data.real.hyperreal ⟷ Mathlib.Data.Real.Hyperreal

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

@@ -523,7 +523,7 @@ theorem isSt_inj_real {r₁ r₂ s : ℝ} (h1 : IsSt r₁ s) (h2 : IsSt r₂ s)
 
 #print Hyperreal.isSt_iff_abs_sub_lt_delta /-
 theorem isSt_iff_abs_sub_lt_delta {x : ℝ*} {r : ℝ} : IsSt x r ↔ ∀ δ : ℝ, 0 < δ → |x - r| < δ := by
-  simp only [abs_sub_lt_iff, sub_lt_iff_lt_add, is_st, and_comm', add_comm]
+  simp only [abs_sub_lt_iff, sub_lt_iff_lt_add, is_st, and_comm, add_comm]
 #align hyperreal.is_st_iff_abs_sub_lt_delta Hyperreal.isSt_iff_abs_sub_lt_delta
 -/
 

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

@@ -960,7 +960,7 @@ theorem Hyperreal.IsSt.mul {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
             (div_pos hd (coe_pos.1 (lt_of_le_of_lt (abs_nonneg x) ht)))
         rw [hs, coe_zero, sub_zero] at hys'
         rw [hs, MulZeroClass.mul_zero, coe_zero, sub_zero, abs_mul, mul_comm, ←
-          div_mul_cancel (d : ℝ*) (ne_of_gt (lt_of_le_of_lt (abs_nonneg x) ht)), ← coe_div]
+          div_mul_cancel₀ (d : ℝ*) (ne_of_gt (lt_of_le_of_lt (abs_nonneg x) ht)), ← coe_div]
         exact mul_lt_mul'' hys' ht (abs_nonneg _) (abs_nonneg _)
       exact is_st_mul' hxr hys hs
 #align hyperreal.is_st_mul Hyperreal.IsSt.mul
@@ -1254,7 +1254,7 @@ theorem infinitePos_mul_of_infinitePos_not_infinitesimal_pos {x y : ℝ*} :
   Exists.dcases_on hy₁' fun r₁ hy₁'' =>
     by
     have hyr := by rw [not_imp, ← abs_lt, not_lt, abs_of_pos hy₂] at hy₁'' <;> exact hy₁''
-    rw [← div_mul_cancel r (ne_of_gt hyr.1), coe_mul] <;>
+    rw [← div_mul_cancel₀ r (ne_of_gt hyr.1), coe_mul] <;>
       exact mul_lt_mul (hx (r / r₁)) hyr.2 (coe_lt_coe.2 hyr.1) (le_of_lt (hx 0))
 #align hyperreal.infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos
 -/

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

@@ -284,7 +284,7 @@ theorem lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝
 theorem neg_lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝 0)) :
     ∀ {r : ℝ}, 0 < r → (-r : ℝ*) < ofSeq f := fun r hr =>
   have hg := hf.neg
-  neg_lt_of_neg_lt (by rw [neg_zero] at hg  <;> exact lt_of_tendsto_zero_of_pos hg hr)
+  neg_lt_of_neg_lt (by rw [neg_zero] at hg <;> exact lt_of_tendsto_zero_of_pos hg hr)
 #align hyperreal.neg_lt_of_tendsto_zero_of_pos Hyperreal.neg_lt_of_tendsto_zero_of_pos
 -/
 
@@ -354,7 +354,7 @@ private theorem is_st_unique' (x : ℝ*) (r s : ℝ) (hr : IsSt x r) (hs : IsSt
   have hs' := (hs _ hrs').1
   have h : s - (s - r) / 2 = r + (s - r) / 2 := by linarith
   norm_cast at *
-  rw [h] at hs' 
+  rw [h] at hs'
   exact not_lt_of_lt hs' hr'
 
 #print Hyperreal.IsSt.unique /-
@@ -559,8 +559,8 @@ theorem Hyperreal.IsSt.lt {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
   have H1 : r + (s - r) / 2 = (r + s) / 2 := by linarith
   have H2 : s - (s - r) / 2 = (r + s) / 2 := by linarith
   norm_cast at *
-  rw [H1] at hxr' 
-  rw [H2] at hys' 
+  rw [H1] at hxr'
+  rw [H2] at hys'
   exact lt_trans hxr' hys'
 #align hyperreal.lt_of_is_st_lt Hyperreal.IsSt.lt
 -/
@@ -745,9 +745,9 @@ theorem infinitePos_abs_iff_infinite {x : ℝ*} : Infinite x ↔ InfinitePos |x|
       rw [abs_of_neg (hin 0)] <;> exact lt_neg.mp (hin (-d)),
     fun hipa => by
     rcases lt_trichotomy x 0 with (h | h | h)
-    · exact Or.inr (infinite_neg_iff_infinite_pos_neg.mpr (by rwa [abs_of_neg h] at hipa ))
-    · exact False.elim (ne_zero_of_infinite (Or.inl (by rw [h] <;> rwa [h, abs_zero] at hipa )) h)
-    · exact Or.inl (by rwa [abs_of_pos h] at hipa )⟩
+    · exact Or.inr (infinite_neg_iff_infinite_pos_neg.mpr (by rwa [abs_of_neg h] at hipa))
+    · exact False.elim (ne_zero_of_infinite (Or.inl (by rw [h] <;> rwa [h, abs_zero] at hipa)) h)
+    · exact Or.inl (by rwa [abs_of_pos h] at hipa)⟩
 #align hyperreal.infinite_iff_infinite_pos_abs Hyperreal.infinitePos_abs_iff_infiniteₓ
 
 theorem infinite_abs_iff {x : ℝ*} : Infinite x ↔ Infinite |x| := by
@@ -874,7 +874,7 @@ theorem not_infinite_iff_exist_lt_gt {x : ℝ*} : ¬Infinite x ↔ ∃ r s : ℝ
   ⟨fun hni =>
     Exists.dcases_on (Classical.not_forall.mp (not_or.mp hni).1) <|
       Exists.dcases_on (Classical.not_forall.mp (not_or.mp hni).2) fun r hr s hs => by
-        rw [not_lt] at hr hs  <;>
+        rw [not_lt] at hr hs <;>
           exact
             ⟨r - 1, s + 1,
               ⟨lt_of_lt_of_le (by rw [sub_eq_add_neg] <;> norm_num) hr,
@@ -958,7 +958,7 @@ theorem Hyperreal.IsSt.mul {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
         have hys' : _ :=
           is_st_iff_abs_sub_lt_delta.mp hys (d / t)
             (div_pos hd (coe_pos.1 (lt_of_le_of_lt (abs_nonneg x) ht)))
-        rw [hs, coe_zero, sub_zero] at hys' 
+        rw [hs, coe_zero, sub_zero] at hys'
         rw [hs, MulZeroClass.mul_zero, coe_zero, sub_zero, abs_mul, mul_comm, ←
           div_mul_cancel (d : ℝ*) (ne_of_gt (lt_of_le_of_lt (abs_nonneg x) ht)), ← coe_div]
         exact mul_lt_mul'' hys' ht (abs_nonneg _) (abs_nonneg _)
@@ -1145,7 +1145,7 @@ theorem infiniteNeg_iff_infinitesimal_inv_neg {x : ℝ*} :
     have hin' := infinitePos_iff_infinitesimal_inv_pos.mp (Hyperreal.InfiniteNeg.neg hin)
     rwa [infinitesimal_neg_iff, ← neg_pos, neg_inv], fun hin => by
     rwa [← neg_pos, infinitesimal_neg_iff, neg_inv, ← infinite_pos_iff_infinitesimal_inv_pos, ←
-      infinite_neg_iff_infinite_pos_neg] at hin ⟩
+      infinite_neg_iff_infinite_pos_neg] at hin⟩
 #align hyperreal.infinite_neg_iff_infinitesimal_inv_neg Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg
 -/
 
@@ -1250,10 +1250,10 @@ theorem infinite_omega : Infinite ω :=
 #print Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos /-
 theorem infinitePos_mul_of_infinitePos_not_infinitesimal_pos {x y : ℝ*} :
     InfinitePos x → ¬Infinitesimal y → 0 < y → InfinitePos (x * y) := fun hx hy₁ hy₂ r =>
-  have hy₁' := Classical.not_forall.mp (by rw [infinitesimal_def] at hy₁  <;> exact hy₁)
+  have hy₁' := Classical.not_forall.mp (by rw [infinitesimal_def] at hy₁ <;> exact hy₁)
   Exists.dcases_on hy₁' fun r₁ hy₁'' =>
     by
-    have hyr := by rw [not_imp, ← abs_lt, not_lt, abs_of_pos hy₂] at hy₁''  <;> exact hy₁''
+    have hyr := by rw [not_imp, ← abs_lt, not_lt, abs_of_pos hy₂] at hy₁'' <;> exact hy₁''
     rw [← div_mul_cancel r (ne_of_gt hyr.1), coe_mul] <;>
       exact mul_lt_mul (hx (r / r₁)) hyr.2 (coe_lt_coe.2 hyr.1) (le_of_lt (hx 0))
 #align hyperreal.infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos

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

@@ -297,7 +297,7 @@ theorem gt_of_tendsto_zero_of_neg {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝
 
 #print Hyperreal.epsilon_lt_pos /-
 theorem epsilon_lt_pos (x : ℝ) : 0 < x → ε < x :=
-  lt_of_tendsto_zero_of_pos tendsto_inverse_atTop_nhds_0_nat
+  lt_of_tendsto_zero_of_pos tendsto_inverse_atTop_nhds_zero_nat
 #align hyperreal.epsilon_lt_pos Hyperreal.epsilon_lt_pos
 -/
 
@@ -1095,7 +1095,7 @@ theorem infinitesimal_of_tendsto_zero {f : ℕ → ℝ} :
 
 #print Hyperreal.infinitesimal_epsilon /-
 theorem infinitesimal_epsilon : Infinitesimal ε :=
-  infinitesimal_of_tendsto_zero tendsto_inverse_atTop_nhds_0_nat
+  infinitesimal_of_tendsto_zero tendsto_inverse_atTop_nhds_zero_nat
 #align hyperreal.infinitesimal_epsilon Hyperreal.infinitesimal_epsilon
 -/
 

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

@@ -759,7 +759,7 @@ theorem infinite_iff_abs_lt_abs {x : ℝ*} : Infinite x ↔ ∀ r : ℝ, (|r| :
   ⟨fun hI r => coe_abs r ▸ infinitePos_abs_iff_infinite.mp hI |r|, fun hR =>
     Or.cases_on (max_choice x (-x))
       (fun h => Or.inl fun r => lt_of_le_of_lt (le_abs_self _) (h ▸ hR r)) fun h =>
-      Or.inr fun r => neg_lt_neg_iff.mp <| lt_of_le_of_lt (neg_le_abs_self _) (h ▸ hR r)⟩
+      Or.inr fun r => neg_lt_neg_iff.mp <| lt_of_le_of_lt (neg_le_abs _) (h ▸ hR r)⟩
 #align hyperreal.infinite_iff_abs_lt_abs Hyperreal.infinite_iff_abs_lt_abs
 -/
 

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

@@ -379,8 +379,8 @@ theorem not_infinite_of_exists_st {x : ℝ*} : (∃ r : ℝ, IsSt x r) → ¬Inf
 theorem isSt_sSup {x : ℝ*} (hni : ¬Infinite x) : IsSt x (sSup {y : ℝ | (y : ℝ*) < x}) :=
   let S : Set ℝ := {y : ℝ | (y : ℝ*) < x}
   let R : _ := sSup S
-  have hnile := not_forall.mp (not_or.mp hni).1
-  have hnige := not_forall.mp (not_or.mp hni).2
+  have hnile := Classical.not_forall.mp (not_or.mp hni).1
+  have hnige := Classical.not_forall.mp (not_or.mp hni).2
   Exists.dcases_on hnile <|
     Exists.dcases_on hnige fun r₁ hr₁ r₂ hr₂ =>
       have HR₁ : S.Nonempty :=
@@ -872,8 +872,8 @@ theorem not_infinite_add {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) :
 #print Hyperreal.not_infinite_iff_exist_lt_gt /-
 theorem not_infinite_iff_exist_lt_gt {x : ℝ*} : ¬Infinite x ↔ ∃ r s : ℝ, (r : ℝ*) < x ∧ x < s :=
   ⟨fun hni =>
-    Exists.dcases_on (not_forall.mp (not_or.mp hni).1) <|
-      Exists.dcases_on (not_forall.mp (not_or.mp hni).2) fun r hr s hs => by
+    Exists.dcases_on (Classical.not_forall.mp (not_or.mp hni).1) <|
+      Exists.dcases_on (Classical.not_forall.mp (not_or.mp hni).2) fun r hr s hs => by
         rw [not_lt] at hr hs  <;>
           exact
             ⟨r - 1, s + 1,
@@ -882,7 +882,9 @@ theorem not_infinite_iff_exist_lt_gt {x : ℝ*} : ¬Infinite x ↔ ∃ r s : ℝ
     fun hrs =>
     Exists.dcases_on hrs fun r hr =>
       Exists.dcases_on hr fun s hs =>
-        not_or.mpr ⟨not_forall.mpr ⟨s, lt_asymm hs.2⟩, not_forall.mpr ⟨r, lt_asymm hs.1⟩⟩⟩
+        not_or.mpr
+          ⟨Classical.not_forall.mpr ⟨s, lt_asymm hs.2⟩,
+            Classical.not_forall.mpr ⟨r, lt_asymm hs.1⟩⟩⟩
 #align hyperreal.not_infinite_iff_exist_lt_gt Hyperreal.not_infinite_iff_exist_lt_gt
 -/
 
@@ -1248,7 +1250,7 @@ theorem infinite_omega : Infinite ω :=
 #print Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos /-
 theorem infinitePos_mul_of_infinitePos_not_infinitesimal_pos {x y : ℝ*} :
     InfinitePos x → ¬Infinitesimal y → 0 < y → InfinitePos (x * y) := fun hx hy₁ hy₂ r =>
-  have hy₁' := not_forall.mp (by rw [infinitesimal_def] at hy₁  <;> exact hy₁)
+  have hy₁' := Classical.not_forall.mp (by rw [infinitesimal_def] at hy₁  <;> exact hy₁)
   Exists.dcases_on hy₁' fun r₁ hy₁'' =>
     by
     have hyr := by rw [not_imp, ← abs_lt, not_lt, abs_of_pos hy₂] at hy₁''  <;> exact hy₁''

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

@@ -3,8 +3,8 @@ Copyright (c) 2019 Abhimanyu Pallavi Sudhir. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Abhimanyu Pallavi Sudhir
 -/
-import Mathbin.Order.Filter.FilterProduct
-import Mathbin.Analysis.SpecificLimits.Basic
+import Order.Filter.FilterProduct
+import Analysis.SpecificLimits.Basic
 
 #align_import data.real.hyperreal from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Abhimanyu Pallavi Sudhir. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Abhimanyu Pallavi Sudhir
-
-! This file was ported from Lean 3 source module data.real.hyperreal
-! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Order.Filter.FilterProduct
 import Mathbin.Analysis.SpecificLimits.Basic
 
+#align_import data.real.hyperreal from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+
 /-!
 # Construction of the hyperreal numbers as an ultraproduct of real sequences.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

@@ -737,12 +737,12 @@ theorem infiniteNeg_iff_infinite_of_neg {x : ℝ*} (hn : x < 0) : InfiniteNeg x
 -/
 
 #print Hyperreal.infinitePos_abs_iff_infinite_abs /-
-theorem infinitePos_abs_iff_infinite_abs {x : ℝ*} : InfinitePos (|x|) ↔ Infinite (|x|) :=
+theorem infinitePos_abs_iff_infinite_abs {x : ℝ*} : InfinitePos |x| ↔ Infinite |x| :=
   infinitePos_iff_infinite_of_nonneg (abs_nonneg _)
 #align hyperreal.infinite_pos_abs_iff_infinite_abs Hyperreal.infinitePos_abs_iff_infinite_abs
 -/
 
-theorem infinitePos_abs_iff_infinite {x : ℝ*} : Infinite x ↔ InfinitePos (|x|) :=
+theorem infinitePos_abs_iff_infinite {x : ℝ*} : Infinite x ↔ InfinitePos |x| :=
   ⟨fun hi d =>
     Or.cases_on hi (fun hip => by rw [abs_of_pos (hip 0)] <;> exact hip d) fun hin => by
       rw [abs_of_neg (hin 0)] <;> exact lt_neg.mp (hin (-d)),
@@ -753,13 +753,13 @@ theorem infinitePos_abs_iff_infinite {x : ℝ*} : Infinite x ↔ InfinitePos (|x
     · exact Or.inl (by rwa [abs_of_pos h] at hipa )⟩
 #align hyperreal.infinite_iff_infinite_pos_abs Hyperreal.infinitePos_abs_iff_infiniteₓ
 
-theorem infinite_abs_iff {x : ℝ*} : Infinite x ↔ Infinite (|x|) := by
+theorem infinite_abs_iff {x : ℝ*} : Infinite x ↔ Infinite |x| := by
   rw [← infinite_pos_iff_infinite_of_nonneg (abs_nonneg _), infinite_iff_infinite_pos_abs]
 #align hyperreal.infinite_iff_infinite_abs Hyperreal.infinite_abs_iffₓ
 
 #print Hyperreal.infinite_iff_abs_lt_abs /-
 theorem infinite_iff_abs_lt_abs {x : ℝ*} : Infinite x ↔ ∀ r : ℝ, (|r| : ℝ*) < |x| :=
-  ⟨fun hI r => coe_abs r ▸ infinitePos_abs_iff_infinite.mp hI (|r|), fun hR =>
+  ⟨fun hI r => coe_abs r ▸ infinitePos_abs_iff_infinite.mp hI |r|, fun hR =>
     Or.cases_on (max_choice x (-x))
       (fun h => Or.inl fun r => lt_of_le_of_lt (le_abs_self _) (h ▸ hR r)) fun h =>
       Or.inr fun r => neg_lt_neg_iff.mp <| lt_of_le_of_lt (neg_le_abs_self _) (h ▸ hR r)⟩
@@ -1040,7 +1040,7 @@ theorem gt_of_neg_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r : ℝ,
 #print Hyperreal.abs_lt_real_iff_infinitesimal /-
 theorem abs_lt_real_iff_infinitesimal {x : ℝ*} : Infinitesimal x ↔ ∀ r : ℝ, r ≠ 0 → |x| < |r| :=
   ⟨fun hi r hr =>
-    abs_lt.mpr (by rw [← coe_abs] <;> exact infinitesimal_def.mp hi (|r|) (abs_pos.2 hr)), fun hR =>
+    abs_lt.mpr (by rw [← coe_abs] <;> exact infinitesimal_def.mp hi |r| (abs_pos.2 hr)), fun hR =>
     infinitesimal_def.mpr fun r hr =>
       abs_lt.mp <| (abs_of_pos <| coe_pos.2 hr) ▸ hR r <| ne_of_gt hr⟩
 #align hyperreal.abs_lt_real_iff_infinitesimal Hyperreal.abs_lt_real_iff_infinitesimal
@@ -1134,7 +1134,7 @@ theorem infinitePos_iff_infinitesimal_inv_pos {x : ℝ*} :
     @by_cases (r = 0) (↑r < x) (fun h => Eq.substr h (inv_pos.mp hp)) fun h =>
       lt_of_le_of_lt (coe_le_coe.2 (le_abs_self r))
         ((inv_lt_inv (inv_pos.mp hp) (coe_lt_coe.2 (abs_pos.2 h))).mp
-          ((infinitesimal_def.mp hi) (|r|)⁻¹ (inv_pos.2 (abs_pos.2 h))).2)⟩
+          ((infinitesimal_def.mp hi) |r|⁻¹ (inv_pos.2 (abs_pos.2 h))).2)⟩
 #align hyperreal.infinite_pos_iff_infinitesimal_inv_pos Hyperreal.infinitePos_iff_infinitesimal_inv_pos
 -/
 

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

@@ -33,7 +33,6 @@ deriving LinearOrderedField, Inhabited
 
 namespace Hyperreal
 
--- mathport name: «exprℝ*»
 notation "ℝ*" => Hyperreal
 
 noncomputable instance : CoeTC ℝ ℝ* :=
@@ -52,50 +51,68 @@ theorem coe_ne_coe {x y : ℝ} : (x : ℝ*) ≠ y ↔ x ≠ y :=
 #align hyperreal.coe_ne_coe Hyperreal.coe_ne_coe
 -/
 
+#print Hyperreal.coe_eq_zero /-
 @[simp, norm_cast]
 theorem coe_eq_zero {x : ℝ} : (x : ℝ*) = 0 ↔ x = 0 :=
   coe_eq_coe
 #align hyperreal.coe_eq_zero Hyperreal.coe_eq_zero
+-/
 
+#print Hyperreal.coe_eq_one /-
 @[simp, norm_cast]
 theorem coe_eq_one {x : ℝ} : (x : ℝ*) = 1 ↔ x = 1 :=
   coe_eq_coe
 #align hyperreal.coe_eq_one Hyperreal.coe_eq_one
+-/
 
+#print Hyperreal.coe_ne_zero /-
 @[norm_cast]
 theorem coe_ne_zero {x : ℝ} : (x : ℝ*) ≠ 0 ↔ x ≠ 0 :=
   coe_ne_coe
 #align hyperreal.coe_ne_zero Hyperreal.coe_ne_zero
+-/
 
+#print Hyperreal.coe_ne_one /-
 @[norm_cast]
 theorem coe_ne_one {x : ℝ} : (x : ℝ*) ≠ 1 ↔ x ≠ 1 :=
   coe_ne_coe
 #align hyperreal.coe_ne_one Hyperreal.coe_ne_one
+-/
 
+#print Hyperreal.coe_one /-
 @[simp, norm_cast]
 theorem coe_one : ↑(1 : ℝ) = (1 : ℝ*) :=
   rfl
 #align hyperreal.coe_one Hyperreal.coe_one
+-/
 
+#print Hyperreal.coe_zero /-
 @[simp, norm_cast]
 theorem coe_zero : ↑(0 : ℝ) = (0 : ℝ*) :=
   rfl
 #align hyperreal.coe_zero Hyperreal.coe_zero
+-/
 
+#print Hyperreal.coe_inv /-
 @[simp, norm_cast]
 theorem coe_inv (x : ℝ) : ↑x⁻¹ = (x⁻¹ : ℝ*) :=
   rfl
 #align hyperreal.coe_inv Hyperreal.coe_inv
+-/
 
+#print Hyperreal.coe_neg /-
 @[simp, norm_cast]
 theorem coe_neg (x : ℝ) : ↑(-x) = (-x : ℝ*) :=
   rfl
 #align hyperreal.coe_neg Hyperreal.coe_neg
+-/
 
+#print Hyperreal.coe_add /-
 @[simp, norm_cast]
 theorem coe_add (x y : ℝ) : ↑(x + y) = (x + y : ℝ*) :=
   rfl
 #align hyperreal.coe_add Hyperreal.coe_add
+-/
 
 @[simp, norm_cast]
 theorem coe_bit0 (x : ℝ) : ↑(bit0 x) = (bit0 x : ℝ*) :=
@@ -107,55 +124,75 @@ theorem coe_bit1 (x : ℝ) : ↑(bit1 x) = (bit1 x : ℝ*) :=
   rfl
 #align hyperreal.coe_bit1 Hyperreal.coe_bit1
 
+#print Hyperreal.coe_mul /-
 @[simp, norm_cast]
 theorem coe_mul (x y : ℝ) : ↑(x * y) = (x * y : ℝ*) :=
   rfl
 #align hyperreal.coe_mul Hyperreal.coe_mul
+-/
 
+#print Hyperreal.coe_div /-
 @[simp, norm_cast]
 theorem coe_div (x y : ℝ) : ↑(x / y) = (x / y : ℝ*) :=
   rfl
 #align hyperreal.coe_div Hyperreal.coe_div
+-/
 
+#print Hyperreal.coe_sub /-
 @[simp, norm_cast]
 theorem coe_sub (x y : ℝ) : ↑(x - y) = (x - y : ℝ*) :=
   rfl
 #align hyperreal.coe_sub Hyperreal.coe_sub
+-/
 
+#print Hyperreal.coe_le_coe /-
 @[simp, norm_cast]
 theorem coe_le_coe {x y : ℝ} : (x : ℝ*) ≤ y ↔ x ≤ y :=
   Germ.const_le_iff
 #align hyperreal.coe_le_coe Hyperreal.coe_le_coe
+-/
 
+#print Hyperreal.coe_lt_coe /-
 @[simp, norm_cast]
 theorem coe_lt_coe {x y : ℝ} : (x : ℝ*) < y ↔ x < y :=
   Germ.const_lt_iff
 #align hyperreal.coe_lt_coe Hyperreal.coe_lt_coe
+-/
 
+#print Hyperreal.coe_nonneg /-
 @[simp, norm_cast]
 theorem coe_nonneg {x : ℝ} : 0 ≤ (x : ℝ*) ↔ 0 ≤ x :=
   coe_le_coe
 #align hyperreal.coe_nonneg Hyperreal.coe_nonneg
+-/
 
+#print Hyperreal.coe_pos /-
 @[simp, norm_cast]
 theorem coe_pos {x : ℝ} : 0 < (x : ℝ*) ↔ 0 < x :=
   coe_lt_coe
 #align hyperreal.coe_pos Hyperreal.coe_pos
+-/
 
+#print Hyperreal.coe_abs /-
 @[simp, norm_cast]
 theorem coe_abs (x : ℝ) : ((|x| : ℝ) : ℝ*) = |x| :=
   const_abs x
 #align hyperreal.coe_abs Hyperreal.coe_abs
+-/
 
+#print Hyperreal.coe_max /-
 @[simp, norm_cast]
 theorem coe_max (x y : ℝ) : ((max x y : ℝ) : ℝ*) = max x y :=
   Germ.const_max _ _
 #align hyperreal.coe_max Hyperreal.coe_max
+-/
 
+#print Hyperreal.coe_min /-
 @[simp, norm_cast]
 theorem coe_min (x y : ℝ) : ((min x y : ℝ) : ℝ*) = min x y :=
   Germ.const_min _ _
 #align hyperreal.coe_min Hyperreal.coe_min
+-/
 
 #print Hyperreal.ofSeq /-
 /-- Construct a hyperreal number from a sequence of real numbers. -/
@@ -178,22 +215,25 @@ noncomputable def omega : ℝ* :=
 #align hyperreal.omega Hyperreal.omega
 -/
 
--- mathport name: hyperreal.epsilon
 scoped notation "ε" => Hyperreal.epsilon
 
--- mathport name: hyperreal.omega
 scoped notation "ω" => Hyperreal.omega
 
+#print Hyperreal.inv_omega /-
 @[simp]
 theorem inv_omega : ω⁻¹ = ε :=
   rfl
 #align hyperreal.inv_omega Hyperreal.inv_omega
+-/
 
+#print Hyperreal.inv_epsilon /-
 @[simp]
 theorem inv_epsilon : ε⁻¹ = ω :=
   @inv_inv _ _ ω
 #align hyperreal.inv_epsilon Hyperreal.inv_epsilon
+-/
 
+#print Hyperreal.omega_pos /-
 theorem omega_pos : 0 < ω :=
   Germ.coe_pos.2 <|
     mem_hyperfilter_of_finite_compl <|
@@ -201,23 +241,33 @@ theorem omega_pos : 0 < ω :=
       convert Set.finite_singleton 0
       simp [Set.eq_singleton_iff_unique_mem]
 #align hyperreal.omega_pos Hyperreal.omega_pos
+-/
 
+#print Hyperreal.epsilon_pos /-
 theorem epsilon_pos : 0 < ε :=
   inv_pos_of_pos omega_pos
 #align hyperreal.epsilon_pos Hyperreal.epsilon_pos
+-/
 
+#print Hyperreal.epsilon_ne_zero /-
 theorem epsilon_ne_zero : ε ≠ 0 :=
   epsilon_pos.ne'
 #align hyperreal.epsilon_ne_zero Hyperreal.epsilon_ne_zero
+-/
 
+#print Hyperreal.omega_ne_zero /-
 theorem omega_ne_zero : ω ≠ 0 :=
   omega_pos.ne'
 #align hyperreal.omega_ne_zero Hyperreal.omega_ne_zero
+-/
 
+#print Hyperreal.epsilon_mul_omega /-
 theorem epsilon_mul_omega : ε * ω = 1 :=
   @inv_mul_cancel _ _ ω omega_ne_zero
 #align hyperreal.epsilon_mul_omega Hyperreal.epsilon_mul_omega
+-/
 
+#print Hyperreal.lt_of_tendsto_zero_of_pos /-
 theorem lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝 0)) :
     ∀ {r : ℝ}, 0 < r → ofSeq f < (r : ℝ*) :=
   by
@@ -231,21 +281,28 @@ theorem lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝
         i < N)
   exact mem_hyperfilter_of_finite_compl ((Set.finite_le_nat N).Subset hs)
 #align hyperreal.lt_of_tendsto_zero_of_pos Hyperreal.lt_of_tendsto_zero_of_pos
+-/
 
+#print Hyperreal.neg_lt_of_tendsto_zero_of_pos /-
 theorem neg_lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝 0)) :
     ∀ {r : ℝ}, 0 < r → (-r : ℝ*) < ofSeq f := fun r hr =>
   have hg := hf.neg
   neg_lt_of_neg_lt (by rw [neg_zero] at hg  <;> exact lt_of_tendsto_zero_of_pos hg hr)
 #align hyperreal.neg_lt_of_tendsto_zero_of_pos Hyperreal.neg_lt_of_tendsto_zero_of_pos
+-/
 
+#print Hyperreal.gt_of_tendsto_zero_of_neg /-
 theorem gt_of_tendsto_zero_of_neg {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝 0)) :
     ∀ {r : ℝ}, r < 0 → (r : ℝ*) < ofSeq f := fun r hr => by
   rw [← neg_neg r, coe_neg] <;> exact neg_lt_of_tendsto_zero_of_pos hf (neg_pos.mpr hr)
 #align hyperreal.gt_of_tendsto_zero_of_neg Hyperreal.gt_of_tendsto_zero_of_neg
+-/
 
+#print Hyperreal.epsilon_lt_pos /-
 theorem epsilon_lt_pos (x : ℝ) : 0 < x → ε < x :=
   lt_of_tendsto_zero_of_pos tendsto_inverse_atTop_nhds_0_nat
 #align hyperreal.epsilon_lt_pos Hyperreal.epsilon_lt_pos
+-/
 
 #print Hyperreal.IsSt /-
 /-- Standard part predicate -/
@@ -321,6 +378,7 @@ theorem not_infinite_of_exists_st {x : ℝ*} : (∃ r : ℝ, IsSt x r) → ¬Inf
 #align hyperreal.not_infinite_of_exists_st Hyperreal.not_infinite_of_exists_st
 -/
 
+#print Hyperreal.isSt_sSup /-
 theorem isSt_sSup {x : ℝ*} (hni : ¬Infinite x) : IsSt x (sSup {y : ℝ | (y : ℝ*) < x}) :=
   let S : Set ℝ := {y : ℝ | (y : ℝ*) < x}
   let R : _ := sSup S
@@ -342,6 +400,7 @@ theorem isSt_sSup {x : ℝ*} (hni : ¬Infinite x) : IsSt x (sSup {y : ℝ | (y :
             lt_of_lt_of_le (add_lt_add_left (coe_lt_coe.2 (half_lt_self hδ)) R) c
           not_lt_of_le (le_csSup HR₂ hc) <| (lt_add_iff_pos_right _).mpr <| half_pos hδ⟩
 #align hyperreal.is_st_Sup Hyperreal.isSt_sSup
+-/
 
 #print Hyperreal.exists_st_of_not_infinite /-
 theorem exists_st_of_not_infinite {x : ℝ*} (hni : ¬Infinite x) : ∃ r : ℝ, IsSt x r :=
@@ -349,6 +408,7 @@ theorem exists_st_of_not_infinite {x : ℝ*} (hni : ¬Infinite x) : ∃ r : ℝ,
 #align hyperreal.exists_st_of_not_infinite Hyperreal.exists_st_of_not_infinite
 -/
 
+#print Hyperreal.st_eq_sSup /-
 theorem st_eq_sSup {x : ℝ*} : st x = sSup {y : ℝ | (y : ℝ*) < x} :=
   by
   unfold st; split_ifs
@@ -363,6 +423,7 @@ theorem st_eq_sSup {x : ℝ*} : st x = sSup {y : ℝ | (y : ℝ*) < x} :=
           {y : ℝ | (y : ℝ*) < x} = ∅)]
       exact real.Sup_empty.symm
 #align hyperreal.st_eq_Sup Hyperreal.st_eq_sSup
+-/
 
 #print Hyperreal.exists_st_iff_not_infinite /-
 theorem exists_st_iff_not_infinite {x : ℝ*} : (∃ r : ℝ, IsSt x r) ↔ ¬Infinite x :=
@@ -376,12 +437,14 @@ theorem infinite_iff_not_exists_st {x : ℝ*} : Infinite x ↔ ¬∃ r : ℝ, Is
 #align hyperreal.infinite_iff_not_exists_st Hyperreal.infinite_iff_not_exists_st
 -/
 
+#print Hyperreal.Infinite.st_eq /-
 theorem Hyperreal.Infinite.st_eq {x : ℝ*} (hi : Infinite x) : st x = 0 :=
   by
   unfold st; split_ifs
   · exact False.elim ((infinite_iff_not_exists_st.mp hi) h)
   · rfl
 #align hyperreal.st_infinite Hyperreal.Infinite.st_eq
+-/
 
 #print Hyperreal.IsSt.st_eq /-
 theorem Hyperreal.IsSt.st_eq {x : ℝ*} {r : ℝ} (hxr : IsSt x r) : st x = r :=
@@ -404,12 +467,14 @@ theorem isSt_st_of_exists_st {x : ℝ*} (hx : ∃ r : ℝ, IsSt x r) : IsSt x (s
 #align hyperreal.is_st_st_of_exists_st Hyperreal.isSt_st_of_exists_st
 -/
 
+#print Hyperreal.isSt_st /-
 theorem isSt_st {x : ℝ*} (hx : st x ≠ 0) : IsSt x (st x) :=
   by
   unfold st; split_ifs
   · exact Classical.choose_spec h
   · exact False.elim (hx (by unfold st <;> split_ifs <;> rfl))
 #align hyperreal.is_st_st Hyperreal.isSt_st
+-/
 
 #print Hyperreal.isSt_st' /-
 theorem isSt_st' {x : ℝ*} (hx : ¬Infinite x) : IsSt x (st x) :=
@@ -459,10 +524,13 @@ theorem isSt_inj_real {r₁ r₂ s : ℝ} (h1 : IsSt r₁ s) (h2 : IsSt r₂ s)
 #align hyperreal.is_st_inj_real Hyperreal.isSt_inj_real
 -/
 
+#print Hyperreal.isSt_iff_abs_sub_lt_delta /-
 theorem isSt_iff_abs_sub_lt_delta {x : ℝ*} {r : ℝ} : IsSt x r ↔ ∀ δ : ℝ, 0 < δ → |x - r| < δ := by
   simp only [abs_sub_lt_iff, sub_lt_iff_lt_add, is_st, and_comm', add_comm]
 #align hyperreal.is_st_iff_abs_sub_lt_delta Hyperreal.isSt_iff_abs_sub_lt_delta
+-/
 
+#print Hyperreal.IsSt.add /-
 theorem Hyperreal.IsSt.add {x y : ℝ*} {r s : ℝ} : IsSt x r → IsSt y s → IsSt (x + y) (r + s) :=
   fun hxr hys d hd =>
   have hxr' := hxr (d / 2) (half_pos hd)
@@ -470,15 +538,21 @@ theorem Hyperreal.IsSt.add {x y : ℝ*} {r s : ℝ} : IsSt x r → IsSt y s →
   ⟨by convert add_lt_add hxr'.1 hys'.1 using 1 <;> norm_cast <;> linarith, by
     convert add_lt_add hxr'.2 hys'.2 using 1 <;> norm_cast <;> linarith⟩
 #align hyperreal.is_st_add Hyperreal.IsSt.add
+-/
 
+#print Hyperreal.IsSt.neg /-
 theorem Hyperreal.IsSt.neg {x : ℝ*} {r : ℝ} (hxr : IsSt x r) : IsSt (-x) (-r) := fun d hd =>
   show -(r : ℝ*) - d < -x ∧ -x < -r + d by cases hxr d hd <;> constructor <;> linarith
 #align hyperreal.is_st_neg Hyperreal.IsSt.neg
+-/
 
+#print Hyperreal.IsSt.sub /-
 theorem Hyperreal.IsSt.sub {x y : ℝ*} {r s : ℝ} : IsSt x r → IsSt y s → IsSt (x - y) (r - s) :=
   fun hxr hys => by rw [sub_eq_add_neg, sub_eq_add_neg] <;> exact is_st_add hxr (is_st_neg hys)
 #align hyperreal.is_st_sub Hyperreal.IsSt.sub
+-/
 
+#print Hyperreal.IsSt.lt /-
 -- (st x < st y) → (x < y) → (x ≤ y) → (st x ≤ st y)
 theorem Hyperreal.IsSt.lt {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt y s) : r < s → x < y :=
   fun hrs => by
@@ -492,47 +566,66 @@ theorem Hyperreal.IsSt.lt {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
   rw [H2] at hys' 
   exact lt_trans hxr' hys'
 #align hyperreal.lt_of_is_st_lt Hyperreal.IsSt.lt
+-/
 
+#print Hyperreal.IsSt.le /-
 theorem Hyperreal.IsSt.le {x y : ℝ*} {r s : ℝ} (hrx : IsSt x r) (hsy : IsSt y s) : x ≤ y → r ≤ s :=
   by rw [← not_lt, ← not_lt, not_imp_not] <;> exact lt_of_is_st_lt hsy hrx
 #align hyperreal.is_st_le_of_le Hyperreal.IsSt.le
+-/
 
