {l : α} (hf : Antitone f)
+    (hg : Tendsto φ atTop atTop) : Tendsto f atTop (𝓝 l) ↔ Tendsto (f ∘ φ) atTop (𝓝 l) :=
+  tendsto_iff_tendsto_subseq_of_monotone (α := αᵒᵈ) hf hg
+
 /-! The next family of results, such as `isLUB_of_tendsto_atTop` and `iSup_eq_of_tendsto`, are
 converses to the standard fact that bounded monotone functions converge. They state, that if a
 monotone function `f` tends to `a` along `Filter.atTop`, then that value `a` is a least upper bound

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -190,7 +190,7 @@ instance Prod.supConvergenceClass
   have B : Tendsto (fun x : s => (x : α × β).2) atTop (𝓝 b) :=
     tendsto_atTop_isLUB (monotone_snd.restrict s) h.2
   convert A.prod_mk_nhds B
-  -- porting note: previously required below to close
+  -- Porting note: previously required below to close
   -- ext1 ⟨⟨x, y⟩, h⟩
   -- rfl
 

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

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

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

@@ -74,7 +74,7 @@ instance (priority := 100) LinearOrder.supConvergenceClass [TopologicalSpace α]
   refine' ⟨fun a s ha => tendsto_order.2 ⟨fun b hb => _, fun b hb => _⟩⟩
   · rcases ha.exists_between hb with ⟨c, hcs, bc, bca⟩
     lift c to s using hcs
-    refine' (eventually_ge_atTop c).mono fun x hx => bc.trans_le hx
+    exact (eventually_ge_atTop c).mono fun x hx => bc.trans_le hx
   · exact eventually_of_forall fun x => (ha.1 x.2).trans_lt hb
 #align linear_order.Sup_convergence_class LinearOrder.supConvergenceClass
 

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

This follows on from #6964.

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

@@ -94,8 +94,8 @@ variable [Preorder α] [SupConvergenceClass α] {f : ι → α} {a : α}
 
 theorem tendsto_atTop_isLUB (h_mono : Monotone f) (ha : IsLUB (Set.range f) a) :
     Tendsto f atTop (𝓝 a) := by
-  suffices : Tendsto (rangeFactorization f) atTop atTop
-  exact (SupConvergenceClass.tendsto_coe_atTop_isLUB _ _ ha).comp this
+  suffices Tendsto (rangeFactorization f) atTop atTop from
+    (SupConvergenceClass.tendsto_coe_atTop_isLUB _ _ ha).comp this
   exact h_mono.rangeFactorization.tendsto_atTop_atTop fun b => b.2.imp fun a ha => ha.ge
 #align tendsto_at_top_is_lub tendsto_atTop_isLUB
 

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

@@ -227,6 +227,12 @@ theorem tendsto_of_monotone {ι α : Type*} [Preorder ι] [TopologicalSpace α]
   else Or.inl <| tendsto_atTop_atTop_of_monotone' h_mono H
 #align tendsto_of_monotone tendsto_of_monotone
 
+theorem tendsto_of_antitone {ι α : Type*} [Preorder ι] [TopologicalSpace α]
+    [ConditionallyCompleteLinearOrder α] [OrderTopology α] {f : ι → α} (h_mono : Antitone f) :
+    Tendsto f atTop atBot ∨ ∃ l, Tendsto f atTop (𝓝 l) :=
+  @tendsto_of_monotone ι αᵒᵈ _ _ _ _ _ h_mono
+#align tendsto_of_antitone tendsto_of_antitone
+
 theorem tendsto_iff_tendsto_subseq_of_monotone {ι₁ ι₂ α : Type*} [SemilatticeSup ι₁] [Preorder ι₂]
     [Nonempty ι₁] [TopologicalSpace α] [ConditionallyCompleteLinearOrder α] [OrderTopology α]
     [NoMaxOrder α] {f : ι₂ → α} {φ : ι₁ → ι₂} {l : α} (hf : Monotone f)

@@ -319,8 +319,22 @@ theorem iSup_eq_iSup_subseq_of_monotone {ι₁ ι₂ α : Type*} [Preorder ι₂
     (iSup_mono' fun i => ⟨φ i, le_rfl⟩)
 #align supr_eq_supr_subseq_of_monotone iSup_eq_iSup_subseq_of_monotone
 
+theorem iSup_eq_iSup_subseq_of_antitone {ι₁ ι₂ α : Type*} [Preorder ι₂] [CompleteLattice α]
+    {l : Filter ι₁} [l.NeBot] {f : ι₂ → α} {φ : ι₁ → ι₂} (hf : Antitone f)
+    (hφ : Tendsto φ l atBot) : ⨆ i, f i = ⨆ i, f (φ i) :=
+  le_antisymm
+    (iSup_mono' fun i =>
+      Exists.imp (fun j (hj : φ j ≤ i) => hf hj) (hφ.eventually <| eventually_le_atBot i).exists)
+    (iSup_mono' fun i => ⟨φ i, le_rfl⟩)
+#align supr_eq_supr_subseq_of_antitone iSup_eq_iSup_subseq_of_antitone
+
 theorem iInf_eq_iInf_subseq_of_monotone {ι₁ ι₂ α : Type*} [Preorder ι₂] [CompleteLattice α]
     {l : Filter ι₁} [l.NeBot] {f : ι₂ → α} {φ : ι₁ → ι₂} (hf : Monotone f)
     (hφ : Tendsto φ l atBot) : ⨅ i, f i = ⨅ i, f (φ i) :=
   iSup_eq_iSup_subseq_of_monotone hf.dual hφ
 #align infi_eq_infi_subseq_of_monotone iInf_eq_iInf_subseq_of_monotone
+
+theorem iInf_eq_iInf_subseq_of_antitone {ι₁ ι₂ α : Type*} [Preorder ι₂] [CompleteLattice α]
+    {l : Filter ι₁} [l.NeBot] {f : ι₂ → α} {φ : ι₁ → ι₂} (hf : Antitone f)
+    (hφ : Tendsto φ l atTop) : ⨅ i, f i = ⨅ i, f (φ i) :=
+  iSup_eq_iSup_subseq_of_antitone hf.dual hφ

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

This has nice performance benefits.

