topology.instances.ereal ⟷ Mathlib.Topology.Instances.EReal

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

@@ -64,7 +64,7 @@ instance : SecondCountableTopology EReal :=
         [rw [show s = ⋃ q ∈ {q : ℚ | a < (q : ℝ)}, {b | ((q : ℝ) : EReal) < b} by ext x;
             simpa only [hs, exists_prop, mem_Union] using lt_iff_exists_rat_btwn];
         rw [show s = ⋃ q ∈ {q : ℚ | ((q : ℝ) : EReal) < a}, {b | b < ((q : ℝ) : EReal)} by ext x;
-            simpa only [hs, and_comm', exists_prop, mem_Union] using lt_iff_exists_rat_btwn]] <;>
+            simpa only [hs, and_comm, exists_prop, mem_Union] using lt_iff_exists_rat_btwn]] <;>
       · apply isOpen_iUnion; intro q
         apply isOpen_iUnion; intro hq
         apply generate_open.basic

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

@@ -4,9 +4,9 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
 import Data.Rat.Encodable
-import Data.Real.Ereal
-import Topology.Algebra.Order.MonotoneContinuity
-import Topology.Instances.Ennreal
+import Data.Real.EReal
+import Topology.Order.MonotoneContinuity
+import Topology.Instances.ENNReal
 
 #align_import topology.instances.ereal from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
 
@@ -239,7 +239,7 @@ theorem continuous_coe_ennreal_iff {f : α → ℝ≥0∞} :
 /-! ### Neighborhoods of infinity -/
 
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a «expr ≠ » «expr⊤»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (a «expr ≠ » «expr⊤»()) -/
 #print EReal.nhds_top /-
 theorem nhds_top : 𝓝 (⊤ : EReal) = ⨅ (a) (_ : a ≠ ⊤), 𝓟 (Ioi a) :=
   nhds_top_order.trans <| by simp [lt_top_iff_ne_top, Ioi]
@@ -276,7 +276,7 @@ theorem tendsto_nhds_top_iff_real {α : Type _} {m : α → EReal} {f : Filter 
 #align ereal.tendsto_nhds_top_iff_real EReal.tendsto_nhds_top_iff_real
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a «expr ≠ » «expr⊥»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (a «expr ≠ » «expr⊥»()) -/
 #print EReal.nhds_bot /-
 theorem nhds_bot : 𝓝 (⊥ : EReal) = ⨅ (a) (_ : a ≠ ⊥), 𝓟 (Iio a) :=
   nhds_bot_order.trans <| by simp [bot_lt_iff_ne_bot]

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

@@ -157,7 +157,7 @@ theorem tendsto_toReal {a : EReal} (ha : a ≠ ⊤) (h'a : a ≠ ⊥) :
 #print EReal.continuousOn_toReal /-
 theorem continuousOn_toReal : ContinuousOn EReal.toReal ({⊥, ⊤}ᶜ : Set EReal) := fun a ha =>
   ContinuousAt.continuousWithinAt
-    (tendsto_toReal (by simp [not_or] at ha ; exact ha.2) (by simp [not_or] at ha ; exact ha.1))
+    (tendsto_toReal (by simp [not_or] at ha; exact ha.2) (by simp [not_or] at ha; exact ha.1))
 #align ereal.continuous_on_to_real EReal.continuousOn_toReal
 -/
 

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

@@ -3,10 +3,10 @@ Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathbin.Data.Rat.Encodable
-import Mathbin.Data.Real.Ereal
-import Mathbin.Topology.Algebra.Order.MonotoneContinuity
-import Mathbin.Topology.Instances.Ennreal
+import Data.Rat.Encodable
+import Data.Real.Ereal
+import Topology.Algebra.Order.MonotoneContinuity
+import Topology.Instances.Ennreal
 
 #align_import topology.instances.ereal from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
 
@@ -239,7 +239,7 @@ theorem continuous_coe_ennreal_iff {f : α → ℝ≥0∞} :
 /-! ### Neighborhoods of infinity -/
 
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ≠ » «expr⊤»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a «expr ≠ » «expr⊤»()) -/
 #print EReal.nhds_top /-
 theorem nhds_top : 𝓝 (⊤ : EReal) = ⨅ (a) (_ : a ≠ ⊤), 𝓟 (Ioi a) :=
   nhds_top_order.trans <| by simp [lt_top_iff_ne_top, Ioi]
@@ -276,7 +276,7 @@ theorem tendsto_nhds_top_iff_real {α : Type _} {m : α → EReal} {f : Filter 
 #align ereal.tendsto_nhds_top_iff_real EReal.tendsto_nhds_top_iff_real
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ≠ » «expr⊥»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (a «expr ≠ » «expr⊥»()) -/
 #print EReal.nhds_bot /-
 theorem nhds_bot : 𝓝 (⊥ : EReal) = ⨅ (a) (_ : a ≠ ⊥), 𝓟 (Iio a) :=
   nhds_bot_order.trans <| by simp [bot_lt_iff_ne_bot]

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module topology.instances.ereal
-! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Rat.Encodable
 import Mathbin.Data.Real.Ereal
 import Mathbin.Topology.Algebra.Order.MonotoneContinuity
 import Mathbin.Topology.Instances.Ennreal
 
+#align_import topology.instances.ereal from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
+
 /-!
 # Topological structure on `ereal`
 
@@ -242,7 +239,7 @@ theorem continuous_coe_ennreal_iff {f : α → ℝ≥0∞} :
 /-! ### Neighborhoods of infinity -/
 
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a «expr ≠ » «expr⊤»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ≠ » «expr⊤»()) -/
 #print EReal.nhds_top /-
 theorem nhds_top : 𝓝 (⊤ : EReal) = ⨅ (a) (_ : a ≠ ⊤), 𝓟 (Ioi a) :=
   nhds_top_order.trans <| by simp [lt_top_iff_ne_top, Ioi]
@@ -279,7 +276,7 @@ theorem tendsto_nhds_top_iff_real {α : Type _} {m : α → EReal} {f : Filter 
 #align ereal.tendsto_nhds_top_iff_real EReal.tendsto_nhds_top_iff_real
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a «expr ≠ » «expr⊥»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ≠ » «expr⊥»()) -/
 #print EReal.nhds_bot /-
 theorem nhds_bot : 𝓝 (⊥ : EReal) = ⨅ (a) (_ : a ≠ ⊥), 𝓟 (Iio a) :=
   nhds_bot_order.trans <| by simp [bot_lt_iff_ne_bot]

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

@@ -76,6 +76,7 @@ instance : SecondCountableTopology EReal :=
 /-! ### Real coercion -/
 
 
+#print EReal.embedding_coe /-
 theorem embedding_coe : Embedding (coe : ℝ → EReal) :=
   ⟨⟨by
       refine' le_antisymm _ _
@@ -99,7 +100,9 @@ theorem embedding_coe : Embedding (coe : ℝ → EReal) :=
         exact ⟨Iio a, isOpen_Iio, by simp [Iio]⟩⟩, fun a b => by
     simp only [imp_self, EReal.coe_eq_coe_iff]⟩
 #align ereal.embedding_coe EReal.embedding_coe
+-/
 
+#print EReal.openEmbedding_coe /-
 theorem openEmbedding_coe : OpenEmbedding (coe : ℝ → EReal) :=
   ⟨embedding_coe, by
     convert @isOpen_Ioo EReal _ _ _ ⊥ ⊤
@@ -109,30 +112,42 @@ theorem openEmbedding_coe : OpenEmbedding (coe : ℝ → EReal) :=
     · simp only [mem_range_self, mem_Ioo, bot_lt_coe, coe_lt_top, and_self_iff]
     · simp only [mem_range, right_mem_Ioo, exists_false, coe_ne_top]⟩
 #align ereal.open_embedding_coe EReal.openEmbedding_coe
+-/
 
+#print EReal.tendsto_coe /-
 @[norm_cast]
 theorem tendsto_coe {α : Type _} {f : Filter α} {m : α → ℝ} {a : ℝ} :
     Tendsto (fun a => (m a : EReal)) f (𝓝 ↑a) ↔ Tendsto m f (𝓝 a) :=
   embedding_coe.tendsto_nhds_iff.symm
 #align ereal.tendsto_coe EReal.tendsto_coe
+-/
 
+#print continuous_coe_real_ereal /-
 theorem continuous_coe_real_ereal : Continuous (coe : ℝ → EReal) :=
   embedding_coe.Continuous
 #align continuous_coe_real_ereal continuous_coe_real_ereal
+-/
 
+#print EReal.continuous_coe_iff /-
 theorem continuous_coe_iff {f : α → ℝ} : (Continuous fun a => (f a : EReal)) ↔ Continuous f :=
   embedding_coe.continuous_iff.symm
 #align ereal.continuous_coe_iff EReal.continuous_coe_iff
+-/
 
+#print EReal.nhds_coe /-
 theorem nhds_coe {r : ℝ} : 𝓝 (r : EReal) = (𝓝 r).map coe :=
   (openEmbedding_coe.map_nhds_eq r).symm
 #align ereal.nhds_coe EReal.nhds_coe
+-/
 
+#print EReal.nhds_coe_coe /-
 theorem nhds_coe_coe {r p : ℝ} :
     𝓝 ((r : EReal), (p : EReal)) = (𝓝 (r, p)).map fun p : ℝ × ℝ => (p.1, p.2) :=
   ((openEmbedding_coe.Prod openEmbedding_coe).map_nhds_eq (r, p)).symm
 #align ereal.nhds_coe_coe EReal.nhds_coe_coe
+-/
 
+#print EReal.tendsto_toReal /-
 theorem tendsto_toReal {a : EReal} (ha : a ≠ ⊤) (h'a : a ≠ ⊥) :
     Tendsto EReal.toReal (𝓝 a) (𝓝 a.toReal) :=
   by
@@ -140,12 +155,16 @@ theorem tendsto_toReal {a : EReal} (ha : a ≠ ⊤) (h'a : a ≠ ⊥) :
   rw [nhds_coe, tendsto_map'_iff]
   exact tendsto_id
 #align ereal.tendsto_to_real EReal.tendsto_toReal
+-/
 
+#print EReal.continuousOn_toReal /-
 theorem continuousOn_toReal : ContinuousOn EReal.toReal ({⊥, ⊤}ᶜ : Set EReal) := fun a ha =>
   ContinuousAt.continuousWithinAt
     (tendsto_toReal (by simp [not_or] at ha ; exact ha.2) (by simp [not_or] at ha ; exact ha.1))
 #align ereal.continuous_on_to_real EReal.continuousOn_toReal
+-/
 
+#print EReal.neBotTopHomeomorphReal /-
 /-- The set of finite `ereal` numbers is homeomorphic to `ℝ`. -/
 def neBotTopHomeomorphReal : ({⊥, ⊤}ᶜ : Set EReal) ≃ₜ ℝ :=
   {
@@ -153,10 +172,12 @@ def neBotTopHomeomorphReal : ({⊥, ⊤}ᶜ : Set EReal) ≃ₜ ℝ :=
     continuous_toFun := continuousOn_iff_continuous_restrict.1 continuousOn_toReal
     continuous_invFun := continuous_coe_real_ereal.subtype_mk _ }
 #align ereal.ne_bot_top_homeomorph_real EReal.neBotTopHomeomorphReal
+-/
 
 /-! ### ennreal coercion -/
 
 
+#print EReal.embedding_coe_ennreal /-
 theorem embedding_coe_ennreal : Embedding (coe : ℝ≥0∞ → EReal) :=
   ⟨⟨by
       refine' le_antisymm _ _
@@ -195,30 +216,40 @@ theorem embedding_coe_ennreal : Embedding (coe : ℝ≥0∞ → EReal) :=
         exact ⟨Iio a, isOpen_Iio, by simp [Iio]⟩⟩, fun a b => by
     simp only [imp_self, coe_ennreal_eq_coe_ennreal_iff]⟩
 #align ereal.embedding_coe_ennreal EReal.embedding_coe_ennreal
+-/
 
+#print EReal.tendsto_coe_ennreal /-
 @[norm_cast]
 theorem tendsto_coe_ennreal {α : Type _} {f : Filter α} {m : α → ℝ≥0∞} {a : ℝ≥0∞} :
     Tendsto (fun a => (m a : EReal)) f (𝓝 ↑a) ↔ Tendsto m f (𝓝 a) :=
   embedding_coe_ennreal.tendsto_nhds_iff.symm
 #align ereal.tendsto_coe_ennreal EReal.tendsto_coe_ennreal
+-/
 
+#print continuous_coe_ennreal_ereal /-
 theorem continuous_coe_ennreal_ereal : Continuous (coe : ℝ≥0∞ → EReal) :=
   embedding_coe_ennreal.Continuous
 #align continuous_coe_ennreal_ereal continuous_coe_ennreal_ereal
+-/
 
+#print EReal.continuous_coe_ennreal_iff /-
 theorem continuous_coe_ennreal_iff {f : α → ℝ≥0∞} :
     (Continuous fun a => (f a : EReal)) ↔ Continuous f :=
   embedding_coe_ennreal.continuous_iff.symm
 #align ereal.continuous_coe_ennreal_iff EReal.continuous_coe_ennreal_iff
+-/
 
 /-! ### Neighborhoods of infinity -/
 
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a «expr ≠ » «expr⊤»()) -/
+#print EReal.nhds_top /-
 theorem nhds_top : 𝓝 (⊤ : EReal) = ⨅ (a) (_ : a ≠ ⊤), 𝓟 (Ioi a) :=
   nhds_top_order.trans <| by simp [lt_top_iff_ne_top, Ioi]
 #align ereal.nhds_top EReal.nhds_top
+-/
 
+#print EReal.nhds_top' /-
 theorem nhds_top' : 𝓝 (⊤ : EReal) = ⨅ a : ℝ, 𝓟 (Ioi a) :=
   by
   rw [nhds_top]
@@ -230,24 +261,32 @@ theorem nhds_top' : 𝓝 (⊤ : EReal) = ⨅ a : ℝ, 𝓟 (Ioi a) :=
     · exact iInf_le _ _
     · simpa using hr
 #align ereal.nhds_top' EReal.nhds_top'
+-/
 
+#print EReal.mem_nhds_top_iff /-
 theorem mem_nhds_top_iff {s : Set EReal} : s ∈ 𝓝 (⊤ : EReal) ↔ ∃ y : ℝ, Ioi (y : EReal) ⊆ s :=
   by
   rw [nhds_top', mem_infi_of_directed]
   · rfl
   exact fun x y => ⟨max x y, by simp [le_refl], by simp [le_refl]⟩
 #align ereal.mem_nhds_top_iff EReal.mem_nhds_top_iff
+-/
 
+#print EReal.tendsto_nhds_top_iff_real /-
 theorem tendsto_nhds_top_iff_real {α : Type _} {m : α → EReal} {f : Filter α} :
     Tendsto m f (𝓝 ⊤) ↔ ∀ x : ℝ, ∀ᶠ a in f, ↑x < m a := by
   simp only [nhds_top', mem_Ioi, tendsto_infi, tendsto_principal]
 #align ereal.tendsto_nhds_top_iff_real EReal.tendsto_nhds_top_iff_real
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a «expr ≠ » «expr⊥»()) -/
+#print EReal.nhds_bot /-
 theorem nhds_bot : 𝓝 (⊥ : EReal) = ⨅ (a) (_ : a ≠ ⊥), 𝓟 (Iio a) :=
   nhds_bot_order.trans <| by simp [bot_lt_iff_ne_bot]
 #align ereal.nhds_bot EReal.nhds_bot
+-/
 
+#print EReal.nhds_bot' /-
 theorem nhds_bot' : 𝓝 (⊥ : EReal) = ⨅ a : ℝ, 𝓟 (Iio a) :=
   by
   rw [nhds_bot]
@@ -259,28 +298,36 @@ theorem nhds_bot' : 𝓝 (⊥ : EReal) = ⨅ a : ℝ, 𝓟 (Iio a) :=
     · exact iInf_le _ _
     · exact (iInf_le _ 0).trans (by simp)
 #align ereal.nhds_bot' EReal.nhds_bot'
+-/
 
+#print EReal.mem_nhds_bot_iff /-
 theorem mem_nhds_bot_iff {s : Set EReal} : s ∈ 𝓝 (⊥ : EReal) ↔ ∃ y : ℝ, Iio (y : EReal) ⊆ s :=
   by
   rw [nhds_bot', mem_infi_of_directed]
   · rfl
   exact fun x y => ⟨min x y, by simp [le_refl], by simp [le_refl]⟩
 #align ereal.mem_nhds_bot_iff EReal.mem_nhds_bot_iff
+-/
 
+#print EReal.tendsto_nhds_bot_iff_real /-
 theorem tendsto_nhds_bot_iff_real {α : Type _} {m : α → EReal} {f : Filter α} :
     Tendsto m f (𝓝 ⊥) ↔ ∀ x : ℝ, ∀ᶠ a in f, m a < x := by
   simp only [nhds_bot', mem_Iio, tendsto_infi, tendsto_principal]
 #align ereal.tendsto_nhds_bot_iff_real EReal.tendsto_nhds_bot_iff_real
+-/
 
 /-! ### Continuity of addition -/
 
 
+#print EReal.continuousAt_add_coe_coe /-
 theorem continuousAt_add_coe_coe (a b : ℝ) :
     ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (a, b) := by
   simp only [ContinuousAt, nhds_coe_coe, ← coe_add, tendsto_map'_iff, (· ∘ ·), tendsto_coe,
     tendsto_add]
 #align ereal.continuous_at_add_coe_coe EReal.continuousAt_add_coe_coe
+-/
 
+#print EReal.continuousAt_add_top_coe /-
 theorem continuousAt_add_top_coe (a : ℝ) :
     ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (⊤, a) :=
   by
@@ -294,7 +341,9 @@ theorem continuousAt_add_top_coe (a : ℝ) :
   convert add_lt_add hx hy
   simp
 #align ereal.continuous_at_add_top_coe EReal.continuousAt_add_top_coe
+-/
 
+#print EReal.continuousAt_add_coe_top /-
 theorem continuousAt_add_coe_top (a : ℝ) :
     ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (a, ⊤) :=
   by
@@ -303,7 +352,9 @@ theorem continuousAt_add_coe_top (a : ℝ) :
   simp_rw [add_comm]
   exact continuous_at_add_top_coe a
 #align ereal.continuous_at_add_coe_top EReal.continuousAt_add_coe_top
+-/
 
+#print EReal.continuousAt_add_top_top /-
 theorem continuousAt_add_top_top : ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (⊤, ⊤) :=
   by
   simp only [ContinuousAt, tendsto_nhds_top_iff_real, top_add_top, nhds_prod_eq]
@@ -316,7 +367,9 @@ theorem continuousAt_add_top_top : ContinuousAt (fun p : EReal × EReal => p.1 +
   convert add_lt_add hx hy
   simp
 #align ereal.continuous_at_add_top_top EReal.continuousAt_add_top_top
+-/
 
+#print EReal.continuousAt_add_bot_coe /-
 theorem continuousAt_add_bot_coe (a : ℝ) :
     ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (⊥, a) :=
   by
@@ -329,7 +382,9 @@ theorem continuousAt_add_bot_coe (a : ℝ) :
   convert add_lt_add hx hy
   rw [sub_add_cancel]
 #align ereal.continuous_at_add_bot_coe EReal.continuousAt_add_bot_coe
+-/
 
+#print EReal.continuousAt_add_coe_bot /-
 theorem continuousAt_add_coe_bot (a : ℝ) :
     ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (a, ⊥) :=
   by
@@ -338,7 +393,9 @@ theorem continuousAt_add_coe_bot (a : ℝ) :
   simp_rw [add_comm]
   exact continuous_at_add_bot_coe a
 #align ereal.continuous_at_add_coe_bot EReal.continuousAt_add_coe_bot
+-/
 
+#print EReal.continuousAt_add_bot_bot /-
 theorem continuousAt_add_bot_bot : ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (⊥, ⊥) :=
   by
   simp only [ContinuousAt, tendsto_nhds_bot_iff_real, nhds_prod_eq, bot_add]
@@ -351,7 +408,9 @@ theorem continuousAt_add_bot_bot : ContinuousAt (fun p : EReal × EReal => p.1 +
   convert add_lt_add hx hy
   simp
 #align ereal.continuous_at_add_bot_bot EReal.continuousAt_add_bot_bot
+-/
 
+#print EReal.continuousAt_add /-
 /-- The addition on `ereal` is continuous except where it doesn't make sense (i.e., at `(⊥, ⊤)`
 and at `(⊤, ⊥)`). -/
 theorem continuousAt_add {p : EReal × EReal} (h : p.1 ≠ ⊤ ∨ p.2 ≠ ⊥) (h' : p.1 ≠ ⊥ ∨ p.2 ≠ ⊤) :
@@ -369,18 +428,23 @@ theorem continuousAt_add {p : EReal × EReal} (h : p.1 ≠ ⊤ ∨ p.2 ≠ ⊥)
   · exact continuous_at_add_top_coe _
   · exact continuous_at_add_top_top
 #align ereal.continuous_at_add EReal.continuousAt_add
+-/
 
 /-! ### Negation-/
 
 
+#print EReal.negHomeo /-
 /-- Negation on `ereal` as a homeomorphism -/
 def negHomeo : EReal ≃ₜ EReal :=
   negOrderIso.toHomeomorph
 #align ereal.neg_homeo EReal.negHomeo
+-/
 
+#print EReal.continuous_neg /-
 theorem continuous_neg : Continuous fun x : EReal => -x :=
   negHomeo.Continuous
 #align ereal.continuous_neg EReal.continuous_neg
+-/
 
 end EReal
 

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

@@ -214,7 +214,7 @@ theorem continuous_coe_ennreal_iff {f : α → ℝ≥0∞} :
 /-! ### Neighborhoods of infinity -/
 