+#print Hyperreal.st_le_of_le /-
 theorem st_le_of_le {x y : ℝ*} (hix : ¬Infinite x) (hiy : ¬Infinite y) : x ≤ y → st x ≤ st y :=
   have hx' := isSt_st' hix
   have hy' := isSt_st' hiy
   Hyperreal.IsSt.le hx' hy'
 #align hyperreal.st_le_of_le Hyperreal.st_le_of_le
+-/
 
+#print Hyperreal.lt_of_st_lt /-
 theorem lt_of_st_lt {x y : ℝ*} (hix : ¬Infinite x) (hiy : ¬Infinite y) : st x < st y → x < y :=
   have hx' := isSt_st' hix
   have hy' := isSt_st' hiy
   Hyperreal.IsSt.lt hx' hy'
 #align hyperreal.lt_of_st_lt Hyperreal.lt_of_st_lt
+-/
 
 /-!
 ### Basic lemmas about infinite
 -/
 
 
+#print Hyperreal.infinitePos_def /-
 theorem infinitePos_def {x : ℝ*} : InfinitePos x ↔ ∀ r : ℝ, ↑r < x := by rw [iff_eq_eq] <;> rfl
 #align hyperreal.infinite_pos_def Hyperreal.infinitePos_def
+-/
 
+#print Hyperreal.infiniteNeg_def /-
 theorem infiniteNeg_def {x : ℝ*} : InfiniteNeg x ↔ ∀ r : ℝ, x < r := by rw [iff_eq_eq] <;> rfl
 #align hyperreal.infinite_neg_def Hyperreal.infiniteNeg_def
+-/
 
+#print Hyperreal.Infinite.ne_zero /-
 theorem Hyperreal.Infinite.ne_zero {x : ℝ*} : Infinite x → x ≠ 0 := fun hI h0 =>
   Or.cases_on hI (fun hip => lt_irrefl (0 : ℝ*) ((by rwa [← h0] : InfinitePos 0) 0)) fun hin =>
     lt_irrefl (0 : ℝ*) ((by rwa [← h0] : InfiniteNeg 0) 0)
 #align hyperreal.ne_zero_of_infinite Hyperreal.Infinite.ne_zero
+-/
 
+#print Hyperreal.not_infinite_zero /-
 theorem not_infinite_zero : ¬Infinite 0 := fun hI => Hyperreal.Infinite.ne_zero hI rfl
 #align hyperreal.not_infinite_zero Hyperreal.not_infinite_zero
+-/
 
+#print Hyperreal.InfinitePos.pos /-
 theorem Hyperreal.InfinitePos.pos {x : ℝ*} : InfinitePos x → 0 < x := fun hip => hip 0
 #align hyperreal.pos_of_infinite_pos Hyperreal.InfinitePos.pos
+-/
 
+#print Hyperreal.InfiniteNeg.lt_zero /-
 theorem Hyperreal.InfiniteNeg.lt_zero {x : ℝ*} : InfiniteNeg x → x < 0 := fun hin => hin 0
 #align hyperreal.neg_of_infinite_neg Hyperreal.InfiniteNeg.lt_zero
+-/
 
 #print Hyperreal.InfiniteNeg.not_infinitePos /-
 theorem Hyperreal.InfiniteNeg.not_infinitePos {x : ℝ*} : InfiniteNeg x → ¬InfinitePos x :=
@@ -546,13 +639,17 @@ theorem Hyperreal.InfinitePos.not_infiniteNeg {x : ℝ*} : InfinitePos x → ¬I
 #align hyperreal.not_infinite_neg_of_infinite_pos Hyperreal.InfinitePos.not_infiniteNeg
 -/
 
+#print Hyperreal.InfinitePos.neg /-
 theorem Hyperreal.InfinitePos.neg {x : ℝ*} : InfinitePos x → InfiniteNeg (-x) := fun hp r =>
   neg_lt.mp (hp (-r))
 #align hyperreal.infinite_neg_neg_of_infinite_pos Hyperreal.InfinitePos.neg
+-/
 
+#print Hyperreal.InfiniteNeg.neg /-
 theorem Hyperreal.InfiniteNeg.neg {x : ℝ*} : InfiniteNeg x → InfinitePos (-x) := fun hp r =>
   lt_neg.mp (hp (-r))
 #align hyperreal.infinite_pos_neg_of_infinite_neg Hyperreal.InfiniteNeg.neg
+-/
 
 theorem infiniteNeg_neg {x : ℝ*} : InfinitePos x ↔ InfiniteNeg (-x) :=
   ⟨Hyperreal.InfinitePos.neg, fun hin => neg_neg x ▸ Hyperreal.InfiniteNeg.neg hin⟩
@@ -603,20 +700,27 @@ theorem Hyperreal.InfiniteNeg.not_infinitesimal {x : ℝ*} : InfiniteNeg x → 
 #align hyperreal.not_infinitesimal_of_infinite_neg Hyperreal.InfiniteNeg.not_infinitesimal
 -/
 
+#print Hyperreal.infinitePos_iff_infinite_and_pos /-
 theorem infinitePos_iff_infinite_and_pos {x : ℝ*} : InfinitePos x ↔ Infinite x ∧ 0 < x :=
   ⟨fun hip => ⟨Or.inl hip, hip 0⟩, fun ⟨hi, hp⟩ =>
     hi.casesOn (fun hip => hip) fun hin => False.elim (not_lt_of_lt hp (hin 0))⟩
 #align hyperreal.infinite_pos_iff_infinite_and_pos Hyperreal.infinitePos_iff_infinite_and_pos
+-/
 
+#print Hyperreal.infiniteNeg_iff_infinite_and_neg /-
 theorem infiniteNeg_iff_infinite_and_neg {x : ℝ*} : InfiniteNeg x ↔ Infinite x ∧ x < 0 :=
   ⟨fun hip => ⟨Or.inr hip, hip 0⟩, fun ⟨hi, hp⟩ =>
     hi.casesOn (fun hin => False.elim (not_lt_of_lt hp (hin 0))) fun hip => hip⟩
 #align hyperreal.infinite_neg_iff_infinite_and_neg Hyperreal.infiniteNeg_iff_infinite_and_neg
+-/
 
+#print Hyperreal.infinitePos_iff_infinite_of_pos /-
 theorem infinitePos_iff_infinite_of_pos {x : ℝ*} (hp : 0 < x) : InfinitePos x ↔ Infinite x := by
   rw [infinite_pos_iff_infinite_and_pos] <;> exact ⟨fun hI => hI.1, fun hI => ⟨hI, hp⟩⟩
 #align hyperreal.infinite_pos_iff_infinite_of_pos Hyperreal.infinitePos_iff_infinite_of_pos
+-/
 
+#print Hyperreal.infinitePos_iff_infinite_of_nonneg /-
 theorem infinitePos_iff_infinite_of_nonneg {x : ℝ*} (hp : 0 ≤ x) : InfinitePos x ↔ Infinite x :=
   Or.cases_on (lt_or_eq_of_le hp) infinitePos_iff_infinite_of_pos fun h => by
     rw [h.symm] <;>
@@ -624,14 +728,19 @@ theorem infinitePos_iff_infinite_of_nonneg {x : ℝ*} (hp : 0 ≤ x) : InfiniteP
         ⟨fun hIP => False.elim (not_infinite_zero (Or.inl hIP)), fun hI =>
           False.elim (not_infinite_zero hI)⟩
 #align hyperreal.infinite_pos_iff_infinite_of_nonneg Hyperreal.infinitePos_iff_infinite_of_nonneg
+-/
 
+#print Hyperreal.infiniteNeg_iff_infinite_of_neg /-
 theorem infiniteNeg_iff_infinite_of_neg {x : ℝ*} (hn : x < 0) : InfiniteNeg x ↔ Infinite x := by
   rw [infinite_neg_iff_infinite_and_neg] <;> exact ⟨fun hI => hI.1, fun hI => ⟨hI, hn⟩⟩
 #align hyperreal.infinite_neg_iff_infinite_of_neg Hyperreal.infiniteNeg_iff_infinite_of_neg
+-/
 
+#print Hyperreal.infinitePos_abs_iff_infinite_abs /-
 theorem infinitePos_abs_iff_infinite_abs {x : ℝ*} : InfinitePos (|x|) ↔ Infinite (|x|) :=
   infinitePos_iff_infinite_of_nonneg (abs_nonneg _)
 #align hyperreal.infinite_pos_abs_iff_infinite_abs Hyperreal.infinitePos_abs_iff_infinite_abs
+-/
 
 theorem infinitePos_abs_iff_infinite {x : ℝ*} : Infinite x ↔ InfinitePos (|x|) :=
   ⟨fun hi d =>
@@ -648,13 +757,16 @@ theorem infinite_abs_iff {x : ℝ*} : Infinite x ↔ Infinite (|x|) := by
   rw [← infinite_pos_iff_infinite_of_nonneg (abs_nonneg _), infinite_iff_infinite_pos_abs]
 #align hyperreal.infinite_iff_infinite_abs Hyperreal.infinite_abs_iffₓ
 
+#print Hyperreal.infinite_iff_abs_lt_abs /-
 theorem infinite_iff_abs_lt_abs {x : ℝ*} : Infinite x ↔ ∀ r : ℝ, (|r| : ℝ*) < |x| :=
   ⟨fun hI r => coe_abs r ▸ infinitePos_abs_iff_infinite.mp hI (|r|), fun hR =>
     Or.cases_on (max_choice x (-x))
       (fun h => Or.inl fun r => lt_of_le_of_lt (le_abs_self _) (h ▸ hR r)) fun h =>
       Or.inr fun r => neg_lt_neg_iff.mp <| lt_of_le_of_lt (neg_le_abs_self _) (h ▸ hR r)⟩
 #align hyperreal.infinite_iff_abs_lt_abs Hyperreal.infinite_iff_abs_lt_abs
+-/
 
+#print Hyperreal.infinitePos_add_not_infiniteNeg /-
 theorem infinitePos_add_not_infiniteNeg {x y : ℝ*} :
     InfinitePos x → ¬InfiniteNeg y → InfinitePos (x + y) :=
   by
@@ -663,43 +775,58 @@ theorem infinitePos_add_not_infiniteNeg {x y : ℝ*} :
   convert add_lt_add_of_lt_of_le (hip (r + -r₂)) (not_lt.mp hr₂) using 1
   simp
 #align hyperreal.infinite_pos_add_not_infinite_neg Hyperreal.infinitePos_add_not_infiniteNeg
+-/
 
+#print Hyperreal.not_infiniteNeg_add_infinitePos /-
 theorem not_infiniteNeg_add_infinitePos {x y : ℝ*} :
     ¬InfiniteNeg x → InfinitePos y → InfinitePos (x + y) := fun hx hy => by
   rw [add_comm] <;> exact infinite_pos_add_not_infinite_neg hy hx
 #align hyperreal.not_infinite_neg_add_infinite_pos Hyperreal.not_infiniteNeg_add_infinitePos
+-/
 
+#print Hyperreal.infiniteNeg_add_not_infinitePos /-
 theorem infiniteNeg_add_not_infinitePos {x y : ℝ*} :
     InfiniteNeg x → ¬InfinitePos y → InfiniteNeg (x + y) := by
   rw [@infinite_neg_iff_infinite_pos_neg x, @infinite_pos_iff_infinite_neg_neg y,
       @infinite_neg_iff_infinite_pos_neg (x + y), neg_add] <;>
     exact infinite_pos_add_not_infinite_neg
 #align hyperreal.infinite_neg_add_not_infinite_pos Hyperreal.infiniteNeg_add_not_infinitePos
+-/
 
+#print Hyperreal.not_infinitePos_add_infiniteNeg /-
 theorem not_infinitePos_add_infiniteNeg {x y : ℝ*} :
     ¬InfinitePos x → InfiniteNeg y → InfiniteNeg (x + y) := fun hx hy => by
   rw [add_comm] <;> exact infinite_neg_add_not_infinite_pos hy hx
 #align hyperreal.not_infinite_pos_add_infinite_neg Hyperreal.not_infinitePos_add_infiniteNeg
+-/
 
+#print Hyperreal.infinitePos_add_infinitePos /-
 theorem infinitePos_add_infinitePos {x y : ℝ*} :
     InfinitePos x → InfinitePos y → InfinitePos (x + y) := fun hx hy =>
   infinitePos_add_not_infiniteNeg hx (Hyperreal.InfinitePos.not_infiniteNeg hy)
 #align hyperreal.infinite_pos_add_infinite_pos Hyperreal.infinitePos_add_infinitePos
+-/
 
+#print Hyperreal.infiniteNeg_add_infiniteNeg /-
 theorem infiniteNeg_add_infiniteNeg {x y : ℝ*} :
     InfiniteNeg x → InfiniteNeg y → InfiniteNeg (x + y) := fun hx hy =>
   infiniteNeg_add_not_infinitePos hx (Hyperreal.InfiniteNeg.not_infinitePos hy)
 #align hyperreal.infinite_neg_add_infinite_neg Hyperreal.infiniteNeg_add_infiniteNeg
+-/
 
+#print Hyperreal.infinitePos_add_not_infinite /-
 theorem infinitePos_add_not_infinite {x y : ℝ*} :
     InfinitePos x → ¬Infinite y → InfinitePos (x + y) := fun hx hy =>
   infinitePos_add_not_infiniteNeg hx (not_or.mp hy).2
 #align hyperreal.infinite_pos_add_not_infinite Hyperreal.infinitePos_add_not_infinite
+-/
 
+#print Hyperreal.infiniteNeg_add_not_infinite /-
 theorem infiniteNeg_add_not_infinite {x y : ℝ*} :
     InfiniteNeg x → ¬Infinite y → InfiniteNeg (x + y) := fun hx hy =>
   infiniteNeg_add_not_infinitePos hx (not_or.mp hy).1
 #align hyperreal.infinite_neg_add_not_infinite Hyperreal.infiniteNeg_add_not_infinite
+-/
 
 #print Hyperreal.infinitePos_of_tendsto_top /-
 theorem infinitePos_of_tendsto_top {f : ℕ → ℝ} (hf : Tendsto f atTop atTop) :
@@ -729,10 +856,13 @@ theorem infiniteNeg_of_tendsto_bot {f : ℕ → ℝ} (hf : Tendsto f atTop atBot
 #align hyperreal.infinite_neg_of_tendsto_bot Hyperreal.infiniteNeg_of_tendsto_bot
 -/
 
+#print Hyperreal.not_infinite_neg /-
 theorem not_infinite_neg {x : ℝ*} : ¬Infinite x → ¬Infinite (-x) :=
   not_imp_not.mpr infinite_neg.mpr
 #align hyperreal.not_infinite_neg Hyperreal.not_infinite_neg
+-/
 
+#print Hyperreal.not_infinite_add /-
 theorem not_infinite_add {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : ¬Infinite (x + y) :=
   have hx' := exists_st_of_not_infinite hx
   have hy' := exists_st_of_not_infinite hy
@@ -740,7 +870,9 @@ theorem not_infinite_add {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) :
     Exists.cases_on hy' fun r hr s hs =>
       not_infinite_of_exists_st <| ⟨s + r, Hyperreal.IsSt.add hs hr⟩
 #align hyperreal.not_infinite_add Hyperreal.not_infinite_add
+-/
 
+#print Hyperreal.not_infinite_iff_exist_lt_gt /-
 theorem not_infinite_iff_exist_lt_gt {x : ℝ*} : ¬Infinite x ↔ ∃ r s : ℝ, (r : ℝ*) < x ∧ x < s :=
   ⟨fun hni =>
     Exists.dcases_on (not_forall.mp (not_or.mp hni).1) <|
@@ -755,6 +887,7 @@ theorem not_infinite_iff_exist_lt_gt {x : ℝ*} : ¬Infinite x ↔ ∃ r s : ℝ
       Exists.dcases_on hr fun s hs =>
         not_or.mpr ⟨not_forall.mpr ⟨s, lt_asymm hs.2⟩, not_forall.mpr ⟨r, lt_asymm hs.1⟩⟩⟩
 #align hyperreal.not_infinite_iff_exist_lt_gt Hyperreal.not_infinite_iff_exist_lt_gt
+-/
 
 #print Hyperreal.not_infinite_real /-
 theorem not_infinite_real (r : ℝ) : ¬Infinite r := by
@@ -813,6 +946,7 @@ private theorem is_st_mul' {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
               _)
           _ = (d : ℝ*) := by rw [mul_one, add_halves]
 
+#print Hyperreal.IsSt.mul /-
 theorem Hyperreal.IsSt.mul {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt y s) :
     IsSt (x * y) (r * s) :=
   have h :=
@@ -831,7 +965,9 @@ theorem Hyperreal.IsSt.mul {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
         exact mul_lt_mul'' hys' ht (abs_nonneg _) (abs_nonneg _)
       exact is_st_mul' hxr hys hs
 #align hyperreal.is_st_mul Hyperreal.IsSt.mul
+-/
 
+#print Hyperreal.not_infinite_mul /-
 --AN INFINITE LEMMA THAT REQUIRES SOME MORE ST MACHINERY
 theorem not_infinite_mul {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : ¬Infinite (x * y) :=
   have hx' := exists_st_of_not_infinite hx
@@ -840,7 +976,9 @@ theorem not_infinite_mul {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) :
     Exists.cases_on hy' fun r hr s hs =>
       not_infinite_of_exists_st <| ⟨s * r, Hyperreal.IsSt.mul hs hr⟩
 #align hyperreal.not_infinite_mul Hyperreal.not_infinite_mul
+-/
 
+#print Hyperreal.st_add /-
 ---
 theorem st_add {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : st (x + y) = st x + st y :=
   have hx' := isSt_st' hx
@@ -849,13 +987,17 @@ theorem st_add {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : st (x + y)
   have hxy' := Hyperreal.IsSt.add hx' hy'
   Hyperreal.IsSt.unique hxy hxy'
 #align hyperreal.st_add Hyperreal.st_add
+-/
 
+#print Hyperreal.st_neg /-
 theorem st_neg (x : ℝ*) : st (-x) = -st x :=
   if h : Infinite x then by
     rw [st_infinite h, st_infinite (infinite_iff_infinite_neg.mp h), neg_zero]
   else Hyperreal.IsSt.unique (isSt_st' (not_infinite_neg h)) (Hyperreal.IsSt.neg (isSt_st' h))
 #align hyperreal.st_neg Hyperreal.st_neg
+-/
 
+#print Hyperreal.st_mul /-
 theorem st_mul {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : st (x * y) = st x * st y :=
   have hx' := isSt_st' hx
   have hy' := isSt_st' hy
@@ -863,69 +1005,94 @@ theorem st_mul {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : st (x * y)
   have hxy' := Hyperreal.IsSt.mul hx' hy'
   Hyperreal.IsSt.unique hxy hxy'
 #align hyperreal.st_mul Hyperreal.st_mul
+-/
 
 /-!
 ### Basic lemmas about infinitesimal
 -/
 
 
+#print Hyperreal.infinitesimal_def /-
 theorem infinitesimal_def {x : ℝ*} : Infinitesimal x ↔ ∀ r : ℝ, 0 < r → -(r : ℝ*) < x ∧ x < r :=
   ⟨fun hi r hr => by convert hi r hr <;> simp, fun hi d hd => by convert hi d hd <;> simp⟩
 #align hyperreal.infinitesimal_def Hyperreal.infinitesimal_def
+-/
 
+#print Hyperreal.lt_of_pos_of_infinitesimal /-
 theorem lt_of_pos_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r : ℝ, 0 < r → x < r :=
   fun hi r hr => ((infinitesimal_def.mp hi) r hr).2
 #align hyperreal.lt_of_pos_of_infinitesimal Hyperreal.lt_of_pos_of_infinitesimal
+-/
 
+#print Hyperreal.lt_neg_of_pos_of_infinitesimal /-
 theorem lt_neg_of_pos_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r : ℝ, 0 < r → -↑r < x :=
   fun hi r hr => ((infinitesimal_def.mp hi) r hr).1
 #align hyperreal.lt_neg_of_pos_of_infinitesimal Hyperreal.lt_neg_of_pos_of_infinitesimal
+-/
 
+#print Hyperreal.gt_of_neg_of_infinitesimal /-
 theorem gt_of_neg_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r : ℝ, r < 0 → ↑r < x :=
   fun hi r hr => by
   convert ((infinitesimal_def.mp hi) (-r) (neg_pos.mpr hr)).1 <;> exact (neg_neg ↑r).symm
 #align hyperreal.gt_of_neg_of_infinitesimal Hyperreal.gt_of_neg_of_infinitesimal
+-/
 
+#print Hyperreal.abs_lt_real_iff_infinitesimal /-
 theorem abs_lt_real_iff_infinitesimal {x : ℝ*} : Infinitesimal x ↔ ∀ r : ℝ, r ≠ 0 → |x| < |r| :=
   ⟨fun hi r hr =>
     abs_lt.mpr (by rw [← coe_abs] <;> exact infinitesimal_def.mp hi (|r|) (abs_pos.2 hr)), fun hR =>
     infinitesimal_def.mpr fun r hr =>
       abs_lt.mp <| (abs_of_pos <| coe_pos.2 hr) ▸ hR r <| ne_of_gt hr⟩
 #align hyperreal.abs_lt_real_iff_infinitesimal Hyperreal.abs_lt_real_iff_infinitesimal
+-/
 
+#print Hyperreal.infinitesimal_zero /-
 theorem infinitesimal_zero : Infinitesimal 0 :=
   isSt_refl_real 0
 #align hyperreal.infinitesimal_zero Hyperreal.infinitesimal_zero
+-/
 
+#print Hyperreal.Infinitesimal.eq_zero /-
 theorem Hyperreal.Infinitesimal.eq_zero {r : ℝ} : Infinitesimal r → r = 0 :=
   eq_of_isSt_real
 #align hyperreal.zero_of_infinitesimal_real Hyperreal.Infinitesimal.eq_zero
+-/
 
+#print Hyperreal.infinitesimal_real_iff /-
 theorem infinitesimal_real_iff {r : ℝ} : Infinitesimal r ↔ r = 0 :=
   ⟨Hyperreal.Infinitesimal.eq_zero, fun hr => by rw [hr] <;> exact infinitesimal_zero⟩
 #align hyperreal.zero_iff_infinitesimal_real Hyperreal.infinitesimal_real_iff
+-/
 
+#print Hyperreal.Infinitesimal.add /-
 theorem Hyperreal.Infinitesimal.add {x y : ℝ*} (hx : Infinitesimal x) (hy : Infinitesimal y) :
     Infinitesimal (x + y) := by simpa only [add_zero] using is_st_add hx hy
 #align hyperreal.infinitesimal_add Hyperreal.Infinitesimal.add
+-/
 
+#print Hyperreal.Infinitesimal.neg /-
 theorem Hyperreal.Infinitesimal.neg {x : ℝ*} (hx : Infinitesimal x) : Infinitesimal (-x) := by
   simpa only [neg_zero] using is_st_neg hx
 #align hyperreal.infinitesimal_neg Hyperreal.Infinitesimal.neg
+-/
 
 theorem infinitesimal_neg {x : ℝ*} : Infinitesimal x ↔ Infinitesimal (-x) :=
   ⟨Hyperreal.Infinitesimal.neg, fun h => neg_neg x ▸ @Hyperreal.Infinitesimal.neg (-x) h⟩
 #align hyperreal.infinitesimal_neg_iff Hyperreal.infinitesimal_negₓ
 
+#print Hyperreal.Infinitesimal.mul /-
 theorem Hyperreal.Infinitesimal.mul {x y : ℝ*} (hx : Infinitesimal x) (hy : Infinitesimal y) :
     Infinitesimal (x * y) := by simpa only [MulZeroClass.mul_zero] using is_st_mul hx hy
 #align hyperreal.infinitesimal_mul Hyperreal.Infinitesimal.mul
+-/
 
+#print Hyperreal.infinitesimal_of_tendsto_zero /-
 theorem infinitesimal_of_tendsto_zero {f : ℕ → ℝ} :
     Tendsto f atTop (𝓝 0) → Infinitesimal (ofSeq f) := fun hf d hd => by
   rw [sub_eq_add_neg, ← coe_neg, ← coe_add, ← coe_add, zero_add, zero_add] <;>
     exact ⟨neg_lt_of_tendsto_zero_of_pos hf hd, lt_of_tendsto_zero_of_pos hf hd⟩
 #align hyperreal.infinitesimal_of_tendsto_zero Hyperreal.infinitesimal_of_tendsto_zero
+-/
 
 #print Hyperreal.infinitesimal_epsilon /-
 theorem infinitesimal_epsilon : Infinitesimal ε :=
@@ -933,22 +1100,29 @@ theorem infinitesimal_epsilon : Infinitesimal ε :=
 #align hyperreal.infinitesimal_epsilon Hyperreal.infinitesimal_epsilon
 -/
 
+#print Hyperreal.not_real_of_infinitesimal_ne_zero /-
 theorem not_real_of_infinitesimal_ne_zero (x : ℝ*) : Infinitesimal x → x ≠ 0 → ∀ r : ℝ, x ≠ r :=
   fun hi hx r hr =>
   hx <|
     hr.trans <| coe_eq_zero.2 <| Hyperreal.IsSt.unique (hr.symm ▸ isSt_refl_real r : IsSt x r) hi
 #align hyperreal.not_real_of_infinitesimal_ne_zero Hyperreal.not_real_of_infinitesimal_ne_zero
+-/
 
+#print Hyperreal.IsSt.infinitesimal_sub /-
 theorem Hyperreal.IsSt.infinitesimal_sub {x : ℝ*} {r : ℝ} (hxr : IsSt x r) :
     Infinitesimal (x - r) :=
   show IsSt (x - r) 0 by rw [sub_eq_add_neg, ← add_neg_self r];
     exact is_st_add hxr (is_st_refl_real (-r))
 #align hyperreal.infinitesimal_sub_is_st Hyperreal.IsSt.infinitesimal_sub
+-/
 
+#print Hyperreal.infinitesimal_sub_st /-
 theorem infinitesimal_sub_st {x : ℝ*} (hx : ¬Infinite x) : Infinitesimal (x - st x) :=
   Hyperreal.IsSt.infinitesimal_sub <| isSt_st' hx
 #align hyperreal.infinitesimal_sub_st Hyperreal.infinitesimal_sub_st
+-/
 
+#print Hyperreal.infinitePos_iff_infinitesimal_inv_pos /-
 theorem infinitePos_iff_infinitesimal_inv_pos {x : ℝ*} :
     InfinitePos x ↔ Infinitesimal x⁻¹ ∧ 0 < x⁻¹ :=
   ⟨fun hip =>
@@ -962,7 +1136,9 @@ theorem infinitePos_iff_infinitesimal_inv_pos {x : ℝ*} :
         ((inv_lt_inv (inv_pos.mp hp) (coe_lt_coe.2 (abs_pos.2 h))).mp
           ((infinitesimal_def.mp hi) (|r|)⁻¹ (inv_pos.2 (abs_pos.2 h))).2)⟩
 #align hyperreal.infinite_pos_iff_infinitesimal_inv_pos Hyperreal.infinitePos_iff_infinitesimal_inv_pos
+-/
 
+#print Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg /-
 theorem infiniteNeg_iff_infinitesimal_inv_neg {x : ℝ*} :
     InfiniteNeg x ↔ Infinitesimal x⁻¹ ∧ x⁻¹ < 0 :=
   ⟨fun hin =>
@@ -972,36 +1148,49 @@ theorem infiniteNeg_iff_infinitesimal_inv_neg {x : ℝ*} :
     rwa [← neg_pos, infinitesimal_neg_iff, neg_inv, ← infinite_pos_iff_infinitesimal_inv_pos, ←
       infinite_neg_iff_infinite_pos_neg] at hin ⟩
 #align hyperreal.infinite_neg_iff_infinitesimal_inv_neg Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg
+-/
 
+#print Hyperreal.infinitesimal_inv_of_infinite /-
 theorem infinitesimal_inv_of_infinite {x : ℝ*} : Infinite x → Infinitesimal x⁻¹ := fun hi =>
   Or.cases_on hi (fun hip => (infinitePos_iff_infinitesimal_inv_pos.mp hip).1) fun hin =>
     (infiniteNeg_iff_infinitesimal_inv_neg.mp hin).1
 #align hyperreal.infinitesimal_inv_of_infinite Hyperreal.infinitesimal_inv_of_infinite
+-/
 
+#print Hyperreal.infinite_of_infinitesimal_inv /-
 theorem infinite_of_infinitesimal_inv {x : ℝ*} (h0 : x ≠ 0) (hi : Infinitesimal x⁻¹) : Infinite x :=
   by
   cases' lt_or_gt_of_ne h0 with hn hp
   · exact Or.inr (infinite_neg_iff_infinitesimal_inv_neg.mpr ⟨hi, inv_lt_zero.mpr hn⟩)
   · exact Or.inl (infinite_pos_iff_infinitesimal_inv_pos.mpr ⟨hi, inv_pos.mpr hp⟩)
 #align hyperreal.infinite_of_infinitesimal_inv Hyperreal.infinite_of_infinitesimal_inv
+-/
 
+#print Hyperreal.infinite_iff_infinitesimal_inv /-
 theorem infinite_iff_infinitesimal_inv {x : ℝ*} (h0 : x ≠ 0) : Infinite x ↔ Infinitesimal x⁻¹ :=
   ⟨infinitesimal_inv_of_infinite, infinite_of_infinitesimal_inv h0⟩
 #align hyperreal.infinite_iff_infinitesimal_inv Hyperreal.infinite_iff_infinitesimal_inv
+-/
 
+#print Hyperreal.infinitesimal_pos_iff_infinitePos_inv /-
 theorem infinitesimal_pos_iff_infinitePos_inv {x : ℝ*} :
     InfinitePos x⁻¹ ↔ Infinitesimal x ∧ 0 < x := by
   convert infinite_pos_iff_infinitesimal_inv_pos <;> simp only [inv_inv]
 #align hyperreal.infinitesimal_pos_iff_infinite_pos_inv Hyperreal.infinitesimal_pos_iff_infinitePos_inv
+-/
 
+#print Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv /-
 theorem infinitesimal_neg_iff_infiniteNeg_inv {x : ℝ*} :
     InfiniteNeg x⁻¹ ↔ Infinitesimal x ∧ x < 0 := by
   convert infinite_neg_iff_infinitesimal_inv_neg <;> simp only [inv_inv]
 #align hyperreal.infinitesimal_neg_iff_infinite_neg_inv Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv
+-/
 
+#print Hyperreal.infinitesimal_iff_infinite_inv /-
 theorem infinitesimal_iff_infinite_inv {x : ℝ*} (h : x ≠ 0) : Infinitesimal x ↔ Infinite x⁻¹ := by
   convert (infinite_iff_infinitesimal_inv (inv_ne_zero h)).symm <;> simp only [inv_inv]
 #align hyperreal.infinitesimal_iff_infinite_inv Hyperreal.infinitesimal_iff_infinite_inv
+-/
 
 /-!
 ### `st` stuff that requires infinitesimal machinery
@@ -1017,6 +1206,7 @@ theorem isSt_of_tendsto {f : ℕ → ℝ} {r : ℝ} (hf : Tendsto f atTop (𝓝
 #align hyperreal.is_st_of_tendsto Hyperreal.isSt_of_tendsto
 -/
 
+#print Hyperreal.IsSt.inv /-
 theorem Hyperreal.IsSt.inv {x : ℝ*} {r : ℝ} (hi : ¬Infinitesimal x) : IsSt x r → IsSt x⁻¹ r⁻¹ :=
   fun hxr =>
   have h : x ≠ 0 := fun h => hi (h.symm ▸ infinitesimal_zero)
@@ -1026,7 +1216,9 @@ theorem Hyperreal.IsSt.inv {x : ℝ*} {r : ℝ} (hi : ¬Infinitesimal x) : IsSt
     have H'' : s = r⁻¹ := one_div r ▸ eq_one_div_of_mul_eq_one_right (eq_of_isSt_real H').symm
     H'' ▸ hs
 #align hyperreal.is_st_inv Hyperreal.IsSt.inv
+-/
 
+#print Hyperreal.st_inv /-
 theorem st_inv (x : ℝ*) : st x⁻¹ = (st x)⁻¹ :=
   by
   by_cases h0 : x = 0
@@ -1037,6 +1229,7 @@ theorem st_inv (x : ℝ*) : st x⁻¹ = (st x)⁻¹ :=
   rw [st_of_is_st (infinitesimal_inv_of_infinite h2), st_infinite h2, inv_zero]
   exact st_of_is_st (is_st_inv h1 (is_st_st' h2))
 #align hyperreal.st_inv Hyperreal.st_inv
+-/
 
 /-!
 ### Infinite stuff that requires infinitesimal machinery
@@ -1055,6 +1248,7 @@ theorem infinite_omega : Infinite ω :=
 #align hyperreal.infinite_omega Hyperreal.infinite_omega
 -/
 
+#print Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos /-
 theorem infinitePos_mul_of_infinitePos_not_infinitesimal_pos {x y : ℝ*} :
     InfinitePos x → ¬Infinitesimal y → 0 < y → InfinitePos (x * y) := fun hx hy₁ hy₂ r =>
   have hy₁' := not_forall.mp (by rw [infinitesimal_def] at hy₁  <;> exact hy₁)
@@ -1064,69 +1258,93 @@ theorem infinitePos_mul_of_infinitePos_not_infinitesimal_pos {x y : ℝ*} :
     rw [← div_mul_cancel r (ne_of_gt hyr.1), coe_mul] <;>
       exact mul_lt_mul (hx (r / r₁)) hyr.2 (coe_lt_coe.2 hyr.1) (le_of_lt (hx 0))
 #align hyperreal.infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos
+-/
 
+#print Hyperreal.infinitePos_mul_of_not_infinitesimal_pos_infinitePos /-
 theorem infinitePos_mul_of_not_infinitesimal_pos_infinitePos {x y : ℝ*} :
     ¬Infinitesimal x → 0 < x → InfinitePos y → InfinitePos (x * y) := fun hx hp hy => by
   rw [mul_comm] <;> exact infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos hy hx hp
 #align hyperreal.infinite_pos_mul_of_not_infinitesimal_pos_infinite_pos Hyperreal.infinitePos_mul_of_not_infinitesimal_pos_infinitePos
+-/
 
+#print Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg /-
 theorem infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg {x y : ℝ*} :
     InfiniteNeg x → ¬Infinitesimal y → y < 0 → InfinitePos (x * y) := by
   rw [infinite_neg_iff_infinite_pos_neg, ← neg_pos, ← neg_mul_neg, infinitesimal_neg_iff] <;>
     exact infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos
 #align hyperreal.infinite_pos_mul_of_infinite_neg_not_infinitesimal_neg Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg
+-/
 
+#print Hyperreal.infinitePos_mul_of_not_infinitesimal_neg_infiniteNeg /-
 theorem infinitePos_mul_of_not_infinitesimal_neg_infiniteNeg {x y : ℝ*} :
     ¬Infinitesimal x → x < 0 → InfiniteNeg y → InfinitePos (x * y) := fun hx hp hy => by
   rw [mul_comm] <;> exact infinite_pos_mul_of_infinite_neg_not_infinitesimal_neg hy hx hp
 #align hyperreal.infinite_pos_mul_of_not_infinitesimal_neg_infinite_neg Hyperreal.infinitePos_mul_of_not_infinitesimal_neg_infiniteNeg
+-/
 
+#print Hyperreal.infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg /-
 theorem infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg {x y : ℝ*} :
     InfinitePos x → ¬Infinitesimal y → y < 0 → InfiniteNeg (x * y) := by
   rw [infinite_neg_iff_infinite_pos_neg, ← neg_pos, neg_mul_eq_mul_neg, infinitesimal_neg_iff] <;>
     exact infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos
 #align hyperreal.infinite_neg_mul_of_infinite_pos_not_infinitesimal_neg Hyperreal.infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg
+-/
 
+#print Hyperreal.infiniteNeg_mul_of_not_infinitesimal_neg_infinitePos /-
 theorem infiniteNeg_mul_of_not_infinitesimal_neg_infinitePos {x y : ℝ*} :
     ¬Infinitesimal x → x < 0 → InfinitePos y → InfiniteNeg (x * y) := fun hx hp hy => by
   rw [mul_comm] <;> exact infinite_neg_mul_of_infinite_pos_not_infinitesimal_neg hy hx hp
 #align hyperreal.infinite_neg_mul_of_not_infinitesimal_neg_infinite_pos Hyperreal.infiniteNeg_mul_of_not_infinitesimal_neg_infinitePos
+-/
 
+#print Hyperreal.infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos /-
 theorem infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos {x y : ℝ*} :
     InfiniteNeg x → ¬Infinitesimal y → 0 < y → InfiniteNeg (x * y) := by
   rw [infinite_neg_iff_infinite_pos_neg, infinite_neg_iff_infinite_pos_neg, neg_mul_eq_neg_mul] <;>
     exact infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos
 #align hyperreal.infinite_neg_mul_of_infinite_neg_not_infinitesimal_pos Hyperreal.infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos
+-/
 
+#print Hyperreal.infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNeg /-
 theorem infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNeg {x y : ℝ*} :
     ¬Infinitesimal x → 0 < x → InfiniteNeg y → InfiniteNeg (x * y) := fun hx hp hy => by
   rw [mul_comm] <;> exact infinite_neg_mul_of_infinite_neg_not_infinitesimal_pos hy hx hp
 #align hyperreal.infinite_neg_mul_of_not_infinitesimal_pos_infinite_neg Hyperreal.infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNeg
+-/
 
+#print Hyperreal.infinitePos_mul_infinitePos /-
 theorem infinitePos_mul_infinitePos {x y : ℝ*} :
     InfinitePos x → InfinitePos y → InfinitePos (x * y) := fun hx hy =>
   infinitePos_mul_of_infinitePos_not_infinitesimal_pos hx
     (Hyperreal.InfinitePos.not_infinitesimal hy) (hy 0)
 #align hyperreal.infinite_pos_mul_infinite_pos Hyperreal.infinitePos_mul_infinitePos
+-/
 