@@ -32,7 +32,7 @@ open Filter Set Function
 
 open Filter Topology Classical
 
-variable {α β : Type _}
+variable {α β : Type*}
 
 /-- We say that `α` is a `SupConvergenceClass` if the following holds. Let `f : ι → α` be a
 monotone function, let `a : α` be a least upper bound of `Set.range f`. Then `f x` tends to `𝓝 a`
@@ -40,7 +40,7 @@ monotone function, let `a : α` be a least upper bound of `Set.range f`. Then `f
 `f = CoeTC.coe` in the definition, then prove it for any `f` in `tendsto_atTop_isLUB`.
 
 This property holds for linear orders with order topology as well as their products. -/
-class SupConvergenceClass (α : Type _) [Preorder α] [TopologicalSpace α] : Prop where
+class SupConvergenceClass (α : Type*) [Preorder α] [TopologicalSpace α] : Prop where
   /-- proof that a monotone function tends to `𝓝 a` as `x → ∞` -/
   tendsto_coe_atTop_isLUB :
     ∀ (a : α) (s : Set α), IsLUB s a → Tendsto (CoeTC.coe : s → α) atTop (𝓝 a)
@@ -52,7 +52,7 @@ as `x → -∞` (formally, at the filter `Filter.atBot`). We require this for `
 `f = CoeTC.coe` in the definition, then prove it for any `f` in `tendsto_atBot_isGLB`.
 
 This property holds for linear orders with order topology as well as their products. -/
-class InfConvergenceClass (α : Type _) [Preorder α] [TopologicalSpace α] : Prop where
+class InfConvergenceClass (α : Type*) [Preorder α] [TopologicalSpace α] : Prop where
   /-- proof that a monotone function tends to `𝓝 a` as `x → -∞`-/
   tendsto_coe_atBot_isGLB :
     ∀ (a : α) (s : Set α), IsGLB s a → Tendsto (CoeTC.coe : s → α) atBot (𝓝 a)
@@ -86,7 +86,7 @@ instance (priority := 100) LinearOrder.infConvergenceClass [TopologicalSpace α]
 
 section
 
-variable {ι : Type _} [Preorder ι] [TopologicalSpace α]
+variable {ι : Type*} [Preorder ι] [TopologicalSpace α]
 
 section IsLUB
 
@@ -199,35 +199,35 @@ instance [Preorder α] [Preorder β] [TopologicalSpace α] [TopologicalSpace β]
   show InfConvergenceClass (αᵒᵈ × βᵒᵈ)ᵒᵈ from OrderDual.infConvergenceClass
 
 instance Pi.supConvergenceClass
-    {ι : Type _} {α : ι → Type _} [∀ i, Preorder (α i)] [∀ i, TopologicalSpace (α i)]
+    {ι : Type*} {α : ι → Type*} [∀ i, Preorder (α i)] [∀ i, TopologicalSpace (α i)]
     [∀ i, SupConvergenceClass (α i)] : SupConvergenceClass (∀ i, α i) := by
   refine' ⟨fun f s h => _⟩
   simp only [isLUB_pi, ← range_restrict] at h
   exact tendsto_pi_nhds.2 fun i => tendsto_atTop_isLUB ((monotone_eval _).restrict _) (h i)
 
 instance Pi.infConvergenceClass
-    {ι : Type _} {α : ι → Type _} [∀ i, Preorder (α i)] [∀ i, TopologicalSpace (α i)]
+    {ι : Type*} {α : ι → Type*} [∀ i, Preorder (α i)] [∀ i, TopologicalSpace (α i)]
     [∀ i, InfConvergenceClass (α i)] : InfConvergenceClass (∀ i, α i) :=
   show InfConvergenceClass (∀ i, (α i)ᵒᵈ)ᵒᵈ from OrderDual.infConvergenceClass
 
-instance Pi.supConvergenceClass' {ι : Type _} [Preorder α] [TopologicalSpace α]
+instance Pi.supConvergenceClass' {ι : Type*} [Preorder α] [TopologicalSpace α]
     [SupConvergenceClass α] : SupConvergenceClass (ι → α) :=
   supConvergenceClass
 #align pi.Sup_convergence_class' Pi.supConvergenceClass'
 
-instance Pi.infConvergenceClass' {ι : Type _} [Preorder α] [TopologicalSpace α]
+instance Pi.infConvergenceClass' {ι : Type*} [Preorder α] [TopologicalSpace α]
     [InfConvergenceClass α] : InfConvergenceClass (ι → α) :=
   Pi.infConvergenceClass
 #align pi.Inf_convergence_class' Pi.infConvergenceClass'
 