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ≠ » «expr⊤»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a «expr ≠ » «expr⊤»()) -/
 theorem nhds_top : 𝓝 (⊤ : EReal) = ⨅ (a) (_ : a ≠ ⊤), 𝓟 (Ioi a) :=
   nhds_top_order.trans <| by simp [lt_top_iff_ne_top, Ioi]
 #align ereal.nhds_top EReal.nhds_top
@@ -243,7 +243,7 @@ theorem tendsto_nhds_top_iff_real {α : Type _} {m : α → EReal} {f : Filter 
   simp only [nhds_top', mem_Ioi, tendsto_infi, tendsto_principal]
 #align ereal.tendsto_nhds_top_iff_real EReal.tendsto_nhds_top_iff_real
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ≠ » «expr⊥»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (a «expr ≠ » «expr⊥»()) -/
 theorem nhds_bot : 𝓝 (⊥ : EReal) = ⨅ (a) (_ : a ≠ ⊥), 𝓟 (Iio a) :=
   nhds_bot_order.trans <| by simp [bot_lt_iff_ne_bot]
 #align ereal.nhds_bot EReal.nhds_bot

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

@@ -55,7 +55,7 @@ instance : T2Space EReal := by infer_instance
 instance : SecondCountableTopology EReal :=
   ⟨by
     refine'
-      ⟨⋃ q : ℚ, {{ a : EReal | a < (q : ℝ) }, { a : EReal | ((q : ℝ) : EReal) < a }},
+      ⟨⋃ q : ℚ, {{a : EReal | a < (q : ℝ)}, {a : EReal | ((q : ℝ) : EReal) < a}},
         countable_Union fun a => (countable_singleton _).insert _, _⟩
     refine'
       le_antisymm
@@ -64,10 +64,9 @@ instance : SecondCountableTopology EReal :=
         _
     apply le_generateFrom fun s h => _
     rcases h with ⟨a, hs | hs⟩ <;>
-        [rw [show s = ⋃ q ∈ { q : ℚ | a < (q : ℝ) }, { b | ((q : ℝ) : EReal) < b } by ext x;
+        [rw [show s = ⋃ q ∈ {q : ℚ | a < (q : ℝ)}, {b | ((q : ℝ) : EReal) < b} by ext x;
             simpa only [hs, exists_prop, mem_Union] using lt_iff_exists_rat_btwn];
-        rw [show s = ⋃ q ∈ { q : ℚ | ((q : ℝ) : EReal) < a }, { b | b < ((q : ℝ) : EReal) } by
-            ext x;
+        rw [show s = ⋃ q ∈ {q : ℚ | ((q : ℝ) : EReal) < a}, {b | b < ((q : ℝ) : EReal)} by ext x;
             simpa only [hs, and_comm', exists_prop, mem_Union] using lt_iff_exists_rat_btwn]] <;>
       · apply isOpen_iUnion; intro q
         apply isOpen_iUnion; intro hq
@@ -83,12 +82,12 @@ theorem embedding_coe : Embedding (coe : ℝ → EReal) :=
       · rw [@OrderTopology.topology_eq_generate_intervals EReal _, ← coinduced_le_iff_le_induced]
         refine' le_generateFrom fun s ha => _
         rcases ha with ⟨a, rfl | rfl⟩
-        show IsOpen { b : ℝ | a < ↑b }
+        show IsOpen {b : ℝ | a < ↑b}
         · induction a using EReal.rec
           · simp only [isOpen_univ, bot_lt_coe, set_of_true]
           · simp only [EReal.coe_lt_coe_iff]; exact isOpen_Ioi
           · simp only [set_of_false, isOpen_empty, not_top_lt]
-        show IsOpen { b : ℝ | ↑b < a }
+        show IsOpen {b : ℝ | ↑b < a}
         · induction a using EReal.rec
           · simp only [not_lt_bot, set_of_false, isOpen_empty]
           · simp only [EReal.coe_lt_coe_iff]; exact isOpen_Iio
@@ -103,7 +102,7 @@ theorem embedding_coe : Embedding (coe : ℝ → EReal) :=
 
 theorem openEmbedding_coe : OpenEmbedding (coe : ℝ → EReal) :=
   ⟨embedding_coe, by
-    convert@isOpen_Ioo EReal _ _ _ ⊥ ⊤
+    convert @isOpen_Ioo EReal _ _ _ ⊥ ⊤
     ext x
     induction x using EReal.rec
     · simp only [left_mem_Ioo, mem_range, coe_ne_bot, exists_false, not_false_iff]
@@ -164,7 +163,7 @@ theorem embedding_coe_ennreal : Embedding (coe : ℝ≥0∞ → EReal) :=
       · rw [@OrderTopology.topology_eq_generate_intervals EReal _, ← coinduced_le_iff_le_induced]
         refine' le_generateFrom fun s ha => _
         rcases ha with ⟨a, rfl | rfl⟩
-        show IsOpen { b : ℝ≥0∞ | a < ↑b }
+        show IsOpen {b : ℝ≥0∞ | a < ↑b}
         · induction' a using EReal.rec with x
           · simp only [isOpen_univ, bot_lt_coe_ennreal, set_of_true]
           · rcases le_or_lt 0 x with (h | h)
@@ -176,7 +175,7 @@ theorem embedding_coe_ennreal : Embedding (coe : ℝ≥0∞ → EReal) :=
                 (EReal.coe_lt_coe_iff.2 h).trans_le (coe_ennreal_nonneg _)
               simp only [this, isOpen_univ, set_of_true]
           · simp only [set_of_false, isOpen_empty, not_top_lt]
-        show IsOpen { b : ℝ≥0∞ | ↑b < a }
+        show IsOpen {b : ℝ≥0∞ | ↑b < a}
         · induction' a using EReal.rec with x
           · simp only [not_lt_bot, set_of_false, isOpen_empty]
           · rcases le_or_lt 0 x with (h | h)

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

@@ -65,9 +65,9 @@ instance : SecondCountableTopology EReal :=
     apply le_generateFrom fun s h => _
     rcases h with ⟨a, hs | hs⟩ <;>
         [rw [show s = ⋃ q ∈ { q : ℚ | a < (q : ℝ) }, { b | ((q : ℝ) : EReal) < b } by ext x;
-            simpa only [hs, exists_prop, mem_Union] using
-              lt_iff_exists_rat_btwn];rw [show
-            s = ⋃ q ∈ { q : ℚ | ((q : ℝ) : EReal) < a }, { b | b < ((q : ℝ) : EReal) } by ext x;
+            simpa only [hs, exists_prop, mem_Union] using lt_iff_exists_rat_btwn];
+        rw [show s = ⋃ q ∈ { q : ℚ | ((q : ℝ) : EReal) < a }, { b | b < ((q : ℝ) : EReal) } by
+            ext x;
             simpa only [hs, and_comm', exists_prop, mem_Union] using lt_iff_exists_rat_btwn]] <;>
       · apply isOpen_iUnion; intro q
         apply isOpen_iUnion; intro hq
@@ -144,7 +144,7 @@ theorem tendsto_toReal {a : EReal} (ha : a ≠ ⊤) (h'a : a ≠ ⊥) :
 
 theorem continuousOn_toReal : ContinuousOn EReal.toReal ({⊥, ⊤}ᶜ : Set EReal) := fun a ha =>
   ContinuousAt.continuousWithinAt
-    (tendsto_toReal (by simp [not_or] at ha; exact ha.2) (by simp [not_or] at ha; exact ha.1))
+    (tendsto_toReal (by simp [not_or] at ha ; exact ha.2) (by simp [not_or] at ha ; exact ha.1))
 #align ereal.continuous_on_to_real EReal.continuousOn_toReal
 
 /-- The set of finite `ereal` numbers is homeomorphic to `ℝ`. -/

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

@@ -38,7 +38,7 @@ noncomputable section
 
 open Classical Set Filter Metric TopologicalSpace
 
-open Classical Topology ENNReal NNReal BigOperators Filter
+open scoped Classical Topology ENNReal NNReal BigOperators Filter
 
 variable {α : Type _} [TopologicalSpace α]
 

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

@@ -77,12 +77,6 @@ instance : SecondCountableTopology EReal :=
 /-! ### Real coercion -/
 
 
-/- warning: ereal.embedding_coe -> EReal.embedding_coe is a dubious translation:
-lean 3 declaration is
-  Embedding.{0, 0} Real EReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) EReal.topologicalSpace ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))))
-but is expected to have type
-  Embedding.{0, 0} Real EReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) EReal.instTopologicalSpaceEReal Real.toEReal
-Case conversion may be inaccurate. Consider using '#align ereal.embedding_coe EReal.embedding_coeₓ'. -/
 theorem embedding_coe : Embedding (coe : ℝ → EReal) :=
   ⟨⟨by
       refine' le_antisymm _ _
@@ -107,12 +101,6 @@ theorem embedding_coe : Embedding (coe : ℝ → EReal) :=
     simp only [imp_self, EReal.coe_eq_coe_iff]⟩
 #align ereal.embedding_coe EReal.embedding_coe
 
-/- warning: ereal.open_embedding_coe -> EReal.openEmbedding_coe is a dubious translation:
-lean 3 declaration is
-  OpenEmbedding.{0, 0} Real EReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) EReal.topologicalSpace ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))))
-but is expected to have type
-  OpenEmbedding.{0, 0} Real EReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) EReal.instTopologicalSpaceEReal Real.toEReal
-Case conversion may be inaccurate. Consider using '#align ereal.open_embedding_coe EReal.openEmbedding_coeₓ'. -/
 theorem openEmbedding_coe : OpenEmbedding (coe : ℝ → EReal) :=
   ⟨embedding_coe, by
     convert@isOpen_Ioo EReal _ _ _ ⊥ ⊤
@@ -123,65 +111,29 @@ theorem openEmbedding_coe : OpenEmbedding (coe : ℝ → EReal) :=
     · simp only [mem_range, right_mem_Ioo, exists_false, coe_ne_top]⟩
 #align ereal.open_embedding_coe EReal.openEmbedding_coe
 
-/- warning: ereal.tendsto_coe -> EReal.tendsto_coe is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {f : Filter.{u1} α} {m : α -> Real} {a : Real}, Iff (Filter.Tendsto.{u1, 0} α EReal (fun (a : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) (m a)) f (nhds.{0} EReal EReal.topologicalSpace ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a))) (Filter.Tendsto.{u1, 0} α Real m f (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) a))
-but is expected to have type
-  forall {α : Type.{u1}} {f : Filter.{u1} α} {m : α -> Real} {a : Real}, Iff (Filter.Tendsto.{u1, 0} α EReal (fun (a : α) => Real.toEReal (m a)) f (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Real.toEReal a))) (Filter.Tendsto.{u1, 0} α Real m f (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) a))
-Case conversion may be inaccurate. Consider using '#align ereal.tendsto_coe EReal.tendsto_coeₓ'. -/
 @[norm_cast]
 theorem tendsto_coe {α : Type _} {f : Filter α} {m : α → ℝ} {a : ℝ} :
     Tendsto (fun a => (m a : EReal)) f (𝓝 ↑a) ↔ Tendsto m f (𝓝 a) :=
   embedding_coe.tendsto_nhds_iff.symm
 #align ereal.tendsto_coe EReal.tendsto_coe
 
-/- warning: continuous_coe_real_ereal -> continuous_coe_real_ereal is a dubious translation:
-lean 3 declaration is
-  Continuous.{0, 0} Real EReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) EReal.topologicalSpace ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))))
-but is expected to have type
-  Continuous.{0, 0} Real EReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) EReal.instTopologicalSpaceEReal Real.toEReal
-Case conversion may be inaccurate. Consider using '#align continuous_coe_real_ereal continuous_coe_real_erealₓ'. -/
 theorem continuous_coe_real_ereal : Continuous (coe : ℝ → EReal) :=
   embedding_coe.Continuous
 #align continuous_coe_real_ereal continuous_coe_real_ereal
 
-/- warning: ereal.continuous_coe_iff -> EReal.continuous_coe_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real}, Iff (Continuous.{u1, 0} α EReal _inst_1 EReal.topologicalSpace (fun (a : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) (f a))) (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real}, Iff (Continuous.{u1, 0} α EReal _inst_1 EReal.instTopologicalSpaceEReal (fun (a : α) => Real.toEReal (f a))) (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f)
-Case conversion may be inaccurate. Consider using '#align ereal.continuous_coe_iff EReal.continuous_coe_iffₓ'. -/
 theorem continuous_coe_iff {f : α → ℝ} : (Continuous fun a => (f a : EReal)) ↔ Continuous f :=
   embedding_coe.continuous_iff.symm
 #align ereal.continuous_coe_iff EReal.continuous_coe_iff
 
-/- warning: ereal.nhds_coe -> EReal.nhds_coe is a dubious translation:
-lean 3 declaration is
-  forall {r : Real}, Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) r)) (Filter.map.{0, 0} Real EReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) r))
-but is expected to have type
-  forall {r : Real}, Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Real.toEReal r)) (Filter.map.{0, 0} Real EReal Real.toEReal (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) r))
-Case conversion may be inaccurate. Consider using '#align ereal.nhds_coe EReal.nhds_coeₓ'. -/
 theorem nhds_coe {r : ℝ} : 𝓝 (r : EReal) = (𝓝 r).map coe :=
   (openEmbedding_coe.map_nhds_eq r).symm
 #align ereal.nhds_coe EReal.nhds_coe
 
-/- warning: ereal.nhds_coe_coe -> EReal.nhds_coe_coe is a dubious translation:
-lean 3 declaration is
-  forall {r : Real} {p : Real}, Eq.{1} (Filter.{0} (Prod.{0, 0} EReal EReal)) (nhds.{0} (Prod.{0, 0} EReal EReal) (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) (Prod.mk.{0, 0} EReal EReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) r) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) p))) (Filter.map.{0, 0} (Prod.{0, 0} Real Real) (Prod.{0, 0} EReal EReal) (fun (p : Prod.{0, 0} Real Real) => Prod.mk.{0, 0} EReal EReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) (Prod.fst.{0, 0} Real Real p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) (Prod.snd.{0, 0} Real Real p))) (nhds.{0} (Prod.{0, 0} Real Real) (Prod.topologicalSpace.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (Prod.mk.{0, 0} Real Real r p)))
-but is expected to have type
-  forall {r : Real} {p : Real}, Eq.{1} (Filter.{0} (Prod.{0, 0} EReal EReal)) (nhds.{0} (Prod.{0, 0} EReal EReal) (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) (Prod.mk.{0, 0} EReal EReal (Real.toEReal r) (Real.toEReal p))) (Filter.map.{0, 0} (Prod.{0, 0} Real Real) (Prod.{0, 0} EReal EReal) (fun (p : Prod.{0, 0} Real Real) => Prod.mk.{0, 0} EReal EReal (Real.toEReal (Prod.fst.{0, 0} Real Real p)) (Real.toEReal (Prod.snd.{0, 0} Real Real p))) (nhds.{0} (Prod.{0, 0} Real Real) (instTopologicalSpaceProd.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (Prod.mk.{0, 0} Real Real r p)))
-Case conversion may be inaccurate. Consider using '#align ereal.nhds_coe_coe EReal.nhds_coe_coeₓ'. -/
 theorem nhds_coe_coe {r p : ℝ} :
     𝓝 ((r : EReal), (p : EReal)) = (𝓝 (r, p)).map fun p : ℝ × ℝ => (p.1, p.2) :=
   ((openEmbedding_coe.Prod openEmbedding_coe).map_nhds_eq (r, p)).symm
 #align ereal.nhds_coe_coe EReal.nhds_coe_coe
 
-/- warning: ereal.tendsto_to_real -> EReal.tendsto_toReal is a dubious translation:
-lean 3 declaration is
-  forall {a : EReal}, (Ne.{1} EReal a (Top.top.{0} EReal EReal.hasTop)) -> (Ne.{1} EReal a (Bot.bot.{0} EReal EReal.hasBot)) -> (Filter.Tendsto.{0, 0} EReal Real EReal.toReal (nhds.{0} EReal EReal.topologicalSpace a) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (EReal.toReal a)))
-but is expected to have type
-  forall {a : EReal}, (Ne.{1} EReal a (Top.top.{0} EReal EReal.instTopEReal)) -> (Ne.{1} EReal a (Bot.bot.{0} EReal instERealBot)) -> (Filter.Tendsto.{0, 0} EReal Real EReal.toReal (nhds.{0} EReal EReal.instTopologicalSpaceEReal a) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (EReal.toReal a)))
-Case conversion may be inaccurate. Consider using '#align ereal.tendsto_to_real EReal.tendsto_toRealₓ'. -/
 theorem tendsto_toReal {a : EReal} (ha : a ≠ ⊤) (h'a : a ≠ ⊥) :
     Tendsto EReal.toReal (𝓝 a) (𝓝 a.toReal) :=
   by
@@ -190,23 +142,11 @@ theorem tendsto_toReal {a : EReal} (ha : a ≠ ⊤) (h'a : a ≠ ⊥) :
   exact tendsto_id
 #align ereal.tendsto_to_real EReal.tendsto_toReal
 
-/- warning: ereal.continuous_on_to_real -> EReal.continuousOn_toReal is a dubious translation:
-lean 3 declaration is
-  ContinuousOn.{0, 0} EReal Real EReal.topologicalSpace (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) EReal.toReal (HasCompl.compl.{0} (Set.{0} EReal) (BooleanAlgebra.toHasCompl.{0} (Set.{0} EReal) (Set.booleanAlgebra.{0} EReal)) (Insert.insert.{0, 0} EReal (Set.{0} EReal) (Set.hasInsert.{0} EReal) (Bot.bot.{0} EReal EReal.hasBot) (Singleton.singleton.{0, 0} EReal (Set.{0} EReal) (Set.hasSingleton.{0} EReal) (Top.top.{0} EReal EReal.hasTop))))
-but is expected to have type
-  ContinuousOn.{0, 0} EReal Real EReal.instTopologicalSpaceEReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) EReal.toReal (HasCompl.compl.{0} (Set.{0} EReal) (BooleanAlgebra.toHasCompl.{0} (Set.{0} EReal) (Set.instBooleanAlgebraSet.{0} EReal)) (Insert.insert.{0, 0} EReal (Set.{0} EReal) (Set.instInsertSet.{0} EReal) (Bot.bot.{0} EReal instERealBot) (Singleton.singleton.{0, 0} EReal (Set.{0} EReal) (Set.instSingletonSet.{0} EReal) (Top.top.{0} EReal EReal.instTopEReal))))
-Case conversion may be inaccurate. Consider using '#align ereal.continuous_on_to_real EReal.continuousOn_toRealₓ'. -/
 theorem continuousOn_toReal : ContinuousOn EReal.toReal ({⊥, ⊤}ᶜ : Set EReal) := fun a ha =>
   ContinuousAt.continuousWithinAt
     (tendsto_toReal (by simp [not_or] at ha; exact ha.2) (by simp [not_or] at ha; exact ha.1))
 #align ereal.continuous_on_to_real EReal.continuousOn_toReal
 
-/- warning: ereal.ne_bot_top_homeomorph_real -> EReal.neBotTopHomeomorphReal is a dubious translation:
-lean 3 declaration is
-  Homeomorph.{0, 0} (coeSort.{1, 2} (Set.{0} EReal) Type (Set.hasCoeToSort.{0} EReal) (HasCompl.compl.{0} (Set.{0} EReal) (BooleanAlgebra.toHasCompl.{0} (Set.{0} EReal) (Set.booleanAlgebra.{0} EReal)) (Insert.insert.{0, 0} EReal (Set.{0} EReal) (Set.hasInsert.{0} EReal) (Bot.bot.{0} EReal EReal.hasBot) (Singleton.singleton.{0, 0} EReal (Set.{0} EReal) (Set.hasSingleton.{0} EReal) (Top.top.{0} EReal EReal.hasTop))))) Real (Subtype.topologicalSpace.{0} EReal (fun (x : EReal) => Membership.Mem.{0, 0} EReal (Set.{0} EReal) (Set.hasMem.{0} EReal) x (HasCompl.compl.{0} (Set.{0} EReal) (BooleanAlgebra.toHasCompl.{0} (Set.{0} EReal) (Set.booleanAlgebra.{0} EReal)) (Insert.insert.{0, 0} EReal (Set.{0} EReal) (Set.hasInsert.{0} EReal) (Bot.bot.{0} EReal EReal.hasBot) (Singleton.singleton.{0, 0} EReal (Set.{0} EReal) (Set.hasSingleton.{0} EReal) (Top.top.{0} EReal EReal.hasTop))))) EReal.topologicalSpace) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))
-but is expected to have type
-  Homeomorph.{0, 0} (Set.Elem.{0} EReal (HasCompl.compl.{0} (Set.{0} EReal) (BooleanAlgebra.toHasCompl.{0} (Set.{0} EReal) (Set.instBooleanAlgebraSet.{0} EReal)) (Insert.insert.{0, 0} EReal (Set.{0} EReal) (Set.instInsertSet.{0} EReal) (Bot.bot.{0} EReal instERealBot) (Singleton.singleton.{0, 0} EReal (Set.{0} EReal) (Set.instSingletonSet.{0} EReal) (Top.top.{0} EReal EReal.instTopEReal))))) Real (instTopologicalSpaceSubtype.{0} EReal (fun (x : EReal) => Membership.mem.{0, 0} EReal (Set.{0} EReal) (Set.instMembershipSet.{0} EReal) x (HasCompl.compl.{0} (Set.{0} EReal) (BooleanAlgebra.toHasCompl.{0} (Set.{0} EReal) (Set.instBooleanAlgebraSet.{0} EReal)) (Insert.insert.{0, 0} EReal (Set.{0} EReal) (Set.instInsertSet.{0} EReal) (Bot.bot.{0} EReal instERealBot) (Singleton.singleton.{0, 0} EReal (Set.{0} EReal) (Set.instSingletonSet.{0} EReal) (Top.top.{0} EReal EReal.instTopEReal))))) EReal.instTopologicalSpaceEReal) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))
-Case conversion may be inaccurate. Consider using '#align ereal.ne_bot_top_homeomorph_real EReal.neBotTopHomeomorphRealₓ'. -/
 /-- The set of finite `ereal` numbers is homeomorphic to `ℝ`. -/
 def neBotTopHomeomorphReal : ({⊥, ⊤}ᶜ : Set EReal) ≃ₜ ℝ :=
   {
@@ -218,12 +158,6 @@ def neBotTopHomeomorphReal : ({⊥, ⊤}ᶜ : Set EReal) ≃ₜ ℝ :=
 /-! ### ennreal coercion -/
 