+#print Hyperreal.infiniteNeg_mul_infiniteNeg /-
 theorem infiniteNeg_mul_infiniteNeg {x y : ℝ*} :
     InfiniteNeg x → InfiniteNeg y → InfinitePos (x * y) := fun hx hy =>
   infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg hx
     (Hyperreal.InfiniteNeg.not_infinitesimal hy) (hy 0)
 #align hyperreal.infinite_neg_mul_infinite_neg Hyperreal.infiniteNeg_mul_infiniteNeg
+-/
 
+#print Hyperreal.infinitePos_mul_infiniteNeg /-
 theorem infinitePos_mul_infiniteNeg {x y : ℝ*} :
     InfinitePos x → InfiniteNeg y → InfiniteNeg (x * y) := fun hx hy =>
   infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg hx
     (Hyperreal.InfiniteNeg.not_infinitesimal hy) (hy 0)
 #align hyperreal.infinite_pos_mul_infinite_neg Hyperreal.infinitePos_mul_infiniteNeg
+-/
 
+#print Hyperreal.infiniteNeg_mul_infinitePos /-
 theorem infiniteNeg_mul_infinitePos {x y : ℝ*} :
     InfiniteNeg x → InfinitePos y → InfiniteNeg (x * y) := fun hx hy =>
   infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos hx
     (Hyperreal.InfinitePos.not_infinitesimal hy) (hy 0)
 #align hyperreal.infinite_neg_mul_infinite_pos Hyperreal.infiniteNeg_mul_infinitePos
+-/
 
+#print Hyperreal.infinite_mul_of_infinite_not_infinitesimal /-
 theorem infinite_mul_of_infinite_not_infinitesimal {x y : ℝ*} :
     Infinite x → ¬Infinitesimal y → Infinite (x * y) := fun hx hy =>
   have h0 : y < 0 ∨ 0 < y := lt_or_gt_of_ne fun H0 => hy (Eq.substr H0 (isSt_refl_real 0))
@@ -1138,15 +1356,20 @@ theorem infinite_mul_of_infinite_not_infinitesimal {x y : ℝ*} :
       (fun H0 Hx => Or.inl (infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg Hx hy H0))
       fun H0 Hx => Or.inr (infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos Hx hy H0))
 #align hyperreal.infinite_mul_of_infinite_not_infinitesimal Hyperreal.infinite_mul_of_infinite_not_infinitesimal
+-/
 
+#print Hyperreal.infinite_mul_of_not_infinitesimal_infinite /-
 theorem infinite_mul_of_not_infinitesimal_infinite {x y : ℝ*} :
     ¬Infinitesimal x → Infinite y → Infinite (x * y) := fun hx hy => by
   rw [mul_comm] <;> exact infinite_mul_of_infinite_not_infinitesimal hy hx
 #align hyperreal.infinite_mul_of_not_infinitesimal_infinite Hyperreal.infinite_mul_of_not_infinitesimal_infinite
+-/
 
+#print Hyperreal.Infinite.mul /-
 theorem Infinite.mul {x y : ℝ*} : Infinite x → Infinite y → Infinite (x * y) := fun hx hy =>
   infinite_mul_of_infinite_not_infinitesimal hx (Hyperreal.Infinite.not_infinitesimal hy)
 #align hyperreal.infinite.mul Hyperreal.Infinite.mul
+-/
 
 end Hyperreal
 

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

@@ -812,7 +812,6 @@ private theorem is_st_mul' {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
                 half_pos <| coe_pos.2 hd)
               _)
           _ = (d : ℝ*) := by rw [mul_one, add_halves]
-          
 
 theorem Hyperreal.IsSt.mul {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt y s) :
     IsSt (x * y) (r * s) :=

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

@@ -223,7 +223,7 @@ theorem lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝
   by
   simp only [Metric.tendsto_atTop, Real.dist_eq, sub_zero, lt_def] at hf ⊢
   intro r hr; cases' hf r hr with N hf'
-  have hs : { i : ℕ | f i < r }ᶜ ⊆ { i : ℕ | i ≤ N } := fun i hi1 =>
+  have hs : {i : ℕ | f i < r}ᶜ ⊆ {i : ℕ | i ≤ N} := fun i hi1 =>
     le_of_lt
       (by
         simp only [lt_iff_not_ge] <;>
@@ -299,7 +299,7 @@ private theorem is_st_unique' (x : ℝ*) (r s : ℝ) (hr : IsSt x r) (hs : IsSt
   have hr' := (hr _ hrs').2
   have hs' := (hs _ hrs').1
   have h : s - (s - r) / 2 = r + (s - r) / 2 := by linarith
-  norm_cast  at *
+  norm_cast at *
   rw [h] at hs' 
   exact not_lt_of_lt hs' hr'
 
@@ -321,8 +321,8 @@ theorem not_infinite_of_exists_st {x : ℝ*} : (∃ r : ℝ, IsSt x r) → ¬Inf
 #align hyperreal.not_infinite_of_exists_st Hyperreal.not_infinite_of_exists_st
 -/
 
-theorem isSt_sSup {x : ℝ*} (hni : ¬Infinite x) : IsSt x (sSup { y : ℝ | (y : ℝ*) < x }) :=
-  let S : Set ℝ := { y : ℝ | (y : ℝ*) < x }
+theorem isSt_sSup {x : ℝ*} (hni : ¬Infinite x) : IsSt x (sSup {y : ℝ | (y : ℝ*) < x}) :=
+  let S : Set ℝ := {y : ℝ | (y : ℝ*) < x}
   let R : _ := sSup S
   have hnile := not_forall.mp (not_or.mp hni).1
   have hnige := not_forall.mp (not_or.mp hni).2
@@ -345,22 +345,22 @@ theorem isSt_sSup {x : ℝ*} (hni : ¬Infinite x) : IsSt x (sSup { y : ℝ | (y
 
 #print Hyperreal.exists_st_of_not_infinite /-
 theorem exists_st_of_not_infinite {x : ℝ*} (hni : ¬Infinite x) : ∃ r : ℝ, IsSt x r :=
-  ⟨sSup { y : ℝ | (y : ℝ*) < x }, isSt_sSup hni⟩
+  ⟨sSup {y : ℝ | (y : ℝ*) < x}, isSt_sSup hni⟩
 #align hyperreal.exists_st_of_not_infinite Hyperreal.exists_st_of_not_infinite
 -/
 
-theorem st_eq_sSup {x : ℝ*} : st x = sSup { y : ℝ | (y : ℝ*) < x } :=
+theorem st_eq_sSup {x : ℝ*} : st x = sSup {y : ℝ | (y : ℝ*) < x} :=
   by
   unfold st; split_ifs
   · exact is_st_unique (Classical.choose_spec h) (is_st_Sup (not_infinite_of_exists_st h))
   · cases' not_imp_comm.mp exists_st_of_not_infinite h with H H
     · rw [(Set.ext fun i => ⟨fun hi => Set.mem_univ i, fun hi => H i⟩ :
-          { y : ℝ | (y : ℝ*) < x } = Set.univ)]
+          {y : ℝ | (y : ℝ*) < x} = Set.univ)]
       exact real.Sup_univ.symm
     · rw [(Set.ext fun i =>
             ⟨fun hi => False.elim (not_lt_of_lt (H i) hi), fun hi =>
               False.elim (Set.not_mem_empty i hi)⟩ :
-          { y : ℝ | (y : ℝ*) < x } = ∅)]
+          {y : ℝ | (y : ℝ*) < x} = ∅)]
       exact real.Sup_empty.symm
 #align hyperreal.st_eq_Sup Hyperreal.st_eq_sSup
 
@@ -487,7 +487,7 @@ theorem Hyperreal.IsSt.lt {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
   have hys' := (hys _ hrs').1
   have H1 : r + (s - r) / 2 = (r + s) / 2 := by linarith
   have H2 : s - (s - r) / 2 = (r + s) / 2 := by linarith
-  norm_cast  at *
+  norm_cast at *
   rw [H1] at hxr' 
   rw [H2] at hys' 
   exact lt_trans hxr' hys'
@@ -708,7 +708,7 @@ theorem infinitePos_of_tendsto_top {f : ℕ → ℝ} (hf : Tendsto f atTop atTop
   Exists.cases_on (hf' (r + 1)) fun i hi =>
     have hi' : ∀ a : ℕ, f a < r + 1 → a < i := fun a => by
       rw [← not_le, ← not_le] <;> exact not_imp_not.mpr (hi a)
-    have hS : { a : ℕ | r < f a }ᶜ ⊆ { a : ℕ | a ≤ i } := by
+    have hS : {a : ℕ | r < f a}ᶜ ⊆ {a : ℕ | a ≤ i} := by
       simp only [Set.compl_setOf, not_lt] <;>
         exact fun a har => le_of_lt (hi' a (lt_of_le_of_lt har (lt_add_one _)))
     Germ.coe_lt.2 <| mem_hyperfilter_of_finite_compl <| (Set.finite_le_nat _).Subset hS
@@ -722,7 +722,7 @@ theorem infiniteNeg_of_tendsto_bot {f : ℕ → ℝ} (hf : Tendsto f atTop atBot
   Exists.cases_on (hf' (r - 1)) fun i hi =>
     have hi' : ∀ a : ℕ, r - 1 < f a → a < i := fun a => by
       rw [← not_le, ← not_le] <;> exact not_imp_not.mpr (hi a)
-    have hS : { a : ℕ | f a < r }ᶜ ⊆ { a : ℕ | a ≤ i } := by
+    have hS : {a : ℕ | f a < r}ᶜ ⊆ {a : ℕ | a ≤ i} := by
       simp only [Set.compl_setOf, not_lt] <;>
         exact fun a har => le_of_lt (hi' a (lt_of_lt_of_le (sub_one_lt _) har))
     Germ.coe_lt.2 <| mem_hyperfilter_of_finite_compl <| (Set.finite_le_nat _).Subset hS
@@ -884,7 +884,7 @@ theorem lt_neg_of_pos_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r :
 
 theorem gt_of_neg_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r : ℝ, r < 0 → ↑r < x :=
   fun hi r hr => by
-  convert((infinitesimal_def.mp hi) (-r) (neg_pos.mpr hr)).1 <;> exact (neg_neg ↑r).symm
+  convert ((infinitesimal_def.mp hi) (-r) (neg_pos.mpr hr)).1 <;> exact (neg_neg ↑r).symm
 #align hyperreal.gt_of_neg_of_infinitesimal Hyperreal.gt_of_neg_of_infinitesimal
 
 theorem abs_lt_real_iff_infinitesimal {x : ℝ*} : Infinitesimal x ↔ ∀ r : ℝ, r ≠ 0 → |x| < |r| :=
@@ -1001,7 +1001,7 @@ theorem infinitesimal_neg_iff_infiniteNeg_inv {x : ℝ*} :
 #align hyperreal.infinitesimal_neg_iff_infinite_neg_inv Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv
 
 theorem infinitesimal_iff_infinite_inv {x : ℝ*} (h : x ≠ 0) : Infinitesimal x ↔ Infinite x⁻¹ := by
-  convert(infinite_iff_infinitesimal_inv (inv_ne_zero h)).symm <;> simp only [inv_inv]
+  convert (infinite_iff_infinitesimal_inv (inv_ne_zero h)).symm <;> simp only [inv_inv]
 #align hyperreal.infinitesimal_iff_infinite_inv Hyperreal.infinitesimal_iff_infinite_inv
 
 /-!

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

@@ -26,7 +26,8 @@ open scoped Topology Classical
 #print Hyperreal /-
 /-- Hyperreal numbers on the ultrafilter extending the cofinite filter -/
 def Hyperreal : Type :=
-  Germ (hyperfilter ℕ : Filter ℕ) ℝ deriving LinearOrderedField, Inhabited
+  Germ (hyperfilter ℕ : Filter ℕ) ℝ
+deriving LinearOrderedField, Inhabited
 #align hyperreal Hyperreal
 -/
 
@@ -220,7 +221,7 @@ theorem epsilon_mul_omega : ε * ω = 1 :=
 theorem lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝 0)) :
     ∀ {r : ℝ}, 0 < r → ofSeq f < (r : ℝ*) :=
   by
-  simp only [Metric.tendsto_atTop, Real.dist_eq, sub_zero, lt_def] at hf⊢
+  simp only [Metric.tendsto_atTop, Real.dist_eq, sub_zero, lt_def] at hf ⊢
   intro r hr; cases' hf r hr with N hf'
   have hs : { i : ℕ | f i < r }ᶜ ⊆ { i : ℕ | i ≤ N } := fun i hi1 =>
     le_of_lt
@@ -234,7 +235,7 @@ theorem lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝
 theorem neg_lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝 0)) :
     ∀ {r : ℝ}, 0 < r → (-r : ℝ*) < ofSeq f := fun r hr =>
   have hg := hf.neg
-  neg_lt_of_neg_lt (by rw [neg_zero] at hg <;> exact lt_of_tendsto_zero_of_pos hg hr)
+  neg_lt_of_neg_lt (by rw [neg_zero] at hg  <;> exact lt_of_tendsto_zero_of_pos hg hr)
 #align hyperreal.neg_lt_of_tendsto_zero_of_pos Hyperreal.neg_lt_of_tendsto_zero_of_pos
 
 theorem gt_of_tendsto_zero_of_neg {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝 0)) :
@@ -299,7 +300,7 @@ private theorem is_st_unique' (x : ℝ*) (r s : ℝ) (hr : IsSt x r) (hs : IsSt
   have hs' := (hs _ hrs').1
   have h : s - (s - r) / 2 = r + (s - r) / 2 := by linarith
   norm_cast  at *
-  rw [h] at hs'
+  rw [h] at hs' 
   exact not_lt_of_lt hs' hr'
 
 #print Hyperreal.IsSt.unique /-
@@ -487,8 +488,8 @@ theorem Hyperreal.IsSt.lt {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
   have H1 : r + (s - r) / 2 = (r + s) / 2 := by linarith
   have H2 : s - (s - r) / 2 = (r + s) / 2 := by linarith
   norm_cast  at *
-  rw [H1] at hxr'
-  rw [H2] at hys'
+  rw [H1] at hxr' 
+  rw [H2] at hys' 
   exact lt_trans hxr' hys'
 #align hyperreal.lt_of_is_st_lt Hyperreal.IsSt.lt
 
@@ -638,9 +639,9 @@ theorem infinitePos_abs_iff_infinite {x : ℝ*} : Infinite x ↔ InfinitePos (|x
       rw [abs_of_neg (hin 0)] <;> exact lt_neg.mp (hin (-d)),
     fun hipa => by
     rcases lt_trichotomy x 0 with (h | h | h)
-    · exact Or.inr (infinite_neg_iff_infinite_pos_neg.mpr (by rwa [abs_of_neg h] at hipa))
-    · exact False.elim (ne_zero_of_infinite (Or.inl (by rw [h] <;> rwa [h, abs_zero] at hipa)) h)
-    · exact Or.inl (by rwa [abs_of_pos h] at hipa)⟩
+    · exact Or.inr (infinite_neg_iff_infinite_pos_neg.mpr (by rwa [abs_of_neg h] at hipa ))
+    · exact False.elim (ne_zero_of_infinite (Or.inl (by rw [h] <;> rwa [h, abs_zero] at hipa )) h)
+    · exact Or.inl (by rwa [abs_of_pos h] at hipa )⟩
 #align hyperreal.infinite_iff_infinite_pos_abs Hyperreal.infinitePos_abs_iff_infiniteₓ
 
 theorem infinite_abs_iff {x : ℝ*} : Infinite x ↔ Infinite (|x|) := by
@@ -744,7 +745,7 @@ theorem not_infinite_iff_exist_lt_gt {x : ℝ*} : ¬Infinite x ↔ ∃ r s : ℝ
   ⟨fun hni =>
     Exists.dcases_on (not_forall.mp (not_or.mp hni).1) <|
       Exists.dcases_on (not_forall.mp (not_or.mp hni).2) fun r hr s hs => by
-        rw [not_lt] at hr hs <;>
+        rw [not_lt] at hr hs  <;>
           exact
             ⟨r - 1, s + 1,
               ⟨lt_of_lt_of_le (by rw [sub_eq_add_neg] <;> norm_num) hr,
@@ -825,7 +826,7 @@ theorem Hyperreal.IsSt.mul {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
         have hys' : _ :=
           is_st_iff_abs_sub_lt_delta.mp hys (d / t)
             (div_pos hd (coe_pos.1 (lt_of_le_of_lt (abs_nonneg x) ht)))
-        rw [hs, coe_zero, sub_zero] at hys'
+        rw [hs, coe_zero, sub_zero] at hys' 
         rw [hs, MulZeroClass.mul_zero, coe_zero, sub_zero, abs_mul, mul_comm, ←
           div_mul_cancel (d : ℝ*) (ne_of_gt (lt_of_le_of_lt (abs_nonneg x) ht)), ← coe_div]
         exact mul_lt_mul'' hys' ht (abs_nonneg _) (abs_nonneg _)
@@ -970,7 +971,7 @@ theorem infiniteNeg_iff_infinitesimal_inv_neg {x : ℝ*} :
     have hin' := infinitePos_iff_infinitesimal_inv_pos.mp (Hyperreal.InfiniteNeg.neg hin)
     rwa [infinitesimal_neg_iff, ← neg_pos, neg_inv], fun hin => by
     rwa [← neg_pos, infinitesimal_neg_iff, neg_inv, ← infinite_pos_iff_infinitesimal_inv_pos, ←
-      infinite_neg_iff_infinite_pos_neg] at hin⟩
+      infinite_neg_iff_infinite_pos_neg] at hin ⟩
 #align hyperreal.infinite_neg_iff_infinitesimal_inv_neg Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg
 
 theorem infinitesimal_inv_of_infinite {x : ℝ*} : Infinite x → Infinitesimal x⁻¹ := fun hi =>
@@ -1057,10 +1058,10 @@ theorem infinite_omega : Infinite ω :=
 
 theorem infinitePos_mul_of_infinitePos_not_infinitesimal_pos {x y : ℝ*} :
     InfinitePos x → ¬Infinitesimal y → 0 < y → InfinitePos (x * y) := fun hx hy₁ hy₂ r =>
-  have hy₁' := not_forall.mp (by rw [infinitesimal_def] at hy₁ <;> exact hy₁)
+  have hy₁' := not_forall.mp (by rw [infinitesimal_def] at hy₁  <;> exact hy₁)
   Exists.dcases_on hy₁' fun r₁ hy₁'' =>
     by
-    have hyr := by rw [not_imp, ← abs_lt, not_lt, abs_of_pos hy₂] at hy₁'' <;> exact hy₁''
+    have hyr := by rw [not_imp, ← abs_lt, not_lt, abs_of_pos hy₂] at hy₁''  <;> exact hy₁''
     rw [← div_mul_cancel r (ne_of_gt hyr.1), coe_mul] <;>
       exact mul_lt_mul (hx (r / r₁)) hyr.2 (coe_lt_coe.2 hyr.1) (le_of_lt (hx 0))
 #align hyperreal.infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos

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

@@ -96,19 +96,15 @@ theorem coe_add (x y : ℝ) : ↑(x + y) = (x + y : ℝ*) :=
   rfl
 #align hyperreal.coe_add Hyperreal.coe_add
 
-/- warning: hyperreal.coe_bit0 clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_bit0 [anonymous]ₓ'. -/
 @[simp, norm_cast]
-theorem [anonymous] (x : ℝ) : ↑(bit0 x) = (bit0 x : ℝ*) :=
+theorem coe_bit0 (x : ℝ) : ↑(bit0 x) = (bit0 x : ℝ*) :=
   rfl
-#align hyperreal.coe_bit0 [anonymous]
+#align hyperreal.coe_bit0 Hyperreal.coe_bit0
 
-/- warning: hyperreal.coe_bit1 clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_bit1 [anonymous]ₓ'. -/
 @[simp, norm_cast]
-theorem [anonymous] (x : ℝ) : ↑(bit1 x) = (bit1 x : ℝ*) :=
+theorem coe_bit1 (x : ℝ) : ↑(bit1 x) = (bit1 x : ℝ*) :=
   rfl
-#align hyperreal.coe_bit1 [anonymous]
+#align hyperreal.coe_bit1 Hyperreal.coe_bit1
 
 @[simp, norm_cast]
 theorem coe_mul (x y : ℝ) : ↑(x * y) = (x * y : ℝ*) :=

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

@@ -21,7 +21,7 @@ import Mathbin.Analysis.SpecificLimits.Basic
 
 open Filter Filter.Germ
 
-open Topology Classical
+open scoped Topology Classical
 
 #print Hyperreal /-
 /-- Hyperreal numbers on the ultrafilter extending the cofinite filter -/

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

@@ -51,111 +51,52 @@ theorem coe_ne_coe {x y : ℝ} : (x : ℝ*) ≠ y ↔ x ≠ y :=
 #align hyperreal.coe_ne_coe Hyperreal.coe_ne_coe
 -/
 
-/- warning: hyperreal.coe_eq_zero -> Hyperreal.coe_eq_zero is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, Iff (Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall {x : Real}, Iff (Eq.{1} Hyperreal (Hyperreal.ofReal x) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_eq_zero Hyperreal.coe_eq_zeroₓ'. -/
 @[simp, norm_cast]
 theorem coe_eq_zero {x : ℝ} : (x : ℝ*) = 0 ↔ x = 0 :=
   coe_eq_coe
 #align hyperreal.coe_eq_zero Hyperreal.coe_eq_zero
 
-/- warning: hyperreal.coe_eq_one -> Hyperreal.coe_eq_one is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, Iff (Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) (OfNat.ofNat.{0} Hyperreal 1 (OfNat.mk.{0} Hyperreal 1 (One.one.{0} Hyperreal (AddMonoidWithOne.toOne.{0} Hyperreal (AddGroupWithOne.toAddMonoidWithOne.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
-but is expected to have type
-  forall {x : Real}, Iff (Eq.{1} Hyperreal (Hyperreal.ofReal x) (OfNat.ofNat.{0} Hyperreal 1 (One.toOfNat1.{0} Hyperreal (Semiring.toOne.{0} Hyperreal (StrictOrderedSemiring.toSemiring.{0} Hyperreal (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Hyperreal (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Hyperreal (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_eq_one Hyperreal.coe_eq_oneₓ'. -/
 @[simp, norm_cast]
 theorem coe_eq_one {x : ℝ} : (x : ℝ*) = 1 ↔ x = 1 :=
   coe_eq_coe
 #align hyperreal.coe_eq_one Hyperreal.coe_eq_one
 
-/- warning: hyperreal.coe_ne_zero -> Hyperreal.coe_ne_zero is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, Iff (Ne.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall {x : Real}, Iff (Ne.{1} Hyperreal (Hyperreal.ofReal x) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_ne_zero Hyperreal.coe_ne_zeroₓ'. -/
 @[norm_cast]
 theorem coe_ne_zero {x : ℝ} : (x : ℝ*) ≠ 0 ↔ x ≠ 0 :=
   coe_ne_coe
 #align hyperreal.coe_ne_zero Hyperreal.coe_ne_zero
 
-/- warning: hyperreal.coe_ne_one -> Hyperreal.coe_ne_one is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, Iff (Ne.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) (OfNat.ofNat.{0} Hyperreal 1 (OfNat.mk.{0} Hyperreal 1 (One.one.{0} Hyperreal (AddMonoidWithOne.toOne.{0} Hyperreal (AddGroupWithOne.toAddMonoidWithOne.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) (Ne.{1} Real x (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
-but is expected to have type
-  forall {x : Real}, Iff (Ne.{1} Hyperreal (Hyperreal.ofReal x) (OfNat.ofNat.{0} Hyperreal 1 (One.toOfNat1.{0} Hyperreal (Semiring.toOne.{0} Hyperreal (StrictOrderedSemiring.toSemiring.{0} Hyperreal (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Hyperreal (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Hyperreal (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))) (Ne.{1} Real x (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_ne_one Hyperreal.coe_ne_oneₓ'. -/
 @[norm_cast]
 theorem coe_ne_one {x : ℝ} : (x : ℝ*) ≠ 1 ↔ x ≠ 1 :=
   coe_ne_coe
 #align hyperreal.coe_ne_one Hyperreal.coe_ne_one
 
-/- warning: hyperreal.coe_one -> Hyperreal.coe_one is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Hyperreal 1 (OfNat.mk.{0} Hyperreal 1 (One.one.{0} Hyperreal (AddMonoidWithOne.toOne.{0} Hyperreal (AddGroupWithOne.toAddMonoidWithOne.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))
-but is expected to have type
-  Eq.{1} Hyperreal (Hyperreal.ofReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Hyperreal 1 (One.toOfNat1.{0} Hyperreal (Semiring.toOne.{0} Hyperreal (StrictOrderedSemiring.toSemiring.{0} Hyperreal (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Hyperreal (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Hyperreal (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_one Hyperreal.coe_oneₓ'. -/
 @[simp, norm_cast]
 theorem coe_one : ↑(1 : ℝ) = (1 : ℝ*) :=
   rfl
 #align hyperreal.coe_one Hyperreal.coe_one
 
-/- warning: hyperreal.coe_zero -> Hyperreal.coe_zero is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))
-but is expected to have type
-  Eq.{1} Hyperreal (Hyperreal.ofReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_zero Hyperreal.coe_zeroₓ'. -/
 @[simp, norm_cast]
 theorem coe_zero : ↑(0 : ℝ) = (0 : ℝ*) :=
   rfl
 #align hyperreal.coe_zero Hyperreal.coe_zero
 
-/- warning: hyperreal.coe_inv -> Hyperreal.coe_inv is a dubious translation:
-lean 3 declaration is
-  forall (x : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (Inv.inv.{0} Real Real.hasInv x)) (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x))
-but is expected to have type
-  forall (x : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (Inv.inv.{0} Real Real.instInvReal x)) (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) (Hyperreal.ofReal x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_inv Hyperreal.coe_invₓ'. -/
 @[simp, norm_cast]
 theorem coe_inv (x : ℝ) : ↑x⁻¹ = (x⁻¹ : ℝ*) :=
   rfl
 #align hyperreal.coe_inv Hyperreal.coe_inv
 
-/- warning: hyperreal.coe_neg -> Hyperreal.coe_neg is a dubious translation:
-lean 3 declaration is
-  forall (x : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (Neg.neg.{0} Real Real.hasNeg x)) (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x))
-but is expected to have type
-  forall (x : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (Neg.neg.{0} Real Real.instNegReal x)) (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (Hyperreal.ofReal x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_neg Hyperreal.coe_negₓ'. -/
 @[simp, norm_cast]
 theorem coe_neg (x : ℝ) : ↑(-x) = (-x : ℝ*) :=
   rfl
 #align hyperreal.coe_neg Hyperreal.coe_neg
 
-/- warning: hyperreal.coe_add -> Hyperreal.coe_add is a dubious translation:
-lean 3 declaration is
-  forall (x : Real) (y : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) x y)) (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y))
-but is expected to have type
-  forall (x : Real) (y : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) x y)) (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) (Hyperreal.ofReal x) (Hyperreal.ofReal y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_add Hyperreal.coe_addₓ'. -/
 @[simp, norm_cast]
 theorem coe_add (x y : ℝ) : ↑(x + y) = (x + y : ℝ*) :=
   rfl
 #align hyperreal.coe_add Hyperreal.coe_add
 
 /- warning: hyperreal.coe_bit0 clashes with [anonymous] -> [anonymous]
-warning: hyperreal.coe_bit0 -> [anonymous] is a dubious translation:
-lean 3 declaration is
-  forall (x : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (bit0.{0} Real Real.hasAdd x)) (bit0.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x))
-but is expected to have type
-  forall {x : Type.{u}} {β : Type.{v}}, (Nat -> x -> β) -> Nat -> (List.{u} x) -> (List.{v} β)
 Case conversion may be inaccurate. Consider using '#align hyperreal.coe_bit0 [anonymous]ₓ'. -/
 @[simp, norm_cast]
 theorem [anonymous] (x : ℝ) : ↑(bit0 x) = (bit0 x : ℝ*) :=
@@ -163,122 +104,57 @@ theorem [anonymous] (x : ℝ) : ↑(bit0 x) = (bit0 x : ℝ*) :=
 #align hyperreal.coe_bit0 [anonymous]
 
 /- warning: hyperreal.coe_bit1 clashes with [anonymous] -> [anonymous]
-warning: hyperreal.coe_bit1 -> [anonymous] is a dubious translation:
-lean 3 declaration is
-  forall (x : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (bit1.{0} Real Real.hasOne Real.hasAdd x)) (bit1.{0} Hyperreal (AddMonoidWithOne.toOne.{0} Hyperreal (AddGroupWithOne.toAddMonoidWithOne.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))) (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x))
-but is expected to have type
-  forall {x : Type.{u}} {β : Type.{v}}, (Nat -> x -> β) -> Nat -> (List.{u} x) -> (List.{v} β)
 Case conversion may be inaccurate. Consider using '#align hyperreal.coe_bit1 [anonymous]ₓ'. -/
 @[simp, norm_cast]
 theorem [anonymous] (x : ℝ) : ↑(bit1 x) = (bit1 x : ℝ*) :=
   rfl
 #align hyperreal.coe_bit1 [anonymous]
 
-/- warning: hyperreal.coe_mul -> Hyperreal.coe_mul is a dubious translation:
-lean 3 declaration is
-  forall (x : Real) (y : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) x y)) (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y))
-but is expected to have type
-  forall (x : Real) (y : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) x y)) (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (Hyperreal.ofReal x) (Hyperreal.ofReal y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_mul Hyperreal.coe_mulₓ'. -/
 @[simp, norm_cast]
 theorem coe_mul (x y : ℝ) : ↑(x * y) = (x * y : ℝ*) :=
   rfl
 #align hyperreal.coe_mul Hyperreal.coe_mul
 
-/- warning: hyperreal.coe_div -> Hyperreal.coe_div is a dubious translation:
-lean 3 declaration is
-  forall (x : Real) (y : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) x y)) (HDiv.hDiv.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHDiv.{0} Hyperreal (DivInvMonoid.toHasDiv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y))
-but is expected to have type
-  forall (x : Real) (y : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) x y)) (HDiv.hDiv.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHDiv.{0} Hyperreal (LinearOrderedField.toDiv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)) (Hyperreal.ofReal x) (Hyperreal.ofReal y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_div Hyperreal.coe_divₓ'. -/
 @[simp, norm_cast]
 theorem coe_div (x y : ℝ) : ↑(x / y) = (x / y : ℝ*) :=
   rfl
 #align hyperreal.coe_div Hyperreal.coe_div
 
-/- warning: hyperreal.coe_sub -> Hyperreal.coe_sub is a dubious translation:
-lean 3 declaration is
-  forall (x : Real) (y : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) x y)) (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (SubNegMonoid.toHasSub.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y))
-but is expected to have type
-  forall (x : Real) (y : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) x y)) (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (Ring.toSub.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal x) (Hyperreal.ofReal y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_sub Hyperreal.coe_subₓ'. -/
 @[simp, norm_cast]
 theorem coe_sub (x y : ℝ) : ↑(x - y) = (x - y : ℝ*) :=
   rfl
 #align hyperreal.coe_sub Hyperreal.coe_sub
 
-/- warning: hyperreal.coe_le_coe -> Hyperreal.coe_le_coe is a dubious translation:
-lean 3 declaration is
-  forall {x : Real} {y : Real}, Iff (LE.le.{0} Hyperreal (Preorder.toHasLe.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y)) (LE.le.{0} Real Real.hasLe x y)
-but is expected to have type
-  forall {x : Real} {y : Real}, Iff (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal x) (Hyperreal.ofReal y)) (LE.le.{0} Real Real.instLEReal x y)
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_le_coe Hyperreal.coe_le_coeₓ'. -/
 @[simp, norm_cast]
 theorem coe_le_coe {x y : ℝ} : (x : ℝ*) ≤ y ↔ x ≤ y :=
   Germ.const_le_iff
 #align hyperreal.coe_le_coe Hyperreal.coe_le_coe
 
-/- warning: hyperreal.coe_lt_coe -> Hyperreal.coe_lt_coe is a dubious translation:
-lean 3 declaration is
-  forall {x : Real} {y : Real}, Iff (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y)) (LT.lt.{0} Real Real.hasLt x y)
-but is expected to have type
-  forall {x : Real} {y : Real}, Iff (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal x) (Hyperreal.ofReal y)) (LT.lt.{0} Real Real.instLTReal x y)
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_lt_coe Hyperreal.coe_lt_coeₓ'. -/
 @[simp, norm_cast]
 theorem coe_lt_coe {x y : ℝ} : (x : ℝ*) < y ↔ x < y :=
   Germ.const_lt_iff
 #align hyperreal.coe_lt_coe Hyperreal.coe_lt_coe
 
-/- warning: hyperreal.coe_nonneg -> Hyperreal.coe_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, Iff (LE.le.{0} Hyperreal (Preorder.toHasLe.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x)) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x)
-but is expected to have type
-  forall {x : Real}, Iff (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) (Hyperreal.ofReal x)) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x)
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_nonneg Hyperreal.coe_nonnegₓ'. -/
 @[simp, norm_cast]
 theorem coe_nonneg {x : ℝ} : 0 ≤ (x : ℝ*) ↔ 0 ≤ x :=
   coe_le_coe
 #align hyperreal.coe_nonneg Hyperreal.coe_nonneg
 
-/- warning: hyperreal.coe_pos -> Hyperreal.coe_pos is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, Iff (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x)) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x)
-but is expected to have type
-  forall {x : Real}, Iff (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) (Hyperreal.ofReal x)) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x)
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_pos Hyperreal.coe_posₓ'. -/
 @[simp, norm_cast]
 theorem coe_pos {x : ℝ} : 0 < (x : ℝ*) ↔ 0 < x :=
   coe_lt_coe
 #align hyperreal.coe_pos Hyperreal.coe_pos
 
-/- warning: hyperreal.coe_abs -> Hyperreal.coe_abs is a dubious translation:
-lean 3 declaration is
-  forall (x : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) x)) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x))
-but is expected to have type
-  forall (x : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (Hyperreal.ofReal x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_abs Hyperreal.coe_absₓ'. -/
 @[simp, norm_cast]
 theorem coe_abs (x : ℝ) : ((|x| : ℝ) : ℝ*) = |x| :=
   const_abs x
 #align hyperreal.coe_abs Hyperreal.coe_abs
 
-/- warning: hyperreal.coe_max -> Hyperreal.coe_max is a dubious translation:
-lean 3 declaration is
-  forall (x : Real) (y : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (LinearOrder.max.{0} Real Real.linearOrder x y)) (LinearOrder.max.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y))
-but is expected to have type
-  forall (x : Real) (y : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) x y)) (Max.max.{0} Hyperreal (LinearOrderedRing.toMax.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))) (Hyperreal.ofReal x) (Hyperreal.ofReal y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_max Hyperreal.coe_maxₓ'. -/
 @[simp, norm_cast]
 theorem coe_max (x y : ℝ) : ((max x y : ℝ) : ℝ*) = max x y :=
   Germ.const_max _ _
 #align hyperreal.coe_max Hyperreal.coe_max
 
-/- warning: hyperreal.coe_min -> Hyperreal.coe_min is a dubious translation:
-lean 3 declaration is
-  forall (x : Real) (y : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (LinearOrder.min.{0} Real Real.linearOrder x y)) (LinearOrder.min.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y))
-but is expected to have type
-  forall (x : Real) (y : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) x y)) (Min.min.{0} Hyperreal (LinearOrderedRing.toMin.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))) (Hyperreal.ofReal x) (Hyperreal.ofReal y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.coe_min Hyperreal.coe_minₓ'. -/
 @[simp, norm_cast]
 theorem coe_min (x y : ℝ) : ((min x y : ℝ) : ℝ*) = min x y :=
   Germ.const_min _ _
@@ -311,34 +187,16 @@ scoped notation "ε" => Hyperreal.epsilon
 -- mathport name: hyperreal.omega
 scoped notation "ω" => Hyperreal.omega
 
-/- warning: hyperreal.inv_omega -> Hyperreal.inv_omega is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Hyperreal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) Hyperreal.omega) Hyperreal.epsilon
-but is expected to have type
-  Eq.{1} Hyperreal (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) Hyperreal.omega) Hyperreal.epsilon
-Case conversion may be inaccurate. Consider using '#align hyperreal.inv_omega Hyperreal.inv_omegaₓ'. -/
 @[simp]
 theorem inv_omega : ω⁻¹ = ε :=
   rfl
 #align hyperreal.inv_omega Hyperreal.inv_omega
 
-/- warning: hyperreal.inv_epsilon -> Hyperreal.inv_epsilon is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Hyperreal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) Hyperreal.epsilon) Hyperreal.omega
-but is expected to have type
-  Eq.{1} Hyperreal (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) Hyperreal.epsilon) Hyperreal.omega
-Case conversion may be inaccurate. Consider using '#align hyperreal.inv_epsilon Hyperreal.inv_epsilonₓ'. -/
 @[simp]
 theorem inv_epsilon : ε⁻¹ = ω :=
   @inv_inv _ _ ω
 #align hyperreal.inv_epsilon Hyperreal.inv_epsilon
 
-/- warning: hyperreal.omega_pos -> Hyperreal.omega_pos is a dubious translation:
-lean 3 declaration is
-  LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) Hyperreal.omega
-but is expected to have type
-  LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) Hyperreal.omega
-Case conversion may be inaccurate. Consider using '#align hyperreal.omega_pos Hyperreal.omega_posₓ'. -/
 theorem omega_pos : 0 < ω :=
   Germ.coe_pos.2 <|
     mem_hyperfilter_of_finite_compl <|
@@ -347,52 +205,22 @@ theorem omega_pos : 0 < ω :=
       simp [Set.eq_singleton_iff_unique_mem]
 #align hyperreal.omega_pos Hyperreal.omega_pos
 
-/- warning: hyperreal.epsilon_pos -> Hyperreal.epsilon_pos is a dubious translation:
-lean 3 declaration is
-  LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) Hyperreal.epsilon
-but is expected to have type
-  LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) Hyperreal.epsilon
-Case conversion may be inaccurate. Consider using '#align hyperreal.epsilon_pos Hyperreal.epsilon_posₓ'. -/
 theorem epsilon_pos : 0 < ε :=
   inv_pos_of_pos omega_pos
 #align hyperreal.epsilon_pos Hyperreal.epsilon_pos
 