-theorem tendsto_of_monotone {ι α : Type _} [Preorder ι] [TopologicalSpace α]
+theorem tendsto_of_monotone {ι α : Type*} [Preorder ι] [TopologicalSpace α]
     [ConditionallyCompleteLinearOrder α] [OrderTopology α] {f : ι → α} (h_mono : Monotone f) :
     Tendsto f atTop atTop ∨ ∃ l, Tendsto f atTop (𝓝 l) :=
   if H : BddAbove (range f) then Or.inr ⟨_, tendsto_atTop_ciSup h_mono H⟩
   else Or.inl <| tendsto_atTop_atTop_of_monotone' h_mono H
 #align tendsto_of_monotone tendsto_of_monotone
 
-theorem tendsto_iff_tendsto_subseq_of_monotone {ι₁ ι₂ α : Type _} [SemilatticeSup ι₁] [Preorder ι₂]
+theorem tendsto_iff_tendsto_subseq_of_monotone {ι₁ ι₂ α : Type*} [SemilatticeSup ι₁] [Preorder ι₂]
     [Nonempty ι₁] [TopologicalSpace α] [ConditionallyCompleteLinearOrder α] [OrderTopology α]
     [NoMaxOrder α] {f : ι₂ → α} {φ : ι₁ → ι₂} {l : α} (hf : Monotone f)
     (hg : Tendsto φ atTop atTop) : Tendsto f atTop (𝓝 l) ↔ Tendsto (f ∘ φ) atTop (𝓝 l) := by
@@ -310,7 +310,7 @@ theorem iInf_eq_of_tendsto {α} [TopologicalSpace α] [CompleteLinearOrder α] [
   tendsto_nhds_unique (tendsto_atTop_iInf hf)
 #align infi_eq_of_tendsto iInf_eq_of_tendsto
 
-theorem iSup_eq_iSup_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι₂] [CompleteLattice α]
+theorem iSup_eq_iSup_subseq_of_monotone {ι₁ ι₂ α : Type*} [Preorder ι₂] [CompleteLattice α]
     {l : Filter ι₁} [l.NeBot] {f : ι₂ → α} {φ : ι₁ → ι₂} (hf : Monotone f)
     (hφ : Tendsto φ l atTop) : ⨆ i, f i = ⨆ i, f (φ i) :=
   le_antisymm
@@ -319,7 +319,7 @@ theorem iSup_eq_iSup_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι
     (iSup_mono' fun i => ⟨φ i, le_rfl⟩)
 #align supr_eq_supr_subseq_of_monotone iSup_eq_iSup_subseq_of_monotone
 
-theorem iInf_eq_iInf_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι₂] [CompleteLattice α]
+theorem iInf_eq_iInf_subseq_of_monotone {ι₁ ι₂ α : Type*} [Preorder ι₂] [CompleteLattice α]
     {l : Filter ι₁} [l.NeBot] {f : ι₂ → α} {φ : ι₁ → ι₂} (hf : Monotone f)
     (hφ : Tendsto φ l atBot) : ⨅ i, f i = ⨅ i, f (φ i) :=
   iSup_eq_iSup_subseq_of_monotone hf.dual hφ

@@ -179,8 +179,9 @@ end iInf
 
 end
 
-instance supConvergenceClassProd [Preorder α] [Preorder β] [TopologicalSpace α] [TopologicalSpace β]
-  [SupConvergenceClass α] [SupConvergenceClass β] : SupConvergenceClass (α × β) := by
+instance Prod.supConvergenceClass
+    [Preorder α] [Preorder β] [TopologicalSpace α] [TopologicalSpace β]
+    [SupConvergenceClass α] [SupConvergenceClass β] : SupConvergenceClass (α × β) := by
   constructor
   rintro ⟨a, b⟩ s h
   rw [isLUB_prod, ← range_restrict, ← range_restrict] at h
@@ -209,15 +210,15 @@ instance Pi.infConvergenceClass
     [∀ i, InfConvergenceClass (α i)] : InfConvergenceClass (∀ i, α i) :=
   show InfConvergenceClass (∀ i, (α i)ᵒᵈ)ᵒᵈ from OrderDual.infConvergenceClass
 
-instance Pi.Sup_convergence_class' {ι : Type _} [Preorder α] [TopologicalSpace α]
+instance Pi.supConvergenceClass' {ι : Type _} [Preorder α] [TopologicalSpace α]
     [SupConvergenceClass α] : SupConvergenceClass (ι → α) :=
   supConvergenceClass
-#align pi.Sup_convergence_class' Pi.Sup_convergence_class'
+#align pi.Sup_convergence_class' Pi.supConvergenceClass'
 
-instance Pi.Inf_convergence_class' {ι : Type _} [Preorder α] [TopologicalSpace α]
+instance Pi.infConvergenceClass' {ι : Type _} [Preorder α] [TopologicalSpace α]
     [InfConvergenceClass α] : InfConvergenceClass (ι → α) :=
   Pi.infConvergenceClass
-#align pi.Inf_convergence_class' Pi.Inf_convergence_class'
+#align pi.Inf_convergence_class' Pi.infConvergenceClass'
 
 theorem tendsto_of_monotone {ι α : Type _} [Preorder ι] [TopologicalSpace α]
     [ConditionallyCompleteLinearOrder α] [OrderTopology α] {f : ι → α} (h_mono : Monotone f) :

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

@@ -245,7 +245,6 @@ for the range of `f`.
 Related theorems above (`IsLUB.isLUB_of_tendsto`, `IsGLB.isGLB_of_tendsto` etc) cover the case
 when `f x` tends to `a` as `x` tends to some point `b` in the domain. -/
 