 
-/- warning: ereal.embedding_coe_ennreal -> EReal.embedding_coe_ennreal is a dubious translation:
-lean 3 declaration is
-  Embedding.{0, 0} ENNReal EReal ENNReal.topologicalSpace EReal.topologicalSpace ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) ENNReal EReal (HasLiftT.mk.{1, 1} ENNReal EReal (CoeTCₓ.coe.{1, 1} ENNReal EReal (coeBase.{1, 1} ENNReal EReal EReal.hasCoeENNReal))))
-but is expected to have type
-  Embedding.{0, 0} ENNReal EReal ENNReal.instTopologicalSpaceENNReal EReal.instTopologicalSpaceEReal ENNReal.toEReal
-Case conversion may be inaccurate. Consider using '#align ereal.embedding_coe_ennreal EReal.embedding_coe_ennrealₓ'. -/
 theorem embedding_coe_ennreal : Embedding (coe : ℝ≥0∞ → EReal) :=
   ⟨⟨by
       refine' le_antisymm _ _
@@ -263,34 +197,16 @@ theorem embedding_coe_ennreal : Embedding (coe : ℝ≥0∞ → EReal) :=
     simp only [imp_self, coe_ennreal_eq_coe_ennreal_iff]⟩
 #align ereal.embedding_coe_ennreal EReal.embedding_coe_ennreal
 
-/- warning: ereal.tendsto_coe_ennreal -> EReal.tendsto_coe_ennreal is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {f : Filter.{u1} α} {m : α -> ENNReal} {a : ENNReal}, Iff (Filter.Tendsto.{u1, 0} α EReal (fun (a : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) ENNReal EReal (HasLiftT.mk.{1, 1} ENNReal EReal (CoeTCₓ.coe.{1, 1} ENNReal EReal (coeBase.{1, 1} ENNReal EReal EReal.hasCoeENNReal))) (m a)) f (nhds.{0} EReal EReal.topologicalSpace ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) ENNReal EReal (HasLiftT.mk.{1, 1} ENNReal EReal (CoeTCₓ.coe.{1, 1} ENNReal EReal (coeBase.{1, 1} ENNReal EReal EReal.hasCoeENNReal))) a))) (Filter.Tendsto.{u1, 0} α ENNReal m f (nhds.{0} ENNReal ENNReal.topologicalSpace a))
-but is expected to have type
-  forall {α : Type.{u1}} {f : Filter.{u1} α} {m : α -> ENNReal} {a : ENNReal}, Iff (Filter.Tendsto.{u1, 0} α EReal (fun (a : α) => ENNReal.toEReal (m a)) f (nhds.{0} EReal EReal.instTopologicalSpaceEReal (ENNReal.toEReal a))) (Filter.Tendsto.{u1, 0} α ENNReal m f (nhds.{0} ENNReal ENNReal.instTopologicalSpaceENNReal a))
-Case conversion may be inaccurate. Consider using '#align ereal.tendsto_coe_ennreal EReal.tendsto_coe_ennrealₓ'. -/
 @[norm_cast]
 theorem tendsto_coe_ennreal {α : Type _} {f : Filter α} {m : α → ℝ≥0∞} {a : ℝ≥0∞} :
     Tendsto (fun a => (m a : EReal)) f (𝓝 ↑a) ↔ Tendsto m f (𝓝 a) :=
   embedding_coe_ennreal.tendsto_nhds_iff.symm
 #align ereal.tendsto_coe_ennreal EReal.tendsto_coe_ennreal
 
-/- warning: continuous_coe_ennreal_ereal -> continuous_coe_ennreal_ereal is a dubious translation:
-lean 3 declaration is
-  Continuous.{0, 0} ENNReal EReal ENNReal.topologicalSpace EReal.topologicalSpace ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) ENNReal EReal (HasLiftT.mk.{1, 1} ENNReal EReal (CoeTCₓ.coe.{1, 1} ENNReal EReal (coeBase.{1, 1} ENNReal EReal EReal.hasCoeENNReal))))
-but is expected to have type
-  Continuous.{0, 0} ENNReal EReal ENNReal.instTopologicalSpaceENNReal EReal.instTopologicalSpaceEReal ENNReal.toEReal
-Case conversion may be inaccurate. Consider using '#align continuous_coe_ennreal_ereal continuous_coe_ennreal_erealₓ'. -/
 theorem continuous_coe_ennreal_ereal : Continuous (coe : ℝ≥0∞ → EReal) :=
   embedding_coe_ennreal.Continuous
 #align continuous_coe_ennreal_ereal continuous_coe_ennreal_ereal
 
-/- warning: ereal.continuous_coe_ennreal_iff -> EReal.continuous_coe_ennreal_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> ENNReal}, Iff (Continuous.{u1, 0} α EReal _inst_1 EReal.topologicalSpace (fun (a : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) ENNReal EReal (HasLiftT.mk.{1, 1} ENNReal EReal (CoeTCₓ.coe.{1, 1} ENNReal EReal (coeBase.{1, 1} ENNReal EReal EReal.hasCoeENNReal))) (f a))) (Continuous.{u1, 0} α ENNReal _inst_1 ENNReal.topologicalSpace f)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> ENNReal}, Iff (Continuous.{u1, 0} α EReal _inst_1 EReal.instTopologicalSpaceEReal (fun (a : α) => ENNReal.toEReal (f a))) (Continuous.{u1, 0} α ENNReal _inst_1 ENNReal.instTopologicalSpaceENNReal f)
-Case conversion may be inaccurate. Consider using '#align ereal.continuous_coe_ennreal_iff EReal.continuous_coe_ennreal_iffₓ'. -/
 theorem continuous_coe_ennreal_iff {f : α → ℝ≥0∞} :
     (Continuous fun a => (f a : EReal)) ↔ Continuous f :=
   embedding_coe_ennreal.continuous_iff.symm
@@ -299,23 +215,11 @@ theorem continuous_coe_ennreal_iff {f : α → ℝ≥0∞} :
 /-! ### Neighborhoods of infinity -/
 
 
-/- warning: ereal.nhds_top -> EReal.nhds_top is a dubious translation:
-lean 3 declaration is
-  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace (Top.top.{0} EReal EReal.hasTop)) (iInf.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) EReal (fun (a : EReal) => iInf.{0, 0} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) (Ne.{1} EReal a (Top.top.{0} EReal EReal.hasTop)) (fun (H : Ne.{1} EReal a (Top.top.{0} EReal EReal.hasTop)) => Filter.principal.{0} EReal (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) a))))
-but is expected to have type
-  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Top.top.{0} EReal EReal.instTopEReal)) (iInf.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) EReal (fun (a : EReal) => iInf.{0, 0} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) (Ne.{1} EReal a (Top.top.{0} EReal EReal.instTopEReal)) (fun (H : Ne.{1} EReal a (Top.top.{0} EReal EReal.instTopEReal)) => Filter.principal.{0} EReal (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) a))))
-Case conversion may be inaccurate. Consider using '#align ereal.nhds_top EReal.nhds_topₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ≠ » «expr⊤»()) -/
 theorem nhds_top : 𝓝 (⊤ : EReal) = ⨅ (a) (_ : a ≠ ⊤), 𝓟 (Ioi a) :=
   nhds_top_order.trans <| by simp [lt_top_iff_ne_top, Ioi]
 #align ereal.nhds_top EReal.nhds_top
 
-/- warning: ereal.nhds_top' -> EReal.nhds_top' is a dubious translation:
-lean 3 declaration is
-  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace (Top.top.{0} EReal EReal.hasTop)) (iInf.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) Real (fun (a : Real) => Filter.principal.{0} EReal (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a))))
-but is expected to have type
-  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Top.top.{0} EReal EReal.instTopEReal)) (iInf.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) Real (fun (a : Real) => Filter.principal.{0} EReal (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) (Real.toEReal a))))
-Case conversion may be inaccurate. Consider using '#align ereal.nhds_top' EReal.nhds_top'ₓ'. -/
 theorem nhds_top' : 𝓝 (⊤ : EReal) = ⨅ a : ℝ, 𝓟 (Ioi a) :=
   by
   rw [nhds_top]
@@ -328,12 +232,6 @@ theorem nhds_top' : 𝓝 (⊤ : EReal) = ⨅ a : ℝ, 𝓟 (Ioi a) :=
     · simpa using hr
 #align ereal.nhds_top' EReal.nhds_top'
 
-/- warning: ereal.mem_nhds_top_iff -> EReal.mem_nhds_top_iff is a dubious translation:
-lean 3 declaration is
-  forall {s : Set.{0} EReal}, Iff (Membership.Mem.{0, 0} (Set.{0} EReal) (Filter.{0} EReal) (Filter.hasMem.{0} EReal) s (nhds.{0} EReal EReal.topologicalSpace (Top.top.{0} EReal EReal.hasTop))) (Exists.{1} Real (fun (y : Real) => HasSubset.Subset.{0} (Set.{0} EReal) (Set.hasSubset.{0} EReal) (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) y)) s))
-but is expected to have type
-  forall {s : Set.{0} EReal}, Iff (Membership.mem.{0, 0} (Set.{0} EReal) (Filter.{0} EReal) (instMembershipSetFilter.{0} EReal) s (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Top.top.{0} EReal EReal.instTopEReal))) (Exists.{1} Real (fun (y : Real) => HasSubset.Subset.{0} (Set.{0} EReal) (Set.instHasSubsetSet.{0} EReal) (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) (Real.toEReal y)) s))
-Case conversion may be inaccurate. Consider using '#align ereal.mem_nhds_top_iff EReal.mem_nhds_top_iffₓ'. -/
 theorem mem_nhds_top_iff {s : Set EReal} : s ∈ 𝓝 (⊤ : EReal) ↔ ∃ y : ℝ, Ioi (y : EReal) ⊆ s :=
   by
   rw [nhds_top', mem_infi_of_directed]
@@ -341,34 +239,16 @@ theorem mem_nhds_top_iff {s : Set EReal} : s ∈ 𝓝 (⊤ : EReal) ↔ ∃ y :
   exact fun x y => ⟨max x y, by simp [le_refl], by simp [le_refl]⟩
 #align ereal.mem_nhds_top_iff EReal.mem_nhds_top_iff
 
-/- warning: ereal.tendsto_nhds_top_iff_real -> EReal.tendsto_nhds_top_iff_real is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {m : α -> EReal} {f : Filter.{u1} α}, Iff (Filter.Tendsto.{u1, 0} α EReal m f (nhds.{0} EReal EReal.topologicalSpace (Top.top.{0} EReal EReal.hasTop))) (forall (x : Real), Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{0} EReal (Preorder.toHasLt.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) x) (m a)) f)
-but is expected to have type
-  forall {α : Type.{u1}} {m : α -> EReal} {f : Filter.{u1} α}, Iff (Filter.Tendsto.{u1, 0} α EReal m f (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Top.top.{0} EReal EReal.instTopEReal))) (forall (x : Real), Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{0} EReal (Preorder.toLT.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder)) (Real.toEReal x) (m a)) f)
-Case conversion may be inaccurate. Consider using '#align ereal.tendsto_nhds_top_iff_real EReal.tendsto_nhds_top_iff_realₓ'. -/
 theorem tendsto_nhds_top_iff_real {α : Type _} {m : α → EReal} {f : Filter α} :
     Tendsto m f (𝓝 ⊤) ↔ ∀ x : ℝ, ∀ᶠ a in f, ↑x < m a := by
   simp only [nhds_top', mem_Ioi, tendsto_infi, tendsto_principal]
 #align ereal.tendsto_nhds_top_iff_real EReal.tendsto_nhds_top_iff_real
 
-/- warning: ereal.nhds_bot -> EReal.nhds_bot is a dubious translation:
-lean 3 declaration is
-  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace (Bot.bot.{0} EReal EReal.hasBot)) (iInf.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) EReal (fun (a : EReal) => iInf.{0, 0} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) (Ne.{1} EReal a (Bot.bot.{0} EReal EReal.hasBot)) (fun (H : Ne.{1} EReal a (Bot.bot.{0} EReal EReal.hasBot)) => Filter.principal.{0} EReal (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) a))))
-but is expected to have type
-  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Bot.bot.{0} EReal instERealBot)) (iInf.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) EReal (fun (a : EReal) => iInf.{0, 0} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) (Ne.{1} EReal a (Bot.bot.{0} EReal instERealBot)) (fun (H : Ne.{1} EReal a (Bot.bot.{0} EReal instERealBot)) => Filter.principal.{0} EReal (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) a))))
-Case conversion may be inaccurate. Consider using '#align ereal.nhds_bot EReal.nhds_botₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ≠ » «expr⊥»()) -/
 theorem nhds_bot : 𝓝 (⊥ : EReal) = ⨅ (a) (_ : a ≠ ⊥), 𝓟 (Iio a) :=
   nhds_bot_order.trans <| by simp [bot_lt_iff_ne_bot]
 #align ereal.nhds_bot EReal.nhds_bot
 
-/- warning: ereal.nhds_bot' -> EReal.nhds_bot' is a dubious translation:
-lean 3 declaration is
-  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace (Bot.bot.{0} EReal EReal.hasBot)) (iInf.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) Real (fun (a : Real) => Filter.principal.{0} EReal (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a))))
-but is expected to have type
-  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Bot.bot.{0} EReal instERealBot)) (iInf.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) Real (fun (a : Real) => Filter.principal.{0} EReal (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) (Real.toEReal a))))
-Case conversion may be inaccurate. Consider using '#align ereal.nhds_bot' EReal.nhds_bot'ₓ'. -/
 theorem nhds_bot' : 𝓝 (⊥ : EReal) = ⨅ a : ℝ, 𝓟 (Iio a) :=
   by
   rw [nhds_bot]
@@ -381,12 +261,6 @@ theorem nhds_bot' : 𝓝 (⊥ : EReal) = ⨅ a : ℝ, 𝓟 (Iio a) :=
     · exact (iInf_le _ 0).trans (by simp)
 #align ereal.nhds_bot' EReal.nhds_bot'
 
-/- warning: ereal.mem_nhds_bot_iff -> EReal.mem_nhds_bot_iff is a dubious translation:
-lean 3 declaration is
-  forall {s : Set.{0} EReal}, Iff (Membership.Mem.{0, 0} (Set.{0} EReal) (Filter.{0} EReal) (Filter.hasMem.{0} EReal) s (nhds.{0} EReal EReal.topologicalSpace (Bot.bot.{0} EReal EReal.hasBot))) (Exists.{1} Real (fun (y : Real) => HasSubset.Subset.{0} (Set.{0} EReal) (Set.hasSubset.{0} EReal) (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) y)) s))
-but is expected to have type
-  forall {s : Set.{0} EReal}, Iff (Membership.mem.{0, 0} (Set.{0} EReal) (Filter.{0} EReal) (instMembershipSetFilter.{0} EReal) s (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Bot.bot.{0} EReal instERealBot))) (Exists.{1} Real (fun (y : Real) => HasSubset.Subset.{0} (Set.{0} EReal) (Set.instHasSubsetSet.{0} EReal) (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) (Real.toEReal y)) s))
-Case conversion may be inaccurate. Consider using '#align ereal.mem_nhds_bot_iff EReal.mem_nhds_bot_iffₓ'. -/
 theorem mem_nhds_bot_iff {s : Set EReal} : s ∈ 𝓝 (⊥ : EReal) ↔ ∃ y : ℝ, Iio (y : EReal) ⊆ s :=
   by
   rw [nhds_bot', mem_infi_of_directed]
@@ -394,12 +268,6 @@ theorem mem_nhds_bot_iff {s : Set EReal} : s ∈ 𝓝 (⊥ : EReal) ↔ ∃ y :
   exact fun x y => ⟨min x y, by simp [le_refl], by simp [le_refl]⟩
 #align ereal.mem_nhds_bot_iff EReal.mem_nhds_bot_iff
 
-/- warning: ereal.tendsto_nhds_bot_iff_real -> EReal.tendsto_nhds_bot_iff_real is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {m : α -> EReal} {f : Filter.{u1} α}, Iff (Filter.Tendsto.{u1, 0} α EReal m f (nhds.{0} EReal EReal.topologicalSpace (Bot.bot.{0} EReal EReal.hasBot))) (forall (x : Real), Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{0} EReal (Preorder.toHasLt.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder))))) (m a) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) x)) f)
-but is expected to have type
-  forall {α : Type.{u1}} {m : α -> EReal} {f : Filter.{u1} α}, Iff (Filter.Tendsto.{u1, 0} α EReal m f (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Bot.bot.{0} EReal instERealBot))) (forall (x : Real), Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{0} EReal (Preorder.toLT.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder)) (m a) (Real.toEReal x)) f)
-Case conversion may be inaccurate. Consider using '#align ereal.tendsto_nhds_bot_iff_real EReal.tendsto_nhds_bot_iff_realₓ'. -/
 theorem tendsto_nhds_bot_iff_real {α : Type _} {m : α → EReal} {f : Filter α} :
     Tendsto m f (𝓝 ⊥) ↔ ∀ x : ℝ, ∀ᶠ a in f, m a < x := by
   simp only [nhds_bot', mem_Iio, tendsto_infi, tendsto_principal]
@@ -408,24 +276,12 @@ theorem tendsto_nhds_bot_iff_real {α : Type _} {m : α → EReal} {f : Filter 
 /-! ### Continuity of addition -/
 
 
-/- warning: ereal.continuous_at_add_coe_coe -> EReal.continuousAt_add_coe_coe is a dubious translation:
-lean 3 declaration is
-  forall (a : Real) (b : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) EReal.topologicalSpace (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toHasAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal EReal.addMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) b))
-but is expected to have type
-  forall (a : Real) (b : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) EReal.instTopologicalSpaceEReal (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal instERealAddMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Real.toEReal a) (Real.toEReal b))
-Case conversion may be inaccurate. Consider using '#align ereal.continuous_at_add_coe_coe EReal.continuousAt_add_coe_coeₓ'. -/
 theorem continuousAt_add_coe_coe (a b : ℝ) :
     ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (a, b) := by
   simp only [ContinuousAt, nhds_coe_coe, ← coe_add, tendsto_map'_iff, (· ∘ ·), tendsto_coe,
     tendsto_add]
 #align ereal.continuous_at_add_coe_coe EReal.continuousAt_add_coe_coe
 
-/- warning: ereal.continuous_at_add_top_coe -> EReal.continuousAt_add_top_coe is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) EReal.topologicalSpace (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toHasAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal EReal.addMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Top.top.{0} EReal EReal.hasTop) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a))
-but is expected to have type
-  forall (a : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) EReal.instTopologicalSpaceEReal (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal instERealAddMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Top.top.{0} EReal EReal.instTopEReal) (Real.toEReal a))
-Case conversion may be inaccurate. Consider using '#align ereal.continuous_at_add_top_coe EReal.continuousAt_add_top_coeₓ'. -/
 theorem continuousAt_add_top_coe (a : ℝ) :
     ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (⊤, a) :=
   by
@@ -440,12 +296,6 @@ theorem continuousAt_add_top_coe (a : ℝ) :
   simp
 #align ereal.continuous_at_add_top_coe EReal.continuousAt_add_top_coe
 
-/- warning: ereal.continuous_at_add_coe_top -> EReal.continuousAt_add_coe_top is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) EReal.topologicalSpace (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toHasAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal EReal.addMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a) (Top.top.{0} EReal EReal.hasTop))
-but is expected to have type
-  forall (a : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) EReal.instTopologicalSpaceEReal (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal instERealAddMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Real.toEReal a) (Top.top.{0} EReal EReal.instTopEReal))
-Case conversion may be inaccurate. Consider using '#align ereal.continuous_at_add_coe_top EReal.continuousAt_add_coe_topₓ'. -/
 theorem continuousAt_add_coe_top (a : ℝ) :
     ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (a, ⊤) :=
   by
@@ -455,12 +305,6 @@ theorem continuousAt_add_coe_top (a : ℝ) :
   exact continuous_at_add_top_coe a
 #align ereal.continuous_at_add_coe_top EReal.continuousAt_add_coe_top
 
-/- warning: ereal.continuous_at_add_top_top -> EReal.continuousAt_add_top_top is a dubious translation:
-lean 3 declaration is
-  ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) EReal.topologicalSpace (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toHasAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal EReal.addMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Top.top.{0} EReal EReal.hasTop) (Top.top.{0} EReal EReal.hasTop))
-but is expected to have type
-  ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) EReal.instTopologicalSpaceEReal (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal instERealAddMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Top.top.{0} EReal EReal.instTopEReal) (Top.top.{0} EReal EReal.instTopEReal))
-Case conversion may be inaccurate. Consider using '#align ereal.continuous_at_add_top_top EReal.continuousAt_add_top_topₓ'. -/
 theorem continuousAt_add_top_top : ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (⊤, ⊤) :=
   by
   simp only [ContinuousAt, tendsto_nhds_top_iff_real, top_add_top, nhds_prod_eq]
@@ -474,12 +318,6 @@ theorem continuousAt_add_top_top : ContinuousAt (fun p : EReal × EReal => p.1 +
   simp
 #align ereal.continuous_at_add_top_top EReal.continuousAt_add_top_top
 
-/- warning: ereal.continuous_at_add_bot_coe -> EReal.continuousAt_add_bot_coe is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) EReal.topologicalSpace (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toHasAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal EReal.addMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Bot.bot.{0} EReal EReal.hasBot) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a))
-but is expected to have type
-  forall (a : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) EReal.instTopologicalSpaceEReal (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal instERealAddMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Bot.bot.{0} EReal instERealBot) (Real.toEReal a))
-Case conversion may be inaccurate. Consider using '#align ereal.continuous_at_add_bot_coe EReal.continuousAt_add_bot_coeₓ'. -/
 theorem continuousAt_add_bot_coe (a : ℝ) :
     ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (⊥, a) :=
   by
@@ -493,12 +331,6 @@ theorem continuousAt_add_bot_coe (a : ℝ) :
   rw [sub_add_cancel]
 #align ereal.continuous_at_add_bot_coe EReal.continuousAt_add_bot_coe
 