-/- warning: hyperreal.epsilon_ne_zero -> Hyperreal.epsilon_ne_zero is a dubious translation:
-lean 3 declaration is
-  Ne.{1} Hyperreal Hyperreal.epsilon (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))
-but is expected to have type
-  Ne.{1} Hyperreal Hyperreal.epsilon (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.epsilon_ne_zero Hyperreal.epsilon_ne_zeroₓ'. -/
 theorem epsilon_ne_zero : ε ≠ 0 :=
   epsilon_pos.ne'
 #align hyperreal.epsilon_ne_zero Hyperreal.epsilon_ne_zero
 
-/- warning: hyperreal.omega_ne_zero -> Hyperreal.omega_ne_zero is a dubious translation:
-lean 3 declaration is
-  Ne.{1} Hyperreal Hyperreal.omega (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))
-but is expected to have type
-  Ne.{1} Hyperreal Hyperreal.omega (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.omega_ne_zero Hyperreal.omega_ne_zeroₓ'. -/
 theorem omega_ne_zero : ω ≠ 0 :=
   omega_pos.ne'
 #align hyperreal.omega_ne_zero Hyperreal.omega_ne_zero
 
-/- warning: hyperreal.epsilon_mul_omega -> Hyperreal.epsilon_mul_omega is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Hyperreal (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) Hyperreal.epsilon Hyperreal.omega) (OfNat.ofNat.{0} Hyperreal 1 (OfNat.mk.{0} Hyperreal 1 (One.one.{0} Hyperreal (AddMonoidWithOne.toOne.{0} Hyperreal (AddGroupWithOne.toAddMonoidWithOne.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))
-but is expected to have type
-  Eq.{1} Hyperreal (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) Hyperreal.epsilon Hyperreal.omega) (OfNat.ofNat.{0} Hyperreal 1 (One.toOfNat1.{0} Hyperreal (Semiring.toOne.{0} Hyperreal (StrictOrderedSemiring.toSemiring.{0} Hyperreal (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Hyperreal (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Hyperreal (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.epsilon_mul_omega Hyperreal.epsilon_mul_omegaₓ'. -/
 theorem epsilon_mul_omega : ε * ω = 1 :=
   @inv_mul_cancel _ _ ω omega_ne_zero
 #align hyperreal.epsilon_mul_omega Hyperreal.epsilon_mul_omega
 
-/- warning: hyperreal.lt_of_tendsto_zero_of_pos -> Hyperreal.lt_of_tendsto_zero_of_pos is a dubious translation:
-lean 3 declaration is
-  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Hyperreal.ofSeq f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)))
-but is expected to have type
-  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofSeq f) (Hyperreal.ofReal r)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.lt_of_tendsto_zero_of_pos Hyperreal.lt_of_tendsto_zero_of_posₓ'. -/
 theorem lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝 0)) :
     ∀ {r : ℝ}, 0 < r → ofSeq f < (r : ℝ*) :=
   by
@@ -407,35 +235,17 @@ theorem lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝
   exact mem_hyperfilter_of_finite_compl ((Set.finite_le_nat N).Subset hs)
 #align hyperreal.lt_of_tendsto_zero_of_pos Hyperreal.lt_of_tendsto_zero_of_pos
 
-/- warning: hyperreal.neg_lt_of_tendsto_zero_of_pos -> Hyperreal.neg_lt_of_tendsto_zero_of_pos is a dubious translation:
-lean 3 declaration is
-  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) (Hyperreal.ofSeq f)))
-but is expected to have type
-  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (Hyperreal.ofReal r)) (Hyperreal.ofSeq f)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.neg_lt_of_tendsto_zero_of_pos Hyperreal.neg_lt_of_tendsto_zero_of_posₓ'. -/
 theorem neg_lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝 0)) :
     ∀ {r : ℝ}, 0 < r → (-r : ℝ*) < ofSeq f := fun r hr =>
   have hg := hf.neg
   neg_lt_of_neg_lt (by rw [neg_zero] at hg <;> exact lt_of_tendsto_zero_of_pos hg hr)
 #align hyperreal.neg_lt_of_tendsto_zero_of_pos Hyperreal.neg_lt_of_tendsto_zero_of_pos
 
-/- warning: hyperreal.gt_of_tendsto_zero_of_neg -> Hyperreal.gt_of_tendsto_zero_of_neg is a dubious translation:
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-  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall {r : Real}, (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r) (Hyperreal.ofSeq f)))
-but is expected to have type
-  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall {r : Real}, (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal r) (Hyperreal.ofSeq f)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.gt_of_tendsto_zero_of_neg Hyperreal.gt_of_tendsto_zero_of_negₓ'. -/
 theorem gt_of_tendsto_zero_of_neg {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝 0)) :
     ∀ {r : ℝ}, r < 0 → (r : ℝ*) < ofSeq f := fun r hr => by
   rw [← neg_neg r, coe_neg] <;> exact neg_lt_of_tendsto_zero_of_pos hf (neg_pos.mpr hr)
 #align hyperreal.gt_of_tendsto_zero_of_neg Hyperreal.gt_of_tendsto_zero_of_neg
 
-/- warning: hyperreal.epsilon_lt_pos -> Hyperreal.epsilon_lt_pos is a dubious translation:
-lean 3 declaration is
-  forall (x : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) Hyperreal.epsilon ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x))
-but is expected to have type
-  forall (x : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) Hyperreal.epsilon (Hyperreal.ofReal x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.epsilon_lt_pos Hyperreal.epsilon_lt_posₓ'. -/
 theorem epsilon_lt_pos (x : ℝ) : 0 < x → ε < x :=
   lt_of_tendsto_zero_of_pos tendsto_inverse_atTop_nhds_0_nat
 #align hyperreal.epsilon_lt_pos Hyperreal.epsilon_lt_pos
@@ -514,12 +324,6 @@ theorem not_infinite_of_exists_st {x : ℝ*} : (∃ r : ℝ, IsSt x r) → ¬Inf
 #align hyperreal.not_infinite_of_exists_st Hyperreal.not_infinite_of_exists_st
 -/
 
-/- warning: hyperreal.is_st_Sup -> Hyperreal.isSt_sSup is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Hyperreal.IsSt x (SupSet.sSup.{0} Real Real.hasSup (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y) x))))
-but is expected to have type
-  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Hyperreal.IsSt x (SupSet.sSup.{0} Real Real.instSupSetReal (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal y) x))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_Sup Hyperreal.isSt_sSupₓ'. -/
 theorem isSt_sSup {x : ℝ*} (hni : ¬Infinite x) : IsSt x (sSup { y : ℝ | (y : ℝ*) < x }) :=
   let S : Set ℝ := { y : ℝ | (y : ℝ*) < x }
   let R : _ := sSup S
@@ -548,12 +352,6 @@ theorem exists_st_of_not_infinite {x : ℝ*} (hni : ¬Infinite x) : ∃ r : ℝ,
 #align hyperreal.exists_st_of_not_infinite Hyperreal.exists_st_of_not_infinite
 -/
 
-/- warning: hyperreal.st_eq_Sup -> Hyperreal.st_eq_sSup is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, Eq.{1} Real (Hyperreal.st x) (SupSet.sSup.{0} Real Real.hasSup (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y) x)))
-but is expected to have type
-  forall {x : Hyperreal}, Eq.{1} Real (Hyperreal.st x) (SupSet.sSup.{0} Real Real.instSupSetReal (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal y) x)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.st_eq_Sup Hyperreal.st_eq_sSupₓ'. -/
 theorem st_eq_sSup {x : ℝ*} : st x = sSup { y : ℝ | (y : ℝ*) < x } :=
   by
   unfold st; split_ifs
@@ -581,12 +379,6 @@ theorem infinite_iff_not_exists_st {x : ℝ*} : Infinite x ↔ ¬∃ r : ℝ, Is
 #align hyperreal.infinite_iff_not_exists_st Hyperreal.infinite_iff_not_exists_st
 -/
 
-/- warning: hyperreal.st_infinite -> Hyperreal.Infinite.st_eq is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Hyperreal.Infinite x) -> (Eq.{1} Real (Hyperreal.st x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall {x : Hyperreal}, (Hyperreal.Infinite x) -> (Eq.{1} Real (Hyperreal.st x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.st_infinite Hyperreal.Infinite.st_eqₓ'. -/
 theorem Hyperreal.Infinite.st_eq {x : ℝ*} (hi : Infinite x) : st x = 0 :=
   by
   unfold st; split_ifs
@@ -615,12 +407,6 @@ theorem isSt_st_of_exists_st {x : ℝ*} (hx : ∃ r : ℝ, IsSt x r) : IsSt x (s
 #align hyperreal.is_st_st_of_exists_st Hyperreal.isSt_st_of_exists_st
 -/
 
-/- warning: hyperreal.is_st_st -> Hyperreal.isSt_st is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Ne.{1} Real (Hyperreal.st x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Hyperreal.IsSt x (Hyperreal.st x))
-but is expected to have type
-  forall {x : Hyperreal}, (Ne.{1} Real (Hyperreal.st x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Hyperreal.IsSt x (Hyperreal.st x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_st Hyperreal.isSt_stₓ'. -/
 theorem isSt_st {x : ℝ*} (hx : st x ≠ 0) : IsSt x (st x) :=
   by
   unfold st; split_ifs
@@ -676,22 +462,10 @@ theorem isSt_inj_real {r₁ r₂ s : ℝ} (h1 : IsSt r₁ s) (h2 : IsSt r₂ s)
 #align hyperreal.is_st_inj_real Hyperreal.isSt_inj_real
 -/
 
-/- warning: hyperreal.is_st_iff_abs_sub_lt_delta -> Hyperreal.isSt_iff_abs_sub_lt_delta is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {r : Real}, Iff (Hyperreal.IsSt x r) (forall (δ : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (SubNegMonoid.toHasSub.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) δ)))
-but is expected to have type
-  forall {x : Hyperreal} {r : Real}, Iff (Hyperreal.IsSt x r) (forall (δ : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (Ring.toSub.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal r))) (Hyperreal.ofReal δ)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_iff_abs_sub_lt_delta Hyperreal.isSt_iff_abs_sub_lt_deltaₓ'. -/
 theorem isSt_iff_abs_sub_lt_delta {x : ℝ*} {r : ℝ} : IsSt x r ↔ ∀ δ : ℝ, 0 < δ → |x - r| < δ := by
   simp only [abs_sub_lt_iff, sub_lt_iff_lt_add, is_st, and_comm', add_comm]
 #align hyperreal.is_st_iff_abs_sub_lt_delta Hyperreal.isSt_iff_abs_sub_lt_delta
 
-/- warning: hyperreal.is_st_add -> Hyperreal.IsSt.add is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (Hyperreal.IsSt (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) r s))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (Hyperreal.IsSt (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) r s))
-Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_add Hyperreal.IsSt.addₓ'. -/
 theorem Hyperreal.IsSt.add {x y : ℝ*} {r s : ℝ} : IsSt x r → IsSt y s → IsSt (x + y) (r + s) :=
   fun hxr hys d hd =>
   have hxr' := hxr (d / 2) (half_pos hd)
@@ -700,32 +474,14 @@ theorem Hyperreal.IsSt.add {x y : ℝ*} {r s : ℝ} : IsSt x r → IsSt y s →
     convert add_lt_add hxr'.2 hys'.2 using 1 <;> norm_cast <;> linarith⟩
 #align hyperreal.is_st_add Hyperreal.IsSt.add
 
-/- warning: hyperreal.is_st_neg -> Hyperreal.IsSt.neg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {r : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) x) (Neg.neg.{0} Real Real.hasNeg r))
-but is expected to have type
-  forall {x : Hyperreal} {r : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) x) (Neg.neg.{0} Real Real.instNegReal r))
-Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_neg Hyperreal.IsSt.negₓ'. -/
 theorem Hyperreal.IsSt.neg {x : ℝ*} {r : ℝ} (hxr : IsSt x r) : IsSt (-x) (-r) := fun d hd =>
   show -(r : ℝ*) - d < -x ∧ -x < -r + d by cases hxr d hd <;> constructor <;> linarith
 #align hyperreal.is_st_neg Hyperreal.IsSt.neg
 
-/- warning: hyperreal.is_st_sub -> Hyperreal.IsSt.sub is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (Hyperreal.IsSt (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (SubNegMonoid.toHasSub.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))) x y) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) r s))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (Hyperreal.IsSt (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (Ring.toSub.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x y) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) r s))
-Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_sub Hyperreal.IsSt.subₓ'. -/
 theorem Hyperreal.IsSt.sub {x y : ℝ*} {r s : ℝ} : IsSt x r → IsSt y s → IsSt (x - y) (r - s) :=
   fun hxr hys => by rw [sub_eq_add_neg, sub_eq_add_neg] <;> exact is_st_add hxr (is_st_neg hys)
 #align hyperreal.is_st_sub Hyperreal.IsSt.sub
 
-/- warning: hyperreal.lt_of_is_st_lt -> Hyperreal.IsSt.lt is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (LT.lt.{0} Real Real.hasLt r s) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y)
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (LT.lt.{0} Real Real.instLTReal r s) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x y)
-Case conversion may be inaccurate. Consider using '#align hyperreal.lt_of_is_st_lt Hyperreal.IsSt.ltₓ'. -/
 -- (st x < st y) → (x < y) → (x ≤ y) → (st x ≤ st y)
 theorem Hyperreal.IsSt.lt {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt y s) : r < s → x < y :=
   fun hrs => by
@@ -740,34 +496,16 @@ theorem Hyperreal.IsSt.lt {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
   exact lt_trans hxr' hys'
 #align hyperreal.lt_of_is_st_lt Hyperreal.IsSt.lt
 
-/- warning: hyperreal.is_st_le_of_le -> Hyperreal.IsSt.le is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (LE.le.{0} Hyperreal (Preorder.toHasLe.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y) -> (LE.le.{0} Real Real.hasLe r s)
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x y) -> (LE.le.{0} Real Real.instLEReal r s)
-Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_le_of_le Hyperreal.IsSt.leₓ'. -/
 theorem Hyperreal.IsSt.le {x y : ℝ*} {r s : ℝ} (hrx : IsSt x r) (hsy : IsSt y s) : x ≤ y → r ≤ s :=
   by rw [← not_lt, ← not_lt, not_imp_not] <;> exact lt_of_is_st_lt hsy hrx
 #align hyperreal.is_st_le_of_le Hyperreal.IsSt.le
 
-/- warning: hyperreal.st_le_of_le -> Hyperreal.st_le_of_le is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (LE.le.{0} Hyperreal (Preorder.toHasLe.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y) -> (LE.le.{0} Real Real.hasLe (Hyperreal.st x) (Hyperreal.st y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x y) -> (LE.le.{0} Real Real.instLEReal (Hyperreal.st x) (Hyperreal.st y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.st_le_of_le Hyperreal.st_le_of_leₓ'. -/
 theorem st_le_of_le {x y : ℝ*} (hix : ¬Infinite x) (hiy : ¬Infinite y) : x ≤ y → st x ≤ st y :=
   have hx' := isSt_st' hix
   have hy' := isSt_st' hiy
   Hyperreal.IsSt.le hx' hy'
 #align hyperreal.st_le_of_le Hyperreal.st_le_of_le
 
-/- warning: hyperreal.lt_of_st_lt -> Hyperreal.lt_of_st_lt is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (LT.lt.{0} Real Real.hasLt (Hyperreal.st x) (Hyperreal.st y)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y)
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (LT.lt.{0} Real Real.instLTReal (Hyperreal.st x) (Hyperreal.st y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x y)
-Case conversion may be inaccurate. Consider using '#align hyperreal.lt_of_st_lt Hyperreal.lt_of_st_ltₓ'. -/
 theorem lt_of_st_lt {x y : ℝ*} (hix : ¬Infinite x) (hiy : ¬Infinite y) : st x < st y → x < y :=
   have hx' := isSt_st' hix
   have hy' := isSt_st' hiy
@@ -779,59 +517,23 @@ theorem lt_of_st_lt {x y : ℝ*} (hix : ¬Infinite x) (hiy : ¬Infinite y) : st
 -/
 
 
-/- warning: hyperreal.infinite_pos_def -> Hyperreal.infinitePos_def is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r) x)
-but is expected to have type
-  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal r) x)
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_def Hyperreal.infinitePos_defₓ'. -/
 theorem infinitePos_def {x : ℝ*} : InfinitePos x ↔ ∀ r : ℝ, ↑r < x := by rw [iff_eq_eq] <;> rfl
 #align hyperreal.infinite_pos_def Hyperreal.infinitePos_def
 
-/- warning: hyperreal.infinite_neg_def -> Hyperreal.infiniteNeg_def is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))
-but is expected to have type
-  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal r))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_def Hyperreal.infiniteNeg_defₓ'. -/
 theorem infiniteNeg_def {x : ℝ*} : InfiniteNeg x ↔ ∀ r : ℝ, x < r := by rw [iff_eq_eq] <;> rfl
 #align hyperreal.infinite_neg_def Hyperreal.infiniteNeg_def
 
-/- warning: hyperreal.ne_zero_of_infinite -> Hyperreal.Infinite.ne_zero is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Hyperreal.Infinite x) -> (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))))
-but is expected to have type
-  forall {x : Hyperreal}, (Hyperreal.Infinite x) -> (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.ne_zero_of_infinite Hyperreal.Infinite.ne_zeroₓ'. -/
 theorem Hyperreal.Infinite.ne_zero {x : ℝ*} : Infinite x → x ≠ 0 := fun hI h0 =>
   Or.cases_on hI (fun hip => lt_irrefl (0 : ℝ*) ((by rwa [← h0] : InfinitePos 0) 0)) fun hin =>
     lt_irrefl (0 : ℝ*) ((by rwa [← h0] : InfiniteNeg 0) 0)
 #align hyperreal.ne_zero_of_infinite Hyperreal.Infinite.ne_zero
 
-/- warning: hyperreal.not_infinite_zero -> Hyperreal.not_infinite_zero is a dubious translation:
-lean 3 declaration is
-  Not (Hyperreal.Infinite (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))))
-but is expected to have type
-  Not (Hyperreal.Infinite (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.not_infinite_zero Hyperreal.not_infinite_zeroₓ'. -/
 theorem not_infinite_zero : ¬Infinite 0 := fun hI => Hyperreal.Infinite.ne_zero hI rfl
 #align hyperreal.not_infinite_zero Hyperreal.not_infinite_zero
 
-/- warning: hyperreal.pos_of_infinite_pos -> Hyperreal.InfinitePos.pos is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Hyperreal.InfinitePos x) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x)
-but is expected to have type
-  forall {x : Hyperreal}, (Hyperreal.InfinitePos x) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x)
-Case conversion may be inaccurate. Consider using '#align hyperreal.pos_of_infinite_pos Hyperreal.InfinitePos.posₓ'. -/
 theorem Hyperreal.InfinitePos.pos {x : ℝ*} : InfinitePos x → 0 < x := fun hip => hip 0
 #align hyperreal.pos_of_infinite_pos Hyperreal.InfinitePos.pos
 
-/- warning: hyperreal.neg_of_infinite_neg -> Hyperreal.InfiniteNeg.lt_zero is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))))
-but is expected to have type
-  forall {x : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.neg_of_infinite_neg Hyperreal.InfiniteNeg.lt_zeroₓ'. -/
 theorem Hyperreal.InfiniteNeg.lt_zero {x : ℝ*} : InfiniteNeg x → x < 0 := fun hin => hin 0
 #align hyperreal.neg_of_infinite_neg Hyperreal.InfiniteNeg.lt_zero
 
@@ -847,22 +549,10 @@ theorem Hyperreal.InfinitePos.not_infiniteNeg {x : ℝ*} : InfinitePos x → ¬I
 #align hyperreal.not_infinite_neg_of_infinite_pos Hyperreal.InfinitePos.not_infiniteNeg
 -/
 
-/- warning: hyperreal.infinite_neg_neg_of_infinite_pos -> Hyperreal.InfinitePos.neg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Hyperreal.InfinitePos x) -> (Hyperreal.InfiniteNeg (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) x))
-but is expected to have type
-  forall {x : Hyperreal}, (Hyperreal.InfinitePos x) -> (Hyperreal.InfiniteNeg (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_neg_of_infinite_pos Hyperreal.InfinitePos.negₓ'. -/
 theorem Hyperreal.InfinitePos.neg {x : ℝ*} : InfinitePos x → InfiniteNeg (-x) := fun hp r =>
   neg_lt.mp (hp (-r))
 #align hyperreal.infinite_neg_neg_of_infinite_pos Hyperreal.InfinitePos.neg
 
-/- warning: hyperreal.infinite_pos_neg_of_infinite_neg -> Hyperreal.InfiniteNeg.neg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Hyperreal.InfinitePos (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) x))
-but is expected to have type
-  forall {x : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Hyperreal.InfinitePos (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_neg_of_infinite_neg Hyperreal.InfiniteNeg.negₓ'. -/
 theorem Hyperreal.InfiniteNeg.neg {x : ℝ*} : InfiniteNeg x → InfinitePos (-x) := fun hp r =>
   lt_neg.mp (hp (-r))
 #align hyperreal.infinite_pos_neg_of_infinite_neg Hyperreal.InfiniteNeg.neg
@@ -916,44 +606,20 @@ theorem Hyperreal.InfiniteNeg.not_infinitesimal {x : ℝ*} : InfiniteNeg x → 
 #align hyperreal.not_infinitesimal_of_infinite_neg Hyperreal.InfiniteNeg.not_infinitesimal
 -/
 
-/- warning: hyperreal.infinite_pos_iff_infinite_and_pos -> Hyperreal.infinitePos_iff_infinite_and_pos is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (And (Hyperreal.Infinite x) (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x))
-but is expected to have type
-  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (And (Hyperreal.Infinite x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_iff_infinite_and_pos Hyperreal.infinitePos_iff_infinite_and_posₓ'. -/
 theorem infinitePos_iff_infinite_and_pos {x : ℝ*} : InfinitePos x ↔ Infinite x ∧ 0 < x :=
   ⟨fun hip => ⟨Or.inl hip, hip 0⟩, fun ⟨hi, hp⟩ =>
     hi.casesOn (fun hip => hip) fun hin => False.elim (not_lt_of_lt hp (hin 0))⟩
 #align hyperreal.infinite_pos_iff_infinite_and_pos Hyperreal.infinitePos_iff_infinite_and_pos
 
-/- warning: hyperreal.infinite_neg_iff_infinite_and_neg -> Hyperreal.infiniteNeg_iff_infinite_and_neg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (And (Hyperreal.Infinite x) (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))))
-but is expected to have type
-  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (And (Hyperreal.Infinite x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_iff_infinite_and_neg Hyperreal.infiniteNeg_iff_infinite_and_negₓ'. -/
 theorem infiniteNeg_iff_infinite_and_neg {x : ℝ*} : InfiniteNeg x ↔ Infinite x ∧ x < 0 :=
   ⟨fun hip => ⟨Or.inr hip, hip 0⟩, fun ⟨hi, hp⟩ =>
     hi.casesOn (fun hin => False.elim (not_lt_of_lt hp (hin 0))) fun hip => hip⟩
 #align hyperreal.infinite_neg_iff_infinite_and_neg Hyperreal.infiniteNeg_iff_infinite_and_neg
 
-/- warning: hyperreal.infinite_pos_iff_infinite_of_pos -> Hyperreal.infinitePos_iff_infinite_of_pos is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x) -> (Iff (Hyperreal.InfinitePos x) (Hyperreal.Infinite x))
-but is expected to have type
-  forall {x : Hyperreal}, (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x) -> (Iff (Hyperreal.InfinitePos x) (Hyperreal.Infinite x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_iff_infinite_of_pos Hyperreal.infinitePos_iff_infinite_of_posₓ'. -/
 theorem infinitePos_iff_infinite_of_pos {x : ℝ*} (hp : 0 < x) : InfinitePos x ↔ Infinite x := by
   rw [infinite_pos_iff_infinite_and_pos] <;> exact ⟨fun hI => hI.1, fun hI => ⟨hI, hp⟩⟩
 #align hyperreal.infinite_pos_iff_infinite_of_pos Hyperreal.infinitePos_iff_infinite_of_pos
 
-/- warning: hyperreal.infinite_pos_iff_infinite_of_nonneg -> Hyperreal.infinitePos_iff_infinite_of_nonneg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (LE.le.{0} Hyperreal (Preorder.toHasLe.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x) -> (Iff (Hyperreal.InfinitePos x) (Hyperreal.Infinite x))
-but is expected to have type
-  forall {x : Hyperreal}, (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x) -> (Iff (Hyperreal.InfinitePos x) (Hyperreal.Infinite x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_iff_infinite_of_nonneg Hyperreal.infinitePos_iff_infinite_of_nonnegₓ'. -/
 theorem infinitePos_iff_infinite_of_nonneg {x : ℝ*} (hp : 0 ≤ x) : InfinitePos x ↔ Infinite x :=
   Or.cases_on (lt_or_eq_of_le hp) infinitePos_iff_infinite_of_pos fun h => by
     rw [h.symm] <;>
@@ -962,22 +628,10 @@ theorem infinitePos_iff_infinite_of_nonneg {x : ℝ*} (hp : 0 ≤ x) : InfiniteP
           False.elim (not_infinite_zero hI)⟩
 #align hyperreal.infinite_pos_iff_infinite_of_nonneg Hyperreal.infinitePos_iff_infinite_of_nonneg
 
-/- warning: hyperreal.infinite_neg_iff_infinite_of_neg -> Hyperreal.infiniteNeg_iff_infinite_of_neg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Iff (Hyperreal.InfiniteNeg x) (Hyperreal.Infinite x))
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-  forall {x : Hyperreal}, (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Iff (Hyperreal.InfiniteNeg x) (Hyperreal.Infinite x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_iff_infinite_of_neg Hyperreal.infiniteNeg_iff_infinite_of_negₓ'. -/
 theorem infiniteNeg_iff_infinite_of_neg {x : ℝ*} (hn : x < 0) : InfiniteNeg x ↔ Infinite x := by
   rw [infinite_neg_iff_infinite_and_neg] <;> exact ⟨fun hI => hI.1, fun hI => ⟨hI, hn⟩⟩
 #align hyperreal.infinite_neg_iff_infinite_of_neg Hyperreal.infiniteNeg_iff_infinite_of_neg
 
-/- warning: hyperreal.infinite_pos_abs_iff_infinite_abs -> Hyperreal.infinitePos_abs_iff_infinite_abs is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x)) (Hyperreal.Infinite (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x))
-but is expected to have type
-  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x)) (Hyperreal.Infinite (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_abs_iff_infinite_abs Hyperreal.infinitePos_abs_iff_infinite_absₓ'. -/
 theorem infinitePos_abs_iff_infinite_abs {x : ℝ*} : InfinitePos (|x|) ↔ Infinite (|x|) :=
   infinitePos_iff_infinite_of_nonneg (abs_nonneg _)
 #align hyperreal.infinite_pos_abs_iff_infinite_abs Hyperreal.infinitePos_abs_iff_infinite_abs
@@ -997,12 +651,6 @@ theorem infinite_abs_iff {x : ℝ*} : Infinite x ↔ Infinite (|x|) := by
   rw [← infinite_pos_iff_infinite_of_nonneg (abs_nonneg _), infinite_iff_infinite_pos_abs]
 #align hyperreal.infinite_iff_infinite_abs Hyperreal.infinite_abs_iffₓ
 
-/- warning: hyperreal.infinite_iff_abs_lt_abs -> Hyperreal.infinite_iff_abs_lt_abs is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.Infinite x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x))
-but is expected to have type
-  forall {x : Hyperreal}, Iff (Hyperreal.Infinite x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (Hyperreal.ofReal r)) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_iff_abs_lt_abs Hyperreal.infinite_iff_abs_lt_absₓ'. -/
 theorem infinite_iff_abs_lt_abs {x : ℝ*} : Infinite x ↔ ∀ r : ℝ, (|r| : ℝ*) < |x| :=
   ⟨fun hI r => coe_abs r ▸ infinitePos_abs_iff_infinite.mp hI (|r|), fun hR =>
     Or.cases_on (max_choice x (-x))
@@ -1010,12 +658,6 @@ theorem infinite_iff_abs_lt_abs {x : ℝ*} : Infinite x ↔ ∀ r : ℝ, (|r| :
       Or.inr fun r => neg_lt_neg_iff.mp <| lt_of_le_of_lt (neg_le_abs_self _) (h ▸ hR r)⟩
 #align hyperreal.infinite_iff_abs_lt_abs Hyperreal.infinite_iff_abs_lt_abs
 
-/- warning: hyperreal.infinite_pos_add_not_infinite_neg -> Hyperreal.infinitePos_add_not_infiniteNeg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.InfiniteNeg y)) -> (Hyperreal.InfinitePos (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.InfiniteNeg y)) -> (Hyperreal.InfinitePos (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_add_not_infinite_neg Hyperreal.infinitePos_add_not_infiniteNegₓ'. -/
 theorem infinitePos_add_not_infiniteNeg {x y : ℝ*} :
     InfinitePos x → ¬InfiniteNeg y → InfinitePos (x + y) :=
   by
@@ -1025,23 +667,11 @@ theorem infinitePos_add_not_infiniteNeg {x y : ℝ*} :
   simp
 #align hyperreal.infinite_pos_add_not_infinite_neg Hyperreal.infinitePos_add_not_infiniteNeg
 
-/- warning: hyperreal.not_infinite_neg_add_infinite_pos -> Hyperreal.not_infiniteNeg_add_infinitePos is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.InfiniteNeg x)) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.InfiniteNeg x)) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.not_infinite_neg_add_infinite_pos Hyperreal.not_infiniteNeg_add_infinitePosₓ'. -/
 theorem not_infiniteNeg_add_infinitePos {x y : ℝ*} :
     ¬InfiniteNeg x → InfinitePos y → InfinitePos (x + y) := fun hx hy => by
   rw [add_comm] <;> exact infinite_pos_add_not_infinite_neg hy hx
 #align hyperreal.not_infinite_neg_add_infinite_pos Hyperreal.not_infiniteNeg_add_infinitePos
 
-/- warning: hyperreal.infinite_neg_add_not_infinite_pos -> Hyperreal.infiniteNeg_add_not_infinitePos is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.InfinitePos y)) -> (Hyperreal.InfiniteNeg (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.InfinitePos y)) -> (Hyperreal.InfiniteNeg (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_add_not_infinite_pos Hyperreal.infiniteNeg_add_not_infinitePosₓ'. -/
 theorem infiniteNeg_add_not_infinitePos {x y : ℝ*} :
     InfiniteNeg x → ¬InfinitePos y → InfiniteNeg (x + y) := by
   rw [@infinite_neg_iff_infinite_pos_neg x, @infinite_pos_iff_infinite_neg_neg y,
@@ -1049,56 +679,26 @@ theorem infiniteNeg_add_not_infinitePos {x y : ℝ*} :
     exact infinite_pos_add_not_infinite_neg
 #align hyperreal.infinite_neg_add_not_infinite_pos Hyperreal.infiniteNeg_add_not_infinitePos
 
-/- warning: hyperreal.not_infinite_pos_add_infinite_neg -> Hyperreal.not_infinitePos_add_infiniteNeg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.InfinitePos x)) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.InfinitePos x)) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.not_infinite_pos_add_infinite_neg Hyperreal.not_infinitePos_add_infiniteNegₓ'. -/
 theorem not_infinitePos_add_infiniteNeg {x y : ℝ*} :
     ¬InfinitePos x → InfiniteNeg y → InfiniteNeg (x + y) := fun hx hy => by
   rw [add_comm] <;> exact infinite_neg_add_not_infinite_pos hy hx
 #align hyperreal.not_infinite_pos_add_infinite_neg Hyperreal.not_infinitePos_add_infiniteNeg
 
-/- warning: hyperreal.infinite_pos_add_infinite_pos -> Hyperreal.infinitePos_add_infinitePos is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_add_infinite_pos Hyperreal.infinitePos_add_infinitePosₓ'. -/
 theorem infinitePos_add_infinitePos {x y : ℝ*} :
     InfinitePos x → InfinitePos y → InfinitePos (x + y) := fun hx hy =>
   infinitePos_add_not_infiniteNeg hx (Hyperreal.InfinitePos.not_infiniteNeg hy)
 #align hyperreal.infinite_pos_add_infinite_pos Hyperreal.infinitePos_add_infinitePos
 
-/- warning: hyperreal.infinite_neg_add_infinite_neg -> Hyperreal.infiniteNeg_add_infiniteNeg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_add_infinite_neg Hyperreal.infiniteNeg_add_infiniteNegₓ'. -/
 theorem infiniteNeg_add_infiniteNeg {x y : ℝ*} :
     InfiniteNeg x → InfiniteNeg y → InfiniteNeg (x + y) := fun hx hy =>
   infiniteNeg_add_not_infinitePos hx (Hyperreal.InfiniteNeg.not_infinitePos hy)
 #align hyperreal.infinite_neg_add_infinite_neg Hyperreal.infiniteNeg_add_infiniteNeg
 
-/- warning: hyperreal.infinite_pos_add_not_infinite -> Hyperreal.infinitePos_add_not_infinite is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinite y)) -> (Hyperreal.InfinitePos (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinite y)) -> (Hyperreal.InfinitePos (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_add_not_infinite Hyperreal.infinitePos_add_not_infiniteₓ'. -/
 theorem infinitePos_add_not_infinite {x y : ℝ*} :
     InfinitePos x → ¬Infinite y → InfinitePos (x + y) := fun hx hy =>
   infinitePos_add_not_infiniteNeg hx (not_or.mp hy).2
 #align hyperreal.infinite_pos_add_not_infinite Hyperreal.infinitePos_add_not_infinite
 
-/- warning: hyperreal.infinite_neg_add_not_infinite -> Hyperreal.infiniteNeg_add_not_infinite is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinite y)) -> (Hyperreal.InfiniteNeg (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinite y)) -> (Hyperreal.InfiniteNeg (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_add_not_infinite Hyperreal.infiniteNeg_add_not_infiniteₓ'. -/
 theorem infiniteNeg_add_not_infinite {x y : ℝ*} :
     InfiniteNeg x → ¬Infinite y → InfiniteNeg (x + y) := fun hx hy =>
   infiniteNeg_add_not_infinitePos hx (not_or.mp hy).1
@@ -1132,22 +732,10 @@ theorem infiniteNeg_of_tendsto_bot {f : ℕ → ℝ} (hf : Tendsto f atTop atBot
 #align hyperreal.infinite_neg_of_tendsto_bot Hyperreal.infiniteNeg_of_tendsto_bot
 -/
 
-/- warning: hyperreal.not_infinite_neg -> Hyperreal.not_infinite_neg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) x)))
-but is expected to have type
-  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) x)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.not_infinite_neg Hyperreal.not_infinite_negₓ'. -/
 theorem not_infinite_neg {x : ℝ*} : ¬Infinite x → ¬Infinite (-x) :=
   not_imp_not.mpr infinite_neg.mpr
 #align hyperreal.not_infinite_neg Hyperreal.not_infinite_neg
 
-/- warning: hyperreal.not_infinite_add -> Hyperreal.not_infinite_add is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (Not (Hyperreal.Infinite (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y)))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (Not (Hyperreal.Infinite (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.not_infinite_add Hyperreal.not_infinite_addₓ'. -/
 theorem not_infinite_add {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : ¬Infinite (x + y) :=
   have hx' := exists_st_of_not_infinite hx
   have hy' := exists_st_of_not_infinite hy
@@ -1156,12 +744,6 @@ theorem not_infinite_add {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) :
       not_infinite_of_exists_st <| ⟨s + r, Hyperreal.IsSt.add hs hr⟩
 #align hyperreal.not_infinite_add Hyperreal.not_infinite_add
 
-/- warning: hyperreal.not_infinite_iff_exist_lt_gt -> Hyperreal.not_infinite_iff_exist_lt_gt is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Not (Hyperreal.Infinite x)) (Exists.{1} Real (fun (r : Real) => Exists.{1} Real (fun (s : Real) => And (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r) x) (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) s)))))
-but is expected to have type
-  forall {x : Hyperreal}, Iff (Not (Hyperreal.Infinite x)) (Exists.{1} Real (fun (r : Real) => Exists.{1} Real (fun (s : Real) => And (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal r) x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal s)))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.not_infinite_iff_exist_lt_gt Hyperreal.not_infinite_iff_exist_lt_gtₓ'. -/
 theorem not_infinite_iff_exist_lt_gt {x : ℝ*} : ¬Infinite x ↔ ∃ r s : ℝ, (r : ℝ*) < x ∧ x < s :=
   ⟨fun hni =>
     Exists.dcases_on (not_forall.mp (not_or.mp hni).1) <|
@@ -1235,12 +817,6 @@ private theorem is_st_mul' {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
           _ = (d : ℝ*) := by rw [mul_one, add_halves]
           
 
-/- warning: hyperreal.is_st_mul -> Hyperreal.IsSt.mul is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (Hyperreal.IsSt (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r s))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (Hyperreal.IsSt (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r s))
-Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_mul Hyperreal.IsSt.mulₓ'. -/
 theorem Hyperreal.IsSt.mul {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt y s) :
     IsSt (x * y) (r * s) :=
   have h :=
@@ -1260,12 +836,6 @@ theorem Hyperreal.IsSt.mul {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
       exact is_st_mul' hxr hys hs
 #align hyperreal.is_st_mul Hyperreal.IsSt.mul
 
-/- warning: hyperreal.not_infinite_mul -> Hyperreal.not_infinite_mul is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (Not (Hyperreal.Infinite (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y)))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (Not (Hyperreal.Infinite (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.not_infinite_mul Hyperreal.not_infinite_mulₓ'. -/
 --AN INFINITE LEMMA THAT REQUIRES SOME MORE ST MACHINERY
 theorem not_infinite_mul {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : ¬Infinite (x * y) :=
   have hx' := exists_st_of_not_infinite hx
@@ -1275,12 +845,6 @@ theorem not_infinite_mul {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) :
       not_infinite_of_exists_st <| ⟨s * r, Hyperreal.IsSt.mul hs hr⟩
 #align hyperreal.not_infinite_mul Hyperreal.not_infinite_mul
 