-set_option autoImplicit false
 theorem Monotone.ge_of_tendsto [TopologicalSpace α] [Preorder α] [OrderClosedTopology α]
     [SemilatticeSup β] {f : β → α} {a : α} (hf : Monotone f) (ha : Tendsto f atTop (𝓝 a)) (b : β) :
     f b ≤ a :=

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth, Yury Kudryashov
-
-! This file was ported from Lean 3 source module topology.algebra.order.monotone_convergence
-! leanprover-community/mathlib commit 4c19a16e4b705bf135cf9a80ac18fcc99c438514
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Order.Basic
 
+#align_import topology.algebra.order.monotone_convergence from "leanprover-community/mathlib"@"4c19a16e4b705bf135cf9a80ac18fcc99c438514"
+
 /-!
 # Bounded monotone sequences converge
 

@@ -315,7 +315,7 @@ theorem iInf_eq_of_tendsto {α} [TopologicalSpace α] [CompleteLinearOrder α] [
 
 theorem iSup_eq_iSup_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι₂] [CompleteLattice α]
     {l : Filter ι₁} [l.NeBot] {f : ι₂ → α} {φ : ι₁ → ι₂} (hf : Monotone f)
-    (hφ : Tendsto φ l atTop) : (⨆ i, f i) = ⨆ i, f (φ i) :=
+    (hφ : Tendsto φ l atTop) : ⨆ i, f i = ⨆ i, f (φ i) :=
   le_antisymm
     (iSup_mono' fun i =>
       Exists.imp (fun j (hj : i ≤ φ j) => hf hj) (hφ.eventually <| eventually_ge_atTop i).exists)
@@ -324,6 +324,6 @@ theorem iSup_eq_iSup_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι
 
 theorem iInf_eq_iInf_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι₂] [CompleteLattice α]
     {l : Filter ι₁} [l.NeBot] {f : ι₂ → α} {φ : ι₁ → ι₂} (hf : Monotone f)
-    (hφ : Tendsto φ l atBot) : (⨅ i, f i) = ⨅ i, f (φ i) :=
+    (hφ : Tendsto φ l atBot) : ⨅ i, f i = ⨅ i, f (φ i) :=
   iSup_eq_iSup_subseq_of_monotone hf.dual hφ
 #align infi_eq_infi_subseq_of_monotone iInf_eq_iInf_subseq_of_monotone

Too often tempted to change these during other PRs, so doing a mass edit here.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

@@ -129,7 +129,7 @@ variable [ConditionallyCompleteLattice α] [SupConvergenceClass α] {f : ι →
 theorem tendsto_atTop_ciSup (h_mono : Monotone f) (hbdd : BddAbove <| range f) :
     Tendsto f atTop (𝓝 (⨆ i, f i)) := by
   cases isEmpty_or_nonempty ι
-  exacts[tendsto_of_isEmpty, tendsto_atTop_isLUB h_mono (isLUB_ciSup hbdd)]
+  exacts [tendsto_of_isEmpty, tendsto_atTop_isLUB h_mono (isLUB_ciSup hbdd)]
 #align tendsto_at_top_csupr tendsto_atTop_ciSup
 
 theorem tendsto_atBot_ciSup (h_anti : Antitone f) (hbdd : BddAbove <| range f) :

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>

@@ -122,63 +122,63 @@ theorem tendsto_atTop_isGLB (h_anti : Antitone f) (ha : IsGLB (Set.range f) a) :
 
 end IsGLB
 
-section Csupᵢ
+section CiSup
 
 variable [ConditionallyCompleteLattice α] [SupConvergenceClass α] {f : ι → α} {a : α}
 
-theorem tendsto_atTop_csupᵢ (h_mono : Monotone f) (hbdd : BddAbove <| range f) :
+theorem tendsto_atTop_ciSup (h_mono : Monotone f) (hbdd : BddAbove <| range f) :
     Tendsto f atTop (𝓝 (⨆ i, f i)) := by
   cases isEmpty_or_nonempty ι
-  exacts[tendsto_of_isEmpty, tendsto_atTop_isLUB h_mono (isLUB_csupᵢ hbdd)]
-#align tendsto_at_top_csupr tendsto_atTop_csupᵢ
+  exacts[tendsto_of_isEmpty, tendsto_atTop_isLUB h_mono (isLUB_ciSup hbdd)]
+#align tendsto_at_top_csupr tendsto_atTop_ciSup
 
-theorem tendsto_atBot_csupᵢ (h_anti : Antitone f) (hbdd : BddAbove <| range f) :
-    Tendsto f atBot (𝓝 (⨆ i, f i)) := by convert tendsto_atTop_csupᵢ h_anti.dual hbdd.dual using 1
-#align tendsto_at_bot_csupr tendsto_atBot_csupᵢ
+theorem tendsto_atBot_ciSup (h_anti : Antitone f) (hbdd : BddAbove <| range f) :
+    Tendsto f atBot (𝓝 (⨆ i, f i)) := by convert tendsto_atTop_ciSup h_anti.dual hbdd.dual using 1
+#align tendsto_at_bot_csupr tendsto_atBot_ciSup
 
-end Csupᵢ
+end CiSup
 
-section Cinfᵢ
+section CiInf
 
 variable [ConditionallyCompleteLattice α] [InfConvergenceClass α] {f : ι → α} {a : α}
 