-/- warning: ereal.continuous_at_add_coe_bot -> EReal.continuousAt_add_coe_bot is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) EReal.topologicalSpace (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toHasAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal EReal.addMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a) (Bot.bot.{0} EReal EReal.hasBot))
-but is expected to have type
-  forall (a : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) EReal.instTopologicalSpaceEReal (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal instERealAddMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Real.toEReal a) (Bot.bot.{0} EReal instERealBot))
-Case conversion may be inaccurate. Consider using '#align ereal.continuous_at_add_coe_bot EReal.continuousAt_add_coe_botₓ'. -/
 theorem continuousAt_add_coe_bot (a : ℝ) :
     ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (a, ⊥) :=
   by
@@ -508,12 +340,6 @@ theorem continuousAt_add_coe_bot (a : ℝ) :
   exact continuous_at_add_bot_coe a
 #align ereal.continuous_at_add_coe_bot EReal.continuousAt_add_coe_bot
 
-/- warning: ereal.continuous_at_add_bot_bot -> EReal.continuousAt_add_bot_bot is a dubious translation:
-lean 3 declaration is
-  ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) EReal.topologicalSpace (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toHasAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal EReal.addMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Bot.bot.{0} EReal EReal.hasBot) (Bot.bot.{0} EReal EReal.hasBot))
-but is expected to have type
-  ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) EReal.instTopologicalSpaceEReal (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal instERealAddMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Bot.bot.{0} EReal instERealBot) (Bot.bot.{0} EReal instERealBot))
-Case conversion may be inaccurate. Consider using '#align ereal.continuous_at_add_bot_bot EReal.continuousAt_add_bot_botₓ'. -/
 theorem continuousAt_add_bot_bot : ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (⊥, ⊥) :=
   by
   simp only [ContinuousAt, tendsto_nhds_bot_iff_real, nhds_prod_eq, bot_add]
@@ -527,12 +353,6 @@ theorem continuousAt_add_bot_bot : ContinuousAt (fun p : EReal × EReal => p.1 +
   simp
 #align ereal.continuous_at_add_bot_bot EReal.continuousAt_add_bot_bot
 
-/- warning: ereal.continuous_at_add -> EReal.continuousAt_add is a dubious translation:
-lean 3 declaration is
-  forall {p : Prod.{0, 0} EReal EReal}, (Or (Ne.{1} EReal (Prod.fst.{0, 0} EReal EReal p) (Top.top.{0} EReal EReal.hasTop)) (Ne.{1} EReal (Prod.snd.{0, 0} EReal EReal p) (Bot.bot.{0} EReal EReal.hasBot))) -> (Or (Ne.{1} EReal (Prod.fst.{0, 0} EReal EReal p) (Bot.bot.{0} EReal EReal.hasBot)) (Ne.{1} EReal (Prod.snd.{0, 0} EReal EReal p) (Top.top.{0} EReal EReal.hasTop))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) EReal.topologicalSpace (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toHasAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal EReal.addMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) p)
-but is expected to have type
-  forall {p : Prod.{0, 0} EReal EReal}, (Or (Ne.{1} EReal (Prod.fst.{0, 0} EReal EReal p) (Top.top.{0} EReal EReal.instTopEReal)) (Ne.{1} EReal (Prod.snd.{0, 0} EReal EReal p) (Bot.bot.{0} EReal instERealBot))) -> (Or (Ne.{1} EReal (Prod.fst.{0, 0} EReal EReal p) (Bot.bot.{0} EReal instERealBot)) (Ne.{1} EReal (Prod.snd.{0, 0} EReal EReal p) (Top.top.{0} EReal EReal.instTopEReal))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) EReal.instTopologicalSpaceEReal (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal instERealAddMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) p)
-Case conversion may be inaccurate. Consider using '#align ereal.continuous_at_add EReal.continuousAt_addₓ'. -/
 /-- The addition on `ereal` is continuous except where it doesn't make sense (i.e., at `(⊥, ⊤)`
 and at `(⊤, ⊥)`). -/
 theorem continuousAt_add {p : EReal × EReal} (h : p.1 ≠ ⊤ ∨ p.2 ≠ ⊥) (h' : p.1 ≠ ⊥ ∨ p.2 ≠ ⊤) :
@@ -554,23 +374,11 @@ theorem continuousAt_add {p : EReal × EReal} (h : p.1 ≠ ⊤ ∨ p.2 ≠ ⊥)
 /-! ### Negation-/
 
 
-/- warning: ereal.neg_homeo -> EReal.negHomeo is a dubious translation:
-lean 3 declaration is
-  Homeomorph.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace
-but is expected to have type
-  Homeomorph.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal
-Case conversion may be inaccurate. Consider using '#align ereal.neg_homeo EReal.negHomeoₓ'. -/
 /-- Negation on `ereal` as a homeomorphism -/
 def negHomeo : EReal ≃ₜ EReal :=
   negOrderIso.toHomeomorph
 #align ereal.neg_homeo EReal.negHomeo
 
-/- warning: ereal.continuous_neg -> EReal.continuous_neg is a dubious translation:
-lean 3 declaration is
-  Continuous.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace (fun (x : EReal) => Neg.neg.{0} EReal EReal.hasNeg x)
-but is expected to have type
-  Continuous.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal (fun (x : EReal) => Neg.neg.{0} EReal EReal.instNegEReal x)
-Case conversion may be inaccurate. Consider using '#align ereal.continuous_neg EReal.continuous_negₓ'. -/
 theorem continuous_neg : Continuous fun x : EReal => -x :=
   negHomeo.Continuous
 #align ereal.continuous_neg EReal.continuous_neg

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

@@ -64,19 +64,13 @@ instance : SecondCountableTopology EReal :=
         _
     apply le_generateFrom fun s h => _
     rcases h with ⟨a, hs | hs⟩ <;>
-        [rw [show s = ⋃ q ∈ { q : ℚ | a < (q : ℝ) }, { b | ((q : ℝ) : EReal) < b }
-            by
-            ext x
+        [rw [show s = ⋃ q ∈ { q : ℚ | a < (q : ℝ) }, { b | ((q : ℝ) : EReal) < b } by ext x;
             simpa only [hs, exists_prop, mem_Union] using
               lt_iff_exists_rat_btwn];rw [show
-            s = ⋃ q ∈ { q : ℚ | ((q : ℝ) : EReal) < a }, { b | b < ((q : ℝ) : EReal) }
-            by
-            ext x
+            s = ⋃ q ∈ { q : ℚ | ((q : ℝ) : EReal) < a }, { b | b < ((q : ℝ) : EReal) } by ext x;
             simpa only [hs, and_comm', exists_prop, mem_Union] using lt_iff_exists_rat_btwn]] <;>
-      · apply isOpen_iUnion
-        intro q
-        apply isOpen_iUnion
-        intro hq
+      · apply isOpen_iUnion; intro q
+        apply isOpen_iUnion; intro hq
         apply generate_open.basic
         exact mem_Union.2 ⟨q, by simp⟩⟩
 
@@ -98,14 +92,12 @@ theorem embedding_coe : Embedding (coe : ℝ → EReal) :=
         show IsOpen { b : ℝ | a < ↑b }
         · induction a using EReal.rec
           · simp only [isOpen_univ, bot_lt_coe, set_of_true]
-          · simp only [EReal.coe_lt_coe_iff]
-            exact isOpen_Ioi
+          · simp only [EReal.coe_lt_coe_iff]; exact isOpen_Ioi
           · simp only [set_of_false, isOpen_empty, not_top_lt]
         show IsOpen { b : ℝ | ↑b < a }
         · induction a using EReal.rec
           · simp only [not_lt_bot, set_of_false, isOpen_empty]
-          · simp only [EReal.coe_lt_coe_iff]
-            exact isOpen_Iio
+          · simp only [EReal.coe_lt_coe_iff]; exact isOpen_Iio
           · simp only [isOpen_univ, coe_lt_top, set_of_true]
       · rw [@OrderTopology.topology_eq_generate_intervals ℝ _]
         refine' le_generateFrom fun s ha => _
@@ -206,13 +198,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align ereal.continuous_on_to_real EReal.continuousOn_toRealₓ'. -/
 theorem continuousOn_toReal : ContinuousOn EReal.toReal ({⊥, ⊤}ᶜ : Set EReal) := fun a ha =>
   ContinuousAt.continuousWithinAt
-    (tendsto_toReal
-      (by
-        simp [not_or] at ha
-        exact ha.2)
-      (by
-        simp [not_or] at ha
-        exact ha.1))
+    (tendsto_toReal (by simp [not_or] at ha; exact ha.2) (by simp [not_or] at ha; exact ha.1))
 #align ereal.continuous_on_to_real EReal.continuousOn_toReal
 
 /- warning: ereal.ne_bot_top_homeomorph_real -> EReal.neBotTopHomeomorphReal is a dubious translation:

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

@@ -67,8 +67,9 @@ instance : SecondCountableTopology EReal :=
         [rw [show s = ⋃ q ∈ { q : ℚ | a < (q : ℝ) }, { b | ((q : ℝ) : EReal) < b }
             by
             ext x
-            simpa only [hs, exists_prop, mem_Union] using lt_iff_exists_rat_btwn],
-        rw [show s = ⋃ q ∈ { q : ℚ | ((q : ℝ) : EReal) < a }, { b | b < ((q : ℝ) : EReal) }
+            simpa only [hs, exists_prop, mem_Union] using
+              lt_iff_exists_rat_btwn];rw [show
+            s = ⋃ q ∈ { q : ℚ | ((q : ℝ) : EReal) < a }, { b | b < ((q : ℝ) : EReal) }
             by
             ext x
             simpa only [hs, and_comm', exists_prop, mem_Union] using lt_iff_exists_rat_btwn]] <;>

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

@@ -356,7 +356,7 @@ theorem mem_nhds_top_iff {s : Set EReal} : s ∈ 𝓝 (⊤ : EReal) ↔ ∃ y :
 
 /- warning: ereal.tendsto_nhds_top_iff_real -> EReal.tendsto_nhds_top_iff_real is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {m : α -> EReal} {f : Filter.{u1} α}, Iff (Filter.Tendsto.{u1, 0} α EReal m f (nhds.{0} EReal EReal.topologicalSpace (Top.top.{0} EReal EReal.hasTop))) (forall (x : Real), Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{0} EReal (Preorder.toLT.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) x) (m a)) f)
+  forall {α : Type.{u1}} {m : α -> EReal} {f : Filter.{u1} α}, Iff (Filter.Tendsto.{u1, 0} α EReal m f (nhds.{0} EReal EReal.topologicalSpace (Top.top.{0} EReal EReal.hasTop))) (forall (x : Real), Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{0} EReal (Preorder.toHasLt.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) x) (m a)) f)
 but is expected to have type
   forall {α : Type.{u1}} {m : α -> EReal} {f : Filter.{u1} α}, Iff (Filter.Tendsto.{u1, 0} α EReal m f (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Top.top.{0} EReal EReal.instTopEReal))) (forall (x : Real), Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{0} EReal (Preorder.toLT.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder)) (Real.toEReal x) (m a)) f)
 Case conversion may be inaccurate. Consider using '#align ereal.tendsto_nhds_top_iff_real EReal.tendsto_nhds_top_iff_realₓ'. -/
@@ -409,7 +409,7 @@ theorem mem_nhds_bot_iff {s : Set EReal} : s ∈ 𝓝 (⊥ : EReal) ↔ ∃ y :
 
 /- warning: ereal.tendsto_nhds_bot_iff_real -> EReal.tendsto_nhds_bot_iff_real is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {m : α -> EReal} {f : Filter.{u1} α}, Iff (Filter.Tendsto.{u1, 0} α EReal m f (nhds.{0} EReal EReal.topologicalSpace (Bot.bot.{0} EReal EReal.hasBot))) (forall (x : Real), Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{0} EReal (Preorder.toLT.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder))))) (m a) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) x)) f)
+  forall {α : Type.{u1}} {m : α -> EReal} {f : Filter.{u1} α}, Iff (Filter.Tendsto.{u1, 0} α EReal m f (nhds.{0} EReal EReal.topologicalSpace (Bot.bot.{0} EReal EReal.hasBot))) (forall (x : Real), Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{0} EReal (Preorder.toHasLt.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder))))) (m a) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) x)) f)
 but is expected to have type
   forall {α : Type.{u1}} {m : α -> EReal} {f : Filter.{u1} α}, Iff (Filter.Tendsto.{u1, 0} α EReal m f (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Bot.bot.{0} EReal instERealBot))) (forall (x : Real), Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{0} EReal (Preorder.toLT.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder)) (m a) (Real.toEReal x)) f)
 Case conversion may be inaccurate. Consider using '#align ereal.tendsto_nhds_bot_iff_real EReal.tendsto_nhds_bot_iff_realₓ'. -/

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

@@ -72,9 +72,9 @@ instance : SecondCountableTopology EReal :=
             by
             ext x
             simpa only [hs, and_comm', exists_prop, mem_Union] using lt_iff_exists_rat_btwn]] <;>
-      · apply isOpen_unionᵢ
+      · apply isOpen_iUnion
         intro q
-        apply isOpen_unionᵢ
+        apply isOpen_iUnion
         intro hq
         apply generate_open.basic
         exact mem_Union.2 ⟨q, by simp⟩⟩
@@ -314,9 +314,9 @@ theorem continuous_coe_ennreal_iff {f : α → ℝ≥0∞} :
 
 /- warning: ereal.nhds_top -> EReal.nhds_top is a dubious translation:
 lean 3 declaration is
-  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace (Top.top.{0} EReal EReal.hasTop)) (infᵢ.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) EReal (fun (a : EReal) => infᵢ.{0, 0} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) (Ne.{1} EReal a (Top.top.{0} EReal EReal.hasTop)) (fun (H : Ne.{1} EReal a (Top.top.{0} EReal EReal.hasTop)) => Filter.principal.{0} EReal (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) a))))
+  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace (Top.top.{0} EReal EReal.hasTop)) (iInf.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) EReal (fun (a : EReal) => iInf.{0, 0} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) (Ne.{1} EReal a (Top.top.{0} EReal EReal.hasTop)) (fun (H : Ne.{1} EReal a (Top.top.{0} EReal EReal.hasTop)) => Filter.principal.{0} EReal (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) a))))
 but is expected to have type
-  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Top.top.{0} EReal EReal.instTopEReal)) (infᵢ.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) EReal (fun (a : EReal) => infᵢ.{0, 0} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) (Ne.{1} EReal a (Top.top.{0} EReal EReal.instTopEReal)) (fun (H : Ne.{1} EReal a (Top.top.{0} EReal EReal.instTopEReal)) => Filter.principal.{0} EReal (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) a))))
+  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Top.top.{0} EReal EReal.instTopEReal)) (iInf.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) EReal (fun (a : EReal) => iInf.{0, 0} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) (Ne.{1} EReal a (Top.top.{0} EReal EReal.instTopEReal)) (fun (H : Ne.{1} EReal a (Top.top.{0} EReal EReal.instTopEReal)) => Filter.principal.{0} EReal (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) a))))
 Case conversion may be inaccurate. Consider using '#align ereal.nhds_top EReal.nhds_topₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ≠ » «expr⊤»()) -/
 theorem nhds_top : 𝓝 (⊤ : EReal) = ⨅ (a) (_ : a ≠ ⊤), 𝓟 (Ioi a) :=
@@ -325,19 +325,19 @@ theorem nhds_top : 𝓝 (⊤ : EReal) = ⨅ (a) (_ : a ≠ ⊤), 𝓟 (Ioi a) :=
 
 /- warning: ereal.nhds_top' -> EReal.nhds_top' is a dubious translation:
 lean 3 declaration is
-  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace (Top.top.{0} EReal EReal.hasTop)) (infᵢ.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) Real (fun (a : Real) => Filter.principal.{0} EReal (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a))))
+  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace (Top.top.{0} EReal EReal.hasTop)) (iInf.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) Real (fun (a : Real) => Filter.principal.{0} EReal (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a))))
 but is expected to have type
-  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Top.top.{0} EReal EReal.instTopEReal)) (infᵢ.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) Real (fun (a : Real) => Filter.principal.{0} EReal (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) (Real.toEReal a))))
+  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Top.top.{0} EReal EReal.instTopEReal)) (iInf.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) Real (fun (a : Real) => Filter.principal.{0} EReal (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) (Real.toEReal a))))
 Case conversion may be inaccurate. Consider using '#align ereal.nhds_top' EReal.nhds_top'ₓ'. -/
 theorem nhds_top' : 𝓝 (⊤ : EReal) = ⨅ a : ℝ, 𝓟 (Ioi a) :=
   by
   rw [nhds_top]
   apply le_antisymm
-  · exact infᵢ_mono' fun x => ⟨x, by simp⟩
-  · refine' le_infᵢ fun r => le_infᵢ fun hr => _
+  · exact iInf_mono' fun x => ⟨x, by simp⟩
+  · refine' le_iInf fun r => le_iInf fun hr => _
     induction r using EReal.rec
-    · exact (infᵢ_le _ 0).trans (by simp)
-    · exact infᵢ_le _ _
+    · exact (iInf_le _ 0).trans (by simp)
+    · exact iInf_le _ _
     · simpa using hr
 #align ereal.nhds_top' EReal.nhds_top'
 
@@ -367,9 +367,9 @@ theorem tendsto_nhds_top_iff_real {α : Type _} {m : α → EReal} {f : Filter 
 
 /- warning: ereal.nhds_bot -> EReal.nhds_bot is a dubious translation:
 lean 3 declaration is
-  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace (Bot.bot.{0} EReal EReal.hasBot)) (infᵢ.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) EReal (fun (a : EReal) => infᵢ.{0, 0} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) (Ne.{1} EReal a (Bot.bot.{0} EReal EReal.hasBot)) (fun (H : Ne.{1} EReal a (Bot.bot.{0} EReal EReal.hasBot)) => Filter.principal.{0} EReal (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) a))))
+  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace (Bot.bot.{0} EReal EReal.hasBot)) (iInf.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) EReal (fun (a : EReal) => iInf.{0, 0} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) (Ne.{1} EReal a (Bot.bot.{0} EReal EReal.hasBot)) (fun (H : Ne.{1} EReal a (Bot.bot.{0} EReal EReal.hasBot)) => Filter.principal.{0} EReal (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) a))))
 but is expected to have type
-  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Bot.bot.{0} EReal instERealBot)) (infᵢ.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) EReal (fun (a : EReal) => infᵢ.{0, 0} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) (Ne.{1} EReal a (Bot.bot.{0} EReal instERealBot)) (fun (H : Ne.{1} EReal a (Bot.bot.{0} EReal instERealBot)) => Filter.principal.{0} EReal (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) a))))
+  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Bot.bot.{0} EReal instERealBot)) (iInf.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) EReal (fun (a : EReal) => iInf.{0, 0} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) (Ne.{1} EReal a (Bot.bot.{0} EReal instERealBot)) (fun (H : Ne.{1} EReal a (Bot.bot.{0} EReal instERealBot)) => Filter.principal.{0} EReal (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) a))))
 Case conversion may be inaccurate. Consider using '#align ereal.nhds_bot EReal.nhds_botₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ≠ » «expr⊥»()) -/
 theorem nhds_bot : 𝓝 (⊥ : EReal) = ⨅ (a) (_ : a ≠ ⊥), 𝓟 (Iio a) :=
@@ -378,20 +378,20 @@ theorem nhds_bot : 𝓝 (⊥ : EReal) = ⨅ (a) (_ : a ≠ ⊥), 𝓟 (Iio a) :=
 
 /- warning: ereal.nhds_bot' -> EReal.nhds_bot' is a dubious translation:
 lean 3 declaration is
-  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace (Bot.bot.{0} EReal EReal.hasBot)) (infᵢ.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) Real (fun (a : Real) => Filter.principal.{0} EReal (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a))))
+  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace (Bot.bot.{0} EReal EReal.hasBot)) (iInf.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) Real (fun (a : Real) => Filter.principal.{0} EReal (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a))))
 but is expected to have type
-  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Bot.bot.{0} EReal instERealBot)) (infᵢ.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) Real (fun (a : Real) => Filter.principal.{0} EReal (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) (Real.toEReal a))))
+  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Bot.bot.{0} EReal instERealBot)) (iInf.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) Real (fun (a : Real) => Filter.principal.{0} EReal (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) (Real.toEReal a))))
 Case conversion may be inaccurate. Consider using '#align ereal.nhds_bot' EReal.nhds_bot'ₓ'. -/
 theorem nhds_bot' : 𝓝 (⊥ : EReal) = ⨅ a : ℝ, 𝓟 (Iio a) :=
   by
   rw [nhds_bot]
   apply le_antisymm
-  · exact infᵢ_mono' fun x => ⟨x, by simp⟩
-  · refine' le_infᵢ fun r => le_infᵢ fun hr => _
+  · exact iInf_mono' fun x => ⟨x, by simp⟩
+  · refine' le_iInf fun r => le_iInf fun hr => _
     induction r using EReal.rec
     · simpa using hr
-    · exact infᵢ_le _ _
-    · exact (infᵢ_le _ 0).trans (by simp)
+    · exact iInf_le _ _
+    · exact (iInf_le _ 0).trans (by simp)
 #align ereal.nhds_bot' EReal.nhds_bot'
 
 /- warning: ereal.mem_nhds_bot_iff -> EReal.mem_nhds_bot_iff is a dubious translation:

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

@@ -122,7 +122,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align ereal.open_embedding_coe EReal.openEmbedding_coeₓ'. -/
 theorem openEmbedding_coe : OpenEmbedding (coe : ℝ → EReal) :=
   ⟨embedding_coe, by
-    convert @isOpen_Ioo EReal _ _ _ ⊥ ⊤
+    convert@isOpen_Ioo EReal _ _ _ ⊥ ⊤
     ext x
     induction x using EReal.rec
     · simp only [left_mem_Ioo, mem_range, coe_ne_bot, exists_false, not_false_iff]

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module topology.instances.ereal
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.Instances.Ennreal
 /-!
 # Topological structure on `ereal`
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We endow `ereal` with the order topology, and prove basic properties of this topology.
 