-/- warning: hyperreal.st_add -> Hyperreal.st_add is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (Eq.{1} Real (Hyperreal.st (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Hyperreal.st x) (Hyperreal.st y)))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (Eq.{1} Real (Hyperreal.st (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Hyperreal.st x) (Hyperreal.st y)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.st_add Hyperreal.st_addₓ'. -/
 ---
 theorem st_add {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : st (x + y) = st x + st y :=
   have hx' := isSt_st' hx
@@ -1290,24 +854,12 @@ theorem st_add {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : st (x + y)
   Hyperreal.IsSt.unique hxy hxy'
 #align hyperreal.st_add Hyperreal.st_add
 
-/- warning: hyperreal.st_neg -> Hyperreal.st_neg is a dubious translation:
-lean 3 declaration is
-  forall (x : Hyperreal), Eq.{1} Real (Hyperreal.st (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) x)) (Neg.neg.{0} Real Real.hasNeg (Hyperreal.st x))
-but is expected to have type
-  forall (x : Hyperreal), Eq.{1} Real (Hyperreal.st (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) x)) (Neg.neg.{0} Real Real.instNegReal (Hyperreal.st x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.st_neg Hyperreal.st_negₓ'. -/
 theorem st_neg (x : ℝ*) : st (-x) = -st x :=
   if h : Infinite x then by
     rw [st_infinite h, st_infinite (infinite_iff_infinite_neg.mp h), neg_zero]
   else Hyperreal.IsSt.unique (isSt_st' (not_infinite_neg h)) (Hyperreal.IsSt.neg (isSt_st' h))
 #align hyperreal.st_neg Hyperreal.st_neg
 
-/- warning: hyperreal.st_mul -> Hyperreal.st_mul is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (Eq.{1} Real (Hyperreal.st (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Hyperreal.st x) (Hyperreal.st y)))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (Eq.{1} Real (Hyperreal.st (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Hyperreal.st x) (Hyperreal.st y)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.st_mul Hyperreal.st_mulₓ'. -/
 theorem st_mul {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : st (x * y) = st x * st y :=
   have hx' := isSt_st' hx
   have hy' := isSt_st' hy
@@ -1321,53 +873,23 @@ theorem st_mul {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : st (x * y)
 -/
 
 
-/- warning: hyperreal.infinitesimal_def -> Hyperreal.infinitesimal_def is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.Infinitesimal x) (forall (r : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (And (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) x) (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))))
-but is expected to have type
-  forall {x : Hyperreal}, Iff (Hyperreal.Infinitesimal x) (forall (r : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (And (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (Hyperreal.ofReal r)) x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal r))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_def Hyperreal.infinitesimal_defₓ'. -/
 theorem infinitesimal_def {x : ℝ*} : Infinitesimal x ↔ ∀ r : ℝ, 0 < r → -(r : ℝ*) < x ∧ x < r :=
   ⟨fun hi r hr => by convert hi r hr <;> simp, fun hi d hd => by convert hi d hd <;> simp⟩
 #align hyperreal.infinitesimal_def Hyperreal.infinitesimal_def
 
-/- warning: hyperreal.lt_of_pos_of_infinitesimal -> Hyperreal.lt_of_pos_of_infinitesimal is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)))
-but is expected to have type
-  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal r)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.lt_of_pos_of_infinitesimal Hyperreal.lt_of_pos_of_infinitesimalₓ'. -/
 theorem lt_of_pos_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r : ℝ, 0 < r → x < r :=
   fun hi r hr => ((infinitesimal_def.mp hi) r hr).2
 #align hyperreal.lt_of_pos_of_infinitesimal Hyperreal.lt_of_pos_of_infinitesimal
 
-/- warning: hyperreal.lt_neg_of_pos_of_infinitesimal -> Hyperreal.lt_neg_of_pos_of_infinitesimal is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) x))
-but is expected to have type
-  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (Hyperreal.ofReal r)) x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.lt_neg_of_pos_of_infinitesimal Hyperreal.lt_neg_of_pos_of_infinitesimalₓ'. -/
 theorem lt_neg_of_pos_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r : ℝ, 0 < r → -↑r < x :=
   fun hi r hr => ((infinitesimal_def.mp hi) r hr).1
 #align hyperreal.lt_neg_of_pos_of_infinitesimal Hyperreal.lt_neg_of_pos_of_infinitesimal
 
-/- warning: hyperreal.gt_of_neg_of_infinitesimal -> Hyperreal.gt_of_neg_of_infinitesimal is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r) x))
-but is expected to have type
-  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal r) x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.gt_of_neg_of_infinitesimal Hyperreal.gt_of_neg_of_infinitesimalₓ'. -/
 theorem gt_of_neg_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r : ℝ, r < 0 → ↑r < x :=
   fun hi r hr => by
   convert((infinitesimal_def.mp hi) (-r) (neg_pos.mpr hr)).1 <;> exact (neg_neg ↑r).symm
 #align hyperreal.gt_of_neg_of_infinitesimal Hyperreal.gt_of_neg_of_infinitesimal
 
-/- warning: hyperreal.abs_lt_real_iff_infinitesimal -> Hyperreal.abs_lt_real_iff_infinitesimal is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.Infinitesimal x) (forall (r : Real), (Ne.{1} Real r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))))
-but is expected to have type
-  forall {x : Hyperreal}, Iff (Hyperreal.Infinitesimal x) (forall (r : Real), (Ne.{1} Real r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (Hyperreal.ofReal r))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.abs_lt_real_iff_infinitesimal Hyperreal.abs_lt_real_iff_infinitesimalₓ'. -/
 theorem abs_lt_real_iff_infinitesimal {x : ℝ*} : Infinitesimal x ↔ ∀ r : ℝ, r ≠ 0 → |x| < |r| :=
   ⟨fun hi r hr =>
     abs_lt.mpr (by rw [← coe_abs] <;> exact infinitesimal_def.mp hi (|r|) (abs_pos.2 hr)), fun hR =>
@@ -1375,52 +897,22 @@ theorem abs_lt_real_iff_infinitesimal {x : ℝ*} : Infinitesimal x ↔ ∀ r : 
       abs_lt.mp <| (abs_of_pos <| coe_pos.2 hr) ▸ hR r <| ne_of_gt hr⟩
 #align hyperreal.abs_lt_real_iff_infinitesimal Hyperreal.abs_lt_real_iff_infinitesimal
 
-/- warning: hyperreal.infinitesimal_zero -> Hyperreal.infinitesimal_zero is a dubious translation:
-lean 3 declaration is
-  Hyperreal.Infinitesimal (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))
-but is expected to have type
-  Hyperreal.Infinitesimal (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_zero Hyperreal.infinitesimal_zeroₓ'. -/
 theorem infinitesimal_zero : Infinitesimal 0 :=
   isSt_refl_real 0
 #align hyperreal.infinitesimal_zero Hyperreal.infinitesimal_zero
 
-/- warning: hyperreal.zero_of_infinitesimal_real -> Hyperreal.Infinitesimal.eq_zero is a dubious translation:
-lean 3 declaration is
-  forall {r : Real}, (Hyperreal.Infinitesimal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) -> (Eq.{1} Real r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall {r : Real}, (Hyperreal.Infinitesimal (Hyperreal.ofReal r)) -> (Eq.{1} Real r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.zero_of_infinitesimal_real Hyperreal.Infinitesimal.eq_zeroₓ'. -/
 theorem Hyperreal.Infinitesimal.eq_zero {r : ℝ} : Infinitesimal r → r = 0 :=
   eq_of_isSt_real
 #align hyperreal.zero_of_infinitesimal_real Hyperreal.Infinitesimal.eq_zero
 
-/- warning: hyperreal.zero_iff_infinitesimal_real -> Hyperreal.infinitesimal_real_iff is a dubious translation:
-lean 3 declaration is
-  forall {r : Real}, Iff (Hyperreal.Infinitesimal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) (Eq.{1} Real r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall {r : Real}, Iff (Hyperreal.Infinitesimal (Hyperreal.ofReal r)) (Eq.{1} Real r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.zero_iff_infinitesimal_real Hyperreal.infinitesimal_real_iffₓ'. -/
 theorem infinitesimal_real_iff {r : ℝ} : Infinitesimal r ↔ r = 0 :=
   ⟨Hyperreal.Infinitesimal.eq_zero, fun hr => by rw [hr] <;> exact infinitesimal_zero⟩
 #align hyperreal.zero_iff_infinitesimal_real Hyperreal.infinitesimal_real_iff
 
-/- warning: hyperreal.infinitesimal_add -> Hyperreal.Infinitesimal.add is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.Infinitesimal x) -> (Hyperreal.Infinitesimal y) -> (Hyperreal.Infinitesimal (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.Infinitesimal x) -> (Hyperreal.Infinitesimal y) -> (Hyperreal.Infinitesimal (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_add Hyperreal.Infinitesimal.addₓ'. -/
 theorem Hyperreal.Infinitesimal.add {x y : ℝ*} (hx : Infinitesimal x) (hy : Infinitesimal y) :
     Infinitesimal (x + y) := by simpa only [add_zero] using is_st_add hx hy
 #align hyperreal.infinitesimal_add Hyperreal.Infinitesimal.add
 
-/- warning: hyperreal.infinitesimal_neg -> Hyperreal.Infinitesimal.neg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (Hyperreal.Infinitesimal (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) x))
-but is expected to have type
-  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (Hyperreal.Infinitesimal (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_neg Hyperreal.Infinitesimal.negₓ'. -/
 theorem Hyperreal.Infinitesimal.neg {x : ℝ*} (hx : Infinitesimal x) : Infinitesimal (-x) := by
   simpa only [neg_zero] using is_st_neg hx
 #align hyperreal.infinitesimal_neg Hyperreal.Infinitesimal.neg
@@ -1429,22 +921,10 @@ theorem infinitesimal_neg {x : ℝ*} : Infinitesimal x ↔ Infinitesimal (-x) :=
   ⟨Hyperreal.Infinitesimal.neg, fun h => neg_neg x ▸ @Hyperreal.Infinitesimal.neg (-x) h⟩
 #align hyperreal.infinitesimal_neg_iff Hyperreal.infinitesimal_negₓ
 
-/- warning: hyperreal.infinitesimal_mul -> Hyperreal.Infinitesimal.mul is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.Infinitesimal x) -> (Hyperreal.Infinitesimal y) -> (Hyperreal.Infinitesimal (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.Infinitesimal x) -> (Hyperreal.Infinitesimal y) -> (Hyperreal.Infinitesimal (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_mul Hyperreal.Infinitesimal.mulₓ'. -/
 theorem Hyperreal.Infinitesimal.mul {x y : ℝ*} (hx : Infinitesimal x) (hy : Infinitesimal y) :
     Infinitesimal (x * y) := by simpa only [MulZeroClass.mul_zero] using is_st_mul hx hy
 #align hyperreal.infinitesimal_mul Hyperreal.Infinitesimal.mul
 
-/- warning: hyperreal.infinitesimal_of_tendsto_zero -> Hyperreal.infinitesimal_of_tendsto_zero is a dubious translation:
-lean 3 declaration is
-  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (Hyperreal.Infinitesimal (Hyperreal.ofSeq f))
-but is expected to have type
-  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (Hyperreal.Infinitesimal (Hyperreal.ofSeq f))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_of_tendsto_zero Hyperreal.infinitesimal_of_tendsto_zeroₓ'. -/
 theorem infinitesimal_of_tendsto_zero {f : ℕ → ℝ} :
     Tendsto f atTop (𝓝 0) → Infinitesimal (ofSeq f) := fun hf d hd => by
   rw [sub_eq_add_neg, ← coe_neg, ← coe_add, ← coe_add, zero_add, zero_add] <;>
@@ -1457,46 +937,22 @@ theorem infinitesimal_epsilon : Infinitesimal ε :=
 #align hyperreal.infinitesimal_epsilon Hyperreal.infinitesimal_epsilon
 -/
 
-/- warning: hyperreal.not_real_of_infinitesimal_ne_zero -> Hyperreal.not_real_of_infinitesimal_ne_zero is a dubious translation:
-lean 3 declaration is
-  forall (x : Hyperreal), (Hyperreal.Infinitesimal x) -> (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (forall (r : Real), Ne.{1} Hyperreal x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))
-but is expected to have type
-  forall (x : Hyperreal), (Hyperreal.Infinitesimal x) -> (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (forall (r : Real), Ne.{1} Hyperreal x (Hyperreal.ofReal r))
-Case conversion may be inaccurate. Consider using '#align hyperreal.not_real_of_infinitesimal_ne_zero Hyperreal.not_real_of_infinitesimal_ne_zeroₓ'. -/
 theorem not_real_of_infinitesimal_ne_zero (x : ℝ*) : Infinitesimal x → x ≠ 0 → ∀ r : ℝ, x ≠ r :=
   fun hi hx r hr =>
   hx <|
     hr.trans <| coe_eq_zero.2 <| Hyperreal.IsSt.unique (hr.symm ▸ isSt_refl_real r : IsSt x r) hi
 #align hyperreal.not_real_of_infinitesimal_ne_zero Hyperreal.not_real_of_infinitesimal_ne_zero
 
-/- warning: hyperreal.infinitesimal_sub_is_st -> Hyperreal.IsSt.infinitesimal_sub is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {r : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.Infinitesimal (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (SubNegMonoid.toHasSub.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)))
-but is expected to have type
-  forall {x : Hyperreal} {r : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.Infinitesimal (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (Ring.toSub.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal r)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_sub_is_st Hyperreal.IsSt.infinitesimal_subₓ'. -/
 theorem Hyperreal.IsSt.infinitesimal_sub {x : ℝ*} {r : ℝ} (hxr : IsSt x r) :
     Infinitesimal (x - r) :=
   show IsSt (x - r) 0 by rw [sub_eq_add_neg, ← add_neg_self r];
     exact is_st_add hxr (is_st_refl_real (-r))
 #align hyperreal.infinitesimal_sub_is_st Hyperreal.IsSt.infinitesimal_sub
 
-/- warning: hyperreal.infinitesimal_sub_st -> Hyperreal.infinitesimal_sub_st is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Hyperreal.Infinitesimal (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (SubNegMonoid.toHasSub.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (Hyperreal.st x))))
-but is expected to have type
-  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Hyperreal.Infinitesimal (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (Ring.toSub.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal (Hyperreal.st x))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_sub_st Hyperreal.infinitesimal_sub_stₓ'. -/
 theorem infinitesimal_sub_st {x : ℝ*} (hx : ¬Infinite x) : Infinitesimal (x - st x) :=
   Hyperreal.IsSt.infinitesimal_sub <| isSt_st' hx
 #align hyperreal.infinitesimal_sub_st Hyperreal.infinitesimal_sub_st
 
-/- warning: hyperreal.infinite_pos_iff_infinitesimal_inv_pos -> Hyperreal.infinitePos_iff_infinitesimal_inv_pos is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (And (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)))
-but is expected to have type
-  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (And (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_iff_infinitesimal_inv_pos Hyperreal.infinitePos_iff_infinitesimal_inv_posₓ'. -/
 theorem infinitePos_iff_infinitesimal_inv_pos {x : ℝ*} :
     InfinitePos x ↔ Infinitesimal x⁻¹ ∧ 0 < x⁻¹ :=
   ⟨fun hip =>
@@ -1511,12 +967,6 @@ theorem infinitePos_iff_infinitesimal_inv_pos {x : ℝ*} :
           ((infinitesimal_def.mp hi) (|r|)⁻¹ (inv_pos.2 (abs_pos.2 h))).2)⟩
 #align hyperreal.infinite_pos_iff_infinitesimal_inv_pos Hyperreal.infinitePos_iff_infinitesimal_inv_pos
 
-/- warning: hyperreal.infinite_neg_iff_infinitesimal_inv_neg -> Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (And (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))))
-but is expected to have type
-  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (And (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_iff_infinitesimal_inv_neg Hyperreal.infiniteNeg_iff_infinitesimal_inv_negₓ'. -/
 theorem infiniteNeg_iff_infinitesimal_inv_neg {x : ℝ*} :
     InfiniteNeg x ↔ Infinitesimal x⁻¹ ∧ x⁻¹ < 0 :=
   ⟨fun hin =>
@@ -1527,23 +977,11 @@ theorem infiniteNeg_iff_infinitesimal_inv_neg {x : ℝ*} :
       infinite_neg_iff_infinite_pos_neg] at hin⟩
 #align hyperreal.infinite_neg_iff_infinitesimal_inv_neg Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg
 
-/- warning: hyperreal.infinitesimal_inv_of_infinite -> Hyperreal.infinitesimal_inv_of_infinite is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Hyperreal.Infinite x) -> (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x))
-but is expected to have type
-  forall {x : Hyperreal}, (Hyperreal.Infinite x) -> (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_inv_of_infinite Hyperreal.infinitesimal_inv_of_infiniteₓ'. -/
 theorem infinitesimal_inv_of_infinite {x : ℝ*} : Infinite x → Infinitesimal x⁻¹ := fun hi =>
   Or.cases_on hi (fun hip => (infinitePos_iff_infinitesimal_inv_pos.mp hip).1) fun hin =>
     (infiniteNeg_iff_infinitesimal_inv_neg.mp hin).1
 #align hyperreal.infinitesimal_inv_of_infinite Hyperreal.infinitesimal_inv_of_infinite
 
-/- warning: hyperreal.infinite_of_infinitesimal_inv -> Hyperreal.infinite_of_infinitesimal_inv is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) -> (Hyperreal.Infinite x)
-but is expected to have type
-  forall {x : Hyperreal}, (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)) -> (Hyperreal.Infinite x)
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_of_infinitesimal_inv Hyperreal.infinite_of_infinitesimal_invₓ'. -/
 theorem infinite_of_infinitesimal_inv {x : ℝ*} (h0 : x ≠ 0) (hi : Infinitesimal x⁻¹) : Infinite x :=
   by
   cases' lt_or_gt_of_ne h0 with hn hp
@@ -1551,44 +989,20 @@ theorem infinite_of_infinitesimal_inv {x : ℝ*} (h0 : x ≠ 0) (hi : Infinitesi
   · exact Or.inl (infinite_pos_iff_infinitesimal_inv_pos.mpr ⟨hi, inv_pos.mpr hp⟩)
 #align hyperreal.infinite_of_infinitesimal_inv Hyperreal.infinite_of_infinitesimal_inv
 
-/- warning: hyperreal.infinite_iff_infinitesimal_inv -> Hyperreal.infinite_iff_infinitesimal_inv is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Iff (Hyperreal.Infinite x) (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)))
-but is expected to have type
-  forall {x : Hyperreal}, (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Iff (Hyperreal.Infinite x) (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_iff_infinitesimal_inv Hyperreal.infinite_iff_infinitesimal_invₓ'. -/
 theorem infinite_iff_infinitesimal_inv {x : ℝ*} (h0 : x ≠ 0) : Infinite x ↔ Infinitesimal x⁻¹ :=
   ⟨infinitesimal_inv_of_infinite, infinite_of_infinitesimal_inv h0⟩
 #align hyperreal.infinite_iff_infinitesimal_inv Hyperreal.infinite_iff_infinitesimal_inv
 
-/- warning: hyperreal.infinitesimal_pos_iff_infinite_pos_inv -> Hyperreal.infinitesimal_pos_iff_infinitePos_inv is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (And (Hyperreal.Infinitesimal x) (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x))
-but is expected to have type
-  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)) (And (Hyperreal.Infinitesimal x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_pos_iff_infinite_pos_inv Hyperreal.infinitesimal_pos_iff_infinitePos_invₓ'. -/
 theorem infinitesimal_pos_iff_infinitePos_inv {x : ℝ*} :
     InfinitePos x⁻¹ ↔ Infinitesimal x ∧ 0 < x := by
   convert infinite_pos_iff_infinitesimal_inv_pos <;> simp only [inv_inv]
 #align hyperreal.infinitesimal_pos_iff_infinite_pos_inv Hyperreal.infinitesimal_pos_iff_infinitePos_inv
 
-/- warning: hyperreal.infinitesimal_neg_iff_infinite_neg_inv -> Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (And (Hyperreal.Infinitesimal x) (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))))
-but is expected to have type
-  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)) (And (Hyperreal.Infinitesimal x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_neg_iff_infinite_neg_inv Hyperreal.infinitesimal_neg_iff_infiniteNeg_invₓ'. -/
 theorem infinitesimal_neg_iff_infiniteNeg_inv {x : ℝ*} :
     InfiniteNeg x⁻¹ ↔ Infinitesimal x ∧ x < 0 := by
   convert infinite_neg_iff_infinitesimal_inv_neg <;> simp only [inv_inv]
 #align hyperreal.infinitesimal_neg_iff_infinite_neg_inv Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv
 
-/- warning: hyperreal.infinitesimal_iff_infinite_inv -> Hyperreal.infinitesimal_iff_infinite_inv is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal}, (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Iff (Hyperreal.Infinitesimal x) (Hyperreal.Infinite (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)))
-but is expected to have type
-  forall {x : Hyperreal}, (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Iff (Hyperreal.Infinitesimal x) (Hyperreal.Infinite (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_iff_infinite_inv Hyperreal.infinitesimal_iff_infinite_invₓ'. -/
 theorem infinitesimal_iff_infinite_inv {x : ℝ*} (h : x ≠ 0) : Infinitesimal x ↔ Infinite x⁻¹ := by
   convert(infinite_iff_infinitesimal_inv (inv_ne_zero h)).symm <;> simp only [inv_inv]
 #align hyperreal.infinitesimal_iff_infinite_inv Hyperreal.infinitesimal_iff_infinite_inv
@@ -1607,12 +1021,6 @@ theorem isSt_of_tendsto {f : ℕ → ℝ} {r : ℝ} (hf : Tendsto f atTop (𝓝
 #align hyperreal.is_st_of_tendsto Hyperreal.isSt_of_tendsto
 -/
 
-/- warning: hyperreal.is_st_inv -> Hyperreal.IsSt.inv is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {r : Real}, (Not (Hyperreal.Infinitesimal x)) -> (Hyperreal.IsSt x r) -> (Hyperreal.IsSt (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x) (Inv.inv.{0} Real Real.hasInv r))
-but is expected to have type
-  forall {x : Hyperreal} {r : Real}, (Not (Hyperreal.Infinitesimal x)) -> (Hyperreal.IsSt x r) -> (Hyperreal.IsSt (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x) (Inv.inv.{0} Real Real.instInvReal r))
-Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_inv Hyperreal.IsSt.invₓ'. -/
 theorem Hyperreal.IsSt.inv {x : ℝ*} {r : ℝ} (hi : ¬Infinitesimal x) : IsSt x r → IsSt x⁻¹ r⁻¹ :=
   fun hxr =>
   have h : x ≠ 0 := fun h => hi (h.symm ▸ infinitesimal_zero)
@@ -1623,12 +1031,6 @@ theorem Hyperreal.IsSt.inv {x : ℝ*} {r : ℝ} (hi : ¬Infinitesimal x) : IsSt
     H'' ▸ hs
 #align hyperreal.is_st_inv Hyperreal.IsSt.inv
 
-/- warning: hyperreal.st_inv -> Hyperreal.st_inv is a dubious translation:
-lean 3 declaration is
-  forall (x : Hyperreal), Eq.{1} Real (Hyperreal.st (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (Inv.inv.{0} Real Real.hasInv (Hyperreal.st x))
-but is expected to have type
-  forall (x : Hyperreal), Eq.{1} Real (Hyperreal.st (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)) (Inv.inv.{0} Real Real.instInvReal (Hyperreal.st x))
-Case conversion may be inaccurate. Consider using '#align hyperreal.st_inv Hyperreal.st_invₓ'. -/
 theorem st_inv (x : ℝ*) : st x⁻¹ = (st x)⁻¹ :=
   by
   by_cases h0 : x = 0
@@ -1657,12 +1059,6 @@ theorem infinite_omega : Infinite ω :=
 #align hyperreal.infinite_omega Hyperreal.infinite_omega
 -/
 
-/- warning: hyperreal.infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos -> Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_posₓ'. -/
 theorem infinitePos_mul_of_infinitePos_not_infinitesimal_pos {x y : ℝ*} :
     InfinitePos x → ¬Infinitesimal y → 0 < y → InfinitePos (x * y) := fun hx hy₁ hy₂ r =>
   have hy₁' := not_forall.mp (by rw [infinitesimal_def] at hy₁ <;> exact hy₁)
@@ -1673,140 +1069,68 @@ theorem infinitePos_mul_of_infinitePos_not_infinitesimal_pos {x y : ℝ*} :
       exact mul_lt_mul (hx (r / r₁)) hyr.2 (coe_lt_coe.2 hyr.1) (le_of_lt (hx 0))
 #align hyperreal.infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos
 
-/- warning: hyperreal.infinite_pos_mul_of_not_infinitesimal_pos_infinite_pos -> Hyperreal.infinitePos_mul_of_not_infinitesimal_pos_infinitePos is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_mul_of_not_infinitesimal_pos_infinite_pos Hyperreal.infinitePos_mul_of_not_infinitesimal_pos_infinitePosₓ'. -/
 theorem infinitePos_mul_of_not_infinitesimal_pos_infinitePos {x y : ℝ*} :
     ¬Infinitesimal x → 0 < x → InfinitePos y → InfinitePos (x * y) := fun hx hp hy => by
   rw [mul_comm] <;> exact infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos hy hx hp
 #align hyperreal.infinite_pos_mul_of_not_infinitesimal_pos_infinite_pos Hyperreal.infinitePos_mul_of_not_infinitesimal_pos_infinitePos
 
-/- warning: hyperreal.infinite_pos_mul_of_infinite_neg_not_infinitesimal_neg -> Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) y (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) y (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_mul_of_infinite_neg_not_infinitesimal_neg Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_negₓ'. -/
 theorem infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg {x y : ℝ*} :
     InfiniteNeg x → ¬Infinitesimal y → y < 0 → InfinitePos (x * y) := by
   rw [infinite_neg_iff_infinite_pos_neg, ← neg_pos, ← neg_mul_neg, infinitesimal_neg_iff] <;>
     exact infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos
 #align hyperreal.infinite_pos_mul_of_infinite_neg_not_infinitesimal_neg Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg
 
-/- warning: hyperreal.infinite_pos_mul_of_not_infinitesimal_neg_infinite_neg -> Hyperreal.infinitePos_mul_of_not_infinitesimal_neg_infiniteNeg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_mul_of_not_infinitesimal_neg_infinite_neg Hyperreal.infinitePos_mul_of_not_infinitesimal_neg_infiniteNegₓ'. -/
 theorem infinitePos_mul_of_not_infinitesimal_neg_infiniteNeg {x y : ℝ*} :
     ¬Infinitesimal x → x < 0 → InfiniteNeg y → InfinitePos (x * y) := fun hx hp hy => by
   rw [mul_comm] <;> exact infinite_pos_mul_of_infinite_neg_not_infinitesimal_neg hy hx hp
 #align hyperreal.infinite_pos_mul_of_not_infinitesimal_neg_infinite_neg Hyperreal.infinitePos_mul_of_not_infinitesimal_neg_infiniteNeg
 
-/- warning: hyperreal.infinite_neg_mul_of_infinite_pos_not_infinitesimal_neg -> Hyperreal.infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) y (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) y (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_mul_of_infinite_pos_not_infinitesimal_neg Hyperreal.infiniteNeg_mul_of_infinitePos_not_infinitesimal_negₓ'. -/
 theorem infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg {x y : ℝ*} :
     InfinitePos x → ¬Infinitesimal y → y < 0 → InfiniteNeg (x * y) := by
   rw [infinite_neg_iff_infinite_pos_neg, ← neg_pos, neg_mul_eq_mul_neg, infinitesimal_neg_iff] <;>
     exact infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos
 #align hyperreal.infinite_neg_mul_of_infinite_pos_not_infinitesimal_neg Hyperreal.infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg
 
-/- warning: hyperreal.infinite_neg_mul_of_not_infinitesimal_neg_infinite_pos -> Hyperreal.infiniteNeg_mul_of_not_infinitesimal_neg_infinitePos is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_mul_of_not_infinitesimal_neg_infinite_pos Hyperreal.infiniteNeg_mul_of_not_infinitesimal_neg_infinitePosₓ'. -/
 theorem infiniteNeg_mul_of_not_infinitesimal_neg_infinitePos {x y : ℝ*} :
     ¬Infinitesimal x → x < 0 → InfinitePos y → InfiniteNeg (x * y) := fun hx hp hy => by
   rw [mul_comm] <;> exact infinite_neg_mul_of_infinite_pos_not_infinitesimal_neg hy hx hp
 #align hyperreal.infinite_neg_mul_of_not_infinitesimal_neg_infinite_pos Hyperreal.infiniteNeg_mul_of_not_infinitesimal_neg_infinitePos
 
-/- warning: hyperreal.infinite_neg_mul_of_infinite_neg_not_infinitesimal_pos -> Hyperreal.infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_mul_of_infinite_neg_not_infinitesimal_pos Hyperreal.infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_posₓ'. -/
 theorem infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos {x y : ℝ*} :
     InfiniteNeg x → ¬Infinitesimal y → 0 < y → InfiniteNeg (x * y) := by
   rw [infinite_neg_iff_infinite_pos_neg, infinite_neg_iff_infinite_pos_neg, neg_mul_eq_neg_mul] <;>
     exact infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos
 #align hyperreal.infinite_neg_mul_of_infinite_neg_not_infinitesimal_pos Hyperreal.infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos
 
-/- warning: hyperreal.infinite_neg_mul_of_not_infinitesimal_pos_infinite_neg -> Hyperreal.infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNeg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_mul_of_not_infinitesimal_pos_infinite_neg Hyperreal.infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNegₓ'. -/
 theorem infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNeg {x y : ℝ*} :
     ¬Infinitesimal x → 0 < x → InfiniteNeg y → InfiniteNeg (x * y) := fun hx hp hy => by
   rw [mul_comm] <;> exact infinite_neg_mul_of_infinite_neg_not_infinitesimal_pos hy hx hp
 #align hyperreal.infinite_neg_mul_of_not_infinitesimal_pos_infinite_neg Hyperreal.infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNeg
 
-/- warning: hyperreal.infinite_pos_mul_infinite_pos -> Hyperreal.infinitePos_mul_infinitePos is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_mul_infinite_pos Hyperreal.infinitePos_mul_infinitePosₓ'. -/
 theorem infinitePos_mul_infinitePos {x y : ℝ*} :
     InfinitePos x → InfinitePos y → InfinitePos (x * y) := fun hx hy =>
   infinitePos_mul_of_infinitePos_not_infinitesimal_pos hx
     (Hyperreal.InfinitePos.not_infinitesimal hy) (hy 0)
 #align hyperreal.infinite_pos_mul_infinite_pos Hyperreal.infinitePos_mul_infinitePos
 
-/- warning: hyperreal.infinite_neg_mul_infinite_neg -> Hyperreal.infiniteNeg_mul_infiniteNeg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_mul_infinite_neg Hyperreal.infiniteNeg_mul_infiniteNegₓ'. -/
 theorem infiniteNeg_mul_infiniteNeg {x y : ℝ*} :
     InfiniteNeg x → InfiniteNeg y → InfinitePos (x * y) := fun hx hy =>
   infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg hx
     (Hyperreal.InfiniteNeg.not_infinitesimal hy) (hy 0)
 #align hyperreal.infinite_neg_mul_infinite_neg Hyperreal.infiniteNeg_mul_infiniteNeg
 
-/- warning: hyperreal.infinite_pos_mul_infinite_neg -> Hyperreal.infinitePos_mul_infiniteNeg is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_mul_infinite_neg Hyperreal.infinitePos_mul_infiniteNegₓ'. -/
 theorem infinitePos_mul_infiniteNeg {x y : ℝ*} :
     InfinitePos x → InfiniteNeg y → InfiniteNeg (x * y) := fun hx hy =>
   infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg hx
     (Hyperreal.InfiniteNeg.not_infinitesimal hy) (hy 0)
 #align hyperreal.infinite_pos_mul_infinite_neg Hyperreal.infinitePos_mul_infiniteNeg
 
-/- warning: hyperreal.infinite_neg_mul_infinite_pos -> Hyperreal.infiniteNeg_mul_infinitePos is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_mul_infinite_pos Hyperreal.infiniteNeg_mul_infinitePosₓ'. -/
 theorem infiniteNeg_mul_infinitePos {x y : ℝ*} :
     InfiniteNeg x → InfinitePos y → InfiniteNeg (x * y) := fun hx hy =>
   infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos hx
     (Hyperreal.InfinitePos.not_infinitesimal hy) (hy 0)
 #align hyperreal.infinite_neg_mul_infinite_pos Hyperreal.infiniteNeg_mul_infinitePos
 
-/- warning: hyperreal.infinite_mul_of_infinite_not_infinitesimal -> Hyperreal.infinite_mul_of_infinite_not_infinitesimal is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.Infinite x) -> (Not (Hyperreal.Infinitesimal y)) -> (Hyperreal.Infinite (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.Infinite x) -> (Not (Hyperreal.Infinitesimal y)) -> (Hyperreal.Infinite (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_mul_of_infinite_not_infinitesimal Hyperreal.infinite_mul_of_infinite_not_infinitesimalₓ'. -/
 theorem infinite_mul_of_infinite_not_infinitesimal {x y : ℝ*} :
     Infinite x → ¬Infinitesimal y → Infinite (x * y) := fun hx hy =>
   have h0 : y < 0 ∨ 0 < y := lt_or_gt_of_ne fun H0 => hy (Eq.substr H0 (isSt_refl_real 0))
@@ -1819,23 +1143,11 @@ theorem infinite_mul_of_infinite_not_infinitesimal {x y : ℝ*} :
       fun H0 Hx => Or.inr (infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos Hx hy H0))
 #align hyperreal.infinite_mul_of_infinite_not_infinitesimal Hyperreal.infinite_mul_of_infinite_not_infinitesimal
 
-/- warning: hyperreal.infinite_mul_of_not_infinitesimal_infinite -> Hyperreal.infinite_mul_of_not_infinitesimal_infinite is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (Hyperreal.Infinite y) -> (Hyperreal.Infinite (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (Hyperreal.Infinite y) -> (Hyperreal.Infinite (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_mul_of_not_infinitesimal_infinite Hyperreal.infinite_mul_of_not_infinitesimal_infiniteₓ'. -/
 theorem infinite_mul_of_not_infinitesimal_infinite {x y : ℝ*} :
     ¬Infinitesimal x → Infinite y → Infinite (x * y) := fun hx hy => by
   rw [mul_comm] <;> exact infinite_mul_of_infinite_not_infinitesimal hy hx
 #align hyperreal.infinite_mul_of_not_infinitesimal_infinite Hyperreal.infinite_mul_of_not_infinitesimal_infinite
 
-/- warning: hyperreal.infinite.mul -> Hyperreal.Infinite.mul is a dubious translation:
-lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.Infinite x) -> (Hyperreal.Infinite y) -> (Hyperreal.Infinite (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
-but is expected to have type
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.Infinite x) -> (Hyperreal.Infinite y) -> (Hyperreal.Infinite (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
-Case conversion may be inaccurate. Consider using '#align hyperreal.infinite.mul Hyperreal.Infinite.mulₓ'. -/
 theorem Infinite.mul {x y : ℝ*} : Infinite x → Infinite y → Infinite (x * y) := fun hx hy =>
   infinite_mul_of_infinite_not_infinitesimal hx (Hyperreal.Infinite.not_infinitesimal hy)
 #align hyperreal.infinite.mul Hyperreal.Infinite.mul

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

@@ -1249,8 +1249,7 @@ theorem Hyperreal.IsSt.mul {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
   Exists.cases_on h fun u h' =>
     Exists.cases_on h' fun t ⟨hu, ht⟩ => by
       by_cases hs : s = 0
-      · apply is_st_iff_abs_sub_lt_delta.mpr
-        intro d hd
+      · apply is_st_iff_abs_sub_lt_delta.mpr; intro d hd
         have hys' : _ :=
           is_st_iff_abs_sub_lt_delta.mp hys (d / t)
             (div_pos hd (coe_pos.1 (lt_of_le_of_lt (abs_nonneg x) ht)))
@@ -1478,8 +1477,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_sub_is_st Hyperreal.IsSt.infinitesimal_subₓ'. -/
 theorem Hyperreal.IsSt.infinitesimal_sub {x : ℝ*} {r : ℝ} (hxr : IsSt x r) :
     Infinitesimal (x - r) :=
-  show IsSt (x - r) 0 by
-    rw [sub_eq_add_neg, ← add_neg_self r]
+  show IsSt (x - r) 0 by rw [sub_eq_add_neg, ← add_neg_self r];
     exact is_st_add hxr (is_st_refl_real (-r))
 #align hyperreal.infinitesimal_sub_is_st Hyperreal.IsSt.infinitesimal_sub
 

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

@@ -495,7 +495,6 @@ private theorem is_st_unique' (x : ℝ*) (r s : ℝ) (hr : IsSt x r) (hs : IsSt
   norm_cast  at *
   rw [h] at hs'
   exact not_lt_of_lt hs' hr'
-#align hyperreal.is_st_unique' hyperreal.is_st_unique'
 
 #print Hyperreal.IsSt.unique /-
 theorem Hyperreal.IsSt.unique {x : ℝ*} {r s : ℝ} (hr : IsSt x r) (hs : IsSt x s) : r = s :=
@@ -1235,7 +1234,6 @@ private theorem is_st_mul' {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
               _)
           _ = (d : ℝ*) := by rw [mul_one, add_halves]
           
-#align hyperreal.is_st_mul' hyperreal.is_st_mul'
 