-theorem tendsto_atBot_cinfᵢ (h_mono : Monotone f) (hbdd : BddBelow <| range f) :
-    Tendsto f atBot (𝓝 (⨅ i, f i)) := by convert tendsto_atTop_csupᵢ h_mono.dual hbdd.dual using 1
-#align tendsto_at_bot_cinfi tendsto_atBot_cinfᵢ
+theorem tendsto_atBot_ciInf (h_mono : Monotone f) (hbdd : BddBelow <| range f) :
+    Tendsto f atBot (𝓝 (⨅ i, f i)) := by convert tendsto_atTop_ciSup h_mono.dual hbdd.dual using 1
+#align tendsto_at_bot_cinfi tendsto_atBot_ciInf
 
-theorem tendsto_atTop_cinfᵢ (h_anti : Antitone f) (hbdd : BddBelow <| range f) :
-    Tendsto f atTop (𝓝 (⨅ i, f i)) := by convert tendsto_atBot_csupᵢ h_anti.dual hbdd.dual using 1
-#align tendsto_at_top_cinfi tendsto_atTop_cinfᵢ
+theorem tendsto_atTop_ciInf (h_anti : Antitone f) (hbdd : BddBelow <| range f) :
+    Tendsto f atTop (𝓝 (⨅ i, f i)) := by convert tendsto_atBot_ciSup h_anti.dual hbdd.dual using 1
+#align tendsto_at_top_cinfi tendsto_atTop_ciInf
 
-end Cinfᵢ
+end CiInf
 
-section supᵢ
+section iSup
 
 variable [CompleteLattice α] [SupConvergenceClass α] {f : ι → α} {a : α}
 
-theorem tendsto_atTop_supᵢ (h_mono : Monotone f) : Tendsto f atTop (𝓝 (⨆ i, f i)) :=
-  tendsto_atTop_csupᵢ h_mono (OrderTop.bddAbove _)
-#align tendsto_at_top_supr tendsto_atTop_supᵢ
+theorem tendsto_atTop_iSup (h_mono : Monotone f) : Tendsto f atTop (𝓝 (⨆ i, f i)) :=
+  tendsto_atTop_ciSup h_mono (OrderTop.bddAbove _)
+#align tendsto_at_top_supr tendsto_atTop_iSup
 
-theorem tendsto_atBot_supᵢ (h_anti : Antitone f) : Tendsto f atBot (𝓝 (⨆ i, f i)) :=
-  tendsto_atBot_csupᵢ h_anti (OrderTop.bddAbove _)
-#align tendsto_at_bot_supr tendsto_atBot_supᵢ
+theorem tendsto_atBot_iSup (h_anti : Antitone f) : Tendsto f atBot (𝓝 (⨆ i, f i)) :=
+  tendsto_atBot_ciSup h_anti (OrderTop.bddAbove _)
+#align tendsto_at_bot_supr tendsto_atBot_iSup
 
-end supᵢ
+end iSup
 
-section infᵢ
+section iInf
 
 variable [CompleteLattice α] [InfConvergenceClass α] {f : ι → α} {a : α}
 
-theorem tendsto_atBot_infᵢ (h_mono : Monotone f) : Tendsto f atBot (𝓝 (⨅ i, f i)) :=
-  tendsto_atBot_cinfᵢ h_mono (OrderBot.bddBelow _)
-#align tendsto_at_bot_infi tendsto_atBot_infᵢ
+theorem tendsto_atBot_iInf (h_mono : Monotone f) : Tendsto f atBot (𝓝 (⨅ i, f i)) :=
+  tendsto_atBot_ciInf h_mono (OrderBot.bddBelow _)
+#align tendsto_at_bot_infi tendsto_atBot_iInf
 
-theorem tendsto_atTop_infᵢ (h_anti : Antitone f) : Tendsto f atTop (𝓝 (⨅ i, f i)) :=
-  tendsto_atTop_cinfᵢ h_anti (OrderBot.bddBelow _)
-#align tendsto_at_top_infi tendsto_atTop_infᵢ
+theorem tendsto_atTop_iInf (h_anti : Antitone f) : Tendsto f atTop (𝓝 (⨅ i, f i)) :=
+  tendsto_atTop_ciInf h_anti (OrderBot.bddBelow _)
+#align tendsto_at_top_infi tendsto_atTop_iInf
 
-end infᵢ
+end iInf
 
 end
 
@@ -225,7 +225,7 @@ instance Pi.Inf_convergence_class' {ι : Type _} [Preorder α] [TopologicalSpace
 theorem tendsto_of_monotone {ι α : Type _} [Preorder ι] [TopologicalSpace α]
     [ConditionallyCompleteLinearOrder α] [OrderTopology α] {f : ι → α} (h_mono : Monotone f) :
     Tendsto f atTop atTop ∨ ∃ l, Tendsto f atTop (𝓝 l) :=
-  if H : BddAbove (range f) then Or.inr ⟨_, tendsto_atTop_csupᵢ h_mono H⟩
+  if H : BddAbove (range f) then Or.inr ⟨_, tendsto_atTop_ciSup h_mono H⟩
   else Or.inl <| tendsto_atTop_atTop_of_monotone' h_mono H
 #align tendsto_of_monotone tendsto_of_monotone
 
@@ -240,7 +240,7 @@ theorem tendsto_iff_tendsto_subseq_of_monotone {ι₁ ι₂ α : Type _} [Semila
     · rwa [tendsto_nhds_unique h (hl'.comp hg)]
 #align tendsto_iff_tendsto_subseq_of_monotone tendsto_iff_tendsto_subseq_of_monotone
 