 ## Main results

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

@@ -79,6 +79,12 @@ instance : SecondCountableTopology EReal :=
 /-! ### Real coercion -/
 
 
+/- warning: ereal.embedding_coe -> EReal.embedding_coe is a dubious translation:
+lean 3 declaration is
+  Embedding.{0, 0} Real EReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) EReal.topologicalSpace ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))))
+but is expected to have type
+  Embedding.{0, 0} Real EReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) EReal.instTopologicalSpaceEReal Real.toEReal
+Case conversion may be inaccurate. Consider using '#align ereal.embedding_coe EReal.embedding_coeₓ'. -/
 theorem embedding_coe : Embedding (coe : ℝ → EReal) :=
   ⟨⟨by
       refine' le_antisymm _ _
@@ -105,6 +111,12 @@ theorem embedding_coe : Embedding (coe : ℝ → EReal) :=
     simp only [imp_self, EReal.coe_eq_coe_iff]⟩
 #align ereal.embedding_coe EReal.embedding_coe
 
+/- warning: ereal.open_embedding_coe -> EReal.openEmbedding_coe is a dubious translation:
+lean 3 declaration is
+  OpenEmbedding.{0, 0} Real EReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) EReal.topologicalSpace ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))))
+but is expected to have type
+  OpenEmbedding.{0, 0} Real EReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) EReal.instTopologicalSpaceEReal Real.toEReal
+Case conversion may be inaccurate. Consider using '#align ereal.open_embedding_coe EReal.openEmbedding_coeₓ'. -/
 theorem openEmbedding_coe : OpenEmbedding (coe : ℝ → EReal) :=
   ⟨embedding_coe, by
     convert @isOpen_Ioo EReal _ _ _ ⊥ ⊤
@@ -115,29 +127,65 @@ theorem openEmbedding_coe : OpenEmbedding (coe : ℝ → EReal) :=
     · simp only [mem_range, right_mem_Ioo, exists_false, coe_ne_top]⟩
 #align ereal.open_embedding_coe EReal.openEmbedding_coe
 
+/- warning: ereal.tendsto_coe -> EReal.tendsto_coe is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {f : Filter.{u1} α} {m : α -> Real} {a : Real}, Iff (Filter.Tendsto.{u1, 0} α EReal (fun (a : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) (m a)) f (nhds.{0} EReal EReal.topologicalSpace ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a))) (Filter.Tendsto.{u1, 0} α Real m f (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) a))
+but is expected to have type
+  forall {α : Type.{u1}} {f : Filter.{u1} α} {m : α -> Real} {a : Real}, Iff (Filter.Tendsto.{u1, 0} α EReal (fun (a : α) => Real.toEReal (m a)) f (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Real.toEReal a))) (Filter.Tendsto.{u1, 0} α Real m f (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) a))
+Case conversion may be inaccurate. Consider using '#align ereal.tendsto_coe EReal.tendsto_coeₓ'. -/
 @[norm_cast]
 theorem tendsto_coe {α : Type _} {f : Filter α} {m : α → ℝ} {a : ℝ} :
     Tendsto (fun a => (m a : EReal)) f (𝓝 ↑a) ↔ Tendsto m f (𝓝 a) :=
   embedding_coe.tendsto_nhds_iff.symm
 #align ereal.tendsto_coe EReal.tendsto_coe
 
-theorem continuous_coe_real_eReal : Continuous (coe : ℝ → EReal) :=
+/- warning: continuous_coe_real_ereal -> continuous_coe_real_ereal is a dubious translation:
+lean 3 declaration is
+  Continuous.{0, 0} Real EReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) EReal.topologicalSpace ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))))
+but is expected to have type
+  Continuous.{0, 0} Real EReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) EReal.instTopologicalSpaceEReal Real.toEReal
+Case conversion may be inaccurate. Consider using '#align continuous_coe_real_ereal continuous_coe_real_erealₓ'. -/
+theorem continuous_coe_real_ereal : Continuous (coe : ℝ → EReal) :=
   embedding_coe.Continuous
-#align continuous_coe_real_ereal continuous_coe_real_eReal
-
+#align continuous_coe_real_ereal continuous_coe_real_ereal
+
+/- warning: ereal.continuous_coe_iff -> EReal.continuous_coe_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real}, Iff (Continuous.{u1, 0} α EReal _inst_1 EReal.topologicalSpace (fun (a : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) (f a))) (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> Real}, Iff (Continuous.{u1, 0} α EReal _inst_1 EReal.instTopologicalSpaceEReal (fun (a : α) => Real.toEReal (f a))) (Continuous.{u1, 0} α Real _inst_1 (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) f)
+Case conversion may be inaccurate. Consider using '#align ereal.continuous_coe_iff EReal.continuous_coe_iffₓ'. -/
 theorem continuous_coe_iff {f : α → ℝ} : (Continuous fun a => (f a : EReal)) ↔ Continuous f :=
   embedding_coe.continuous_iff.symm
 #align ereal.continuous_coe_iff EReal.continuous_coe_iff
 
+/- warning: ereal.nhds_coe -> EReal.nhds_coe is a dubious translation:
+lean 3 declaration is
+  forall {r : Real}, Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) r)) (Filter.map.{0, 0} Real EReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) r))
+but is expected to have type
+  forall {r : Real}, Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Real.toEReal r)) (Filter.map.{0, 0} Real EReal Real.toEReal (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) r))
+Case conversion may be inaccurate. Consider using '#align ereal.nhds_coe EReal.nhds_coeₓ'. -/
 theorem nhds_coe {r : ℝ} : 𝓝 (r : EReal) = (𝓝 r).map coe :=
   (openEmbedding_coe.map_nhds_eq r).symm
 #align ereal.nhds_coe EReal.nhds_coe
 
+/- warning: ereal.nhds_coe_coe -> EReal.nhds_coe_coe is a dubious translation:
+lean 3 declaration is
+  forall {r : Real} {p : Real}, Eq.{1} (Filter.{0} (Prod.{0, 0} EReal EReal)) (nhds.{0} (Prod.{0, 0} EReal EReal) (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) (Prod.mk.{0, 0} EReal EReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) r) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) p))) (Filter.map.{0, 0} (Prod.{0, 0} Real Real) (Prod.{0, 0} EReal EReal) (fun (p : Prod.{0, 0} Real Real) => Prod.mk.{0, 0} EReal EReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) (Prod.fst.{0, 0} Real Real p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) (Prod.snd.{0, 0} Real Real p))) (nhds.{0} (Prod.{0, 0} Real Real) (Prod.topologicalSpace.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (Prod.mk.{0, 0} Real Real r p)))
+but is expected to have type
+  forall {r : Real} {p : Real}, Eq.{1} (Filter.{0} (Prod.{0, 0} EReal EReal)) (nhds.{0} (Prod.{0, 0} EReal EReal) (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) (Prod.mk.{0, 0} EReal EReal (Real.toEReal r) (Real.toEReal p))) (Filter.map.{0, 0} (Prod.{0, 0} Real Real) (Prod.{0, 0} EReal EReal) (fun (p : Prod.{0, 0} Real Real) => Prod.mk.{0, 0} EReal EReal (Real.toEReal (Prod.fst.{0, 0} Real Real p)) (Real.toEReal (Prod.snd.{0, 0} Real Real p))) (nhds.{0} (Prod.{0, 0} Real Real) (instTopologicalSpaceProd.{0, 0} Real Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) (Prod.mk.{0, 0} Real Real r p)))
+Case conversion may be inaccurate. Consider using '#align ereal.nhds_coe_coe EReal.nhds_coe_coeₓ'. -/
 theorem nhds_coe_coe {r p : ℝ} :
     𝓝 ((r : EReal), (p : EReal)) = (𝓝 (r, p)).map fun p : ℝ × ℝ => (p.1, p.2) :=
   ((openEmbedding_coe.Prod openEmbedding_coe).map_nhds_eq (r, p)).symm
 #align ereal.nhds_coe_coe EReal.nhds_coe_coe
 
+/- warning: ereal.tendsto_to_real -> EReal.tendsto_toReal is a dubious translation:
+lean 3 declaration is
+  forall {a : EReal}, (Ne.{1} EReal a (Top.top.{0} EReal EReal.hasTop)) -> (Ne.{1} EReal a (Bot.bot.{0} EReal EReal.hasBot)) -> (Filter.Tendsto.{0, 0} EReal Real EReal.toReal (nhds.{0} EReal EReal.topologicalSpace a) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (EReal.toReal a)))
+but is expected to have type
+  forall {a : EReal}, (Ne.{1} EReal a (Top.top.{0} EReal EReal.instTopEReal)) -> (Ne.{1} EReal a (Bot.bot.{0} EReal instERealBot)) -> (Filter.Tendsto.{0, 0} EReal Real EReal.toReal (nhds.{0} EReal EReal.instTopologicalSpaceEReal a) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (EReal.toReal a)))
+Case conversion may be inaccurate. Consider using '#align ereal.tendsto_to_real EReal.tendsto_toRealₓ'. -/
 theorem tendsto_toReal {a : EReal} (ha : a ≠ ⊤) (h'a : a ≠ ⊥) :
     Tendsto EReal.toReal (𝓝 a) (𝓝 a.toReal) :=
   by
@@ -146,6 +194,12 @@ theorem tendsto_toReal {a : EReal} (ha : a ≠ ⊤) (h'a : a ≠ ⊥) :
   exact tendsto_id
 #align ereal.tendsto_to_real EReal.tendsto_toReal
 
+/- warning: ereal.continuous_on_to_real -> EReal.continuousOn_toReal is a dubious translation:
+lean 3 declaration is
+  ContinuousOn.{0, 0} EReal Real EReal.topologicalSpace (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) EReal.toReal (HasCompl.compl.{0} (Set.{0} EReal) (BooleanAlgebra.toHasCompl.{0} (Set.{0} EReal) (Set.booleanAlgebra.{0} EReal)) (Insert.insert.{0, 0} EReal (Set.{0} EReal) (Set.hasInsert.{0} EReal) (Bot.bot.{0} EReal EReal.hasBot) (Singleton.singleton.{0, 0} EReal (Set.{0} EReal) (Set.hasSingleton.{0} EReal) (Top.top.{0} EReal EReal.hasTop))))
+but is expected to have type
+  ContinuousOn.{0, 0} EReal Real EReal.instTopologicalSpaceEReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) EReal.toReal (HasCompl.compl.{0} (Set.{0} EReal) (BooleanAlgebra.toHasCompl.{0} (Set.{0} EReal) (Set.instBooleanAlgebraSet.{0} EReal)) (Insert.insert.{0, 0} EReal (Set.{0} EReal) (Set.instInsertSet.{0} EReal) (Bot.bot.{0} EReal instERealBot) (Singleton.singleton.{0, 0} EReal (Set.{0} EReal) (Set.instSingletonSet.{0} EReal) (Top.top.{0} EReal EReal.instTopEReal))))
+Case conversion may be inaccurate. Consider using '#align ereal.continuous_on_to_real EReal.continuousOn_toRealₓ'. -/
 theorem continuousOn_toReal : ContinuousOn EReal.toReal ({⊥, ⊤}ᶜ : Set EReal) := fun a ha =>
   ContinuousAt.continuousWithinAt
     (tendsto_toReal
@@ -157,18 +211,30 @@ theorem continuousOn_toReal : ContinuousOn EReal.toReal ({⊥, ⊤}ᶜ : Set ERe
         exact ha.1))
 #align ereal.continuous_on_to_real EReal.continuousOn_toReal
 
+/- warning: ereal.ne_bot_top_homeomorph_real -> EReal.neBotTopHomeomorphReal is a dubious translation:
+lean 3 declaration is
+  Homeomorph.{0, 0} (coeSort.{1, 2} (Set.{0} EReal) Type (Set.hasCoeToSort.{0} EReal) (HasCompl.compl.{0} (Set.{0} EReal) (BooleanAlgebra.toHasCompl.{0} (Set.{0} EReal) (Set.booleanAlgebra.{0} EReal)) (Insert.insert.{0, 0} EReal (Set.{0} EReal) (Set.hasInsert.{0} EReal) (Bot.bot.{0} EReal EReal.hasBot) (Singleton.singleton.{0, 0} EReal (Set.{0} EReal) (Set.hasSingleton.{0} EReal) (Top.top.{0} EReal EReal.hasTop))))) Real (Subtype.topologicalSpace.{0} EReal (fun (x : EReal) => Membership.Mem.{0, 0} EReal (Set.{0} EReal) (Set.hasMem.{0} EReal) x (HasCompl.compl.{0} (Set.{0} EReal) (BooleanAlgebra.toHasCompl.{0} (Set.{0} EReal) (Set.booleanAlgebra.{0} EReal)) (Insert.insert.{0, 0} EReal (Set.{0} EReal) (Set.hasInsert.{0} EReal) (Bot.bot.{0} EReal EReal.hasBot) (Singleton.singleton.{0, 0} EReal (Set.{0} EReal) (Set.hasSingleton.{0} EReal) (Top.top.{0} EReal EReal.hasTop))))) EReal.topologicalSpace) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))
+but is expected to have type
+  Homeomorph.{0, 0} (Set.Elem.{0} EReal (HasCompl.compl.{0} (Set.{0} EReal) (BooleanAlgebra.toHasCompl.{0} (Set.{0} EReal) (Set.instBooleanAlgebraSet.{0} EReal)) (Insert.insert.{0, 0} EReal (Set.{0} EReal) (Set.instInsertSet.{0} EReal) (Bot.bot.{0} EReal instERealBot) (Singleton.singleton.{0, 0} EReal (Set.{0} EReal) (Set.instSingletonSet.{0} EReal) (Top.top.{0} EReal EReal.instTopEReal))))) Real (instTopologicalSpaceSubtype.{0} EReal (fun (x : EReal) => Membership.mem.{0, 0} EReal (Set.{0} EReal) (Set.instMembershipSet.{0} EReal) x (HasCompl.compl.{0} (Set.{0} EReal) (BooleanAlgebra.toHasCompl.{0} (Set.{0} EReal) (Set.instBooleanAlgebraSet.{0} EReal)) (Insert.insert.{0, 0} EReal (Set.{0} EReal) (Set.instInsertSet.{0} EReal) (Bot.bot.{0} EReal instERealBot) (Singleton.singleton.{0, 0} EReal (Set.{0} EReal) (Set.instSingletonSet.{0} EReal) (Top.top.{0} EReal EReal.instTopEReal))))) EReal.instTopologicalSpaceEReal) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))
+Case conversion may be inaccurate. Consider using '#align ereal.ne_bot_top_homeomorph_real EReal.neBotTopHomeomorphRealₓ'. -/
 /-- The set of finite `ereal` numbers is homeomorphic to `ℝ`. -/
 def neBotTopHomeomorphReal : ({⊥, ⊤}ᶜ : Set EReal) ≃ₜ ℝ :=
   {
     neTopBotEquivReal with
     continuous_toFun := continuousOn_iff_continuous_restrict.1 continuousOn_toReal
-    continuous_invFun := continuous_coe_real_eReal.subtype_mk _ }
+    continuous_invFun := continuous_coe_real_ereal.subtype_mk _ }
 #align ereal.ne_bot_top_homeomorph_real EReal.neBotTopHomeomorphReal
 
 /-! ### ennreal coercion -/
 
 
-theorem embedding_coe_eNNReal : Embedding (coe : ℝ≥0∞ → EReal) :=
+/- warning: ereal.embedding_coe_ennreal -> EReal.embedding_coe_ennreal is a dubious translation:
+lean 3 declaration is
+  Embedding.{0, 0} ENNReal EReal ENNReal.topologicalSpace EReal.topologicalSpace ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) ENNReal EReal (HasLiftT.mk.{1, 1} ENNReal EReal (CoeTCₓ.coe.{1, 1} ENNReal EReal (coeBase.{1, 1} ENNReal EReal EReal.hasCoeENNReal))))
+but is expected to have type
+  Embedding.{0, 0} ENNReal EReal ENNReal.instTopologicalSpaceENNReal EReal.instTopologicalSpaceEReal ENNReal.toEReal
+Case conversion may be inaccurate. Consider using '#align ereal.embedding_coe_ennreal EReal.embedding_coe_ennrealₓ'. -/
+theorem embedding_coe_ennreal : Embedding (coe : ℝ≥0∞ → EReal) :=
   ⟨⟨by
       refine' le_antisymm _ _
       · rw [@OrderTopology.topology_eq_generate_intervals EReal _, ← coinduced_le_iff_le_induced]
@@ -205,31 +271,61 @@ theorem embedding_coe_eNNReal : Embedding (coe : ℝ≥0∞ → EReal) :=
         exact ⟨Ioi a, isOpen_Ioi, by simp [Ioi]⟩
         exact ⟨Iio a, isOpen_Iio, by simp [Iio]⟩⟩, fun a b => by
     simp only [imp_self, coe_ennreal_eq_coe_ennreal_iff]⟩
-#align ereal.embedding_coe_ennreal EReal.embedding_coe_eNNReal
-
+#align ereal.embedding_coe_ennreal EReal.embedding_coe_ennreal
+
+/- warning: ereal.tendsto_coe_ennreal -> EReal.tendsto_coe_ennreal is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {f : Filter.{u1} α} {m : α -> ENNReal} {a : ENNReal}, Iff (Filter.Tendsto.{u1, 0} α EReal (fun (a : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) ENNReal EReal (HasLiftT.mk.{1, 1} ENNReal EReal (CoeTCₓ.coe.{1, 1} ENNReal EReal (coeBase.{1, 1} ENNReal EReal EReal.hasCoeENNReal))) (m a)) f (nhds.{0} EReal EReal.topologicalSpace ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) ENNReal EReal (HasLiftT.mk.{1, 1} ENNReal EReal (CoeTCₓ.coe.{1, 1} ENNReal EReal (coeBase.{1, 1} ENNReal EReal EReal.hasCoeENNReal))) a))) (Filter.Tendsto.{u1, 0} α ENNReal m f (nhds.{0} ENNReal ENNReal.topologicalSpace a))
+but is expected to have type
+  forall {α : Type.{u1}} {f : Filter.{u1} α} {m : α -> ENNReal} {a : ENNReal}, Iff (Filter.Tendsto.{u1, 0} α EReal (fun (a : α) => ENNReal.toEReal (m a)) f (nhds.{0} EReal EReal.instTopologicalSpaceEReal (ENNReal.toEReal a))) (Filter.Tendsto.{u1, 0} α ENNReal m f (nhds.{0} ENNReal ENNReal.instTopologicalSpaceENNReal a))
+Case conversion may be inaccurate. Consider using '#align ereal.tendsto_coe_ennreal EReal.tendsto_coe_ennrealₓ'. -/
 @[norm_cast]
-theorem tendsto_coe_eNNReal {α : Type _} {f : Filter α} {m : α → ℝ≥0∞} {a : ℝ≥0∞} :
+theorem tendsto_coe_ennreal {α : Type _} {f : Filter α} {m : α → ℝ≥0∞} {a : ℝ≥0∞} :
     Tendsto (fun a => (m a : EReal)) f (𝓝 ↑a) ↔ Tendsto m f (𝓝 a) :=
-  embedding_coe_eNNReal.tendsto_nhds_iff.symm
-#align ereal.tendsto_coe_ennreal EReal.tendsto_coe_eNNReal
-
-theorem continuous_coe_eNNReal_eReal : Continuous (coe : ℝ≥0∞ → EReal) :=
-  embedding_coe_eNNReal.Continuous
-#align continuous_coe_ennreal_ereal continuous_coe_eNNReal_eReal
-
-theorem continuous_coe_eNNReal_iff {f : α → ℝ≥0∞} :
+  embedding_coe_ennreal.tendsto_nhds_iff.symm
+#align ereal.tendsto_coe_ennreal EReal.tendsto_coe_ennreal
+
+/- warning: continuous_coe_ennreal_ereal -> continuous_coe_ennreal_ereal is a dubious translation:
+lean 3 declaration is
+  Continuous.{0, 0} ENNReal EReal ENNReal.topologicalSpace EReal.topologicalSpace ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) ENNReal EReal (HasLiftT.mk.{1, 1} ENNReal EReal (CoeTCₓ.coe.{1, 1} ENNReal EReal (coeBase.{1, 1} ENNReal EReal EReal.hasCoeENNReal))))
+but is expected to have type
+  Continuous.{0, 0} ENNReal EReal ENNReal.instTopologicalSpaceENNReal EReal.instTopologicalSpaceEReal ENNReal.toEReal
+Case conversion may be inaccurate. Consider using '#align continuous_coe_ennreal_ereal continuous_coe_ennreal_erealₓ'. -/
+theorem continuous_coe_ennreal_ereal : Continuous (coe : ℝ≥0∞ → EReal) :=
+  embedding_coe_ennreal.Continuous
+#align continuous_coe_ennreal_ereal continuous_coe_ennreal_ereal
+
+/- warning: ereal.continuous_coe_ennreal_iff -> EReal.continuous_coe_ennreal_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> ENNReal}, Iff (Continuous.{u1, 0} α EReal _inst_1 EReal.topologicalSpace (fun (a : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) ENNReal EReal (HasLiftT.mk.{1, 1} ENNReal EReal (CoeTCₓ.coe.{1, 1} ENNReal EReal (coeBase.{1, 1} ENNReal EReal EReal.hasCoeENNReal))) (f a))) (Continuous.{u1, 0} α ENNReal _inst_1 ENNReal.topologicalSpace f)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {f : α -> ENNReal}, Iff (Continuous.{u1, 0} α EReal _inst_1 EReal.instTopologicalSpaceEReal (fun (a : α) => ENNReal.toEReal (f a))) (Continuous.{u1, 0} α ENNReal _inst_1 ENNReal.instTopologicalSpaceENNReal f)
+Case conversion may be inaccurate. Consider using '#align ereal.continuous_coe_ennreal_iff EReal.continuous_coe_ennreal_iffₓ'. -/
+theorem continuous_coe_ennreal_iff {f : α → ℝ≥0∞} :
     (Continuous fun a => (f a : EReal)) ↔ Continuous f :=
-  embedding_coe_eNNReal.continuous_iff.symm
-#align ereal.continuous_coe_ennreal_iff EReal.continuous_coe_eNNReal_iff
+  embedding_coe_ennreal.continuous_iff.symm
+#align ereal.continuous_coe_ennreal_iff EReal.continuous_coe_ennreal_iff
 