 /- warning: hyperreal.is_st_mul -> Hyperreal.IsSt.mul is a dubious translation:
 lean 3 declaration is
@@ -1852,15 +1850,12 @@ open Positivity
 
 private theorem hyperreal_coe_ne_zero {r : ℝ} : r ≠ 0 → (r : ℝ*) ≠ 0 :=
   Hyperreal.coe_ne_zero.2
-#align tactic.hyperreal_coe_ne_zero tactic.hyperreal_coe_ne_zero
 
 private theorem hyperreal_coe_nonneg {r : ℝ} : 0 ≤ r → 0 ≤ (r : ℝ*) :=
   Hyperreal.coe_nonneg.2
-#align tactic.hyperreal_coe_nonneg tactic.hyperreal_coe_nonneg
 
 private theorem hyperreal_coe_pos {r : ℝ} : 0 < r → 0 < (r : ℝ*) :=
   Hyperreal.coe_pos.2
-#align tactic.hyperreal_coe_pos tactic.hyperreal_coe_pos
 
 /-- Extension for the `positivity` tactic: cast from `ℝ` to `ℝ*`. -/
 @[positivity]

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

@@ -209,7 +209,7 @@ theorem coe_sub (x y : ℝ) : ↑(x - y) = (x - y : ℝ*) :=
 
 /- warning: hyperreal.coe_le_coe -> Hyperreal.coe_le_coe is a dubious translation:
 lean 3 declaration is
-  forall {x : Real} {y : Real}, Iff (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y)) (LE.le.{0} Real Real.hasLe x y)
+  forall {x : Real} {y : Real}, Iff (LE.le.{0} Hyperreal (Preorder.toHasLe.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y)) (LE.le.{0} Real Real.hasLe x y)
 but is expected to have type
   forall {x : Real} {y : Real}, Iff (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal x) (Hyperreal.ofReal y)) (LE.le.{0} Real Real.instLEReal x y)
 Case conversion may be inaccurate. Consider using '#align hyperreal.coe_le_coe Hyperreal.coe_le_coeₓ'. -/
@@ -220,7 +220,7 @@ theorem coe_le_coe {x y : ℝ} : (x : ℝ*) ≤ y ↔ x ≤ y :=
 
 /- warning: hyperreal.coe_lt_coe -> Hyperreal.coe_lt_coe is a dubious translation:
 lean 3 declaration is
-  forall {x : Real} {y : Real}, Iff (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y)) (LT.lt.{0} Real Real.hasLt x y)
+  forall {x : Real} {y : Real}, Iff (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y)) (LT.lt.{0} Real Real.hasLt x y)
 but is expected to have type
   forall {x : Real} {y : Real}, Iff (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal x) (Hyperreal.ofReal y)) (LT.lt.{0} Real Real.instLTReal x y)
 Case conversion may be inaccurate. Consider using '#align hyperreal.coe_lt_coe Hyperreal.coe_lt_coeₓ'. -/
@@ -231,7 +231,7 @@ theorem coe_lt_coe {x y : ℝ} : (x : ℝ*) < y ↔ x < y :=
 
 /- warning: hyperreal.coe_nonneg -> Hyperreal.coe_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {x : Real}, Iff (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x)) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x)
+  forall {x : Real}, Iff (LE.le.{0} Hyperreal (Preorder.toHasLe.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x)) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x)
 but is expected to have type
   forall {x : Real}, Iff (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) (Hyperreal.ofReal x)) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x)
 Case conversion may be inaccurate. Consider using '#align hyperreal.coe_nonneg Hyperreal.coe_nonnegₓ'. -/
@@ -242,7 +242,7 @@ theorem coe_nonneg {x : ℝ} : 0 ≤ (x : ℝ*) ↔ 0 ≤ x :=
 
 /- warning: hyperreal.coe_pos -> Hyperreal.coe_pos is a dubious translation:
 lean 3 declaration is
-  forall {x : Real}, Iff (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x)) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x)
+  forall {x : Real}, Iff (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x)) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x)
 but is expected to have type
   forall {x : Real}, Iff (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) (Hyperreal.ofReal x)) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x)
 Case conversion may be inaccurate. Consider using '#align hyperreal.coe_pos Hyperreal.coe_posₓ'. -/
@@ -335,7 +335,7 @@ theorem inv_epsilon : ε⁻¹ = ω :=
 
 /- warning: hyperreal.omega_pos -> Hyperreal.omega_pos is a dubious translation:
 lean 3 declaration is
-  LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) Hyperreal.omega
+  LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) Hyperreal.omega
 but is expected to have type
   LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) Hyperreal.omega
 Case conversion may be inaccurate. Consider using '#align hyperreal.omega_pos Hyperreal.omega_posₓ'. -/
@@ -349,7 +349,7 @@ theorem omega_pos : 0 < ω :=
 
 /- warning: hyperreal.epsilon_pos -> Hyperreal.epsilon_pos is a dubious translation:
 lean 3 declaration is
-  LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) Hyperreal.epsilon
+  LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) Hyperreal.epsilon
 but is expected to have type
   LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) Hyperreal.epsilon
 Case conversion may be inaccurate. Consider using '#align hyperreal.epsilon_pos Hyperreal.epsilon_posₓ'. -/
@@ -389,7 +389,7 @@ theorem epsilon_mul_omega : ε * ω = 1 :=
 
 /- warning: hyperreal.lt_of_tendsto_zero_of_pos -> Hyperreal.lt_of_tendsto_zero_of_pos is a dubious translation:
 lean 3 declaration is
-  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Hyperreal.ofSeq f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)))
+  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Hyperreal.ofSeq f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)))
 but is expected to have type
   forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofSeq f) (Hyperreal.ofReal r)))
 Case conversion may be inaccurate. Consider using '#align hyperreal.lt_of_tendsto_zero_of_pos Hyperreal.lt_of_tendsto_zero_of_posₓ'. -/
@@ -409,7 +409,7 @@ theorem lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝
 
 /- warning: hyperreal.neg_lt_of_tendsto_zero_of_pos -> Hyperreal.neg_lt_of_tendsto_zero_of_pos is a dubious translation:
 lean 3 declaration is
-  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) (Hyperreal.ofSeq f)))
+  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) (Hyperreal.ofSeq f)))
 but is expected to have type
   forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (Hyperreal.ofReal r)) (Hyperreal.ofSeq f)))
 Case conversion may be inaccurate. Consider using '#align hyperreal.neg_lt_of_tendsto_zero_of_pos Hyperreal.neg_lt_of_tendsto_zero_of_posₓ'. -/
@@ -421,7 +421,7 @@ theorem neg_lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (
 
 /- warning: hyperreal.gt_of_tendsto_zero_of_neg -> Hyperreal.gt_of_tendsto_zero_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall {r : Real}, (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r) (Hyperreal.ofSeq f)))
+  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall {r : Real}, (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r) (Hyperreal.ofSeq f)))
 but is expected to have type
   forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall {r : Real}, (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal r) (Hyperreal.ofSeq f)))
 Case conversion may be inaccurate. Consider using '#align hyperreal.gt_of_tendsto_zero_of_neg Hyperreal.gt_of_tendsto_zero_of_negₓ'. -/
@@ -432,7 +432,7 @@ theorem gt_of_tendsto_zero_of_neg {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝
 
 /- warning: hyperreal.epsilon_lt_pos -> Hyperreal.epsilon_lt_pos is a dubious translation:
 lean 3 declaration is
-  forall (x : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) Hyperreal.epsilon ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x))
+  forall (x : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) Hyperreal.epsilon ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x))
 but is expected to have type
   forall (x : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) Hyperreal.epsilon (Hyperreal.ofReal x))
 Case conversion may be inaccurate. Consider using '#align hyperreal.epsilon_lt_pos Hyperreal.epsilon_lt_posₓ'. -/
@@ -517,7 +517,7 @@ theorem not_infinite_of_exists_st {x : ℝ*} : (∃ r : ℝ, IsSt x r) → ¬Inf
 
 /- warning: hyperreal.is_st_Sup -> Hyperreal.isSt_sSup is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Hyperreal.IsSt x (SupSet.sSup.{0} Real Real.hasSup (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y) x))))
+  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Hyperreal.IsSt x (SupSet.sSup.{0} Real Real.hasSup (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y) x))))
 but is expected to have type
   forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Hyperreal.IsSt x (SupSet.sSup.{0} Real Real.instSupSetReal (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal y) x))))
 Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_Sup Hyperreal.isSt_sSupₓ'. -/
@@ -551,7 +551,7 @@ theorem exists_st_of_not_infinite {x : ℝ*} (hni : ¬Infinite x) : ∃ r : ℝ,
 
 /- warning: hyperreal.st_eq_Sup -> Hyperreal.st_eq_sSup is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, Eq.{1} Real (Hyperreal.st x) (SupSet.sSup.{0} Real Real.hasSup (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y) x)))
+  forall {x : Hyperreal}, Eq.{1} Real (Hyperreal.st x) (SupSet.sSup.{0} Real Real.hasSup (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y) x)))
 but is expected to have type
   forall {x : Hyperreal}, Eq.{1} Real (Hyperreal.st x) (SupSet.sSup.{0} Real Real.instSupSetReal (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal y) x)))
 Case conversion may be inaccurate. Consider using '#align hyperreal.st_eq_Sup Hyperreal.st_eq_sSupₓ'. -/
@@ -679,7 +679,7 @@ theorem isSt_inj_real {r₁ r₂ s : ℝ} (h1 : IsSt r₁ s) (h2 : IsSt r₂ s)
 
 /- warning: hyperreal.is_st_iff_abs_sub_lt_delta -> Hyperreal.isSt_iff_abs_sub_lt_delta is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal} {r : Real}, Iff (Hyperreal.IsSt x r) (forall (δ : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (SubNegMonoid.toHasSub.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) δ)))
+  forall {x : Hyperreal} {r : Real}, Iff (Hyperreal.IsSt x r) (forall (δ : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (SubNegMonoid.toHasSub.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) δ)))
 but is expected to have type
   forall {x : Hyperreal} {r : Real}, Iff (Hyperreal.IsSt x r) (forall (δ : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (Ring.toSub.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal r))) (Hyperreal.ofReal δ)))
 Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_iff_abs_sub_lt_delta Hyperreal.isSt_iff_abs_sub_lt_deltaₓ'. -/
@@ -723,7 +723,7 @@ theorem Hyperreal.IsSt.sub {x y : ℝ*} {r s : ℝ} : IsSt x r → IsSt y s →
 
 /- warning: hyperreal.lt_of_is_st_lt -> Hyperreal.IsSt.lt is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (LT.lt.{0} Real Real.hasLt r s) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y)
+  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (LT.lt.{0} Real Real.hasLt r s) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y)
 but is expected to have type
   forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (LT.lt.{0} Real Real.instLTReal r s) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x y)
 Case conversion may be inaccurate. Consider using '#align hyperreal.lt_of_is_st_lt Hyperreal.IsSt.ltₓ'. -/
@@ -743,7 +743,7 @@ theorem Hyperreal.IsSt.lt {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
 
 /- warning: hyperreal.is_st_le_of_le -> Hyperreal.IsSt.le is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y) -> (LE.le.{0} Real Real.hasLe r s)
+  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (LE.le.{0} Hyperreal (Preorder.toHasLe.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y) -> (LE.le.{0} Real Real.hasLe r s)
 but is expected to have type
   forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x y) -> (LE.le.{0} Real Real.instLEReal r s)
 Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_le_of_le Hyperreal.IsSt.leₓ'. -/
@@ -753,7 +753,7 @@ theorem Hyperreal.IsSt.le {x y : ℝ*} {r s : ℝ} (hrx : IsSt x r) (hsy : IsSt
 
 /- warning: hyperreal.st_le_of_le -> Hyperreal.st_le_of_le is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y) -> (LE.le.{0} Real Real.hasLe (Hyperreal.st x) (Hyperreal.st y))
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (LE.le.{0} Hyperreal (Preorder.toHasLe.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y) -> (LE.le.{0} Real Real.hasLe (Hyperreal.st x) (Hyperreal.st y))
 but is expected to have type
   forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x y) -> (LE.le.{0} Real Real.instLEReal (Hyperreal.st x) (Hyperreal.st y))
 Case conversion may be inaccurate. Consider using '#align hyperreal.st_le_of_le Hyperreal.st_le_of_leₓ'. -/
@@ -765,7 +765,7 @@ theorem st_le_of_le {x y : ℝ*} (hix : ¬Infinite x) (hiy : ¬Infinite y) : x 
 
 /- warning: hyperreal.lt_of_st_lt -> Hyperreal.lt_of_st_lt is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (LT.lt.{0} Real Real.hasLt (Hyperreal.st x) (Hyperreal.st y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y)
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (LT.lt.{0} Real Real.hasLt (Hyperreal.st x) (Hyperreal.st y)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y)
 but is expected to have type
   forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (LT.lt.{0} Real Real.instLTReal (Hyperreal.st x) (Hyperreal.st y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x y)
 Case conversion may be inaccurate. Consider using '#align hyperreal.lt_of_st_lt Hyperreal.lt_of_st_ltₓ'. -/
@@ -782,7 +782,7 @@ theorem lt_of_st_lt {x y : ℝ*} (hix : ¬Infinite x) (hiy : ¬Infinite y) : st
 
 /- warning: hyperreal.infinite_pos_def -> Hyperreal.infinitePos_def is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r) x)
+  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r) x)
 but is expected to have type
   forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal r) x)
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_def Hyperreal.infinitePos_defₓ'. -/
@@ -791,7 +791,7 @@ theorem infinitePos_def {x : ℝ*} : InfinitePos x ↔ ∀ r : ℝ, ↑r < x :=
 
 /- warning: hyperreal.infinite_neg_def -> Hyperreal.infiniteNeg_def is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))
+  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))
 but is expected to have type
   forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal r))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_def Hyperreal.infiniteNeg_defₓ'. -/
@@ -820,7 +820,7 @@ theorem not_infinite_zero : ¬Infinite 0 := fun hI => Hyperreal.Infinite.ne_zero
 
 /- warning: hyperreal.pos_of_infinite_pos -> Hyperreal.InfinitePos.pos is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, (Hyperreal.InfinitePos x) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x)
+  forall {x : Hyperreal}, (Hyperreal.InfinitePos x) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x)
 but is expected to have type
   forall {x : Hyperreal}, (Hyperreal.InfinitePos x) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x)
 Case conversion may be inaccurate. Consider using '#align hyperreal.pos_of_infinite_pos Hyperreal.InfinitePos.posₓ'. -/
@@ -829,7 +829,7 @@ theorem Hyperreal.InfinitePos.pos {x : ℝ*} : InfinitePos x → 0 < x := fun hi
 
 /- warning: hyperreal.neg_of_infinite_neg -> Hyperreal.InfiniteNeg.lt_zero is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))))
+  forall {x : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))))
 but is expected to have type
   forall {x : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))
 Case conversion may be inaccurate. Consider using '#align hyperreal.neg_of_infinite_neg Hyperreal.InfiniteNeg.lt_zeroₓ'. -/
@@ -919,7 +919,7 @@ theorem Hyperreal.InfiniteNeg.not_infinitesimal {x : ℝ*} : InfiniteNeg x → 
 
 /- warning: hyperreal.infinite_pos_iff_infinite_and_pos -> Hyperreal.infinitePos_iff_infinite_and_pos is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (And (Hyperreal.Infinite x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x))
+  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (And (Hyperreal.Infinite x) (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x))
 but is expected to have type
   forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (And (Hyperreal.Infinite x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_iff_infinite_and_pos Hyperreal.infinitePos_iff_infinite_and_posₓ'. -/
@@ -930,7 +930,7 @@ theorem infinitePos_iff_infinite_and_pos {x : ℝ*} : InfinitePos x ↔ Infinite
 
 /- warning: hyperreal.infinite_neg_iff_infinite_and_neg -> Hyperreal.infiniteNeg_iff_infinite_and_neg is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (And (Hyperreal.Infinite x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))))
+  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (And (Hyperreal.Infinite x) (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))))
 but is expected to have type
   forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (And (Hyperreal.Infinite x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_iff_infinite_and_neg Hyperreal.infiniteNeg_iff_infinite_and_negₓ'. -/
@@ -941,7 +941,7 @@ theorem infiniteNeg_iff_infinite_and_neg {x : ℝ*} : InfiniteNeg x ↔ Infinite
 
 /- warning: hyperreal.infinite_pos_iff_infinite_of_pos -> Hyperreal.infinitePos_iff_infinite_of_pos is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x) -> (Iff (Hyperreal.InfinitePos x) (Hyperreal.Infinite x))
+  forall {x : Hyperreal}, (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x) -> (Iff (Hyperreal.InfinitePos x) (Hyperreal.Infinite x))
 but is expected to have type
   forall {x : Hyperreal}, (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x) -> (Iff (Hyperreal.InfinitePos x) (Hyperreal.Infinite x))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_iff_infinite_of_pos Hyperreal.infinitePos_iff_infinite_of_posₓ'. -/
@@ -951,7 +951,7 @@ theorem infinitePos_iff_infinite_of_pos {x : ℝ*} (hp : 0 < x) : InfinitePos x
 
 /- warning: hyperreal.infinite_pos_iff_infinite_of_nonneg -> Hyperreal.infinitePos_iff_infinite_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x) -> (Iff (Hyperreal.InfinitePos x) (Hyperreal.Infinite x))
+  forall {x : Hyperreal}, (LE.le.{0} Hyperreal (Preorder.toHasLe.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x) -> (Iff (Hyperreal.InfinitePos x) (Hyperreal.Infinite x))
 but is expected to have type
   forall {x : Hyperreal}, (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x) -> (Iff (Hyperreal.InfinitePos x) (Hyperreal.Infinite x))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_iff_infinite_of_nonneg Hyperreal.infinitePos_iff_infinite_of_nonnegₓ'. -/
@@ -965,7 +965,7 @@ theorem infinitePos_iff_infinite_of_nonneg {x : ℝ*} (hp : 0 ≤ x) : InfiniteP
 
 /- warning: hyperreal.infinite_neg_iff_infinite_of_neg -> Hyperreal.infiniteNeg_iff_infinite_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Iff (Hyperreal.InfiniteNeg x) (Hyperreal.Infinite x))
+  forall {x : Hyperreal}, (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Iff (Hyperreal.InfiniteNeg x) (Hyperreal.Infinite x))
 but is expected to have type
   forall {x : Hyperreal}, (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Iff (Hyperreal.InfiniteNeg x) (Hyperreal.Infinite x))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_iff_infinite_of_neg Hyperreal.infiniteNeg_iff_infinite_of_negₓ'. -/
@@ -1000,7 +1000,7 @@ theorem infinite_abs_iff {x : ℝ*} : Infinite x ↔ Infinite (|x|) := by
 
 /- warning: hyperreal.infinite_iff_abs_lt_abs -> Hyperreal.infinite_iff_abs_lt_abs is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.Infinite x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x))
+  forall {x : Hyperreal}, Iff (Hyperreal.Infinite x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x))
 but is expected to have type
   forall {x : Hyperreal}, Iff (Hyperreal.Infinite x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (Hyperreal.ofReal r)) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_iff_abs_lt_abs Hyperreal.infinite_iff_abs_lt_absₓ'. -/
@@ -1159,7 +1159,7 @@ theorem not_infinite_add {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) :
 
 /- warning: hyperreal.not_infinite_iff_exist_lt_gt -> Hyperreal.not_infinite_iff_exist_lt_gt is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Not (Hyperreal.Infinite x)) (Exists.{1} Real (fun (r : Real) => Exists.{1} Real (fun (s : Real) => And (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r) x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) s)))))
+  forall {x : Hyperreal}, Iff (Not (Hyperreal.Infinite x)) (Exists.{1} Real (fun (r : Real) => Exists.{1} Real (fun (s : Real) => And (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r) x) (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) s)))))
 but is expected to have type
   forall {x : Hyperreal}, Iff (Not (Hyperreal.Infinite x)) (Exists.{1} Real (fun (r : Real) => Exists.{1} Real (fun (s : Real) => And (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal r) x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal s)))))
 Case conversion may be inaccurate. Consider using '#align hyperreal.not_infinite_iff_exist_lt_gt Hyperreal.not_infinite_iff_exist_lt_gtₓ'. -/
@@ -1326,7 +1326,7 @@ theorem st_mul {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : st (x * y)
 
 /- warning: hyperreal.infinitesimal_def -> Hyperreal.infinitesimal_def is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.Infinitesimal x) (forall (r : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (And (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))))
+  forall {x : Hyperreal}, Iff (Hyperreal.Infinitesimal x) (forall (r : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (And (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) x) (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))))
 but is expected to have type
   forall {x : Hyperreal}, Iff (Hyperreal.Infinitesimal x) (forall (r : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (And (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (Hyperreal.ofReal r)) x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal r))))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_def Hyperreal.infinitesimal_defₓ'. -/
@@ -1336,7 +1336,7 @@ theorem infinitesimal_def {x : ℝ*} : Infinitesimal x ↔ ∀ r : ℝ, 0 < r 
 
 /- warning: hyperreal.lt_of_pos_of_infinitesimal -> Hyperreal.lt_of_pos_of_infinitesimal is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)))
+  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)))
 but is expected to have type
   forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal r)))
 Case conversion may be inaccurate. Consider using '#align hyperreal.lt_of_pos_of_infinitesimal Hyperreal.lt_of_pos_of_infinitesimalₓ'. -/
@@ -1346,7 +1346,7 @@ theorem lt_of_pos_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r : ℝ,
 
 /- warning: hyperreal.lt_neg_of_pos_of_infinitesimal -> Hyperreal.lt_neg_of_pos_of_infinitesimal is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) x))
+  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) x))
 but is expected to have type
   forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (Hyperreal.ofReal r)) x))
 Case conversion may be inaccurate. Consider using '#align hyperreal.lt_neg_of_pos_of_infinitesimal Hyperreal.lt_neg_of_pos_of_infinitesimalₓ'. -/
@@ -1356,7 +1356,7 @@ theorem lt_neg_of_pos_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r :
 
 /- warning: hyperreal.gt_of_neg_of_infinitesimal -> Hyperreal.gt_of_neg_of_infinitesimal is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r) x))
+  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r) x))
 but is expected to have type
   forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal r) x))
 Case conversion may be inaccurate. Consider using '#align hyperreal.gt_of_neg_of_infinitesimal Hyperreal.gt_of_neg_of_infinitesimalₓ'. -/
@@ -1367,7 +1367,7 @@ theorem gt_of_neg_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r : ℝ,
 
 /- warning: hyperreal.abs_lt_real_iff_infinitesimal -> Hyperreal.abs_lt_real_iff_infinitesimal is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.Infinitesimal x) (forall (r : Real), (Ne.{1} Real r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))))
+  forall {x : Hyperreal}, Iff (Hyperreal.Infinitesimal x) (forall (r : Real), (Ne.{1} Real r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))))
 but is expected to have type
   forall {x : Hyperreal}, Iff (Hyperreal.Infinitesimal x) (forall (r : Real), (Ne.{1} Real r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (Hyperreal.ofReal r))))
 Case conversion may be inaccurate. Consider using '#align hyperreal.abs_lt_real_iff_infinitesimal Hyperreal.abs_lt_real_iff_infinitesimalₓ'. -/
@@ -1497,7 +1497,7 @@ theorem infinitesimal_sub_st {x : ℝ*} (hx : ¬Infinite x) : Infinitesimal (x -
 
 /- warning: hyperreal.infinite_pos_iff_infinitesimal_inv_pos -> Hyperreal.infinitePos_iff_infinitesimal_inv_pos is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (And (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)))
+  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (And (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)))
 but is expected to have type
   forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (And (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_iff_infinitesimal_inv_pos Hyperreal.infinitePos_iff_infinitesimal_inv_posₓ'. -/
@@ -1517,7 +1517,7 @@ theorem infinitePos_iff_infinitesimal_inv_pos {x : ℝ*} :
 
 /- warning: hyperreal.infinite_neg_iff_infinitesimal_inv_neg -> Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (And (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))))
+  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (And (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))))
 but is expected to have type
   forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (And (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_iff_infinitesimal_inv_neg Hyperreal.infiniteNeg_iff_infinitesimal_inv_negₓ'. -/
@@ -1567,7 +1567,7 @@ theorem infinite_iff_infinitesimal_inv {x : ℝ*} (h0 : x ≠ 0) : Infinite x 
 
 /- warning: hyperreal.infinitesimal_pos_iff_infinite_pos_inv -> Hyperreal.infinitesimal_pos_iff_infinitePos_inv is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (And (Hyperreal.Infinitesimal x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x))
+  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (And (Hyperreal.Infinitesimal x) (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x))
 but is expected to have type
   forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)) (And (Hyperreal.Infinitesimal x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_pos_iff_infinite_pos_inv Hyperreal.infinitesimal_pos_iff_infinitePos_invₓ'. -/
@@ -1578,7 +1578,7 @@ theorem infinitesimal_pos_iff_infinitePos_inv {x : ℝ*} :
 
 /- warning: hyperreal.infinitesimal_neg_iff_infinite_neg_inv -> Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (And (Hyperreal.Infinitesimal x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))))
+  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (And (Hyperreal.Infinitesimal x) (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))))
 but is expected to have type
   forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)) (And (Hyperreal.Infinitesimal x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_neg_iff_infinite_neg_inv Hyperreal.infinitesimal_neg_iff_infiniteNeg_invₓ'. -/
@@ -1663,7 +1663,7 @@ theorem infinite_omega : Infinite ω :=
 
 /- warning: hyperreal.infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos -> Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
 but is expected to have type
   forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_posₓ'. -/
@@ -1679,7 +1679,7 @@ theorem infinitePos_mul_of_infinitePos_not_infinitesimal_pos {x y : ℝ*} :
 
 /- warning: hyperreal.infinite_pos_mul_of_not_infinitesimal_pos_infinite_pos -> Hyperreal.infinitePos_mul_of_not_infinitesimal_pos_infinitePos is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
 but is expected to have type
   forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_mul_of_not_infinitesimal_pos_infinite_pos Hyperreal.infinitePos_mul_of_not_infinitesimal_pos_infinitePosₓ'. -/
@@ -1690,7 +1690,7 @@ theorem infinitePos_mul_of_not_infinitesimal_pos_infinitePos {x y : ℝ*} :
 
 /- warning: hyperreal.infinite_pos_mul_of_infinite_neg_not_infinitesimal_neg -> Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) y (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) y (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
 but is expected to have type
   forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) y (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_mul_of_infinite_neg_not_infinitesimal_neg Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_negₓ'. -/
@@ -1702,7 +1702,7 @@ theorem infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg {x y : ℝ*} :
 
 /- warning: hyperreal.infinite_pos_mul_of_not_infinitesimal_neg_infinite_neg -> Hyperreal.infinitePos_mul_of_not_infinitesimal_neg_infiniteNeg is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
 but is expected to have type
   forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_mul_of_not_infinitesimal_neg_infinite_neg Hyperreal.infinitePos_mul_of_not_infinitesimal_neg_infiniteNegₓ'. -/
@@ -1713,7 +1713,7 @@ theorem infinitePos_mul_of_not_infinitesimal_neg_infiniteNeg {x y : ℝ*} :
 
 /- warning: hyperreal.infinite_neg_mul_of_infinite_pos_not_infinitesimal_neg -> Hyperreal.infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) y (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) y (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
 but is expected to have type
   forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) y (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_mul_of_infinite_pos_not_infinitesimal_neg Hyperreal.infiniteNeg_mul_of_infinitePos_not_infinitesimal_negₓ'. -/
@@ -1725,7 +1725,7 @@ theorem infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg {x y : ℝ*} :
 
 /- warning: hyperreal.infinite_neg_mul_of_not_infinitesimal_neg_infinite_pos -> Hyperreal.infiniteNeg_mul_of_not_infinitesimal_neg_infinitePos is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
 but is expected to have type
   forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_mul_of_not_infinitesimal_neg_infinite_pos Hyperreal.infiniteNeg_mul_of_not_infinitesimal_neg_infinitePosₓ'. -/
@@ -1736,7 +1736,7 @@ theorem infiniteNeg_mul_of_not_infinitesimal_neg_infinitePos {x y : ℝ*} :
 
 /- warning: hyperreal.infinite_neg_mul_of_infinite_neg_not_infinitesimal_pos -> Hyperreal.infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
 but is expected to have type
   forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_mul_of_infinite_neg_not_infinitesimal_pos Hyperreal.infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_posₓ'. -/
@@ -1748,7 +1748,7 @@ theorem infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos {x y : ℝ*} :
 
 /- warning: hyperreal.infinite_neg_mul_of_not_infinitesimal_pos_infinite_neg -> Hyperreal.infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNeg is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toHasLt.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
 but is expected to have type
   forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
 Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_mul_of_not_infinitesimal_pos_infinite_neg Hyperreal.infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNegₓ'. -/

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

@@ -515,15 +515,15 @@ theorem not_infinite_of_exists_st {x : ℝ*} : (∃ r : ℝ, IsSt x r) → ¬Inf
 #align hyperreal.not_infinite_of_exists_st Hyperreal.not_infinite_of_exists_st
 -/
 
-/- warning: hyperreal.is_st_Sup -> Hyperreal.isSt_supₛ is a dubious translation:
+/- warning: hyperreal.is_st_Sup -> Hyperreal.isSt_sSup is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Hyperreal.IsSt x (SupSet.supₛ.{0} Real Real.hasSup (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y) x))))
+  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Hyperreal.IsSt x (SupSet.sSup.{0} Real Real.hasSup (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y) x))))
 but is expected to have type
-  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Hyperreal.IsSt x (SupSet.supₛ.{0} Real Real.instSupSetReal (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal y) x))))
-Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_Sup Hyperreal.isSt_supₛₓ'. -/
-theorem isSt_supₛ {x : ℝ*} (hni : ¬Infinite x) : IsSt x (supₛ { y : ℝ | (y : ℝ*) < x }) :=
+  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Hyperreal.IsSt x (SupSet.sSup.{0} Real Real.instSupSetReal (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal y) x))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_Sup Hyperreal.isSt_sSupₓ'. -/
+theorem isSt_sSup {x : ℝ*} (hni : ¬Infinite x) : IsSt x (sSup { y : ℝ | (y : ℝ*) < x }) :=
   let S : Set ℝ := { y : ℝ | (y : ℝ*) < x }
-  let R : _ := supₛ S
+  let R : _ := sSup S
   have hnile := not_forall.mp (not_or.mp hni).1
   have hnige := not_forall.mp (not_or.mp hni).2
   Exists.dcases_on hnile <|
@@ -536,26 +536,26 @@ theorem isSt_supₛ {x : ℝ*} (hni : ¬Infinite x) : IsSt x (supₛ { y : ℝ |
       ⟨lt_of_not_le fun c =>
           have hc : ∀ y ∈ S, y ≤ R - δ := fun y hy =>
             coe_le_coe.1 <| le_of_lt <| lt_of_lt_of_le hy c
-          not_lt_of_le (csupₛ_le HR₁ hc) <| sub_lt_self R hδ,
+          not_lt_of_le (csSup_le HR₁ hc) <| sub_lt_self R hδ,
         lt_of_not_le fun c =>
           have hc : ↑(R + δ / 2) < x :=
             lt_of_lt_of_le (add_lt_add_left (coe_lt_coe.2 (half_lt_self hδ)) R) c
-          not_lt_of_le (le_csupₛ HR₂ hc) <| (lt_add_iff_pos_right _).mpr <| half_pos hδ⟩
-#align hyperreal.is_st_Sup Hyperreal.isSt_supₛ
+          not_lt_of_le (le_csSup HR₂ hc) <| (lt_add_iff_pos_right _).mpr <| half_pos hδ⟩
+#align hyperreal.is_st_Sup Hyperreal.isSt_sSup
 
 #print Hyperreal.exists_st_of_not_infinite /-
 theorem exists_st_of_not_infinite {x : ℝ*} (hni : ¬Infinite x) : ∃ r : ℝ, IsSt x r :=
-  ⟨supₛ { y : ℝ | (y : ℝ*) < x }, isSt_supₛ hni⟩
+  ⟨sSup { y : ℝ | (y : ℝ*) < x }, isSt_sSup hni⟩
 #align hyperreal.exists_st_of_not_infinite Hyperreal.exists_st_of_not_infinite
 -/
 
-/- warning: hyperreal.st_eq_Sup -> Hyperreal.st_eq_supₛ is a dubious translation:
+/- warning: hyperreal.st_eq_Sup -> Hyperreal.st_eq_sSup is a dubious translation:
 lean 3 declaration is
-  forall {x : Hyperreal}, Eq.{1} Real (Hyperreal.st x) (SupSet.supₛ.{0} Real Real.hasSup (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y) x)))
+  forall {x : Hyperreal}, Eq.{1} Real (Hyperreal.st x) (SupSet.sSup.{0} Real Real.hasSup (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y) x)))
 but is expected to have type
-  forall {x : Hyperreal}, Eq.{1} Real (Hyperreal.st x) (SupSet.supₛ.{0} Real Real.instSupSetReal (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal y) x)))
-Case conversion may be inaccurate. Consider using '#align hyperreal.st_eq_Sup Hyperreal.st_eq_supₛₓ'. -/
-theorem st_eq_supₛ {x : ℝ*} : st x = supₛ { y : ℝ | (y : ℝ*) < x } :=
+  forall {x : Hyperreal}, Eq.{1} Real (Hyperreal.st x) (SupSet.sSup.{0} Real Real.instSupSetReal (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal y) x)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.st_eq_Sup Hyperreal.st_eq_sSupₓ'. -/
+theorem st_eq_sSup {x : ℝ*} : st x = sSup { y : ℝ | (y : ℝ*) < x } :=
   by
   unfold st; split_ifs
   · exact is_st_unique (Classical.choose_spec h) (is_st_Sup (not_infinite_of_exists_st h))
@@ -568,7 +568,7 @@ theorem st_eq_supₛ {x : ℝ*} : st x = supₛ { y : ℝ | (y : ℝ*) < x } :=
               False.elim (Set.not_mem_empty i hi)⟩ :
           { y : ℝ | (y : ℝ*) < x } = ∅)]
       exact real.Sup_empty.symm
-#align hyperreal.st_eq_Sup Hyperreal.st_eq_supₛ
+#align hyperreal.st_eq_Sup Hyperreal.st_eq_sSup
 
 #print Hyperreal.exists_st_iff_not_infinite /-
 theorem exists_st_iff_not_infinite {x : ℝ*} : (∃ r : ℝ, IsSt x r) ↔ ¬Infinite x :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -66,7 +66,7 @@ theorem coe_eq_zero {x : ℝ} : (x : ℝ*) = 0 ↔ x = 0 :=
 lean 3 declaration is
   forall {x : Real}, Iff (Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) (OfNat.ofNat.{0} Hyperreal 1 (OfNat.mk.{0} Hyperreal 1 (One.one.{0} Hyperreal (AddMonoidWithOne.toOne.{0} Hyperreal (AddGroupWithOne.toAddMonoidWithOne.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
 but is expected to have type
-  forall {x : Real}, Iff (Eq.{1} Hyperreal (Hyperreal.ofReal x) (OfNat.ofNat.{0} Hyperreal 1 (One.toOfNat1.{0} Hyperreal (NonAssocRing.toOne.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+  forall {x : Real}, Iff (Eq.{1} Hyperreal (Hyperreal.ofReal x) (OfNat.ofNat.{0} Hyperreal 1 (One.toOfNat1.{0} Hyperreal (Semiring.toOne.{0} Hyperreal (StrictOrderedSemiring.toSemiring.{0} Hyperreal (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Hyperreal (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Hyperreal (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
 Case conversion may be inaccurate. Consider using '#align hyperreal.coe_eq_one Hyperreal.coe_eq_oneₓ'. -/
 @[simp, norm_cast]
 theorem coe_eq_one {x : ℝ} : (x : ℝ*) = 1 ↔ x = 1 :=
@@ -88,7 +88,7 @@ theorem coe_ne_zero {x : ℝ} : (x : ℝ*) ≠ 0 ↔ x ≠ 0 :=
 lean 3 declaration is
   forall {x : Real}, Iff (Ne.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) (OfNat.ofNat.{0} Hyperreal 1 (OfNat.mk.{0} Hyperreal 1 (One.one.{0} Hyperreal (AddMonoidWithOne.toOne.{0} Hyperreal (AddGroupWithOne.toAddMonoidWithOne.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) (Ne.{1} Real x (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
 but is expected to have type
-  forall {x : Real}, Iff (Ne.{1} Hyperreal (Hyperreal.ofReal x) (OfNat.ofNat.{0} Hyperreal 1 (One.toOfNat1.{0} Hyperreal (NonAssocRing.toOne.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))) (Ne.{1} Real x (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+  forall {x : Real}, Iff (Ne.{1} Hyperreal (Hyperreal.ofReal x) (OfNat.ofNat.{0} Hyperreal 1 (One.toOfNat1.{0} Hyperreal (Semiring.toOne.{0} Hyperreal (StrictOrderedSemiring.toSemiring.{0} Hyperreal (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Hyperreal (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Hyperreal (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))) (Ne.{1} Real x (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
 Case conversion may be inaccurate. Consider using '#align hyperreal.coe_ne_one Hyperreal.coe_ne_oneₓ'. -/
 @[norm_cast]
 theorem coe_ne_one {x : ℝ} : (x : ℝ*) ≠ 1 ↔ x ≠ 1 :=
@@ -99,7 +99,7 @@ theorem coe_ne_one {x : ℝ} : (x : ℝ*) ≠ 1 ↔ x ≠ 1 :=
 lean 3 declaration is
   Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Hyperreal 1 (OfNat.mk.{0} Hyperreal 1 (One.one.{0} Hyperreal (AddMonoidWithOne.toOne.{0} Hyperreal (AddGroupWithOne.toAddMonoidWithOne.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))
 but is expected to have type
-  Eq.{1} Hyperreal (Hyperreal.ofReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Hyperreal 1 (One.toOfNat1.{0} Hyperreal (NonAssocRing.toOne.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))
+  Eq.{1} Hyperreal (Hyperreal.ofReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Hyperreal 1 (One.toOfNat1.{0} Hyperreal (Semiring.toOne.{0} Hyperreal (StrictOrderedSemiring.toSemiring.{0} Hyperreal (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Hyperreal (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Hyperreal (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))
 Case conversion may be inaccurate. Consider using '#align hyperreal.coe_one Hyperreal.coe_oneₓ'. -/
 @[simp, norm_cast]
 theorem coe_one : ↑(1 : ℝ) = (1 : ℝ*) :=
@@ -381,7 +381,7 @@ theorem omega_ne_zero : ω ≠ 0 :=
 lean 3 declaration is
   Eq.{1} Hyperreal (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) Hyperreal.epsilon Hyperreal.omega) (OfNat.ofNat.{0} Hyperreal 1 (OfNat.mk.{0} Hyperreal 1 (One.one.{0} Hyperreal (AddMonoidWithOne.toOne.{0} Hyperreal (AddGroupWithOne.toAddMonoidWithOne.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))
 but is expected to have type
-  Eq.{1} Hyperreal (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) Hyperreal.epsilon Hyperreal.omega) (OfNat.ofNat.{0} Hyperreal 1 (One.toOfNat1.{0} Hyperreal (NonAssocRing.toOne.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))
+  Eq.{1} Hyperreal (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) Hyperreal.epsilon Hyperreal.omega) (OfNat.ofNat.{0} Hyperreal 1 (One.toOfNat1.{0} Hyperreal (Semiring.toOne.{0} Hyperreal (StrictOrderedSemiring.toSemiring.{0} Hyperreal (LinearOrderedSemiring.toStrictOrderedSemiring.{0} Hyperreal (LinearOrderedCommSemiring.toLinearOrderedSemiring.{0} Hyperreal (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))
 Case conversion may be inaccurate. Consider using '#align hyperreal.epsilon_mul_omega Hyperreal.epsilon_mul_omegaₓ'. -/
 theorem epsilon_mul_omega : ε * ω = 1 :=
   @inv_mul_cancel _ _ ω omega_ne_zero

mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Abhimanyu Pallavi Sudhir
 
 ! This file was ported from Lean 3 source module data.real.hyperreal
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Analysis.SpecificLimits.Basic
 