-/-! The next family of results, such as `isLUB_of_tendsto_atTop` and `supᵢ_eq_of_tendsto`, are
+/-! The next family of results, such as `isLUB_of_tendsto_atTop` and `iSup_eq_of_tendsto`, are
 converses to the standard fact that bounded monotone functions converge. They state, that if a
 monotone function `f` tends to `a` along `Filter.atTop`, then that value `a` is a least upper bound
 for the range of `f`.
@@ -301,29 +301,29 @@ theorem isGLB_of_tendsto_atTop [TopologicalSpace α] [Preorder α] [OrderClosedT
   @isGLB_of_tendsto_atBot α βᵒᵈ _ _ _ _ _ _ _ hf.dual_left ha
 #align is_glb_of_tendsto_at_top isGLB_of_tendsto_atTop
 
-theorem supᵢ_eq_of_tendsto {α β} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
+theorem iSup_eq_of_tendsto {α β} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
     [Nonempty β] [SemilatticeSup β] {f : β → α} {a : α} (hf : Monotone f) :
-    Tendsto f atTop (𝓝 a) → supᵢ f = a :=
-  tendsto_nhds_unique (tendsto_atTop_supᵢ hf)
-#align supr_eq_of_tendsto supᵢ_eq_of_tendsto
+    Tendsto f atTop (𝓝 a) → iSup f = a :=
+  tendsto_nhds_unique (tendsto_atTop_iSup hf)
+#align supr_eq_of_tendsto iSup_eq_of_tendsto
 
-theorem infᵢ_eq_of_tendsto {α} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
+theorem iInf_eq_of_tendsto {α} [TopologicalSpace α] [CompleteLinearOrder α] [OrderTopology α]
     [Nonempty β] [SemilatticeSup β] {f : β → α} {a : α} (hf : Antitone f) :
-    Tendsto f atTop (𝓝 a) → infᵢ f = a :=
-  tendsto_nhds_unique (tendsto_atTop_infᵢ hf)
-#align infi_eq_of_tendsto infᵢ_eq_of_tendsto
+    Tendsto f atTop (𝓝 a) → iInf f = a :=
+  tendsto_nhds_unique (tendsto_atTop_iInf hf)
+#align infi_eq_of_tendsto iInf_eq_of_tendsto
 
-theorem supᵢ_eq_supᵢ_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι₂] [CompleteLattice α]
+theorem iSup_eq_iSup_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι₂] [CompleteLattice α]
     {l : Filter ι₁} [l.NeBot] {f : ι₂ → α} {φ : ι₁ → ι₂} (hf : Monotone f)
     (hφ : Tendsto φ l atTop) : (⨆ i, f i) = ⨆ i, f (φ i) :=
   le_antisymm
-    (supᵢ_mono' fun i =>
+    (iSup_mono' fun i =>
       Exists.imp (fun j (hj : i ≤ φ j) => hf hj) (hφ.eventually <| eventually_ge_atTop i).exists)
-    (supᵢ_mono' fun i => ⟨φ i, le_rfl⟩)
-#align supr_eq_supr_subseq_of_monotone supᵢ_eq_supᵢ_subseq_of_monotone
+    (iSup_mono' fun i => ⟨φ i, le_rfl⟩)
+#align supr_eq_supr_subseq_of_monotone iSup_eq_iSup_subseq_of_monotone
 
-theorem infᵢ_eq_infᵢ_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι₂] [CompleteLattice α]
+theorem iInf_eq_iInf_subseq_of_monotone {ι₁ ι₂ α : Type _} [Preorder ι₂] [CompleteLattice α]
     {l : Filter ι₁} [l.NeBot] {f : ι₂ → α} {φ : ι₁ → ι₂} (hf : Monotone f)
     (hφ : Tendsto φ l atBot) : (⨅ i, f i) = ⨅ i, f (φ i) :=
-  supᵢ_eq_supᵢ_subseq_of_monotone hf.dual hφ
-#align infi_eq_infi_subseq_of_monotone infᵢ_eq_infᵢ_subseq_of_monotone
+  iSup_eq_iSup_subseq_of_monotone hf.dual hφ
+#align infi_eq_infi_subseq_of_monotone iInf_eq_iInf_subseq_of_monotone

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

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

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

@@ -103,7 +103,7 @@ theorem tendsto_atTop_isLUB (h_mono : Monotone f) (ha : IsLUB (Set.range f) a) :
 #align tendsto_at_top_is_lub tendsto_atTop_isLUB
 
 theorem tendsto_atBot_isLUB (h_anti : Antitone f) (ha : IsLUB (Set.range f) a) :
-    Tendsto f atBot (𝓝 a) := by convert tendsto_atTop_isLUB h_anti.dual_left ha
+    Tendsto f atBot (𝓝 a) := by convert tendsto_atTop_isLUB h_anti.dual_left ha using 1
 #align tendsto_at_bot_is_lub tendsto_atBot_isLUB
 
 end IsLUB
@@ -113,11 +113,11 @@ section IsGLB
 variable [Preorder α] [InfConvergenceClass α] {f : ι → α} {a : α}
 
 theorem tendsto_atBot_isGLB (h_mono : Monotone f) (ha : IsGLB (Set.range f) a) :
-    Tendsto f atBot (𝓝 a) := by convert tendsto_atTop_isLUB h_mono.dual ha.dual
+    Tendsto f atBot (𝓝 a) := by convert tendsto_atTop_isLUB h_mono.dual ha.dual using 1
 #align tendsto_at_bot_is_glb tendsto_atBot_isGLB
 
 theorem tendsto_atTop_isGLB (h_anti : Antitone f) (ha : IsGLB (Set.range f) a) :
-    Tendsto f atTop (𝓝 a) := by convert tendsto_atBot_isLUB h_anti.dual ha.dual
+    Tendsto f atTop (𝓝 a) := by convert tendsto_atBot_isLUB h_anti.dual ha.dual using 1
 #align tendsto_at_top_is_glb tendsto_atTop_isGLB
 