 /-! ### Neighborhoods of infinity -/
 
 
+/- warning: ereal.nhds_top -> EReal.nhds_top is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace (Top.top.{0} EReal EReal.hasTop)) (infᵢ.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) EReal (fun (a : EReal) => infᵢ.{0, 0} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) (Ne.{1} EReal a (Top.top.{0} EReal EReal.hasTop)) (fun (H : Ne.{1} EReal a (Top.top.{0} EReal EReal.hasTop)) => Filter.principal.{0} EReal (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) a))))
+but is expected to have type
+  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Top.top.{0} EReal EReal.instTopEReal)) (infᵢ.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) EReal (fun (a : EReal) => infᵢ.{0, 0} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) (Ne.{1} EReal a (Top.top.{0} EReal EReal.instTopEReal)) (fun (H : Ne.{1} EReal a (Top.top.{0} EReal EReal.instTopEReal)) => Filter.principal.{0} EReal (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) a))))
+Case conversion may be inaccurate. Consider using '#align ereal.nhds_top EReal.nhds_topₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ≠ » «expr⊤»()) -/
 theorem nhds_top : 𝓝 (⊤ : EReal) = ⨅ (a) (_ : a ≠ ⊤), 𝓟 (Ioi a) :=
   nhds_top_order.trans <| by simp [lt_top_iff_ne_top, Ioi]
 #align ereal.nhds_top EReal.nhds_top
 
+/- warning: ereal.nhds_top' -> EReal.nhds_top' is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace (Top.top.{0} EReal EReal.hasTop)) (infᵢ.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) Real (fun (a : Real) => Filter.principal.{0} EReal (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a))))
+but is expected to have type
+  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Top.top.{0} EReal EReal.instTopEReal)) (infᵢ.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) Real (fun (a : Real) => Filter.principal.{0} EReal (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) (Real.toEReal a))))
+Case conversion may be inaccurate. Consider using '#align ereal.nhds_top' EReal.nhds_top'ₓ'. -/
 theorem nhds_top' : 𝓝 (⊤ : EReal) = ⨅ a : ℝ, 𝓟 (Ioi a) :=
   by
   rw [nhds_top]
@@ -242,6 +338,12 @@ theorem nhds_top' : 𝓝 (⊤ : EReal) = ⨅ a : ℝ, 𝓟 (Ioi a) :=
     · simpa using hr
 #align ereal.nhds_top' EReal.nhds_top'
 
+/- warning: ereal.mem_nhds_top_iff -> EReal.mem_nhds_top_iff is a dubious translation:
+lean 3 declaration is
+  forall {s : Set.{0} EReal}, Iff (Membership.Mem.{0, 0} (Set.{0} EReal) (Filter.{0} EReal) (Filter.hasMem.{0} EReal) s (nhds.{0} EReal EReal.topologicalSpace (Top.top.{0} EReal EReal.hasTop))) (Exists.{1} Real (fun (y : Real) => HasSubset.Subset.{0} (Set.{0} EReal) (Set.hasSubset.{0} EReal) (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) y)) s))
+but is expected to have type
+  forall {s : Set.{0} EReal}, Iff (Membership.mem.{0, 0} (Set.{0} EReal) (Filter.{0} EReal) (instMembershipSetFilter.{0} EReal) s (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Top.top.{0} EReal EReal.instTopEReal))) (Exists.{1} Real (fun (y : Real) => HasSubset.Subset.{0} (Set.{0} EReal) (Set.instHasSubsetSet.{0} EReal) (Set.Ioi.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) (Real.toEReal y)) s))
+Case conversion may be inaccurate. Consider using '#align ereal.mem_nhds_top_iff EReal.mem_nhds_top_iffₓ'. -/
 theorem mem_nhds_top_iff {s : Set EReal} : s ∈ 𝓝 (⊤ : EReal) ↔ ∃ y : ℝ, Ioi (y : EReal) ⊆ s :=
   by
   rw [nhds_top', mem_infi_of_directed]
@@ -249,16 +351,34 @@ theorem mem_nhds_top_iff {s : Set EReal} : s ∈ 𝓝 (⊤ : EReal) ↔ ∃ y :
   exact fun x y => ⟨max x y, by simp [le_refl], by simp [le_refl]⟩
 #align ereal.mem_nhds_top_iff EReal.mem_nhds_top_iff
 
+/- warning: ereal.tendsto_nhds_top_iff_real -> EReal.tendsto_nhds_top_iff_real is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {m : α -> EReal} {f : Filter.{u1} α}, Iff (Filter.Tendsto.{u1, 0} α EReal m f (nhds.{0} EReal EReal.topologicalSpace (Top.top.{0} EReal EReal.hasTop))) (forall (x : Real), Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{0} EReal (Preorder.toLT.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) x) (m a)) f)
+but is expected to have type
+  forall {α : Type.{u1}} {m : α -> EReal} {f : Filter.{u1} α}, Iff (Filter.Tendsto.{u1, 0} α EReal m f (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Top.top.{0} EReal EReal.instTopEReal))) (forall (x : Real), Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{0} EReal (Preorder.toLT.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder)) (Real.toEReal x) (m a)) f)
+Case conversion may be inaccurate. Consider using '#align ereal.tendsto_nhds_top_iff_real EReal.tendsto_nhds_top_iff_realₓ'. -/
 theorem tendsto_nhds_top_iff_real {α : Type _} {m : α → EReal} {f : Filter α} :
     Tendsto m f (𝓝 ⊤) ↔ ∀ x : ℝ, ∀ᶠ a in f, ↑x < m a := by
   simp only [nhds_top', mem_Ioi, tendsto_infi, tendsto_principal]
 #align ereal.tendsto_nhds_top_iff_real EReal.tendsto_nhds_top_iff_real
 
+/- warning: ereal.nhds_bot -> EReal.nhds_bot is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace (Bot.bot.{0} EReal EReal.hasBot)) (infᵢ.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) EReal (fun (a : EReal) => infᵢ.{0, 0} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) (Ne.{1} EReal a (Bot.bot.{0} EReal EReal.hasBot)) (fun (H : Ne.{1} EReal a (Bot.bot.{0} EReal EReal.hasBot)) => Filter.principal.{0} EReal (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) a))))
+but is expected to have type
+  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Bot.bot.{0} EReal instERealBot)) (infᵢ.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) EReal (fun (a : EReal) => infᵢ.{0, 0} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) (Ne.{1} EReal a (Bot.bot.{0} EReal instERealBot)) (fun (H : Ne.{1} EReal a (Bot.bot.{0} EReal instERealBot)) => Filter.principal.{0} EReal (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) a))))
+Case conversion may be inaccurate. Consider using '#align ereal.nhds_bot EReal.nhds_botₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ≠ » «expr⊥»()) -/
 theorem nhds_bot : 𝓝 (⊥ : EReal) = ⨅ (a) (_ : a ≠ ⊥), 𝓟 (Iio a) :=
   nhds_bot_order.trans <| by simp [bot_lt_iff_ne_bot]
 #align ereal.nhds_bot EReal.nhds_bot
 
+/- warning: ereal.nhds_bot' -> EReal.nhds_bot' is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.topologicalSpace (Bot.bot.{0} EReal EReal.hasBot)) (infᵢ.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toHasInf.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.completeLattice.{0} EReal))) Real (fun (a : Real) => Filter.principal.{0} EReal (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a))))
+but is expected to have type
+  Eq.{1} (Filter.{0} EReal) (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Bot.bot.{0} EReal instERealBot)) (infᵢ.{0, 1} (Filter.{0} EReal) (ConditionallyCompleteLattice.toInfSet.{0} (Filter.{0} EReal) (CompleteLattice.toConditionallyCompleteLattice.{0} (Filter.{0} EReal) (Filter.instCompleteLatticeFilter.{0} EReal))) Real (fun (a : Real) => Filter.principal.{0} EReal (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) (Real.toEReal a))))
+Case conversion may be inaccurate. Consider using '#align ereal.nhds_bot' EReal.nhds_bot'ₓ'. -/
 theorem nhds_bot' : 𝓝 (⊥ : EReal) = ⨅ a : ℝ, 𝓟 (Iio a) :=
   by
   rw [nhds_bot]
@@ -271,6 +391,12 @@ theorem nhds_bot' : 𝓝 (⊥ : EReal) = ⨅ a : ℝ, 𝓟 (Iio a) :=
     · exact (infᵢ_le _ 0).trans (by simp)
 #align ereal.nhds_bot' EReal.nhds_bot'
 
+/- warning: ereal.mem_nhds_bot_iff -> EReal.mem_nhds_bot_iff is a dubious translation:
+lean 3 declaration is
+  forall {s : Set.{0} EReal}, Iff (Membership.Mem.{0, 0} (Set.{0} EReal) (Filter.{0} EReal) (Filter.hasMem.{0} EReal) s (nhds.{0} EReal EReal.topologicalSpace (Bot.bot.{0} EReal EReal.hasBot))) (Exists.{1} Real (fun (y : Real) => HasSubset.Subset.{0} (Set.{0} EReal) (Set.hasSubset.{0} EReal) (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) y)) s))
+but is expected to have type
+  forall {s : Set.{0} EReal}, Iff (Membership.mem.{0, 0} (Set.{0} EReal) (Filter.{0} EReal) (instMembershipSetFilter.{0} EReal) s (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Bot.bot.{0} EReal instERealBot))) (Exists.{1} Real (fun (y : Real) => HasSubset.Subset.{0} (Set.{0} EReal) (Set.instHasSubsetSet.{0} EReal) (Set.Iio.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder) (Real.toEReal y)) s))
+Case conversion may be inaccurate. Consider using '#align ereal.mem_nhds_bot_iff EReal.mem_nhds_bot_iffₓ'. -/
 theorem mem_nhds_bot_iff {s : Set EReal} : s ∈ 𝓝 (⊥ : EReal) ↔ ∃ y : ℝ, Iio (y : EReal) ⊆ s :=
   by
   rw [nhds_bot', mem_infi_of_directed]
@@ -278,6 +404,12 @@ theorem mem_nhds_bot_iff {s : Set EReal} : s ∈ 𝓝 (⊥ : EReal) ↔ ∃ y :
   exact fun x y => ⟨min x y, by simp [le_refl], by simp [le_refl]⟩
 #align ereal.mem_nhds_bot_iff EReal.mem_nhds_bot_iff
 
+/- warning: ereal.tendsto_nhds_bot_iff_real -> EReal.tendsto_nhds_bot_iff_real is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {m : α -> EReal} {f : Filter.{u1} α}, Iff (Filter.Tendsto.{u1, 0} α EReal m f (nhds.{0} EReal EReal.topologicalSpace (Bot.bot.{0} EReal EReal.hasBot))) (forall (x : Real), Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{0} EReal (Preorder.toLT.{0} EReal (PartialOrder.toPreorder.{0} EReal (CompleteSemilatticeInf.toPartialOrder.{0} EReal (CompleteLattice.toCompleteSemilatticeInf.{0} EReal (CompleteLinearOrder.toCompleteLattice.{0} EReal EReal.completeLinearOrder))))) (m a) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) x)) f)
+but is expected to have type
+  forall {α : Type.{u1}} {m : α -> EReal} {f : Filter.{u1} α}, Iff (Filter.Tendsto.{u1, 0} α EReal m f (nhds.{0} EReal EReal.instTopologicalSpaceEReal (Bot.bot.{0} EReal instERealBot))) (forall (x : Real), Filter.Eventually.{u1} α (fun (a : α) => LT.lt.{0} EReal (Preorder.toLT.{0} EReal (PartialOrder.toPreorder.{0} EReal instERealPartialOrder)) (m a) (Real.toEReal x)) f)
+Case conversion may be inaccurate. Consider using '#align ereal.tendsto_nhds_bot_iff_real EReal.tendsto_nhds_bot_iff_realₓ'. -/
 theorem tendsto_nhds_bot_iff_real {α : Type _} {m : α → EReal} {f : Filter α} :
     Tendsto m f (𝓝 ⊥) ↔ ∀ x : ℝ, ∀ᶠ a in f, m a < x := by
   simp only [nhds_bot', mem_Iio, tendsto_infi, tendsto_principal]
@@ -286,12 +418,24 @@ theorem tendsto_nhds_bot_iff_real {α : Type _} {m : α → EReal} {f : Filter 
 /-! ### Continuity of addition -/
 
 
+/- warning: ereal.continuous_at_add_coe_coe -> EReal.continuousAt_add_coe_coe is a dubious translation:
+lean 3 declaration is
+  forall (a : Real) (b : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) EReal.topologicalSpace (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toHasAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal EReal.addMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) b))
+but is expected to have type
+  forall (a : Real) (b : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) EReal.instTopologicalSpaceEReal (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal instERealAddMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Real.toEReal a) (Real.toEReal b))
+Case conversion may be inaccurate. Consider using '#align ereal.continuous_at_add_coe_coe EReal.continuousAt_add_coe_coeₓ'. -/
 theorem continuousAt_add_coe_coe (a b : ℝ) :
     ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (a, b) := by
   simp only [ContinuousAt, nhds_coe_coe, ← coe_add, tendsto_map'_iff, (· ∘ ·), tendsto_coe,
     tendsto_add]
 #align ereal.continuous_at_add_coe_coe EReal.continuousAt_add_coe_coe
 
+/- warning: ereal.continuous_at_add_top_coe -> EReal.continuousAt_add_top_coe is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) EReal.topologicalSpace (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toHasAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal EReal.addMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Top.top.{0} EReal EReal.hasTop) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a))
+but is expected to have type
+  forall (a : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) EReal.instTopologicalSpaceEReal (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal instERealAddMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Top.top.{0} EReal EReal.instTopEReal) (Real.toEReal a))
+Case conversion may be inaccurate. Consider using '#align ereal.continuous_at_add_top_coe EReal.continuousAt_add_top_coeₓ'. -/
 theorem continuousAt_add_top_coe (a : ℝ) :
     ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (⊤, a) :=
   by
@@ -306,6 +450,12 @@ theorem continuousAt_add_top_coe (a : ℝ) :
   simp
 #align ereal.continuous_at_add_top_coe EReal.continuousAt_add_top_coe
 
+/- warning: ereal.continuous_at_add_coe_top -> EReal.continuousAt_add_coe_top is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) EReal.topologicalSpace (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toHasAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal EReal.addMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a) (Top.top.{0} EReal EReal.hasTop))
+but is expected to have type
+  forall (a : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) EReal.instTopologicalSpaceEReal (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal instERealAddMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Real.toEReal a) (Top.top.{0} EReal EReal.instTopEReal))
+Case conversion may be inaccurate. Consider using '#align ereal.continuous_at_add_coe_top EReal.continuousAt_add_coe_topₓ'. -/
 theorem continuousAt_add_coe_top (a : ℝ) :
     ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (a, ⊤) :=
   by
@@ -315,6 +465,12 @@ theorem continuousAt_add_coe_top (a : ℝ) :
   exact continuous_at_add_top_coe a
 #align ereal.continuous_at_add_coe_top EReal.continuousAt_add_coe_top
 
+/- warning: ereal.continuous_at_add_top_top -> EReal.continuousAt_add_top_top is a dubious translation:
+lean 3 declaration is
+  ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) EReal.topologicalSpace (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toHasAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal EReal.addMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Top.top.{0} EReal EReal.hasTop) (Top.top.{0} EReal EReal.hasTop))
+but is expected to have type
+  ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) EReal.instTopologicalSpaceEReal (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal instERealAddMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Top.top.{0} EReal EReal.instTopEReal) (Top.top.{0} EReal EReal.instTopEReal))
+Case conversion may be inaccurate. Consider using '#align ereal.continuous_at_add_top_top EReal.continuousAt_add_top_topₓ'. -/
 theorem continuousAt_add_top_top : ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (⊤, ⊤) :=
   by
   simp only [ContinuousAt, tendsto_nhds_top_iff_real, top_add_top, nhds_prod_eq]
@@ -328,6 +484,12 @@ theorem continuousAt_add_top_top : ContinuousAt (fun p : EReal × EReal => p.1 +
   simp
 #align ereal.continuous_at_add_top_top EReal.continuousAt_add_top_top
 
+/- warning: ereal.continuous_at_add_bot_coe -> EReal.continuousAt_add_bot_coe is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) EReal.topologicalSpace (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toHasAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal EReal.addMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Bot.bot.{0} EReal EReal.hasBot) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a))
+but is expected to have type
+  forall (a : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) EReal.instTopologicalSpaceEReal (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal instERealAddMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Bot.bot.{0} EReal instERealBot) (Real.toEReal a))
+Case conversion may be inaccurate. Consider using '#align ereal.continuous_at_add_bot_coe EReal.continuousAt_add_bot_coeₓ'. -/
 theorem continuousAt_add_bot_coe (a : ℝ) :
     ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (⊥, a) :=
   by
@@ -341,6 +503,12 @@ theorem continuousAt_add_bot_coe (a : ℝ) :
   rw [sub_add_cancel]
 #align ereal.continuous_at_add_bot_coe EReal.continuousAt_add_bot_coe
 
+/- warning: ereal.continuous_at_add_coe_bot -> EReal.continuousAt_add_coe_bot is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) EReal.topologicalSpace (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toHasAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal EReal.addMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real EReal (HasLiftT.mk.{1, 1} Real EReal (CoeTCₓ.coe.{1, 1} Real EReal (coeBase.{1, 1} Real EReal EReal.hasCoe))) a) (Bot.bot.{0} EReal EReal.hasBot))
+but is expected to have type
+  forall (a : Real), ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) EReal.instTopologicalSpaceEReal (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal instERealAddMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Real.toEReal a) (Bot.bot.{0} EReal instERealBot))
+Case conversion may be inaccurate. Consider using '#align ereal.continuous_at_add_coe_bot EReal.continuousAt_add_coe_botₓ'. -/
 theorem continuousAt_add_coe_bot (a : ℝ) :
     ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (a, ⊥) :=
   by
@@ -350,6 +518,12 @@ theorem continuousAt_add_coe_bot (a : ℝ) :
   exact continuous_at_add_bot_coe a
 #align ereal.continuous_at_add_coe_bot EReal.continuousAt_add_coe_bot
 
+/- warning: ereal.continuous_at_add_bot_bot -> EReal.continuousAt_add_bot_bot is a dubious translation:
+lean 3 declaration is
+  ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) EReal.topologicalSpace (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toHasAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal EReal.addMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Bot.bot.{0} EReal EReal.hasBot) (Bot.bot.{0} EReal EReal.hasBot))
+but is expected to have type
+  ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) EReal.instTopologicalSpaceEReal (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal instERealAddMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) (Prod.mk.{0, 0} EReal EReal (Bot.bot.{0} EReal instERealBot) (Bot.bot.{0} EReal instERealBot))
+Case conversion may be inaccurate. Consider using '#align ereal.continuous_at_add_bot_bot EReal.continuousAt_add_bot_botₓ'. -/
 theorem continuousAt_add_bot_bot : ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (⊥, ⊥) :=
   by
   simp only [ContinuousAt, tendsto_nhds_bot_iff_real, nhds_prod_eq, bot_add]
@@ -363,6 +537,12 @@ theorem continuousAt_add_bot_bot : ContinuousAt (fun p : EReal × EReal => p.1 +
   simp
 #align ereal.continuous_at_add_bot_bot EReal.continuousAt_add_bot_bot
 
+/- warning: ereal.continuous_at_add -> EReal.continuousAt_add is a dubious translation:
+lean 3 declaration is
+  forall {p : Prod.{0, 0} EReal EReal}, (Or (Ne.{1} EReal (Prod.fst.{0, 0} EReal EReal p) (Top.top.{0} EReal EReal.hasTop)) (Ne.{1} EReal (Prod.snd.{0, 0} EReal EReal p) (Bot.bot.{0} EReal EReal.hasBot))) -> (Or (Ne.{1} EReal (Prod.fst.{0, 0} EReal EReal p) (Bot.bot.{0} EReal EReal.hasBot)) (Ne.{1} EReal (Prod.snd.{0, 0} EReal EReal p) (Top.top.{0} EReal EReal.hasTop))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (Prod.topologicalSpace.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace) EReal.topologicalSpace (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toHasAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal EReal.addMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) p)
+but is expected to have type
+  forall {p : Prod.{0, 0} EReal EReal}, (Or (Ne.{1} EReal (Prod.fst.{0, 0} EReal EReal p) (Top.top.{0} EReal EReal.instTopEReal)) (Ne.{1} EReal (Prod.snd.{0, 0} EReal EReal p) (Bot.bot.{0} EReal instERealBot))) -> (Or (Ne.{1} EReal (Prod.fst.{0, 0} EReal EReal p) (Bot.bot.{0} EReal instERealBot)) (Ne.{1} EReal (Prod.snd.{0, 0} EReal EReal p) (Top.top.{0} EReal EReal.instTopEReal))) -> (ContinuousAt.{0, 0} (Prod.{0, 0} EReal EReal) EReal (instTopologicalSpaceProd.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal) EReal.instTopologicalSpaceEReal (fun (p : Prod.{0, 0} EReal EReal) => HAdd.hAdd.{0, 0, 0} EReal EReal EReal (instHAdd.{0} EReal (AddZeroClass.toAdd.{0} EReal (AddMonoid.toAddZeroClass.{0} EReal instERealAddMonoid))) (Prod.fst.{0, 0} EReal EReal p) (Prod.snd.{0, 0} EReal EReal p)) p)
+Case conversion may be inaccurate. Consider using '#align ereal.continuous_at_add EReal.continuousAt_addₓ'. -/
 /-- The addition on `ereal` is continuous except where it doesn't make sense (i.e., at `(⊥, ⊤)`
 and at `(⊤, ⊥)`). -/
 theorem continuousAt_add {p : EReal × EReal} (h : p.1 ≠ ⊤ ∨ p.2 ≠ ⊥) (h' : p.1 ≠ ⊥ ∨ p.2 ≠ ⊤) :
@@ -384,11 +564,23 @@ theorem continuousAt_add {p : EReal × EReal} (h : p.1 ≠ ⊤ ∨ p.2 ≠ ⊥)
 /-! ### Negation-/
 