 /-!
 # Construction of the hyperreal numbers as an ultraproduct of real sequences.
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 -/
 
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -20,10 +20,12 @@ open Filter Filter.Germ
 
 open Topology Classical
 
+#print Hyperreal /-
 /-- Hyperreal numbers on the ultrafilter extending the cofinite filter -/
 def Hyperreal : Type :=
   Germ (hyperfilter ℕ : Filter ℕ) ℝ deriving LinearOrderedField, Inhabited
 #align hyperreal Hyperreal
+-/
 
 namespace Hyperreal
 
@@ -33,134 +35,272 @@ notation "ℝ*" => Hyperreal
 noncomputable instance : CoeTC ℝ ℝ* :=
   ⟨fun x => (↑x : Germ _ _)⟩
 
+#print Hyperreal.coe_eq_coe /-
 @[simp, norm_cast]
 theorem coe_eq_coe {x y : ℝ} : (x : ℝ*) = y ↔ x = y :=
   Germ.const_inj
 #align hyperreal.coe_eq_coe Hyperreal.coe_eq_coe
+-/
 
+#print Hyperreal.coe_ne_coe /-
 theorem coe_ne_coe {x y : ℝ} : (x : ℝ*) ≠ y ↔ x ≠ y :=
   coe_eq_coe.Not
 #align hyperreal.coe_ne_coe Hyperreal.coe_ne_coe
+-/
 
+/- warning: hyperreal.coe_eq_zero -> Hyperreal.coe_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Iff (Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {x : Real}, Iff (Eq.{1} Hyperreal (Hyperreal.ofReal x) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_eq_zero Hyperreal.coe_eq_zeroₓ'. -/
 @[simp, norm_cast]
 theorem coe_eq_zero {x : ℝ} : (x : ℝ*) = 0 ↔ x = 0 :=
   coe_eq_coe
 #align hyperreal.coe_eq_zero Hyperreal.coe_eq_zero
 
+/- warning: hyperreal.coe_eq_one -> Hyperreal.coe_eq_one is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Iff (Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) (OfNat.ofNat.{0} Hyperreal 1 (OfNat.mk.{0} Hyperreal 1 (One.one.{0} Hyperreal (AddMonoidWithOne.toOne.{0} Hyperreal (AddGroupWithOne.toAddMonoidWithOne.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  forall {x : Real}, Iff (Eq.{1} Hyperreal (Hyperreal.ofReal x) (OfNat.ofNat.{0} Hyperreal 1 (One.toOfNat1.{0} Hyperreal (NonAssocRing.toOne.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))) (Eq.{1} Real x (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_eq_one Hyperreal.coe_eq_oneₓ'. -/
 @[simp, norm_cast]
 theorem coe_eq_one {x : ℝ} : (x : ℝ*) = 1 ↔ x = 1 :=
   coe_eq_coe
 #align hyperreal.coe_eq_one Hyperreal.coe_eq_one
 
+/- warning: hyperreal.coe_ne_zero -> Hyperreal.coe_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Iff (Ne.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {x : Real}, Iff (Ne.{1} Hyperreal (Hyperreal.ofReal x) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (Ne.{1} Real x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_ne_zero Hyperreal.coe_ne_zeroₓ'. -/
 @[norm_cast]
 theorem coe_ne_zero {x : ℝ} : (x : ℝ*) ≠ 0 ↔ x ≠ 0 :=
   coe_ne_coe
 #align hyperreal.coe_ne_zero Hyperreal.coe_ne_zero
 
+/- warning: hyperreal.coe_ne_one -> Hyperreal.coe_ne_one is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Iff (Ne.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) (OfNat.ofNat.{0} Hyperreal 1 (OfNat.mk.{0} Hyperreal 1 (One.one.{0} Hyperreal (AddMonoidWithOne.toOne.{0} Hyperreal (AddGroupWithOne.toAddMonoidWithOne.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) (Ne.{1} Real x (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  forall {x : Real}, Iff (Ne.{1} Hyperreal (Hyperreal.ofReal x) (OfNat.ofNat.{0} Hyperreal 1 (One.toOfNat1.{0} Hyperreal (NonAssocRing.toOne.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))) (Ne.{1} Real x (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_ne_one Hyperreal.coe_ne_oneₓ'. -/
 @[norm_cast]
 theorem coe_ne_one {x : ℝ} : (x : ℝ*) ≠ 1 ↔ x ≠ 1 :=
   coe_ne_coe
 #align hyperreal.coe_ne_one Hyperreal.coe_ne_one
 
+/- warning: hyperreal.coe_one -> Hyperreal.coe_one is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Hyperreal 1 (OfNat.mk.{0} Hyperreal 1 (One.one.{0} Hyperreal (AddMonoidWithOne.toOne.{0} Hyperreal (AddGroupWithOne.toAddMonoidWithOne.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))
+but is expected to have type
+  Eq.{1} Hyperreal (Hyperreal.ofReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Hyperreal 1 (One.toOfNat1.{0} Hyperreal (NonAssocRing.toOne.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_one Hyperreal.coe_oneₓ'. -/
 @[simp, norm_cast]
 theorem coe_one : ↑(1 : ℝ) = (1 : ℝ*) :=
   rfl
 #align hyperreal.coe_one Hyperreal.coe_one
 
+/- warning: hyperreal.coe_zero -> Hyperreal.coe_zero is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))
+but is expected to have type
+  Eq.{1} Hyperreal (Hyperreal.ofReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_zero Hyperreal.coe_zeroₓ'. -/
 @[simp, norm_cast]
 theorem coe_zero : ↑(0 : ℝ) = (0 : ℝ*) :=
   rfl
 #align hyperreal.coe_zero Hyperreal.coe_zero
 
+/- warning: hyperreal.coe_inv -> Hyperreal.coe_inv is a dubious translation:
+lean 3 declaration is
+  forall (x : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (Inv.inv.{0} Real Real.hasInv x)) (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x))
+but is expected to have type
+  forall (x : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (Inv.inv.{0} Real Real.instInvReal x)) (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) (Hyperreal.ofReal x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_inv Hyperreal.coe_invₓ'. -/
 @[simp, norm_cast]
 theorem coe_inv (x : ℝ) : ↑x⁻¹ = (x⁻¹ : ℝ*) :=
   rfl
 #align hyperreal.coe_inv Hyperreal.coe_inv
 
+/- warning: hyperreal.coe_neg -> Hyperreal.coe_neg is a dubious translation:
+lean 3 declaration is
+  forall (x : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (Neg.neg.{0} Real Real.hasNeg x)) (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x))
+but is expected to have type
+  forall (x : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (Neg.neg.{0} Real Real.instNegReal x)) (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (Hyperreal.ofReal x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_neg Hyperreal.coe_negₓ'. -/
 @[simp, norm_cast]
 theorem coe_neg (x : ℝ) : ↑(-x) = (-x : ℝ*) :=
   rfl
 #align hyperreal.coe_neg Hyperreal.coe_neg
 
+/- warning: hyperreal.coe_add -> Hyperreal.coe_add is a dubious translation:
+lean 3 declaration is
+  forall (x : Real) (y : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) x y)) (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y))
+but is expected to have type
+  forall (x : Real) (y : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) x y)) (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) (Hyperreal.ofReal x) (Hyperreal.ofReal y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_add Hyperreal.coe_addₓ'. -/
 @[simp, norm_cast]
 theorem coe_add (x y : ℝ) : ↑(x + y) = (x + y : ℝ*) :=
   rfl
 #align hyperreal.coe_add Hyperreal.coe_add
 
+/- warning: hyperreal.coe_bit0 clashes with [anonymous] -> [anonymous]
+warning: hyperreal.coe_bit0 -> [anonymous] is a dubious translation:
+lean 3 declaration is
+  forall (x : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (bit0.{0} Real Real.hasAdd x)) (bit0.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x))
+but is expected to have type
+  forall {x : Type.{u}} {β : Type.{v}}, (Nat -> x -> β) -> Nat -> (List.{u} x) -> (List.{v} β)
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_bit0 [anonymous]ₓ'. -/
 @[simp, norm_cast]
-theorem coe_bit0 (x : ℝ) : ↑(bit0 x) = (bit0 x : ℝ*) :=
+theorem [anonymous] (x : ℝ) : ↑(bit0 x) = (bit0 x : ℝ*) :=
   rfl
-#align hyperreal.coe_bit0 Hyperreal.coe_bit0
-
+#align hyperreal.coe_bit0 [anonymous]
+
+/- warning: hyperreal.coe_bit1 clashes with [anonymous] -> [anonymous]
+warning: hyperreal.coe_bit1 -> [anonymous] is a dubious translation:
+lean 3 declaration is
+  forall (x : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (bit1.{0} Real Real.hasOne Real.hasAdd x)) (bit1.{0} Hyperreal (AddMonoidWithOne.toOne.{0} Hyperreal (AddGroupWithOne.toAddMonoidWithOne.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))) (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x))
+but is expected to have type
+  forall {x : Type.{u}} {β : Type.{v}}, (Nat -> x -> β) -> Nat -> (List.{u} x) -> (List.{v} β)
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_bit1 [anonymous]ₓ'. -/
 @[simp, norm_cast]
-theorem coe_bit1 (x : ℝ) : ↑(bit1 x) = (bit1 x : ℝ*) :=
+theorem [anonymous] (x : ℝ) : ↑(bit1 x) = (bit1 x : ℝ*) :=
   rfl
-#align hyperreal.coe_bit1 Hyperreal.coe_bit1
-
+#align hyperreal.coe_bit1 [anonymous]
+
+/- warning: hyperreal.coe_mul -> Hyperreal.coe_mul is a dubious translation:
+lean 3 declaration is
+  forall (x : Real) (y : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) x y)) (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y))
+but is expected to have type
+  forall (x : Real) (y : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) x y)) (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (Hyperreal.ofReal x) (Hyperreal.ofReal y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_mul Hyperreal.coe_mulₓ'. -/
 @[simp, norm_cast]
 theorem coe_mul (x y : ℝ) : ↑(x * y) = (x * y : ℝ*) :=
   rfl
 #align hyperreal.coe_mul Hyperreal.coe_mul
 
+/- warning: hyperreal.coe_div -> Hyperreal.coe_div is a dubious translation:
+lean 3 declaration is
+  forall (x : Real) (y : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) x y)) (HDiv.hDiv.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHDiv.{0} Hyperreal (DivInvMonoid.toHasDiv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y))
+but is expected to have type
+  forall (x : Real) (y : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) x y)) (HDiv.hDiv.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHDiv.{0} Hyperreal (LinearOrderedField.toDiv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)) (Hyperreal.ofReal x) (Hyperreal.ofReal y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_div Hyperreal.coe_divₓ'. -/
 @[simp, norm_cast]
 theorem coe_div (x y : ℝ) : ↑(x / y) = (x / y : ℝ*) :=
   rfl
 #align hyperreal.coe_div Hyperreal.coe_div
 
+/- warning: hyperreal.coe_sub -> Hyperreal.coe_sub is a dubious translation:
+lean 3 declaration is
+  forall (x : Real) (y : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) x y)) (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (SubNegMonoid.toHasSub.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y))
+but is expected to have type
+  forall (x : Real) (y : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) x y)) (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (Ring.toSub.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal x) (Hyperreal.ofReal y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_sub Hyperreal.coe_subₓ'. -/
 @[simp, norm_cast]
 theorem coe_sub (x y : ℝ) : ↑(x - y) = (x - y : ℝ*) :=
   rfl
 #align hyperreal.coe_sub Hyperreal.coe_sub
 
+/- warning: hyperreal.coe_le_coe -> Hyperreal.coe_le_coe is a dubious translation:
+lean 3 declaration is
+  forall {x : Real} {y : Real}, Iff (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y)) (LE.le.{0} Real Real.hasLe x y)
+but is expected to have type
+  forall {x : Real} {y : Real}, Iff (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal x) (Hyperreal.ofReal y)) (LE.le.{0} Real Real.instLEReal x y)
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_le_coe Hyperreal.coe_le_coeₓ'. -/
 @[simp, norm_cast]
 theorem coe_le_coe {x y : ℝ} : (x : ℝ*) ≤ y ↔ x ≤ y :=
   Germ.const_le_iff
 #align hyperreal.coe_le_coe Hyperreal.coe_le_coe
 
+/- warning: hyperreal.coe_lt_coe -> Hyperreal.coe_lt_coe is a dubious translation:
+lean 3 declaration is
+  forall {x : Real} {y : Real}, Iff (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y)) (LT.lt.{0} Real Real.hasLt x y)
+but is expected to have type
+  forall {x : Real} {y : Real}, Iff (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal x) (Hyperreal.ofReal y)) (LT.lt.{0} Real Real.instLTReal x y)
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_lt_coe Hyperreal.coe_lt_coeₓ'. -/
 @[simp, norm_cast]
 theorem coe_lt_coe {x y : ℝ} : (x : ℝ*) < y ↔ x < y :=
   Germ.const_lt_iff
 #align hyperreal.coe_lt_coe Hyperreal.coe_lt_coe
 
+/- warning: hyperreal.coe_nonneg -> Hyperreal.coe_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Iff (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x)) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x)
+but is expected to have type
+  forall {x : Real}, Iff (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) (Hyperreal.ofReal x)) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x)
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_nonneg Hyperreal.coe_nonnegₓ'. -/
 @[simp, norm_cast]
 theorem coe_nonneg {x : ℝ} : 0 ≤ (x : ℝ*) ↔ 0 ≤ x :=
   coe_le_coe
 #align hyperreal.coe_nonneg Hyperreal.coe_nonneg
 
+/- warning: hyperreal.coe_pos -> Hyperreal.coe_pos is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Iff (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x)) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x)
+but is expected to have type
+  forall {x : Real}, Iff (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) (Hyperreal.ofReal x)) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x)
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_pos Hyperreal.coe_posₓ'. -/
 @[simp, norm_cast]
 theorem coe_pos {x : ℝ} : 0 < (x : ℝ*) ↔ 0 < x :=
   coe_lt_coe
 #align hyperreal.coe_pos Hyperreal.coe_pos
 
+/- warning: hyperreal.coe_abs -> Hyperreal.coe_abs is a dubious translation:
+lean 3 declaration is
+  forall (x : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) x)) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x))
+but is expected to have type
+  forall (x : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (Hyperreal.ofReal x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_abs Hyperreal.coe_absₓ'. -/
 @[simp, norm_cast]
 theorem coe_abs (x : ℝ) : ((|x| : ℝ) : ℝ*) = |x| :=
   const_abs x
 #align hyperreal.coe_abs Hyperreal.coe_abs
 
+/- warning: hyperreal.coe_max -> Hyperreal.coe_max is a dubious translation:
+lean 3 declaration is
+  forall (x : Real) (y : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (LinearOrder.max.{0} Real Real.linearOrder x y)) (LinearOrder.max.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y))
+but is expected to have type
+  forall (x : Real) (y : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) x y)) (Max.max.{0} Hyperreal (LinearOrderedRing.toMax.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))) (Hyperreal.ofReal x) (Hyperreal.ofReal y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_max Hyperreal.coe_maxₓ'. -/
 @[simp, norm_cast]
 theorem coe_max (x y : ℝ) : ((max x y : ℝ) : ℝ*) = max x y :=
   Germ.const_max _ _
 #align hyperreal.coe_max Hyperreal.coe_max
 
+/- warning: hyperreal.coe_min -> Hyperreal.coe_min is a dubious translation:
+lean 3 declaration is
+  forall (x : Real) (y : Real), Eq.{1} Hyperreal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (LinearOrder.min.{0} Real Real.linearOrder x y)) (LinearOrder.min.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y))
+but is expected to have type
+  forall (x : Real) (y : Real), Eq.{1} Hyperreal (Hyperreal.ofReal (Min.min.{0} Real (LinearOrderedRing.toMin.{0} Real Real.instLinearOrderedRingReal) x y)) (Min.min.{0} Hyperreal (LinearOrderedRing.toMin.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))) (Hyperreal.ofReal x) (Hyperreal.ofReal y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.coe_min Hyperreal.coe_minₓ'. -/
 @[simp, norm_cast]
 theorem coe_min (x y : ℝ) : ((min x y : ℝ) : ℝ*) = min x y :=
   Germ.const_min _ _
 #align hyperreal.coe_min Hyperreal.coe_min
 
+#print Hyperreal.ofSeq /-
 /-- Construct a hyperreal number from a sequence of real numbers. -/
 noncomputable def ofSeq (f : ℕ → ℝ) : ℝ* :=
   (↑f : Germ (hyperfilter ℕ : Filter ℕ) ℝ)
 #align hyperreal.of_seq Hyperreal.ofSeq
+-/
 
+#print Hyperreal.epsilon /-
 /-- A sample infinitesimal hyperreal-/
 noncomputable def epsilon : ℝ* :=
   ofSeq fun n => n⁻¹
 #align hyperreal.epsilon Hyperreal.epsilon
+-/
 
+#print Hyperreal.omega /-
 /-- A sample infinite hyperreal-/
 noncomputable def omega : ℝ* :=
   ofSeq coe
 #align hyperreal.omega Hyperreal.omega
+-/
 
 -- mathport name: hyperreal.epsilon
 scoped notation "ε" => Hyperreal.epsilon
@@ -168,16 +308,34 @@ scoped notation "ε" => Hyperreal.epsilon
 -- mathport name: hyperreal.omega
 scoped notation "ω" => Hyperreal.omega
 
+/- warning: hyperreal.inv_omega -> Hyperreal.inv_omega is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Hyperreal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) Hyperreal.omega) Hyperreal.epsilon
+but is expected to have type
+  Eq.{1} Hyperreal (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) Hyperreal.omega) Hyperreal.epsilon
+Case conversion may be inaccurate. Consider using '#align hyperreal.inv_omega Hyperreal.inv_omegaₓ'. -/
 @[simp]
 theorem inv_omega : ω⁻¹ = ε :=
   rfl
 #align hyperreal.inv_omega Hyperreal.inv_omega
 
+/- warning: hyperreal.inv_epsilon -> Hyperreal.inv_epsilon is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Hyperreal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) Hyperreal.epsilon) Hyperreal.omega
+but is expected to have type
+  Eq.{1} Hyperreal (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) Hyperreal.epsilon) Hyperreal.omega
+Case conversion may be inaccurate. Consider using '#align hyperreal.inv_epsilon Hyperreal.inv_epsilonₓ'. -/
 @[simp]
 theorem inv_epsilon : ε⁻¹ = ω :=
   @inv_inv _ _ ω
 #align hyperreal.inv_epsilon Hyperreal.inv_epsilon
 
+/- warning: hyperreal.omega_pos -> Hyperreal.omega_pos is a dubious translation:
+lean 3 declaration is
+  LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) Hyperreal.omega
+but is expected to have type
+  LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) Hyperreal.omega
+Case conversion may be inaccurate. Consider using '#align hyperreal.omega_pos Hyperreal.omega_posₓ'. -/
 theorem omega_pos : 0 < ω :=
   Germ.coe_pos.2 <|
     mem_hyperfilter_of_finite_compl <|
@@ -186,22 +344,52 @@ theorem omega_pos : 0 < ω :=
       simp [Set.eq_singleton_iff_unique_mem]
 #align hyperreal.omega_pos Hyperreal.omega_pos
 
+/- warning: hyperreal.epsilon_pos -> Hyperreal.epsilon_pos is a dubious translation:
+lean 3 declaration is
+  LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) Hyperreal.epsilon
+but is expected to have type
+  LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) Hyperreal.epsilon
+Case conversion may be inaccurate. Consider using '#align hyperreal.epsilon_pos Hyperreal.epsilon_posₓ'. -/
 theorem epsilon_pos : 0 < ε :=
   inv_pos_of_pos omega_pos
 #align hyperreal.epsilon_pos Hyperreal.epsilon_pos
 
+/- warning: hyperreal.epsilon_ne_zero -> Hyperreal.epsilon_ne_zero is a dubious translation:
+lean 3 declaration is
+  Ne.{1} Hyperreal Hyperreal.epsilon (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))
+but is expected to have type
+  Ne.{1} Hyperreal Hyperreal.epsilon (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.epsilon_ne_zero Hyperreal.epsilon_ne_zeroₓ'. -/
 theorem epsilon_ne_zero : ε ≠ 0 :=
   epsilon_pos.ne'
 #align hyperreal.epsilon_ne_zero Hyperreal.epsilon_ne_zero
 
+/- warning: hyperreal.omega_ne_zero -> Hyperreal.omega_ne_zero is a dubious translation:
+lean 3 declaration is
+  Ne.{1} Hyperreal Hyperreal.omega (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))
+but is expected to have type
+  Ne.{1} Hyperreal Hyperreal.omega (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.omega_ne_zero Hyperreal.omega_ne_zeroₓ'. -/
 theorem omega_ne_zero : ω ≠ 0 :=
   omega_pos.ne'
 #align hyperreal.omega_ne_zero Hyperreal.omega_ne_zero
 
+/- warning: hyperreal.epsilon_mul_omega -> Hyperreal.epsilon_mul_omega is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Hyperreal (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) Hyperreal.epsilon Hyperreal.omega) (OfNat.ofNat.{0} Hyperreal 1 (OfNat.mk.{0} Hyperreal 1 (One.one.{0} Hyperreal (AddMonoidWithOne.toOne.{0} Hyperreal (AddGroupWithOne.toAddMonoidWithOne.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))
+but is expected to have type
+  Eq.{1} Hyperreal (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) Hyperreal.epsilon Hyperreal.omega) (OfNat.ofNat.{0} Hyperreal 1 (One.toOfNat1.{0} Hyperreal (NonAssocRing.toOne.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.epsilon_mul_omega Hyperreal.epsilon_mul_omegaₓ'. -/
 theorem epsilon_mul_omega : ε * ω = 1 :=
   @inv_mul_cancel _ _ ω omega_ne_zero
 #align hyperreal.epsilon_mul_omega Hyperreal.epsilon_mul_omega
 
+/- warning: hyperreal.lt_of_tendsto_zero_of_pos -> Hyperreal.lt_of_tendsto_zero_of_pos is a dubious translation:
+lean 3 declaration is
+  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Hyperreal.ofSeq f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)))
+but is expected to have type
+  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofSeq f) (Hyperreal.ofReal r)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.lt_of_tendsto_zero_of_pos Hyperreal.lt_of_tendsto_zero_of_posₓ'. -/
 theorem lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝 0)) :
     ∀ {r : ℝ}, 0 < r → ofSeq f < (r : ℝ*) :=
   by
@@ -216,49 +404,79 @@ theorem lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝
   exact mem_hyperfilter_of_finite_compl ((Set.finite_le_nat N).Subset hs)
 #align hyperreal.lt_of_tendsto_zero_of_pos Hyperreal.lt_of_tendsto_zero_of_pos
 
+/- warning: hyperreal.neg_lt_of_tendsto_zero_of_pos -> Hyperreal.neg_lt_of_tendsto_zero_of_pos is a dubious translation:
+lean 3 declaration is
+  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) (Hyperreal.ofSeq f)))
+but is expected to have type
+  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (Hyperreal.ofReal r)) (Hyperreal.ofSeq f)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.neg_lt_of_tendsto_zero_of_pos Hyperreal.neg_lt_of_tendsto_zero_of_posₓ'. -/
 theorem neg_lt_of_tendsto_zero_of_pos {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝 0)) :
     ∀ {r : ℝ}, 0 < r → (-r : ℝ*) < ofSeq f := fun r hr =>
   have hg := hf.neg
   neg_lt_of_neg_lt (by rw [neg_zero] at hg <;> exact lt_of_tendsto_zero_of_pos hg hr)
 #align hyperreal.neg_lt_of_tendsto_zero_of_pos Hyperreal.neg_lt_of_tendsto_zero_of_pos
 
+/- warning: hyperreal.gt_of_tendsto_zero_of_neg -> Hyperreal.gt_of_tendsto_zero_of_neg is a dubious translation:
+lean 3 declaration is
+  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (forall {r : Real}, (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r) (Hyperreal.ofSeq f)))
+but is expected to have type
+  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (forall {r : Real}, (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal r) (Hyperreal.ofSeq f)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.gt_of_tendsto_zero_of_neg Hyperreal.gt_of_tendsto_zero_of_negₓ'. -/
 theorem gt_of_tendsto_zero_of_neg {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝 0)) :
     ∀ {r : ℝ}, r < 0 → (r : ℝ*) < ofSeq f := fun r hr => by
   rw [← neg_neg r, coe_neg] <;> exact neg_lt_of_tendsto_zero_of_pos hf (neg_pos.mpr hr)
 #align hyperreal.gt_of_tendsto_zero_of_neg Hyperreal.gt_of_tendsto_zero_of_neg
 
+/- warning: hyperreal.epsilon_lt_pos -> Hyperreal.epsilon_lt_pos is a dubious translation:
+lean 3 declaration is
+  forall (x : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) Hyperreal.epsilon ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) x))
+but is expected to have type
+  forall (x : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) Hyperreal.epsilon (Hyperreal.ofReal x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.epsilon_lt_pos Hyperreal.epsilon_lt_posₓ'. -/
 theorem epsilon_lt_pos (x : ℝ) : 0 < x → ε < x :=
   lt_of_tendsto_zero_of_pos tendsto_inverse_atTop_nhds_0_nat
 #align hyperreal.epsilon_lt_pos Hyperreal.epsilon_lt_pos
 
+#print Hyperreal.IsSt /-
 /-- Standard part predicate -/
 def IsSt (x : ℝ*) (r : ℝ) :=
   ∀ δ : ℝ, 0 < δ → (r - δ : ℝ*) < x ∧ x < r + δ
 #align hyperreal.is_st Hyperreal.IsSt
+-/
 
+#print Hyperreal.st /-
 /-- Standard part function: like a "round" to ℝ instead of ℤ -/
 noncomputable def st : ℝ* → ℝ := fun x => if h : ∃ r, IsSt x r then Classical.choose h else 0
 #align hyperreal.st Hyperreal.st
+-/
 
+#print Hyperreal.Infinitesimal /-
 /-- A hyperreal number is infinitesimal if its standard part is 0 -/
 def Infinitesimal (x : ℝ*) :=
   IsSt x 0
 #align hyperreal.infinitesimal Hyperreal.Infinitesimal
+-/
 
+#print Hyperreal.InfinitePos /-
 /-- A hyperreal number is positive infinite if it is larger than all real numbers -/
 def InfinitePos (x : ℝ*) :=
   ∀ r : ℝ, ↑r < x
 #align hyperreal.infinite_pos Hyperreal.InfinitePos
+-/
 
+#print Hyperreal.InfiniteNeg /-
 /-- A hyperreal number is negative infinite if it is smaller than all real numbers -/
 def InfiniteNeg (x : ℝ*) :=
   ∀ r : ℝ, x < r
 #align hyperreal.infinite_neg Hyperreal.InfiniteNeg
+-/
 
+#print Hyperreal.Infinite /-
 /-- A hyperreal number is infinite if it is infinite positive or infinite negative -/
 def Infinite (x : ℝ*) :=
   InfinitePos x ∨ InfiniteNeg x
 #align hyperreal.infinite Hyperreal.Infinite
+-/
 
 /-!
 ### Some facts about `st`
@@ -276,20 +494,30 @@ private theorem is_st_unique' (x : ℝ*) (r s : ℝ) (hr : IsSt x r) (hs : IsSt
   exact not_lt_of_lt hs' hr'
 #align hyperreal.is_st_unique' hyperreal.is_st_unique'
 
-theorem isSt_unique {x : ℝ*} {r s : ℝ} (hr : IsSt x r) (hs : IsSt x s) : r = s :=
+#print Hyperreal.IsSt.unique /-
+theorem Hyperreal.IsSt.unique {x : ℝ*} {r s : ℝ} (hr : IsSt x r) (hs : IsSt x s) : r = s :=
   by
   rcases lt_trichotomy r s with (h | h | h)
   · exact False.elim (is_st_unique' x r s hr hs h)
   · exact h
   · exact False.elim (is_st_unique' x s r hs hr h)
-#align hyperreal.is_st_unique Hyperreal.isSt_unique
+#align hyperreal.is_st_unique Hyperreal.IsSt.unique
+-/
 
+#print Hyperreal.not_infinite_of_exists_st /-
 theorem not_infinite_of_exists_st {x : ℝ*} : (∃ r : ℝ, IsSt x r) → ¬Infinite x := fun he hi =>
   Exists.dcases_on he fun r hr =>
     hi.elim (fun hip => not_lt_of_lt (hr 2 zero_lt_two).2 (hip <| r + 2)) fun hin =>
       not_lt_of_lt (hr 2 zero_lt_two).1 (hin <| r - 2)
 #align hyperreal.not_infinite_of_exists_st Hyperreal.not_infinite_of_exists_st
+-/
 
+/- warning: hyperreal.is_st_Sup -> Hyperreal.isSt_supₛ is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Hyperreal.IsSt x (SupSet.supₛ.{0} Real Real.hasSup (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y) x))))
+but is expected to have type
+  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Hyperreal.IsSt x (SupSet.supₛ.{0} Real Real.instSupSetReal (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal y) x))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_Sup Hyperreal.isSt_supₛₓ'. -/
 theorem isSt_supₛ {x : ℝ*} (hni : ¬Infinite x) : IsSt x (supₛ { y : ℝ | (y : ℝ*) < x }) :=
   let S : Set ℝ := { y : ℝ | (y : ℝ*) < x }
   let R : _ := supₛ S
@@ -312,10 +540,18 @@ theorem isSt_supₛ {x : ℝ*} (hni : ¬Infinite x) : IsSt x (supₛ { y : ℝ |
           not_lt_of_le (le_csupₛ HR₂ hc) <| (lt_add_iff_pos_right _).mpr <| half_pos hδ⟩
 #align hyperreal.is_st_Sup Hyperreal.isSt_supₛ
 
+#print Hyperreal.exists_st_of_not_infinite /-
 theorem exists_st_of_not_infinite {x : ℝ*} (hni : ¬Infinite x) : ∃ r : ℝ, IsSt x r :=
   ⟨supₛ { y : ℝ | (y : ℝ*) < x }, isSt_supₛ hni⟩
 #align hyperreal.exists_st_of_not_infinite Hyperreal.exists_st_of_not_infinite
+-/
 
+/- warning: hyperreal.st_eq_Sup -> Hyperreal.st_eq_supₛ is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, Eq.{1} Real (Hyperreal.st x) (SupSet.supₛ.{0} Real Real.hasSup (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) y) x)))
+but is expected to have type
+  forall {x : Hyperreal}, Eq.{1} Real (Hyperreal.st x) (SupSet.supₛ.{0} Real Real.instSupSetReal (setOf.{0} Real (fun (y : Real) => LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal y) x)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.st_eq_Sup Hyperreal.st_eq_supₛₓ'. -/
 theorem st_eq_supₛ {x : ℝ*} : st x = supₛ { y : ℝ | (y : ℝ*) < x } :=
   by
   unfold st; split_ifs
@@ -331,36 +567,58 @@ theorem st_eq_supₛ {x : ℝ*} : st x = supₛ { y : ℝ | (y : ℝ*) < x } :=
       exact real.Sup_empty.symm
 #align hyperreal.st_eq_Sup Hyperreal.st_eq_supₛ
 
+#print Hyperreal.exists_st_iff_not_infinite /-
 theorem exists_st_iff_not_infinite {x : ℝ*} : (∃ r : ℝ, IsSt x r) ↔ ¬Infinite x :=
   ⟨not_infinite_of_exists_st, exists_st_of_not_infinite⟩
 #align hyperreal.exists_st_iff_not_infinite Hyperreal.exists_st_iff_not_infinite
+-/
 
+#print Hyperreal.infinite_iff_not_exists_st /-
 theorem infinite_iff_not_exists_st {x : ℝ*} : Infinite x ↔ ¬∃ r : ℝ, IsSt x r :=
   iff_not_comm.mp exists_st_iff_not_infinite
 #align hyperreal.infinite_iff_not_exists_st Hyperreal.infinite_iff_not_exists_st
+-/
 
-theorem st_infinite {x : ℝ*} (hi : Infinite x) : st x = 0 :=
+/- warning: hyperreal.st_infinite -> Hyperreal.Infinite.st_eq is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Hyperreal.Infinite x) -> (Eq.{1} Real (Hyperreal.st x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {x : Hyperreal}, (Hyperreal.Infinite x) -> (Eq.{1} Real (Hyperreal.st x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.st_infinite Hyperreal.Infinite.st_eqₓ'. -/
+theorem Hyperreal.Infinite.st_eq {x : ℝ*} (hi : Infinite x) : st x = 0 :=
   by
   unfold st; split_ifs
   · exact False.elim ((infinite_iff_not_exists_st.mp hi) h)
   · rfl
-#align hyperreal.st_infinite Hyperreal.st_infinite
+#align hyperreal.st_infinite Hyperreal.Infinite.st_eq
 
-theorem st_of_isSt {x : ℝ*} {r : ℝ} (hxr : IsSt x r) : st x = r :=
+#print Hyperreal.IsSt.st_eq /-
+theorem Hyperreal.IsSt.st_eq {x : ℝ*} {r : ℝ} (hxr : IsSt x r) : st x = r :=
   by
   unfold st; split_ifs
   · exact is_st_unique (Classical.choose_spec h) hxr
   · exact False.elim (h ⟨r, hxr⟩)
-#align hyperreal.st_of_is_st Hyperreal.st_of_isSt
+#align hyperreal.st_of_is_st Hyperreal.IsSt.st_eq
+-/
 
-theorem isSt_st_of_isSt {x : ℝ*} {r : ℝ} (hxr : IsSt x r) : IsSt x (st x) := by
+#print Hyperreal.IsSt.isSt_st /-
+theorem Hyperreal.IsSt.isSt_st {x : ℝ*} {r : ℝ} (hxr : IsSt x r) : IsSt x (st x) := by
   rwa [st_of_is_st hxr]
-#align hyperreal.is_st_st_of_is_st Hyperreal.isSt_st_of_isSt
+#align hyperreal.is_st_st_of_is_st Hyperreal.IsSt.isSt_st
+-/
 
+#print Hyperreal.isSt_st_of_exists_st /-
 theorem isSt_st_of_exists_st {x : ℝ*} (hx : ∃ r : ℝ, IsSt x r) : IsSt x (st x) :=
-  Exists.dcases_on hx fun r => isSt_st_of_isSt
+  Exists.dcases_on hx fun r => Hyperreal.IsSt.isSt_st
 #align hyperreal.is_st_st_of_exists_st Hyperreal.isSt_st_of_exists_st
+-/
 
+/- warning: hyperreal.is_st_st -> Hyperreal.isSt_st is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Ne.{1} Real (Hyperreal.st x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Hyperreal.IsSt x (Hyperreal.st x))
+but is expected to have type
+  forall {x : Hyperreal}, (Ne.{1} Real (Hyperreal.st x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Hyperreal.IsSt x (Hyperreal.st x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_st Hyperreal.isSt_stₓ'. -/
 theorem isSt_st {x : ℝ*} (hx : st x ≠ 0) : IsSt x (st x) :=
   by
   unfold st; split_ifs
@@ -368,60 +626,106 @@ theorem isSt_st {x : ℝ*} (hx : st x ≠ 0) : IsSt x (st x) :=
   · exact False.elim (hx (by unfold st <;> split_ifs <;> rfl))
 #align hyperreal.is_st_st Hyperreal.isSt_st
 
+#print Hyperreal.isSt_st' /-
 theorem isSt_st' {x : ℝ*} (hx : ¬Infinite x) : IsSt x (st x) :=
   isSt_st_of_exists_st <| exists_st_of_not_infinite hx
 #align hyperreal.is_st_st' Hyperreal.isSt_st'
+-/
 
+#print Hyperreal.isSt_refl_real /-
 theorem isSt_refl_real (r : ℝ) : IsSt r r := fun δ hδ =>
   ⟨sub_lt_self _ (coe_lt_coe.2 hδ), lt_add_of_pos_right _ (coe_lt_coe.2 hδ)⟩
 #align hyperreal.is_st_refl_real Hyperreal.isSt_refl_real
+-/
 
+#print Hyperreal.st_id_real /-
 theorem st_id_real (r : ℝ) : st r = r :=
-  st_of_isSt (isSt_refl_real r)
+  Hyperreal.IsSt.st_eq (isSt_refl_real r)
 #align hyperreal.st_id_real Hyperreal.st_id_real
+-/
 