 end IsGLB
@@ -133,7 +133,7 @@ theorem tendsto_atTop_csupᵢ (h_mono : Monotone f) (hbdd : BddAbove <| range f)
 #align tendsto_at_top_csupr tendsto_atTop_csupᵢ
 
 theorem tendsto_atBot_csupᵢ (h_anti : Antitone f) (hbdd : BddAbove <| range f) :
-    Tendsto f atBot (𝓝 (⨆ i, f i)) := by convert tendsto_atTop_csupᵢ h_anti.dual hbdd.dual
+    Tendsto f atBot (𝓝 (⨆ i, f i)) := by convert tendsto_atTop_csupᵢ h_anti.dual hbdd.dual using 1
 #align tendsto_at_bot_csupr tendsto_atBot_csupᵢ
 
 end Csupᵢ
@@ -143,11 +143,11 @@ section Cinfᵢ
 variable [ConditionallyCompleteLattice α] [InfConvergenceClass α] {f : ι → α} {a : α}
 
 theorem tendsto_atBot_cinfᵢ (h_mono : Monotone f) (hbdd : BddBelow <| range f) :
-    Tendsto f atBot (𝓝 (⨅ i, f i)) := by convert tendsto_atTop_csupᵢ h_mono.dual hbdd.dual
+    Tendsto f atBot (𝓝 (⨅ i, f i)) := by convert tendsto_atTop_csupᵢ h_mono.dual hbdd.dual using 1
 #align tendsto_at_bot_cinfi tendsto_atBot_cinfᵢ
 
 theorem tendsto_atTop_cinfᵢ (h_anti : Antitone f) (hbdd : BddBelow <| range f) :
-    Tendsto f atTop (𝓝 (⨅ i, f i)) := by convert tendsto_atBot_csupᵢ h_anti.dual hbdd.dual
+    Tendsto f atTop (𝓝 (⨅ i, f i)) := by convert tendsto_atBot_csupᵢ h_anti.dual hbdd.dual using 1
 #align tendsto_at_top_cinfi tendsto_atTop_cinfᵢ
 
 end Cinfᵢ

API changes:

• Add HasSum.sum_range_add, sum_add_tsum_nat_add', and tsum_eq_zero_add'. We had these (or stronger) results for topological groups. These versions works for monoids.
• Rename tendsto_atTop_csupr to tendsto_atTop_csupᵢ, tendsto_atBot_csupr to tendsto_atBot_csupᵢ, tendsto_atBot_cinfi to tendsto_atBot_cinfᵢ, and tendsto_atTop_cinfi to tendsto_atTop_cinfᵢ.
• Add a shortcut instance for T5Space ENNReal.
• Add ENNReal.nhdsWithin_Ioi_one_neBot, ENNReal.nhdsWithin_Ioi_nat_neBot, ENNReal.nhdsWithin_Ioi_ofNat_nebot, and ENNReal.nhdsWithin_Iio_neBot.
• Add ENNReal.hasBasis_nhds_of_ne_top and ENNReal.hasBasis_nhds_of_ne_top'.
• Add ENNReal.binfᵢ_le_nhds and ENNReal.tendsto_nhds_of_Icc.
• Use Real.nnabs instead of nnnorm to avoid dependency on analysis.normed.group.basic (forward-port of leanprover-community/mathlib#18562).
• Add ENNReal.tsum_eq_limsup_sum_nat.
• Add ENNReal.tsum_comp_le_tsum_of_injective, ENNReal.tsum_le_tsum_comp_of_surjective, use them to golf some proofs.
• Add ENNReal.tsum_bunionᵢ_le_tsum, ENNReal.tsum_unionᵢ_le_tsum. We had versions of these lemmas for finite collections. The proofs for infinite collections are simpler.

Most of these changes were done to fix some long proofs: it was easier for me (@urkud) to add supporting lemmas and golf the proof than to fix the original code.

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

@@ -122,46 +122,46 @@ theorem tendsto_atTop_isGLB (h_anti : Antitone f) (ha : IsGLB (Set.range f) a) :
 
 end IsGLB
 
-section Csupr
+section Csupᵢ
 
 variable [ConditionallyCompleteLattice α] [SupConvergenceClass α] {f : ι → α} {a : α}
 
-theorem tendsto_atTop_csupr (h_mono : Monotone f) (hbdd : BddAbove <| range f) :
+theorem tendsto_atTop_csupᵢ (h_mono : Monotone f) (hbdd : BddAbove <| range f) :
     Tendsto f atTop (𝓝 (⨆ i, f i)) := by
   cases isEmpty_or_nonempty ι
   exacts[tendsto_of_isEmpty, tendsto_atTop_isLUB h_mono (isLUB_csupᵢ hbdd)]
-#align tendsto_at_top_csupr tendsto_atTop_csupr
+#align tendsto_at_top_csupr tendsto_atTop_csupᵢ
 
-theorem tendsto_atBot_csupr (h_anti : Antitone f) (hbdd : BddAbove <| range f) :
-    Tendsto f atBot (𝓝 (⨆ i, f i)) := by convert tendsto_atTop_csupr h_anti.dual hbdd.dual
-#align tendsto_at_bot_csupr tendsto_atBot_csupr
+theorem tendsto_atBot_csupᵢ (h_anti : Antitone f) (hbdd : BddAbove <| range f) :
+    Tendsto f atBot (𝓝 (⨆ i, f i)) := by convert tendsto_atTop_csupᵢ h_anti.dual hbdd.dual
+#align tendsto_at_bot_csupr tendsto_atBot_csupᵢ
 