 
+/- warning: ereal.neg_homeo -> EReal.negHomeo is a dubious translation:
+lean 3 declaration is
+  Homeomorph.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace
+but is expected to have type
+  Homeomorph.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal
+Case conversion may be inaccurate. Consider using '#align ereal.neg_homeo EReal.negHomeoₓ'. -/
 /-- Negation on `ereal` as a homeomorphism -/
 def negHomeo : EReal ≃ₜ EReal :=
   negOrderIso.toHomeomorph
 #align ereal.neg_homeo EReal.negHomeo
 
+/- warning: ereal.continuous_neg -> EReal.continuous_neg is a dubious translation:
+lean 3 declaration is
+  Continuous.{0, 0} EReal EReal EReal.topologicalSpace EReal.topologicalSpace (fun (x : EReal) => Neg.neg.{0} EReal EReal.hasNeg x)
+but is expected to have type
+  Continuous.{0, 0} EReal EReal EReal.instTopologicalSpaceEReal EReal.instTopologicalSpaceEReal (fun (x : EReal) => Neg.neg.{0} EReal EReal.instNegEReal x)
+Case conversion may be inaccurate. Consider using '#align ereal.continuous_neg EReal.continuous_negₓ'. -/
 theorem continuous_neg : Continuous fun x : EReal => -x :=
   negHomeo.Continuous
 #align ereal.continuous_neg EReal.continuous_neg

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

@@ -225,7 +225,7 @@ theorem continuous_coe_eNNReal_iff {f : α → ℝ≥0∞} :
 /-! ### Neighborhoods of infinity -/
 
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (a «expr ≠ » «expr⊤»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ≠ » «expr⊤»()) -/
 theorem nhds_top : 𝓝 (⊤ : EReal) = ⨅ (a) (_ : a ≠ ⊤), 𝓟 (Ioi a) :=
   nhds_top_order.trans <| by simp [lt_top_iff_ne_top, Ioi]
 #align ereal.nhds_top EReal.nhds_top
@@ -254,7 +254,7 @@ theorem tendsto_nhds_top_iff_real {α : Type _} {m : α → EReal} {f : Filter 
   simp only [nhds_top', mem_Ioi, tendsto_infi, tendsto_principal]
 #align ereal.tendsto_nhds_top_iff_real EReal.tendsto_nhds_top_iff_real
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (a «expr ≠ » «expr⊥»()) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (a «expr ≠ » «expr⊥»()) -/
 theorem nhds_bot : 𝓝 (⊥ : EReal) = ⨅ (a) (_ : a ≠ ⊥), 𝓟 (Iio a) :=
   nhds_bot_order.trans <| by simp [bot_lt_iff_ne_bot]
 #align ereal.nhds_bot EReal.nhds_bot

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

@@ -39,20 +39,20 @@ open Classical Topology ENNReal NNReal BigOperators Filter
 
 variable {α : Type _} [TopologicalSpace α]
 
-namespace Ereal
+namespace EReal
 
-instance : TopologicalSpace Ereal :=
-  Preorder.topology Ereal
+instance : TopologicalSpace EReal :=
+  Preorder.topology EReal
 
-instance : OrderTopology Ereal :=
+instance : OrderTopology EReal :=
   ⟨rfl⟩
 
-instance : T2Space Ereal := by infer_instance
+instance : T2Space EReal := by infer_instance
 
-instance : SecondCountableTopology Ereal :=
+instance : SecondCountableTopology EReal :=
   ⟨by
     refine'
-      ⟨⋃ q : ℚ, {{ a : Ereal | a < (q : ℝ) }, { a : Ereal | ((q : ℝ) : Ereal) < a }},
+      ⟨⋃ q : ℚ, {{ a : EReal | a < (q : ℝ) }, { a : EReal | ((q : ℝ) : EReal) < a }},
         countable_Union fun a => (countable_singleton _).insert _, _⟩
     refine'
       le_antisymm
@@ -61,11 +61,11 @@ instance : SecondCountableTopology Ereal :=
         _
     apply le_generateFrom fun s h => _
     rcases h with ⟨a, hs | hs⟩ <;>
-        [rw [show s = ⋃ q ∈ { q : ℚ | a < (q : ℝ) }, { b | ((q : ℝ) : Ereal) < b }
+        [rw [show s = ⋃ q ∈ { q : ℚ | a < (q : ℝ) }, { b | ((q : ℝ) : EReal) < b }
             by
             ext x
             simpa only [hs, exists_prop, mem_Union] using lt_iff_exists_rat_btwn],
-        rw [show s = ⋃ q ∈ { q : ℚ | ((q : ℝ) : Ereal) < a }, { b | b < ((q : ℝ) : Ereal) }
+        rw [show s = ⋃ q ∈ { q : ℚ | ((q : ℝ) : EReal) < a }, { b | b < ((q : ℝ) : EReal) }
             by
             ext x
             simpa only [hs, and_comm', exists_prop, mem_Union] using lt_iff_exists_rat_btwn]] <;>
@@ -79,22 +79,22 @@ instance : SecondCountableTopology Ereal :=
 /-! ### Real coercion -/
 
 
-theorem embedding_coe : Embedding (coe : ℝ → Ereal) :=
+theorem embedding_coe : Embedding (coe : ℝ → EReal) :=
   ⟨⟨by
       refine' le_antisymm _ _
-      · rw [@OrderTopology.topology_eq_generate_intervals Ereal _, ← coinduced_le_iff_le_induced]
+      · rw [@OrderTopology.topology_eq_generate_intervals EReal _, ← coinduced_le_iff_le_induced]
         refine' le_generateFrom fun s ha => _
         rcases ha with ⟨a, rfl | rfl⟩
         show IsOpen { b : ℝ | a < ↑b }
-        · induction a using Ereal.rec
+        · induction a using EReal.rec
           · simp only [isOpen_univ, bot_lt_coe, set_of_true]
-          · simp only [Ereal.coe_lt_coe_iff]
+          · simp only [EReal.coe_lt_coe_iff]
             exact isOpen_Ioi
           · simp only [set_of_false, isOpen_empty, not_top_lt]
         show IsOpen { b : ℝ | ↑b < a }
-        · induction a using Ereal.rec
+        · induction a using EReal.rec
           · simp only [not_lt_bot, set_of_false, isOpen_empty]
-          · simp only [Ereal.coe_lt_coe_iff]
+          · simp only [EReal.coe_lt_coe_iff]
             exact isOpen_Iio
           · simp only [isOpen_univ, coe_lt_top, set_of_true]
       · rw [@OrderTopology.topology_eq_generate_intervals ℝ _]
@@ -102,51 +102,51 @@ theorem embedding_coe : Embedding (coe : ℝ → Ereal) :=
         rcases ha with ⟨a, rfl | rfl⟩
         exact ⟨Ioi a, isOpen_Ioi, by simp [Ioi]⟩
         exact ⟨Iio a, isOpen_Iio, by simp [Iio]⟩⟩, fun a b => by
-    simp only [imp_self, Ereal.coe_eq_coe_iff]⟩
-#align ereal.embedding_coe Ereal.embedding_coe
+    simp only [imp_self, EReal.coe_eq_coe_iff]⟩
+#align ereal.embedding_coe EReal.embedding_coe
 
-theorem openEmbedding_coe : OpenEmbedding (coe : ℝ → Ereal) :=
+theorem openEmbedding_coe : OpenEmbedding (coe : ℝ → EReal) :=
   ⟨embedding_coe, by
-    convert @isOpen_Ioo Ereal _ _ _ ⊥ ⊤
+    convert @isOpen_Ioo EReal _ _ _ ⊥ ⊤
     ext x
-    induction x using Ereal.rec
+    induction x using EReal.rec
     · simp only [left_mem_Ioo, mem_range, coe_ne_bot, exists_false, not_false_iff]
     · simp only [mem_range_self, mem_Ioo, bot_lt_coe, coe_lt_top, and_self_iff]
     · simp only [mem_range, right_mem_Ioo, exists_false, coe_ne_top]⟩
-#align ereal.open_embedding_coe Ereal.openEmbedding_coe
+#align ereal.open_embedding_coe EReal.openEmbedding_coe
 
 @[norm_cast]
 theorem tendsto_coe {α : Type _} {f : Filter α} {m : α → ℝ} {a : ℝ} :
-    Tendsto (fun a => (m a : Ereal)) f (𝓝 ↑a) ↔ Tendsto m f (𝓝 a) :=
+    Tendsto (fun a => (m a : EReal)) f (𝓝 ↑a) ↔ Tendsto m f (𝓝 a) :=
   embedding_coe.tendsto_nhds_iff.symm
-#align ereal.tendsto_coe Ereal.tendsto_coe
+#align ereal.tendsto_coe EReal.tendsto_coe
 
-theorem continuous_coe_real_ereal : Continuous (coe : ℝ → Ereal) :=
+theorem continuous_coe_real_eReal : Continuous (coe : ℝ → EReal) :=
   embedding_coe.Continuous
-#align continuous_coe_real_ereal continuous_coe_real_ereal
+#align continuous_coe_real_ereal continuous_coe_real_eReal
 
-theorem continuous_coe_iff {f : α → ℝ} : (Continuous fun a => (f a : Ereal)) ↔ Continuous f :=
+theorem continuous_coe_iff {f : α → ℝ} : (Continuous fun a => (f a : EReal)) ↔ Continuous f :=
   embedding_coe.continuous_iff.symm
-#align ereal.continuous_coe_iff Ereal.continuous_coe_iff
+#align ereal.continuous_coe_iff EReal.continuous_coe_iff
 
-theorem nhds_coe {r : ℝ} : 𝓝 (r : Ereal) = (𝓝 r).map coe :=
+theorem nhds_coe {r : ℝ} : 𝓝 (r : EReal) = (𝓝 r).map coe :=
   (openEmbedding_coe.map_nhds_eq r).symm
-#align ereal.nhds_coe Ereal.nhds_coe
+#align ereal.nhds_coe EReal.nhds_coe
 
 theorem nhds_coe_coe {r p : ℝ} :
-    𝓝 ((r : Ereal), (p : Ereal)) = (𝓝 (r, p)).map fun p : ℝ × ℝ => (p.1, p.2) :=
+    𝓝 ((r : EReal), (p : EReal)) = (𝓝 (r, p)).map fun p : ℝ × ℝ => (p.1, p.2) :=
   ((openEmbedding_coe.Prod openEmbedding_coe).map_nhds_eq (r, p)).symm
-#align ereal.nhds_coe_coe Ereal.nhds_coe_coe
+#align ereal.nhds_coe_coe EReal.nhds_coe_coe
 
-theorem tendsto_toReal {a : Ereal} (ha : a ≠ ⊤) (h'a : a ≠ ⊥) :
-    Tendsto Ereal.toReal (𝓝 a) (𝓝 a.toReal) :=
+theorem tendsto_toReal {a : EReal} (ha : a ≠ ⊤) (h'a : a ≠ ⊥) :
+    Tendsto EReal.toReal (𝓝 a) (𝓝 a.toReal) :=
   by
   lift a to ℝ using And.intro ha h'a
   rw [nhds_coe, tendsto_map'_iff]
   exact tendsto_id
-#align ereal.tendsto_to_real Ereal.tendsto_toReal
+#align ereal.tendsto_to_real EReal.tendsto_toReal
 
-theorem continuousOn_toReal : ContinuousOn Ereal.toReal ({⊥, ⊤}ᶜ : Set Ereal) := fun a ha =>
+theorem continuousOn_toReal : ContinuousOn EReal.toReal ({⊥, ⊤}ᶜ : Set EReal) := fun a ha =>
   ContinuousAt.continuousWithinAt
     (tendsto_toReal
       (by
@@ -155,48 +155,48 @@ theorem continuousOn_toReal : ContinuousOn Ereal.toReal ({⊥, ⊤}ᶜ : Set Ere
       (by
         simp [not_or] at ha
         exact ha.1))
-#align ereal.continuous_on_to_real Ereal.continuousOn_toReal
+#align ereal.continuous_on_to_real EReal.continuousOn_toReal
 
 /-- The set of finite `ereal` numbers is homeomorphic to `ℝ`. -/
-def neBotTopHomeomorphReal : ({⊥, ⊤}ᶜ : Set Ereal) ≃ₜ ℝ :=
+def neBotTopHomeomorphReal : ({⊥, ⊤}ᶜ : Set EReal) ≃ₜ ℝ :=
   {
     neTopBotEquivReal with
     continuous_toFun := continuousOn_iff_continuous_restrict.1 continuousOn_toReal
-    continuous_invFun := continuous_coe_real_ereal.subtype_mk _ }
-#align ereal.ne_bot_top_homeomorph_real Ereal.neBotTopHomeomorphReal
+    continuous_invFun := continuous_coe_real_eReal.subtype_mk _ }
+#align ereal.ne_bot_top_homeomorph_real EReal.neBotTopHomeomorphReal
 
 /-! ### ennreal coercion -/
 
 
-theorem embedding_coe_eNNReal : Embedding (coe : ℝ≥0∞ → Ereal) :=
+theorem embedding_coe_eNNReal : Embedding (coe : ℝ≥0∞ → EReal) :=
   ⟨⟨by
       refine' le_antisymm _ _
-      · rw [@OrderTopology.topology_eq_generate_intervals Ereal _, ← coinduced_le_iff_le_induced]
+      · rw [@OrderTopology.topology_eq_generate_intervals EReal _, ← coinduced_le_iff_le_induced]
         refine' le_generateFrom fun s ha => _
         rcases ha with ⟨a, rfl | rfl⟩
         show IsOpen { b : ℝ≥0∞ | a < ↑b }
-        · induction' a using Ereal.rec with x
+        · induction' a using EReal.rec with x
           · simp only [isOpen_univ, bot_lt_coe_ennreal, set_of_true]
           · rcases le_or_lt 0 x with (h | h)
-            · have : (x : Ereal) = ((id ⟨x, h⟩ : ℝ≥0) : ℝ≥0∞) := rfl
+            · have : (x : EReal) = ((id ⟨x, h⟩ : ℝ≥0) : ℝ≥0∞) := rfl
               rw [this]
               simp only [id.def, coe_ennreal_lt_coe_ennreal_iff]
               exact isOpen_Ioi
-            · have : ∀ y : ℝ≥0∞, (x : Ereal) < y := fun y =>
-                (Ereal.coe_lt_coe_iff.2 h).trans_le (coe_ennreal_nonneg _)
+            · have : ∀ y : ℝ≥0∞, (x : EReal) < y := fun y =>
+                (EReal.coe_lt_coe_iff.2 h).trans_le (coe_ennreal_nonneg _)
               simp only [this, isOpen_univ, set_of_true]
           · simp only [set_of_false, isOpen_empty, not_top_lt]
         show IsOpen { b : ℝ≥0∞ | ↑b < a }
-        · induction' a using Ereal.rec with x
+        · induction' a using EReal.rec with x
           · simp only [not_lt_bot, set_of_false, isOpen_empty]
           · rcases le_or_lt 0 x with (h | h)
-            · have : (x : Ereal) = ((id ⟨x, h⟩ : ℝ≥0) : ℝ≥0∞) := rfl
+            · have : (x : EReal) = ((id ⟨x, h⟩ : ℝ≥0) : ℝ≥0∞) := rfl
               rw [this]
               simp only [id.def, coe_ennreal_lt_coe_ennreal_iff]
               exact isOpen_Iio
             · convert isOpen_empty
-              apply eq_empty_iff_forall_not_mem.2 fun y hy => lt_irrefl (x : Ereal) _
-              exact ((Ereal.coe_lt_coe_iff.2 h).trans_le (coe_ennreal_nonneg y)).trans hy
+              apply eq_empty_iff_forall_not_mem.2 fun y hy => lt_irrefl (x : EReal) _
+              exact ((EReal.coe_lt_coe_iff.2 h).trans_le (coe_ennreal_nonneg y)).trans hy
           · simp only [← coe_ennreal_top, coe_ennreal_lt_coe_ennreal_iff]
             exact isOpen_Iio
       · rw [@OrderTopology.topology_eq_generate_intervals ℝ≥0∞ _]
@@ -205,152 +205,152 @@ theorem embedding_coe_eNNReal : Embedding (coe : ℝ≥0∞ → Ereal) :=
         exact ⟨Ioi a, isOpen_Ioi, by simp [Ioi]⟩
         exact ⟨Iio a, isOpen_Iio, by simp [Iio]⟩⟩, fun a b => by
     simp only [imp_self, coe_ennreal_eq_coe_ennreal_iff]⟩
-#align ereal.embedding_coe_ennreal Ereal.embedding_coe_eNNReal
+#align ereal.embedding_coe_ennreal EReal.embedding_coe_eNNReal
 
 @[norm_cast]
 theorem tendsto_coe_eNNReal {α : Type _} {f : Filter α} {m : α → ℝ≥0∞} {a : ℝ≥0∞} :
-    Tendsto (fun a => (m a : Ereal)) f (𝓝 ↑a) ↔ Tendsto m f (𝓝 a) :=
+    Tendsto (fun a => (m a : EReal)) f (𝓝 ↑a) ↔ Tendsto m f (𝓝 a) :=
   embedding_coe_eNNReal.tendsto_nhds_iff.symm
-#align ereal.tendsto_coe_ennreal Ereal.tendsto_coe_eNNReal
+#align ereal.tendsto_coe_ennreal EReal.tendsto_coe_eNNReal
 
-theorem continuous_coe_eNNReal_ereal : Continuous (coe : ℝ≥0∞ → Ereal) :=
+theorem continuous_coe_eNNReal_eReal : Continuous (coe : ℝ≥0∞ → EReal) :=
   embedding_coe_eNNReal.Continuous
-#align continuous_coe_ennreal_ereal continuous_coe_eNNReal_ereal
+#align continuous_coe_ennreal_ereal continuous_coe_eNNReal_eReal
 
 theorem continuous_coe_eNNReal_iff {f : α → ℝ≥0∞} :
-    (Continuous fun a => (f a : Ereal)) ↔ Continuous f :=
+    (Continuous fun a => (f a : EReal)) ↔ Continuous f :=
   embedding_coe_eNNReal.continuous_iff.symm
-#align ereal.continuous_coe_ennreal_iff Ereal.continuous_coe_eNNReal_iff
+#align ereal.continuous_coe_ennreal_iff EReal.continuous_coe_eNNReal_iff
 
 /-! ### Neighborhoods of infinity -/
 
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (a «expr ≠ » «expr⊤»()) -/
-theorem nhds_top : 𝓝 (⊤ : Ereal) = ⨅ (a) (_ : a ≠ ⊤), 𝓟 (Ioi a) :=
+theorem nhds_top : 𝓝 (⊤ : EReal) = ⨅ (a) (_ : a ≠ ⊤), 𝓟 (Ioi a) :=
   nhds_top_order.trans <| by simp [lt_top_iff_ne_top, Ioi]
-#align ereal.nhds_top Ereal.nhds_top
+#align ereal.nhds_top EReal.nhds_top
 
-theorem nhds_top' : 𝓝 (⊤ : Ereal) = ⨅ a : ℝ, 𝓟 (Ioi a) :=
+theorem nhds_top' : 𝓝 (⊤ : EReal) = ⨅ a : ℝ, 𝓟 (Ioi a) :=
   by
   rw [nhds_top]
   apply le_antisymm
   · exact infᵢ_mono' fun x => ⟨x, by simp⟩
   · refine' le_infᵢ fun r => le_infᵢ fun hr => _
-    induction r using Ereal.rec
+    induction r using EReal.rec
     · exact (infᵢ_le _ 0).trans (by simp)
     · exact infᵢ_le _ _
     · simpa using hr
-#align ereal.nhds_top' Ereal.nhds_top'
+#align ereal.nhds_top' EReal.nhds_top'
 
-theorem mem_nhds_top_iff {s : Set Ereal} : s ∈ 𝓝 (⊤ : Ereal) ↔ ∃ y : ℝ, Ioi (y : Ereal) ⊆ s :=
+theorem mem_nhds_top_iff {s : Set EReal} : s ∈ 𝓝 (⊤ : EReal) ↔ ∃ y : ℝ, Ioi (y : EReal) ⊆ s :=
   by
   rw [nhds_top', mem_infi_of_directed]
   · rfl
   exact fun x y => ⟨max x y, by simp [le_refl], by simp [le_refl]⟩
-#align ereal.mem_nhds_top_iff Ereal.mem_nhds_top_iff
+#align ereal.mem_nhds_top_iff EReal.mem_nhds_top_iff
 
-theorem tendsto_nhds_top_iff_real {α : Type _} {m : α → Ereal} {f : Filter α} :
+theorem tendsto_nhds_top_iff_real {α : Type _} {m : α → EReal} {f : Filter α} :
     Tendsto m f (𝓝 ⊤) ↔ ∀ x : ℝ, ∀ᶠ a in f, ↑x < m a := by
   simp only [nhds_top', mem_Ioi, tendsto_infi, tendsto_principal]
-#align ereal.tendsto_nhds_top_iff_real Ereal.tendsto_nhds_top_iff_real
+#align ereal.tendsto_nhds_top_iff_real EReal.tendsto_nhds_top_iff_real
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (a «expr ≠ » «expr⊥»()) -/
-theorem nhds_bot : 𝓝 (⊥ : Ereal) = ⨅ (a) (_ : a ≠ ⊥), 𝓟 (Iio a) :=
+theorem nhds_bot : 𝓝 (⊥ : EReal) = ⨅ (a) (_ : a ≠ ⊥), 𝓟 (Iio a) :=
   nhds_bot_order.trans <| by simp [bot_lt_iff_ne_bot]
-#align ereal.nhds_bot Ereal.nhds_bot
+#align ereal.nhds_bot EReal.nhds_bot
 
-theorem nhds_bot' : 𝓝 (⊥ : Ereal) = ⨅ a : ℝ, 𝓟 (Iio a) :=
+theorem nhds_bot' : 𝓝 (⊥ : EReal) = ⨅ a : ℝ, 𝓟 (Iio a) :=
   by
   rw [nhds_bot]
   apply le_antisymm
   · exact infᵢ_mono' fun x => ⟨x, by simp⟩
   · refine' le_infᵢ fun r => le_infᵢ fun hr => _
-    induction r using Ereal.rec
+    induction r using EReal.rec
     · simpa using hr
     · exact infᵢ_le _ _
     · exact (infᵢ_le _ 0).trans (by simp)
-#align ereal.nhds_bot' Ereal.nhds_bot'
+#align ereal.nhds_bot' EReal.nhds_bot'
 
-theorem mem_nhds_bot_iff {s : Set Ereal} : s ∈ 𝓝 (⊥ : Ereal) ↔ ∃ y : ℝ, Iio (y : Ereal) ⊆ s :=
+theorem mem_nhds_bot_iff {s : Set EReal} : s ∈ 𝓝 (⊥ : EReal) ↔ ∃ y : ℝ, Iio (y : EReal) ⊆ s :=
   by
   rw [nhds_bot', mem_infi_of_directed]
   · rfl
   exact fun x y => ⟨min x y, by simp [le_refl], by simp [le_refl]⟩
-#align ereal.mem_nhds_bot_iff Ereal.mem_nhds_bot_iff
+#align ereal.mem_nhds_bot_iff EReal.mem_nhds_bot_iff
 
-theorem tendsto_nhds_bot_iff_real {α : Type _} {m : α → Ereal} {f : Filter α} :
+theorem tendsto_nhds_bot_iff_real {α : Type _} {m : α → EReal} {f : Filter α} :
     Tendsto m f (𝓝 ⊥) ↔ ∀ x : ℝ, ∀ᶠ a in f, m a < x := by
   simp only [nhds_bot', mem_Iio, tendsto_infi, tendsto_principal]
-#align ereal.tendsto_nhds_bot_iff_real Ereal.tendsto_nhds_bot_iff_real
+#align ereal.tendsto_nhds_bot_iff_real EReal.tendsto_nhds_bot_iff_real
 
 /-! ### Continuity of addition -/
 
 
 theorem continuousAt_add_coe_coe (a b : ℝ) :
-    ContinuousAt (fun p : Ereal × Ereal => p.1 + p.2) (a, b) := by
+    ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (a, b) := by
   simp only [ContinuousAt, nhds_coe_coe, ← coe_add, tendsto_map'_iff, (· ∘ ·), tendsto_coe,
     tendsto_add]
-#align ereal.continuous_at_add_coe_coe Ereal.continuousAt_add_coe_coe
+#align ereal.continuous_at_add_coe_coe EReal.continuousAt_add_coe_coe
 
 theorem continuousAt_add_top_coe (a : ℝ) :
-    ContinuousAt (fun p : Ereal × Ereal => p.1 + p.2) (⊤, a) :=
+    ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (⊤, a) :=
   by
   simp only [ContinuousAt, tendsto_nhds_top_iff_real, top_add_coe, nhds_prod_eq]
   intro r
   rw [eventually_prod_iff]
   refine'
-    ⟨fun z => ((r - (a - 1) : ℝ) : Ereal) < z, Ioi_mem_nhds (coe_lt_top _), fun z =>
-      ((a - 1 : ℝ) : Ereal) < z, Ioi_mem_nhds (by simp [-Ereal.coe_sub]), fun x hx y hy => _⟩
+    ⟨fun z => ((r - (a - 1) : ℝ) : EReal) < z, Ioi_mem_nhds (coe_lt_top _), fun z =>
+      ((a - 1 : ℝ) : EReal) < z, Ioi_mem_nhds (by simp [-EReal.coe_sub]), fun x hx y hy => _⟩
   dsimp
   convert add_lt_add hx hy
   simp
-#align ereal.continuous_at_add_top_coe Ereal.continuousAt_add_top_coe
+#align ereal.continuous_at_add_top_coe EReal.continuousAt_add_top_coe
 
 theorem continuousAt_add_coe_top (a : ℝ) :
-    ContinuousAt (fun p : Ereal × Ereal => p.1 + p.2) (a, ⊤) :=
+    ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (a, ⊤) :=
   by
-  change ContinuousAt ((fun p : Ereal × Ereal => p.2 + p.1) ∘ Prod.swap) (a, ⊤)
+  change ContinuousAt ((fun p : EReal × EReal => p.2 + p.1) ∘ Prod.swap) (a, ⊤)
   apply ContinuousAt.comp _ continuous_swap.continuous_at
   simp_rw [add_comm]
   exact continuous_at_add_top_coe a
-#align ereal.continuous_at_add_coe_top Ereal.continuousAt_add_coe_top
+#align ereal.continuous_at_add_coe_top EReal.continuousAt_add_coe_top
 
-theorem continuousAt_add_top_top : ContinuousAt (fun p : Ereal × Ereal => p.1 + p.2) (⊤, ⊤) :=
+theorem continuousAt_add_top_top : ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (⊤, ⊤) :=
   by
   simp only [ContinuousAt, tendsto_nhds_top_iff_real, top_add_top, nhds_prod_eq]
   intro r
   rw [eventually_prod_iff]
   refine'
-    ⟨fun z => (r : Ereal) < z, Ioi_mem_nhds (coe_lt_top _), fun z => ((0 : ℝ) : Ereal) < z,
+    ⟨fun z => (r : EReal) < z, Ioi_mem_nhds (coe_lt_top _), fun z => ((0 : ℝ) : EReal) < z,
       Ioi_mem_nhds (by simp [zero_lt_one]), fun x hx y hy => _⟩
   dsimp
   convert add_lt_add hx hy
   simp
-#align ereal.continuous_at_add_top_top Ereal.continuousAt_add_top_top
+#align ereal.continuous_at_add_top_top EReal.continuousAt_add_top_top
 
 theorem continuousAt_add_bot_coe (a : ℝ) :
-    ContinuousAt (fun p : Ereal × Ereal => p.1 + p.2) (⊥, a) :=
+    ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (⊥, a) :=
   by
   simp only [ContinuousAt, tendsto_nhds_bot_iff_real, nhds_prod_eq, bot_add]
   intro r
   rw [eventually_prod_iff]
   refine'
-    ⟨fun z => z < ((r - (a + 1) : ℝ) : Ereal), Iio_mem_nhds (bot_lt_coe _), fun z =>
-      z < ((a + 1 : ℝ) : Ereal), Iio_mem_nhds (by simp [-coe_add, zero_lt_one]), fun x hx y hy => _⟩
+    ⟨fun z => z < ((r - (a + 1) : ℝ) : EReal), Iio_mem_nhds (bot_lt_coe _), fun z =>
+      z < ((a + 1 : ℝ) : EReal), Iio_mem_nhds (by simp [-coe_add, zero_lt_one]), fun x hx y hy => _⟩
   convert add_lt_add hx hy
   rw [sub_add_cancel]
-#align ereal.continuous_at_add_bot_coe Ereal.continuousAt_add_bot_coe
+#align ereal.continuous_at_add_bot_coe EReal.continuousAt_add_bot_coe
 
 theorem continuousAt_add_coe_bot (a : ℝ) :
-    ContinuousAt (fun p : Ereal × Ereal => p.1 + p.2) (a, ⊥) :=
+    ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (a, ⊥) :=
   by
-  change ContinuousAt ((fun p : Ereal × Ereal => p.2 + p.1) ∘ Prod.swap) (a, ⊥)
+  change ContinuousAt ((fun p : EReal × EReal => p.2 + p.1) ∘ Prod.swap) (a, ⊥)
   apply ContinuousAt.comp _ continuous_swap.continuous_at
   simp_rw [add_comm]
   exact continuous_at_add_bot_coe a
-#align ereal.continuous_at_add_coe_bot Ereal.continuousAt_add_coe_bot
+#align ereal.continuous_at_add_coe_bot EReal.continuousAt_add_coe_bot
 
-theorem continuousAt_add_bot_bot : ContinuousAt (fun p : Ereal × Ereal => p.1 + p.2) (⊥, ⊥) :=
+theorem continuousAt_add_bot_bot : ContinuousAt (fun p : EReal × EReal => p.1 + p.2) (⊥, ⊥) :=
   by
   simp only [ContinuousAt, tendsto_nhds_bot_iff_real, nhds_prod_eq, bot_add]
   intro r
@@ -361,15 +361,15 @@ theorem continuousAt_add_bot_bot : ContinuousAt (fun p : Ereal × Ereal => p.1 +
   dsimp
   convert add_lt_add hx hy
   simp
-#align ereal.continuous_at_add_bot_bot Ereal.continuousAt_add_bot_bot
+#align ereal.continuous_at_add_bot_bot EReal.continuousAt_add_bot_bot
 
 /-- The addition on `ereal` is continuous except where it doesn't make sense (i.e., at `(⊥, ⊤)`
 and at `(⊤, ⊥)`). -/
-theorem continuousAt_add {p : Ereal × Ereal} (h : p.1 ≠ ⊤ ∨ p.2 ≠ ⊥) (h' : p.1 ≠ ⊥ ∨ p.2 ≠ ⊤) :
-    ContinuousAt (fun p : Ereal × Ereal => p.1 + p.2) p :=
+theorem continuousAt_add {p : EReal × EReal} (h : p.1 ≠ ⊤ ∨ p.2 ≠ ⊥) (h' : p.1 ≠ ⊥ ∨ p.2 ≠ ⊤) :
+    ContinuousAt (fun p : EReal × EReal => p.1 + p.2) p :=
   by
   rcases p with ⟨x, y⟩
-  induction x using Ereal.rec <;> induction y using Ereal.rec
+  induction x using EReal.rec <;> induction y using EReal.rec
   · exact continuous_at_add_bot_bot
   · exact continuous_at_add_bot_coe _
   · simpa using h'
@@ -379,19 +379,19 @@ theorem continuousAt_add {p : Ereal × Ereal} (h : p.1 ≠ ⊤ ∨ p.2 ≠ ⊥)
   · simpa using h
   · exact continuous_at_add_top_coe _
   · exact continuous_at_add_top_top
-#align ereal.continuous_at_add Ereal.continuousAt_add
+#align ereal.continuous_at_add EReal.continuousAt_add
 
 /-! ### Negation-/
 
 
 /-- Negation on `ereal` as a homeomorphism -/
-def negHomeo : Ereal ≃ₜ Ereal :=
+def negHomeo : EReal ≃ₜ EReal :=
   negOrderIso.toHomeomorph
-#align ereal.neg_homeo Ereal.negHomeo
+#align ereal.neg_homeo EReal.negHomeo
 
-theorem continuous_neg : Continuous fun x : Ereal => -x :=
+theorem continuous_neg : Continuous fun x : EReal => -x :=
   negHomeo.Continuous
-#align ereal.continuous_neg Ereal.continuous_neg
+#align ereal.continuous_neg EReal.continuous_neg
 
-end Ereal
+end EReal
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -35,7 +35,7 @@ noncomputable section
 
 open Classical Set Filter Metric TopologicalSpace
 
-open Classical Topology Ennreal NNReal BigOperators Filter
+open Classical Topology ENNReal NNReal BigOperators Filter
 
 variable {α : Type _} [TopologicalSpace α]
 
@@ -168,7 +168,7 @@ def neBotTopHomeomorphReal : ({⊥, ⊤}ᶜ : Set Ereal) ≃ₜ ℝ :=
 /-! ### ennreal coercion -/
 
 
-theorem embedding_coe_ennreal : Embedding (coe : ℝ≥0∞ → Ereal) :=
+theorem embedding_coe_eNNReal : Embedding (coe : ℝ≥0∞ → Ereal) :=
   ⟨⟨by
       refine' le_antisymm _ _
       · rw [@OrderTopology.topology_eq_generate_intervals Ereal _, ← coinduced_le_iff_le_induced]
@@ -205,22 +205,22 @@ theorem embedding_coe_ennreal : Embedding (coe : ℝ≥0∞ → Ereal) :=
         exact ⟨Ioi a, isOpen_Ioi, by simp [Ioi]⟩
         exact ⟨Iio a, isOpen_Iio, by simp [Iio]⟩⟩, fun a b => by
     simp only [imp_self, coe_ennreal_eq_coe_ennreal_iff]⟩
-#align ereal.embedding_coe_ennreal Ereal.embedding_coe_ennreal
+#align ereal.embedding_coe_ennreal Ereal.embedding_coe_eNNReal
 
 @[norm_cast]
-theorem tendsto_coe_ennreal {α : Type _} {f : Filter α} {m : α → ℝ≥0∞} {a : ℝ≥0∞} :
+theorem tendsto_coe_eNNReal {α : Type _} {f : Filter α} {m : α → ℝ≥0∞} {a : ℝ≥0∞} :
     Tendsto (fun a => (m a : Ereal)) f (𝓝 ↑a) ↔ Tendsto m f (𝓝 a) :=
-  embedding_coe_ennreal.tendsto_nhds_iff.symm
-#align ereal.tendsto_coe_ennreal Ereal.tendsto_coe_ennreal
+  embedding_coe_eNNReal.tendsto_nhds_iff.symm
+#align ereal.tendsto_coe_ennreal Ereal.tendsto_coe_eNNReal
 
-theorem continuous_coe_ennreal_ereal : Continuous (coe : ℝ≥0∞ → Ereal) :=
-  embedding_coe_ennreal.Continuous
-#align continuous_coe_ennreal_ereal continuous_coe_ennreal_ereal
+theorem continuous_coe_eNNReal_ereal : Continuous (coe : ℝ≥0∞ → Ereal) :=
+  embedding_coe_eNNReal.Continuous
+#align continuous_coe_ennreal_ereal continuous_coe_eNNReal_ereal
 
-theorem continuous_coe_ennreal_iff {f : α → ℝ≥0∞} :
+theorem continuous_coe_eNNReal_iff {f : α → ℝ≥0∞} :
     (Continuous fun a => (f a : Ereal)) ↔ Continuous f :=
-  embedding_coe_ennreal.continuous_iff.symm
-#align ereal.continuous_coe_ennreal_iff Ereal.continuous_coe_ennreal_iff
+  embedding_coe_eNNReal.continuous_iff.symm
+#align ereal.continuous_coe_ennreal_iff Ereal.continuous_coe_eNNReal_iff
 
 /-! ### Neighborhoods of infinity -/
 

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

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

According to git, the moves are:

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

@@ -5,8 +5,8 @@ Authors: Sébastien Gouëzel
 -/
 import Mathlib.Data.Rat.Encodable
 import Mathlib.Data.Real.EReal
-import Mathlib.Topology.Algebra.Order.MonotoneContinuity
 import Mathlib.Topology.Instances.ENNReal
+import Mathlib.Topology.Order.MonotoneContinuity
 
 #align_import topology.instances.ereal from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
 

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 @@ Most proofs are adapted from the corresponding proofs on `ℝ≥0∞`.
 
 noncomputable section
 
-open Classical Set Filter Metric TopologicalSpace Topology
+open scoped Classical
+open Set Filter Metric TopologicalSpace Topology
 open scoped ENNReal NNReal BigOperators Filter
 
 variable {α : Type*} [TopologicalSpace α]

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

This has nice performance benefits.

@@ -33,7 +33,7 @@ noncomputable section
 open Classical Set Filter Metric TopologicalSpace Topology
 open scoped ENNReal NNReal BigOperators Filter
 
-variable {α : Type _} [TopologicalSpace α]
+variable {α : Type*} [TopologicalSpace α]
 
 namespace EReal
 
@@ -60,7 +60,7 @@ theorem openEmbedding_coe : OpenEmbedding ((↑) : ℝ → EReal) :=
 #align ereal.open_embedding_coe EReal.openEmbedding_coe
 
 @[norm_cast]
-theorem tendsto_coe {α : Type _} {f : Filter α} {m : α → ℝ} {a : ℝ} :
+theorem tendsto_coe {α : Type*} {f : Filter α} {m : α → ℝ} {a : ℝ} :
     Tendsto (fun a => (m a : EReal)) f (𝓝 ↑a) ↔ Tendsto m f (𝓝 a) :=
   embedding_coe.tendsto_nhds_iff.symm
 #align ereal.tendsto_coe EReal.tendsto_coe
@@ -111,7 +111,7 @@ theorem closedEmbedding_coe_ennreal : ClosedEmbedding ((↑) : ℝ≥0∞ → ER
   ⟨embedding_coe_ennreal, by rw [range_coe_ennreal]; exact isClosed_Ici⟩
 
 @[norm_cast]
-theorem tendsto_coe_ennreal {α : Type _} {f : Filter α} {m : α → ℝ≥0∞} {a : ℝ≥0∞} :
+theorem tendsto_coe_ennreal {α : Type*} {f : Filter α} {m : α → ℝ≥0∞} {a : ℝ≥0∞} :
     Tendsto (fun a => (m a : EReal)) f (𝓝 ↑a) ↔ Tendsto m f (𝓝 a) :=
   embedding_coe_ennreal.tendsto_nhds_iff.symm
 #align ereal.tendsto_coe_ennreal EReal.tendsto_coe_ennreal
@@ -143,7 +143,7 @@ theorem mem_nhds_top_iff {s : Set EReal} : s ∈ 𝓝 (⊤ : EReal) ↔ ∃ y :
   nhds_top_basis.mem_iff.trans <| by simp only [true_and]
 #align ereal.mem_nhds_top_iff EReal.mem_nhds_top_iff
 
-theorem tendsto_nhds_top_iff_real {α : Type _} {m : α → EReal} {f : Filter α} :
+theorem tendsto_nhds_top_iff_real {α : Type*} {m : α → EReal} {f : Filter α} :
     Tendsto m f (𝓝 ⊤) ↔ ∀ x : ℝ, ∀ᶠ a in f, ↑x < m a :=
   nhds_top_basis.tendsto_right_iff.trans <| by simp only [true_implies, mem_Ioi]
 #align ereal.tendsto_nhds_top_iff_real EReal.tendsto_nhds_top_iff_real
@@ -165,7 +165,7 @@ theorem mem_nhds_bot_iff {s : Set EReal} : s ∈ 𝓝 (⊥ : EReal) ↔ ∃ y :
   nhds_bot_basis.mem_iff.trans <| by simp only [true_and]
 #align ereal.mem_nhds_bot_iff EReal.mem_nhds_bot_iff
 
-theorem tendsto_nhds_bot_iff_real {α : Type _} {m : α → EReal} {f : Filter α} :
+theorem tendsto_nhds_bot_iff_real {α : Type*} {m : α → EReal} {f : Filter α} :
     Tendsto m f (𝓝 ⊥) ↔ ∀ x : ℝ, ∀ᶠ a in f, m a < x :=
   nhds_bot_basis.tendsto_right_iff.trans <| by simp only [true_implies, mem_Iio]
 #align ereal.tendsto_nhds_bot_iff_real EReal.tendsto_nhds_bot_iff_real

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module topology.instances.ereal
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Rat.Encodable
 import Mathlib.Data.Real.EReal
 import Mathlib.Topology.Algebra.Order.MonotoneContinuity
 import Mathlib.Topology.Instances.ENNReal
 
+#align_import topology.instances.ereal from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Topological structure on `EReal`
 

@@ -130,7 +130,7 @@ theorem continuous_coe_ennreal_iff {f : α → ℝ≥0∞} :
 
 /-! ### Neighborhoods of infinity -/
 
-theorem nhds_top : 𝓝 (⊤ : EReal) = ⨅ (a) (_h : a ≠ ⊤), 𝓟 (Ioi a) :=
+theorem nhds_top : 𝓝 (⊤ : EReal) = ⨅ (a) (_ : a ≠ ⊤), 𝓟 (Ioi a) :=
   nhds_top_order.trans <| by simp only [lt_top_iff_ne_top]
 #align ereal.nhds_top EReal.nhds_top
 
@@ -151,7 +151,7 @@ theorem tendsto_nhds_top_iff_real {α : Type _} {m : α → EReal} {f : Filter 
   nhds_top_basis.tendsto_right_iff.trans <| by simp only [true_implies, mem_Ioi]
 #align ereal.tendsto_nhds_top_iff_real EReal.tendsto_nhds_top_iff_real
 
-theorem nhds_bot : 𝓝 (⊥ : EReal) = ⨅ (a) (_h : a ≠ ⊥), 𝓟 (Iio a) :=
+theorem nhds_bot : 𝓝 (⊥ : EReal) = ⨅ (a) (_ : a ≠ ⊥), 𝓟 (Iio a) :=
   nhds_bot_order.trans <| by simp only [bot_lt_iff_ne_bot]
 #align ereal.nhds_bot EReal.nhds_bot
 

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>

@@ -139,7 +139,7 @@ nonrec theorem nhds_top_basis : (𝓝 (⊤ : EReal)).HasBasis (fun _ : ℝ ↦ T
   rcases exists_rat_btwn_of_lt hx with ⟨y, hxy, -⟩
   exact ⟨_, trivial, Ioi_subset_Ioi hxy.le⟩
 
-theorem nhds_top' : 𝓝 (⊤ : EReal) = ⨅ a : ℝ, 𝓟 (Ioi ↑a) := nhds_top_basis.eq_infᵢ
+theorem nhds_top' : 𝓝 (⊤ : EReal) = ⨅ a : ℝ, 𝓟 (Ioi ↑a) := nhds_top_basis.eq_iInf
 #align ereal.nhds_top' EReal.nhds_top'
 
 theorem mem_nhds_top_iff {s : Set EReal} : s ∈ 𝓝 (⊤ : EReal) ↔ ∃ y : ℝ, Ioi (y : EReal) ⊆ s :=
@@ -161,7 +161,7 @@ theorem nhds_bot_basis : (𝓝 (⊥ : EReal)).HasBasis (fun _ : ℝ ↦ True) (I
   exact ⟨_, trivial, Iio_subset_Iio hxy.le⟩
 
 theorem nhds_bot' : 𝓝 (⊥ : EReal) = ⨅ a : ℝ, 𝓟 (Iio ↑a) :=
-  nhds_bot_basis.eq_infᵢ
+  nhds_bot_basis.eq_iInf
 #align ereal.nhds_bot' EReal.nhds_bot'
 
 theorem mem_nhds_bot_iff {s : Set EReal} : s ∈ 𝓝 (⊥ : EReal) ↔ ∃ y : ℝ, Iio (y : EReal) ⊆ s :=

API changes

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