-end Csupr
+end Csupᵢ
 
-section Cinfi
+section Cinfᵢ
 
 variable [ConditionallyCompleteLattice α] [InfConvergenceClass α] {f : ι → α} {a : α}
 
-theorem tendsto_atBot_cinfi (h_mono : Monotone f) (hbdd : BddBelow <| range f) :
-    Tendsto f atBot (𝓝 (⨅ i, f i)) := by convert tendsto_atTop_csupr h_mono.dual hbdd.dual
-#align tendsto_at_bot_cinfi tendsto_atBot_cinfi
+theorem tendsto_atBot_cinfᵢ (h_mono : Monotone f) (hbdd : BddBelow <| range f) :
+    Tendsto f atBot (𝓝 (⨅ i, f i)) := by convert tendsto_atTop_csupᵢ h_mono.dual hbdd.dual
+#align tendsto_at_bot_cinfi tendsto_atBot_cinfᵢ
 
-theorem tendsto_atTop_cinfi (h_anti : Antitone f) (hbdd : BddBelow <| range f) :
-    Tendsto f atTop (𝓝 (⨅ i, f i)) := by convert tendsto_atBot_csupr h_anti.dual hbdd.dual
-#align tendsto_at_top_cinfi tendsto_atTop_cinfi
+theorem tendsto_atTop_cinfᵢ (h_anti : Antitone f) (hbdd : BddBelow <| range f) :
+    Tendsto f atTop (𝓝 (⨅ i, f i)) := by convert tendsto_atBot_csupᵢ h_anti.dual hbdd.dual
+#align tendsto_at_top_cinfi tendsto_atTop_cinfᵢ
 
-end Cinfi
+end Cinfᵢ
 
 section supᵢ
 
 variable [CompleteLattice α] [SupConvergenceClass α] {f : ι → α} {a : α}
 
 theorem tendsto_atTop_supᵢ (h_mono : Monotone f) : Tendsto f atTop (𝓝 (⨆ i, f i)) :=
-  tendsto_atTop_csupr h_mono (OrderTop.bddAbove _)
+  tendsto_atTop_csupᵢ h_mono (OrderTop.bddAbove _)
 #align tendsto_at_top_supr tendsto_atTop_supᵢ
 
 theorem tendsto_atBot_supᵢ (h_anti : Antitone f) : Tendsto f atBot (𝓝 (⨆ i, f i)) :=
-  tendsto_atBot_csupr h_anti (OrderTop.bddAbove _)
+  tendsto_atBot_csupᵢ h_anti (OrderTop.bddAbove _)
 #align tendsto_at_bot_supr tendsto_atBot_supᵢ
 
 end supᵢ
@@ -171,11 +171,11 @@ section infᵢ
 variable [CompleteLattice α] [InfConvergenceClass α] {f : ι → α} {a : α}
 
 theorem tendsto_atBot_infᵢ (h_mono : Monotone f) : Tendsto f atBot (𝓝 (⨅ i, f i)) :=
-  tendsto_atBot_cinfi h_mono (OrderBot.bddBelow _)
+  tendsto_atBot_cinfᵢ h_mono (OrderBot.bddBelow _)
 #align tendsto_at_bot_infi tendsto_atBot_infᵢ
 
 theorem tendsto_atTop_infᵢ (h_anti : Antitone f) : Tendsto f atTop (𝓝 (⨅ i, f i)) :=
-  tendsto_atTop_cinfi h_anti (OrderBot.bddBelow _)
+  tendsto_atTop_cinfᵢ h_anti (OrderBot.bddBelow _)
 #align tendsto_at_top_infi tendsto_atTop_infᵢ
 
 end infᵢ
@@ -225,7 +225,7 @@ instance Pi.Inf_convergence_class' {ι : Type _} [Preorder α] [TopologicalSpace
 theorem tendsto_of_monotone {ι α : Type _} [Preorder ι] [TopologicalSpace α]
     [ConditionallyCompleteLinearOrder α] [OrderTopology α] {f : ι → α} (h_mono : Monotone f) :
     Tendsto f atTop atTop ∨ ∃ l, Tendsto f atTop (𝓝 l) :=
-  if H : BddAbove (range f) then Or.inr ⟨_, tendsto_atTop_csupr h_mono H⟩
+  if H : BddAbove (range f) then Or.inr ⟨_, tendsto_atTop_csupᵢ h_mono H⟩
   else Or.inl <| tendsto_atTop_atTop_of_monotone' h_mono H
 #align tendsto_of_monotone tendsto_of_monotone
 

import Mathlib.Tactic.LibrarySearch is often useful to include while porting a theory file, but should be deleted before committing. This PR cleans up some cases where it did not get deleted:

• Mathlib/Data/Set/Pointwise/SMul.lean in https://github.com/leanprover-community/mathlib4/pull/1473
• Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean in https://github.com/leanprover-community/mathlib4/pull/2097

@@ -9,7 +9,6 @@ Authors: Heather Macbeth, Yury Kudryashov
 ! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Order.Basic
-import Mathlib.Tactic.LibrarySearch
 
 /-!
 # Bounded monotone sequences converge

port of topology.algebra.order.monotone_convergence

Co-authored-by: Moritz Doll <moritz.doll@googlemail.com> Co-authored-by: Johan Commelin <johan@commelin.net>