+#print Hyperreal.eq_of_isSt_real /-
 theorem eq_of_isSt_real {r s : ℝ} : IsSt r s → r = s :=
-  isSt_unique (isSt_refl_real r)
+  Hyperreal.IsSt.unique (isSt_refl_real r)
 #align hyperreal.eq_of_is_st_real Hyperreal.eq_of_isSt_real
+-/
 
+#print Hyperreal.isSt_real_iff_eq /-
 theorem isSt_real_iff_eq {r s : ℝ} : IsSt r s ↔ r = s :=
   ⟨eq_of_isSt_real, fun hrs => by rw [hrs] <;> exact is_st_refl_real s⟩
 #align hyperreal.is_st_real_iff_eq Hyperreal.isSt_real_iff_eq
+-/
 
+#print Hyperreal.isSt_symm_real /-
 theorem isSt_symm_real {r s : ℝ} : IsSt r s ↔ IsSt s r := by
   rw [is_st_real_iff_eq, is_st_real_iff_eq, eq_comm]
 #align hyperreal.is_st_symm_real Hyperreal.isSt_symm_real
+-/
 
+#print Hyperreal.isSt_trans_real /-
 theorem isSt_trans_real {r s t : ℝ} : IsSt r s → IsSt s t → IsSt r t := by
   rw [is_st_real_iff_eq, is_st_real_iff_eq, is_st_real_iff_eq] <;> exact Eq.trans
 #align hyperreal.is_st_trans_real Hyperreal.isSt_trans_real
+-/
 
+#print Hyperreal.isSt_inj_real /-
 theorem isSt_inj_real {r₁ r₂ s : ℝ} (h1 : IsSt r₁ s) (h2 : IsSt r₂ s) : r₁ = r₂ :=
   Eq.trans (eq_of_isSt_real h1) (eq_of_isSt_real h2).symm
 #align hyperreal.is_st_inj_real Hyperreal.isSt_inj_real
+-/
 
+/- warning: hyperreal.is_st_iff_abs_sub_lt_delta -> Hyperreal.isSt_iff_abs_sub_lt_delta is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {r : Real}, Iff (Hyperreal.IsSt x r) (forall (δ : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) δ) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (SubNegMonoid.toHasSub.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) δ)))
+but is expected to have type
+  forall {x : Hyperreal} {r : Real}, Iff (Hyperreal.IsSt x r) (forall (δ : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) δ) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (Ring.toSub.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal r))) (Hyperreal.ofReal δ)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_iff_abs_sub_lt_delta Hyperreal.isSt_iff_abs_sub_lt_deltaₓ'. -/
 theorem isSt_iff_abs_sub_lt_delta {x : ℝ*} {r : ℝ} : IsSt x r ↔ ∀ δ : ℝ, 0 < δ → |x - r| < δ := by
   simp only [abs_sub_lt_iff, sub_lt_iff_lt_add, is_st, and_comm', add_comm]
 #align hyperreal.is_st_iff_abs_sub_lt_delta Hyperreal.isSt_iff_abs_sub_lt_delta
 
-theorem isSt_add {x y : ℝ*} {r s : ℝ} : IsSt x r → IsSt y s → IsSt (x + y) (r + s) :=
+/- warning: hyperreal.is_st_add -> Hyperreal.IsSt.add is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (Hyperreal.IsSt (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) r s))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (Hyperreal.IsSt (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) r s))
+Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_add Hyperreal.IsSt.addₓ'. -/
+theorem Hyperreal.IsSt.add {x y : ℝ*} {r s : ℝ} : IsSt x r → IsSt y s → IsSt (x + y) (r + s) :=
   fun hxr hys d hd =>
   have hxr' := hxr (d / 2) (half_pos hd)
   have hys' := hys (d / 2) (half_pos hd)
   ⟨by convert add_lt_add hxr'.1 hys'.1 using 1 <;> norm_cast <;> linarith, by
     convert add_lt_add hxr'.2 hys'.2 using 1 <;> norm_cast <;> linarith⟩
-#align hyperreal.is_st_add Hyperreal.isSt_add
-
-theorem isSt_neg {x : ℝ*} {r : ℝ} (hxr : IsSt x r) : IsSt (-x) (-r) := fun d hd =>
+#align hyperreal.is_st_add Hyperreal.IsSt.add
+
+/- warning: hyperreal.is_st_neg -> Hyperreal.IsSt.neg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {r : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) x) (Neg.neg.{0} Real Real.hasNeg r))
+but is expected to have type
+  forall {x : Hyperreal} {r : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) x) (Neg.neg.{0} Real Real.instNegReal r))
+Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_neg Hyperreal.IsSt.negₓ'. -/
+theorem Hyperreal.IsSt.neg {x : ℝ*} {r : ℝ} (hxr : IsSt x r) : IsSt (-x) (-r) := fun d hd =>
   show -(r : ℝ*) - d < -x ∧ -x < -r + d by cases hxr d hd <;> constructor <;> linarith
-#align hyperreal.is_st_neg Hyperreal.isSt_neg
-
-theorem isSt_sub {x y : ℝ*} {r s : ℝ} : IsSt x r → IsSt y s → IsSt (x - y) (r - s) := fun hxr hys =>
-  by rw [sub_eq_add_neg, sub_eq_add_neg] <;> exact is_st_add hxr (is_st_neg hys)
-#align hyperreal.is_st_sub Hyperreal.isSt_sub
-
+#align hyperreal.is_st_neg Hyperreal.IsSt.neg
+
+/- warning: hyperreal.is_st_sub -> Hyperreal.IsSt.sub is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (Hyperreal.IsSt (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (SubNegMonoid.toHasSub.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))) x y) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) r s))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (Hyperreal.IsSt (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (Ring.toSub.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x y) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) r s))
+Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_sub Hyperreal.IsSt.subₓ'. -/
+theorem Hyperreal.IsSt.sub {x y : ℝ*} {r s : ℝ} : IsSt x r → IsSt y s → IsSt (x - y) (r - s) :=
+  fun hxr hys => by rw [sub_eq_add_neg, sub_eq_add_neg] <;> exact is_st_add hxr (is_st_neg hys)
+#align hyperreal.is_st_sub Hyperreal.IsSt.sub
+
+/- warning: hyperreal.lt_of_is_st_lt -> Hyperreal.IsSt.lt is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (LT.lt.{0} Real Real.hasLt r s) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y)
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (LT.lt.{0} Real Real.instLTReal r s) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x y)
+Case conversion may be inaccurate. Consider using '#align hyperreal.lt_of_is_st_lt Hyperreal.IsSt.ltₓ'. -/
 -- (st x < st y) → (x < y) → (x ≤ y) → (st x ≤ st y)
-theorem lt_of_isSt_lt {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt y s) : r < s → x < y :=
+theorem Hyperreal.IsSt.lt {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt y s) : r < s → x < y :=
   fun hrs => by
   have hrs' : 0 < (s - r) / 2 := half_pos (sub_pos.mpr hrs)
   have hxr' := (hxr _ hrs').2
@@ -432,22 +736,40 @@ theorem lt_of_isSt_lt {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt y s)
   rw [H1] at hxr'
   rw [H2] at hys'
   exact lt_trans hxr' hys'
-#align hyperreal.lt_of_is_st_lt Hyperreal.lt_of_isSt_lt
-
-theorem isSt_le_of_le {x y : ℝ*} {r s : ℝ} (hrx : IsSt x r) (hsy : IsSt y s) : x ≤ y → r ≤ s := by
-  rw [← not_lt, ← not_lt, not_imp_not] <;> exact lt_of_is_st_lt hsy hrx
-#align hyperreal.is_st_le_of_le Hyperreal.isSt_le_of_le
-
+#align hyperreal.lt_of_is_st_lt Hyperreal.IsSt.lt
+
+/- warning: hyperreal.is_st_le_of_le -> Hyperreal.IsSt.le is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y) -> (LE.le.{0} Real Real.hasLe r s)
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x y) -> (LE.le.{0} Real Real.instLEReal r s)
+Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_le_of_le Hyperreal.IsSt.leₓ'. -/
+theorem Hyperreal.IsSt.le {x y : ℝ*} {r s : ℝ} (hrx : IsSt x r) (hsy : IsSt y s) : x ≤ y → r ≤ s :=
+  by rw [← not_lt, ← not_lt, not_imp_not] <;> exact lt_of_is_st_lt hsy hrx
+#align hyperreal.is_st_le_of_le Hyperreal.IsSt.le
+
+/- warning: hyperreal.st_le_of_le -> Hyperreal.st_le_of_le is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y) -> (LE.le.{0} Real Real.hasLe (Hyperreal.st x) (Hyperreal.st y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x y) -> (LE.le.{0} Real Real.instLEReal (Hyperreal.st x) (Hyperreal.st y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.st_le_of_le Hyperreal.st_le_of_leₓ'. -/
 theorem st_le_of_le {x y : ℝ*} (hix : ¬Infinite x) (hiy : ¬Infinite y) : x ≤ y → st x ≤ st y :=
   have hx' := isSt_st' hix
   have hy' := isSt_st' hiy
-  isSt_le_of_le hx' hy'
+  Hyperreal.IsSt.le hx' hy'
 #align hyperreal.st_le_of_le Hyperreal.st_le_of_le
 
+/- warning: hyperreal.lt_of_st_lt -> Hyperreal.lt_of_st_lt is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (LT.lt.{0} Real Real.hasLt (Hyperreal.st x) (Hyperreal.st y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y)
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (LT.lt.{0} Real Real.instLTReal (Hyperreal.st x) (Hyperreal.st y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x y)
+Case conversion may be inaccurate. Consider using '#align hyperreal.lt_of_st_lt Hyperreal.lt_of_st_ltₓ'. -/
 theorem lt_of_st_lt {x y : ℝ*} (hix : ¬Infinite x) (hiy : ¬Infinite y) : st x < st y → x < y :=
   have hx' := isSt_st' hix
   have hy' := isSt_st' hiy
-  lt_of_isSt_lt hx' hy'
+  Hyperreal.IsSt.lt hx' hy'
 #align hyperreal.lt_of_st_lt Hyperreal.lt_of_st_lt
 
 /-!
@@ -455,60 +777,114 @@ theorem lt_of_st_lt {x y : ℝ*} (hix : ¬Infinite x) (hiy : ¬Infinite y) : st
 -/
 
 
+/- warning: hyperreal.infinite_pos_def -> Hyperreal.infinitePos_def is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r) x)
+but is expected to have type
+  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal r) x)
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_def Hyperreal.infinitePos_defₓ'. -/
 theorem infinitePos_def {x : ℝ*} : InfinitePos x ↔ ∀ r : ℝ, ↑r < x := by rw [iff_eq_eq] <;> rfl
 #align hyperreal.infinite_pos_def Hyperreal.infinitePos_def
 
+/- warning: hyperreal.infinite_neg_def -> Hyperreal.infiniteNeg_def is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))
+but is expected to have type
+  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal r))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_def Hyperreal.infiniteNeg_defₓ'. -/
 theorem infiniteNeg_def {x : ℝ*} : InfiniteNeg x ↔ ∀ r : ℝ, x < r := by rw [iff_eq_eq] <;> rfl
 #align hyperreal.infinite_neg_def Hyperreal.infiniteNeg_def
 
-theorem ne_zero_of_infinite {x : ℝ*} : Infinite x → x ≠ 0 := fun hI h0 =>
+/- warning: hyperreal.ne_zero_of_infinite -> Hyperreal.Infinite.ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Hyperreal.Infinite x) -> (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))))
+but is expected to have type
+  forall {x : Hyperreal}, (Hyperreal.Infinite x) -> (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.ne_zero_of_infinite Hyperreal.Infinite.ne_zeroₓ'. -/
+theorem Hyperreal.Infinite.ne_zero {x : ℝ*} : Infinite x → x ≠ 0 := fun hI h0 =>
   Or.cases_on hI (fun hip => lt_irrefl (0 : ℝ*) ((by rwa [← h0] : InfinitePos 0) 0)) fun hin =>
     lt_irrefl (0 : ℝ*) ((by rwa [← h0] : InfiniteNeg 0) 0)
-#align hyperreal.ne_zero_of_infinite Hyperreal.ne_zero_of_infinite
-
-theorem not_infinite_zero : ¬Infinite 0 := fun hI => ne_zero_of_infinite hI rfl
+#align hyperreal.ne_zero_of_infinite Hyperreal.Infinite.ne_zero
+
+/- warning: hyperreal.not_infinite_zero -> Hyperreal.not_infinite_zero is a dubious translation:
+lean 3 declaration is
+  Not (Hyperreal.Infinite (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))))
+but is expected to have type
+  Not (Hyperreal.Infinite (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.not_infinite_zero Hyperreal.not_infinite_zeroₓ'. -/
+theorem not_infinite_zero : ¬Infinite 0 := fun hI => Hyperreal.Infinite.ne_zero hI rfl
 #align hyperreal.not_infinite_zero Hyperreal.not_infinite_zero
 
-theorem pos_of_infinitePos {x : ℝ*} : InfinitePos x → 0 < x := fun hip => hip 0
-#align hyperreal.pos_of_infinite_pos Hyperreal.pos_of_infinitePos
-
-theorem neg_of_infiniteNeg {x : ℝ*} : InfiniteNeg x → x < 0 := fun hin => hin 0
-#align hyperreal.neg_of_infinite_neg Hyperreal.neg_of_infiniteNeg
-
-theorem not_infinitePos_of_infiniteNeg {x : ℝ*} : InfiniteNeg x → ¬InfinitePos x := fun hn hp =>
-  not_lt_of_lt (hn 1) (hp 1)
-#align hyperreal.not_infinite_pos_of_infinite_neg Hyperreal.not_infinitePos_of_infiniteNeg
+/- warning: hyperreal.pos_of_infinite_pos -> Hyperreal.InfinitePos.pos is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Hyperreal.InfinitePos x) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x)
+but is expected to have type
+  forall {x : Hyperreal}, (Hyperreal.InfinitePos x) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x)
+Case conversion may be inaccurate. Consider using '#align hyperreal.pos_of_infinite_pos Hyperreal.InfinitePos.posₓ'. -/
+theorem Hyperreal.InfinitePos.pos {x : ℝ*} : InfinitePos x → 0 < x := fun hip => hip 0
+#align hyperreal.pos_of_infinite_pos Hyperreal.InfinitePos.pos
+
+/- warning: hyperreal.neg_of_infinite_neg -> Hyperreal.InfiniteNeg.lt_zero is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))))
+but is expected to have type
+  forall {x : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.neg_of_infinite_neg Hyperreal.InfiniteNeg.lt_zeroₓ'. -/
+theorem Hyperreal.InfiniteNeg.lt_zero {x : ℝ*} : InfiniteNeg x → x < 0 := fun hin => hin 0
+#align hyperreal.neg_of_infinite_neg Hyperreal.InfiniteNeg.lt_zero
+
+#print Hyperreal.InfiniteNeg.not_infinitePos /-
+theorem Hyperreal.InfiniteNeg.not_infinitePos {x : ℝ*} : InfiniteNeg x → ¬InfinitePos x :=
+  fun hn hp => not_lt_of_lt (hn 1) (hp 1)
+#align hyperreal.not_infinite_pos_of_infinite_neg Hyperreal.InfiniteNeg.not_infinitePos
+-/
 
-theorem not_infiniteNeg_of_infinitePos {x : ℝ*} : InfinitePos x → ¬InfiniteNeg x :=
-  imp_not_comm.mp not_infinitePos_of_infiniteNeg
-#align hyperreal.not_infinite_neg_of_infinite_pos Hyperreal.not_infiniteNeg_of_infinitePos
+#print Hyperreal.InfinitePos.not_infiniteNeg /-
+theorem Hyperreal.InfinitePos.not_infiniteNeg {x : ℝ*} : InfinitePos x → ¬InfiniteNeg x :=
+  imp_not_comm.mp Hyperreal.InfiniteNeg.not_infinitePos
+#align hyperreal.not_infinite_neg_of_infinite_pos Hyperreal.InfinitePos.not_infiniteNeg
+-/
 
-theorem infiniteNeg_neg_of_infinitePos {x : ℝ*} : InfinitePos x → InfiniteNeg (-x) := fun hp r =>
+/- warning: hyperreal.infinite_neg_neg_of_infinite_pos -> Hyperreal.InfinitePos.neg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Hyperreal.InfinitePos x) -> (Hyperreal.InfiniteNeg (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) x))
+but is expected to have type
+  forall {x : Hyperreal}, (Hyperreal.InfinitePos x) -> (Hyperreal.InfiniteNeg (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_neg_of_infinite_pos Hyperreal.InfinitePos.negₓ'. -/
+theorem Hyperreal.InfinitePos.neg {x : ℝ*} : InfinitePos x → InfiniteNeg (-x) := fun hp r =>
   neg_lt.mp (hp (-r))
-#align hyperreal.infinite_neg_neg_of_infinite_pos Hyperreal.infiniteNeg_neg_of_infinitePos
-
-theorem infinitePos_neg_of_infiniteNeg {x : ℝ*} : InfiniteNeg x → InfinitePos (-x) := fun hp r =>
+#align hyperreal.infinite_neg_neg_of_infinite_pos Hyperreal.InfinitePos.neg
+
+/- warning: hyperreal.infinite_pos_neg_of_infinite_neg -> Hyperreal.InfiniteNeg.neg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Hyperreal.InfinitePos (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) x))
+but is expected to have type
+  forall {x : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Hyperreal.InfinitePos (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_neg_of_infinite_neg Hyperreal.InfiniteNeg.negₓ'. -/
+theorem Hyperreal.InfiniteNeg.neg {x : ℝ*} : InfiniteNeg x → InfinitePos (-x) := fun hp r =>
   lt_neg.mp (hp (-r))
-#align hyperreal.infinite_pos_neg_of_infinite_neg Hyperreal.infinitePos_neg_of_infiniteNeg
+#align hyperreal.infinite_pos_neg_of_infinite_neg Hyperreal.InfiniteNeg.neg
 
-theorem infinitePos_iff_infiniteNeg_neg {x : ℝ*} : InfinitePos x ↔ InfiniteNeg (-x) :=
-  ⟨infiniteNeg_neg_of_infinitePos, fun hin => neg_neg x ▸ infinitePos_neg_of_infiniteNeg hin⟩
-#align hyperreal.infinite_pos_iff_infinite_neg_neg Hyperreal.infinitePos_iff_infiniteNeg_neg
+theorem infiniteNeg_neg {x : ℝ*} : InfinitePos x ↔ InfiniteNeg (-x) :=
+  ⟨Hyperreal.InfinitePos.neg, fun hin => neg_neg x ▸ Hyperreal.InfiniteNeg.neg hin⟩
+#align hyperreal.infinite_pos_iff_infinite_neg_neg Hyperreal.infiniteNeg_negₓ
 
-theorem infiniteNeg_iff_infinitePos_neg {x : ℝ*} : InfiniteNeg x ↔ InfinitePos (-x) :=
-  ⟨infinitePos_neg_of_infiniteNeg, fun hin => neg_neg x ▸ infiniteNeg_neg_of_infinitePos hin⟩
-#align hyperreal.infinite_neg_iff_infinite_pos_neg Hyperreal.infiniteNeg_iff_infinitePos_neg
+theorem infinitePos_neg {x : ℝ*} : InfiniteNeg x ↔ InfinitePos (-x) :=
+  ⟨Hyperreal.InfiniteNeg.neg, fun hin => neg_neg x ▸ Hyperreal.InfinitePos.neg hin⟩
+#align hyperreal.infinite_neg_iff_infinite_pos_neg Hyperreal.infinitePos_negₓ
 
-theorem infinite_iff_infinite_neg {x : ℝ*} : Infinite x ↔ Infinite (-x) :=
+theorem infinite_neg {x : ℝ*} : Infinite x ↔ Infinite (-x) :=
   ⟨fun hi =>
-    Or.cases_on hi (fun hip => Or.inr (infiniteNeg_neg_of_infinitePos hip)) fun hin =>
-      Or.inl (infinitePos_neg_of_infiniteNeg hin),
+    Or.cases_on hi (fun hip => Or.inr (Hyperreal.InfinitePos.neg hip)) fun hin =>
+      Or.inl (Hyperreal.InfiniteNeg.neg hin),
     fun hi =>
-    Or.cases_on hi (fun hipn => Or.inr (infiniteNeg_iff_infinitePos_neg.mpr hipn)) fun hinp =>
-      Or.inl (infinitePos_iff_infiniteNeg_neg.mpr hinp)⟩
-#align hyperreal.infinite_iff_infinite_neg Hyperreal.infinite_iff_infinite_neg
+    Or.cases_on hi (fun hipn => Or.inr (infinitePos_neg.mpr hipn)) fun hinp =>
+      Or.inl (infiniteNeg_neg.mpr hinp)⟩
+#align hyperreal.infinite_iff_infinite_neg Hyperreal.infinite_negₓ
 
-theorem not_infinite_of_infinitesimal {x : ℝ*} : Infinitesimal x → ¬Infinite x := fun hi hI =>
+#print Hyperreal.Infinitesimal.not_infinite /-
+theorem Hyperreal.Infinitesimal.not_infinite {x : ℝ*} : Infinitesimal x → ¬Infinite x :=
+  fun hi hI =>
   have hi' := hi 2 zero_lt_two
   Or.dcases_on hI
     (fun hip =>
@@ -517,34 +893,65 @@ theorem not_infinite_of_infinitesimal {x : ℝ*} : Infinitesimal x → ¬Infinit
     fun hin =>
     have hin' := hin (-2)
     not_lt_of_lt hin' (by convert hi'.1 <;> exact (zero_sub 2).symm)
-#align hyperreal.not_infinite_of_infinitesimal Hyperreal.not_infinite_of_infinitesimal
+#align hyperreal.not_infinite_of_infinitesimal Hyperreal.Infinitesimal.not_infinite
+-/
 
-theorem not_infinitesimal_of_infinite {x : ℝ*} : Infinite x → ¬Infinitesimal x :=
-  imp_not_comm.mp not_infinite_of_infinitesimal
-#align hyperreal.not_infinitesimal_of_infinite Hyperreal.not_infinitesimal_of_infinite
+#print Hyperreal.Infinite.not_infinitesimal /-
+theorem Hyperreal.Infinite.not_infinitesimal {x : ℝ*} : Infinite x → ¬Infinitesimal x :=
+  imp_not_comm.mp Hyperreal.Infinitesimal.not_infinite
+#align hyperreal.not_infinitesimal_of_infinite Hyperreal.Infinite.not_infinitesimal
+-/
 
-theorem not_infinitesimal_of_infinitePos {x : ℝ*} : InfinitePos x → ¬Infinitesimal x := fun hp =>
-  not_infinitesimal_of_infinite (Or.inl hp)
-#align hyperreal.not_infinitesimal_of_infinite_pos Hyperreal.not_infinitesimal_of_infinitePos
+#print Hyperreal.InfinitePos.not_infinitesimal /-
+theorem Hyperreal.InfinitePos.not_infinitesimal {x : ℝ*} : InfinitePos x → ¬Infinitesimal x :=
+  fun hp => Hyperreal.Infinite.not_infinitesimal (Or.inl hp)
+#align hyperreal.not_infinitesimal_of_infinite_pos Hyperreal.InfinitePos.not_infinitesimal
+-/
 
-theorem not_infinitesimal_of_infiniteNeg {x : ℝ*} : InfiniteNeg x → ¬Infinitesimal x := fun hn =>
-  not_infinitesimal_of_infinite (Or.inr hn)
-#align hyperreal.not_infinitesimal_of_infinite_neg Hyperreal.not_infinitesimal_of_infiniteNeg
+#print Hyperreal.InfiniteNeg.not_infinitesimal /-
+theorem Hyperreal.InfiniteNeg.not_infinitesimal {x : ℝ*} : InfiniteNeg x → ¬Infinitesimal x :=
+  fun hn => Hyperreal.Infinite.not_infinitesimal (Or.inr hn)
+#align hyperreal.not_infinitesimal_of_infinite_neg Hyperreal.InfiniteNeg.not_infinitesimal
+-/
 
+/- warning: hyperreal.infinite_pos_iff_infinite_and_pos -> Hyperreal.infinitePos_iff_infinite_and_pos is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (And (Hyperreal.Infinite x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x))
+but is expected to have type
+  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (And (Hyperreal.Infinite x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_iff_infinite_and_pos Hyperreal.infinitePos_iff_infinite_and_posₓ'. -/
 theorem infinitePos_iff_infinite_and_pos {x : ℝ*} : InfinitePos x ↔ Infinite x ∧ 0 < x :=
   ⟨fun hip => ⟨Or.inl hip, hip 0⟩, fun ⟨hi, hp⟩ =>
     hi.casesOn (fun hip => hip) fun hin => False.elim (not_lt_of_lt hp (hin 0))⟩
 #align hyperreal.infinite_pos_iff_infinite_and_pos Hyperreal.infinitePos_iff_infinite_and_pos
 
+/- warning: hyperreal.infinite_neg_iff_infinite_and_neg -> Hyperreal.infiniteNeg_iff_infinite_and_neg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (And (Hyperreal.Infinite x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))))
+but is expected to have type
+  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (And (Hyperreal.Infinite x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_iff_infinite_and_neg Hyperreal.infiniteNeg_iff_infinite_and_negₓ'. -/
 theorem infiniteNeg_iff_infinite_and_neg {x : ℝ*} : InfiniteNeg x ↔ Infinite x ∧ x < 0 :=
   ⟨fun hip => ⟨Or.inr hip, hip 0⟩, fun ⟨hi, hp⟩ =>
     hi.casesOn (fun hin => False.elim (not_lt_of_lt hp (hin 0))) fun hip => hip⟩
 #align hyperreal.infinite_neg_iff_infinite_and_neg Hyperreal.infiniteNeg_iff_infinite_and_neg
 
+/- warning: hyperreal.infinite_pos_iff_infinite_of_pos -> Hyperreal.infinitePos_iff_infinite_of_pos is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x) -> (Iff (Hyperreal.InfinitePos x) (Hyperreal.Infinite x))
+but is expected to have type
+  forall {x : Hyperreal}, (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x) -> (Iff (Hyperreal.InfinitePos x) (Hyperreal.Infinite x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_iff_infinite_of_pos Hyperreal.infinitePos_iff_infinite_of_posₓ'. -/
 theorem infinitePos_iff_infinite_of_pos {x : ℝ*} (hp : 0 < x) : InfinitePos x ↔ Infinite x := by
   rw [infinite_pos_iff_infinite_and_pos] <;> exact ⟨fun hI => hI.1, fun hI => ⟨hI, hp⟩⟩
 #align hyperreal.infinite_pos_iff_infinite_of_pos Hyperreal.infinitePos_iff_infinite_of_pos
 
+/- warning: hyperreal.infinite_pos_iff_infinite_of_nonneg -> Hyperreal.infinitePos_iff_infinite_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x) -> (Iff (Hyperreal.InfinitePos x) (Hyperreal.Infinite x))
+but is expected to have type
+  forall {x : Hyperreal}, (LE.le.{0} Hyperreal (Preorder.toLE.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x) -> (Iff (Hyperreal.InfinitePos x) (Hyperreal.Infinite x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_iff_infinite_of_nonneg Hyperreal.infinitePos_iff_infinite_of_nonnegₓ'. -/
 theorem infinitePos_iff_infinite_of_nonneg {x : ℝ*} (hp : 0 ≤ x) : InfinitePos x ↔ Infinite x :=
   Or.cases_on (lt_or_eq_of_le hp) infinitePos_iff_infinite_of_pos fun h => by
     rw [h.symm] <;>
@@ -553,15 +960,27 @@ theorem infinitePos_iff_infinite_of_nonneg {x : ℝ*} (hp : 0 ≤ x) : InfiniteP
           False.elim (not_infinite_zero hI)⟩
 #align hyperreal.infinite_pos_iff_infinite_of_nonneg Hyperreal.infinitePos_iff_infinite_of_nonneg
 
+/- warning: hyperreal.infinite_neg_iff_infinite_of_neg -> Hyperreal.infiniteNeg_iff_infinite_of_neg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Iff (Hyperreal.InfiniteNeg x) (Hyperreal.Infinite x))
+but is expected to have type
+  forall {x : Hyperreal}, (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Iff (Hyperreal.InfiniteNeg x) (Hyperreal.Infinite x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_iff_infinite_of_neg Hyperreal.infiniteNeg_iff_infinite_of_negₓ'. -/
 theorem infiniteNeg_iff_infinite_of_neg {x : ℝ*} (hn : x < 0) : InfiniteNeg x ↔ Infinite x := by
   rw [infinite_neg_iff_infinite_and_neg] <;> exact ⟨fun hI => hI.1, fun hI => ⟨hI, hn⟩⟩
 #align hyperreal.infinite_neg_iff_infinite_of_neg Hyperreal.infiniteNeg_iff_infinite_of_neg
 
+/- warning: hyperreal.infinite_pos_abs_iff_infinite_abs -> Hyperreal.infinitePos_abs_iff_infinite_abs is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x)) (Hyperreal.Infinite (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x))
+but is expected to have type
+  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x)) (Hyperreal.Infinite (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_abs_iff_infinite_abs Hyperreal.infinitePos_abs_iff_infinite_absₓ'. -/
 theorem infinitePos_abs_iff_infinite_abs {x : ℝ*} : InfinitePos (|x|) ↔ Infinite (|x|) :=
   infinitePos_iff_infinite_of_nonneg (abs_nonneg _)
 #align hyperreal.infinite_pos_abs_iff_infinite_abs Hyperreal.infinitePos_abs_iff_infinite_abs
 
-theorem infinite_iff_infinitePos_abs {x : ℝ*} : Infinite x ↔ InfinitePos (|x|) :=
+theorem infinitePos_abs_iff_infinite {x : ℝ*} : Infinite x ↔ InfinitePos (|x|) :=
   ⟨fun hi d =>
     Or.cases_on hi (fun hip => by rw [abs_of_pos (hip 0)] <;> exact hip d) fun hin => by
       rw [abs_of_neg (hin 0)] <;> exact lt_neg.mp (hin (-d)),
@@ -570,19 +989,31 @@ theorem infinite_iff_infinitePos_abs {x : ℝ*} : Infinite x ↔ InfinitePos (|x
     · exact Or.inr (infinite_neg_iff_infinite_pos_neg.mpr (by rwa [abs_of_neg h] at hipa))
     · exact False.elim (ne_zero_of_infinite (Or.inl (by rw [h] <;> rwa [h, abs_zero] at hipa)) h)
     · exact Or.inl (by rwa [abs_of_pos h] at hipa)⟩
-#align hyperreal.infinite_iff_infinite_pos_abs Hyperreal.infinite_iff_infinitePos_abs
+#align hyperreal.infinite_iff_infinite_pos_abs Hyperreal.infinitePos_abs_iff_infiniteₓ
 
-theorem infinite_iff_infinite_abs {x : ℝ*} : Infinite x ↔ Infinite (|x|) := by
+theorem infinite_abs_iff {x : ℝ*} : Infinite x ↔ Infinite (|x|) := by
   rw [← infinite_pos_iff_infinite_of_nonneg (abs_nonneg _), infinite_iff_infinite_pos_abs]
-#align hyperreal.infinite_iff_infinite_abs Hyperreal.infinite_iff_infinite_abs
-
+#align hyperreal.infinite_iff_infinite_abs Hyperreal.infinite_abs_iffₓ
+
+/- warning: hyperreal.infinite_iff_abs_lt_abs -> Hyperreal.infinite_iff_abs_lt_abs is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, Iff (Hyperreal.Infinite x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x))
+but is expected to have type
+  forall {x : Hyperreal}, Iff (Hyperreal.Infinite x) (forall (r : Real), LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (Hyperreal.ofReal r)) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_iff_abs_lt_abs Hyperreal.infinite_iff_abs_lt_absₓ'. -/
 theorem infinite_iff_abs_lt_abs {x : ℝ*} : Infinite x ↔ ∀ r : ℝ, (|r| : ℝ*) < |x| :=
-  ⟨fun hI r => coe_abs r ▸ infinite_iff_infinitePos_abs.mp hI (|r|), fun hR =>
+  ⟨fun hI r => coe_abs r ▸ infinitePos_abs_iff_infinite.mp hI (|r|), fun hR =>
     Or.cases_on (max_choice x (-x))
       (fun h => Or.inl fun r => lt_of_le_of_lt (le_abs_self _) (h ▸ hR r)) fun h =>
       Or.inr fun r => neg_lt_neg_iff.mp <| lt_of_le_of_lt (neg_le_abs_self _) (h ▸ hR r)⟩
 #align hyperreal.infinite_iff_abs_lt_abs Hyperreal.infinite_iff_abs_lt_abs
 
+/- warning: hyperreal.infinite_pos_add_not_infinite_neg -> Hyperreal.infinitePos_add_not_infiniteNeg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.InfiniteNeg y)) -> (Hyperreal.InfinitePos (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.InfiniteNeg y)) -> (Hyperreal.InfinitePos (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_add_not_infinite_neg Hyperreal.infinitePos_add_not_infiniteNegₓ'. -/
 theorem infinitePos_add_not_infiniteNeg {x y : ℝ*} :
     InfinitePos x → ¬InfiniteNeg y → InfinitePos (x + y) :=
   by
@@ -592,11 +1023,23 @@ theorem infinitePos_add_not_infiniteNeg {x y : ℝ*} :
   simp
 #align hyperreal.infinite_pos_add_not_infinite_neg Hyperreal.infinitePos_add_not_infiniteNeg
 
+/- warning: hyperreal.not_infinite_neg_add_infinite_pos -> Hyperreal.not_infiniteNeg_add_infinitePos is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.InfiniteNeg x)) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.InfiniteNeg x)) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.not_infinite_neg_add_infinite_pos Hyperreal.not_infiniteNeg_add_infinitePosₓ'. -/
 theorem not_infiniteNeg_add_infinitePos {x y : ℝ*} :
     ¬InfiniteNeg x → InfinitePos y → InfinitePos (x + y) := fun hx hy => by
   rw [add_comm] <;> exact infinite_pos_add_not_infinite_neg hy hx
 #align hyperreal.not_infinite_neg_add_infinite_pos Hyperreal.not_infiniteNeg_add_infinitePos
 
+/- warning: hyperreal.infinite_neg_add_not_infinite_pos -> Hyperreal.infiniteNeg_add_not_infinitePos is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.InfinitePos y)) -> (Hyperreal.InfiniteNeg (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.InfinitePos y)) -> (Hyperreal.InfiniteNeg (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_add_not_infinite_pos Hyperreal.infiniteNeg_add_not_infinitePosₓ'. -/
 theorem infiniteNeg_add_not_infinitePos {x y : ℝ*} :
     InfiniteNeg x → ¬InfinitePos y → InfiniteNeg (x + y) := by
   rw [@infinite_neg_iff_infinite_pos_neg x, @infinite_pos_iff_infinite_neg_neg y,
@@ -604,31 +1047,62 @@ theorem infiniteNeg_add_not_infinitePos {x y : ℝ*} :
     exact infinite_pos_add_not_infinite_neg
 #align hyperreal.infinite_neg_add_not_infinite_pos Hyperreal.infiniteNeg_add_not_infinitePos
 
+/- warning: hyperreal.not_infinite_pos_add_infinite_neg -> Hyperreal.not_infinitePos_add_infiniteNeg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.InfinitePos x)) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.InfinitePos x)) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.not_infinite_pos_add_infinite_neg Hyperreal.not_infinitePos_add_infiniteNegₓ'. -/
 theorem not_infinitePos_add_infiniteNeg {x y : ℝ*} :
     ¬InfinitePos x → InfiniteNeg y → InfiniteNeg (x + y) := fun hx hy => by
   rw [add_comm] <;> exact infinite_neg_add_not_infinite_pos hy hx
 #align hyperreal.not_infinite_pos_add_infinite_neg Hyperreal.not_infinitePos_add_infiniteNeg
 
+/- warning: hyperreal.infinite_pos_add_infinite_pos -> Hyperreal.infinitePos_add_infinitePos is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_add_infinite_pos Hyperreal.infinitePos_add_infinitePosₓ'. -/
 theorem infinitePos_add_infinitePos {x y : ℝ*} :
     InfinitePos x → InfinitePos y → InfinitePos (x + y) := fun hx hy =>
-  infinitePos_add_not_infiniteNeg hx (not_infiniteNeg_of_infinitePos hy)
+  infinitePos_add_not_infiniteNeg hx (Hyperreal.InfinitePos.not_infiniteNeg hy)
 #align hyperreal.infinite_pos_add_infinite_pos Hyperreal.infinitePos_add_infinitePos
 
+/- warning: hyperreal.infinite_neg_add_infinite_neg -> Hyperreal.infiniteNeg_add_infiniteNeg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_add_infinite_neg Hyperreal.infiniteNeg_add_infiniteNegₓ'. -/
 theorem infiniteNeg_add_infiniteNeg {x y : ℝ*} :
     InfiniteNeg x → InfiniteNeg y → InfiniteNeg (x + y) := fun hx hy =>
-  infiniteNeg_add_not_infinitePos hx (not_infinitePos_of_infiniteNeg hy)
+  infiniteNeg_add_not_infinitePos hx (Hyperreal.InfiniteNeg.not_infinitePos hy)
 #align hyperreal.infinite_neg_add_infinite_neg Hyperreal.infiniteNeg_add_infiniteNeg
 
+/- warning: hyperreal.infinite_pos_add_not_infinite -> Hyperreal.infinitePos_add_not_infinite is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinite y)) -> (Hyperreal.InfinitePos (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinite y)) -> (Hyperreal.InfinitePos (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_add_not_infinite Hyperreal.infinitePos_add_not_infiniteₓ'. -/
 theorem infinitePos_add_not_infinite {x y : ℝ*} :
     InfinitePos x → ¬Infinite y → InfinitePos (x + y) := fun hx hy =>
   infinitePos_add_not_infiniteNeg hx (not_or.mp hy).2
 #align hyperreal.infinite_pos_add_not_infinite Hyperreal.infinitePos_add_not_infinite
 
+/- warning: hyperreal.infinite_neg_add_not_infinite -> Hyperreal.infiniteNeg_add_not_infinite is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinite y)) -> (Hyperreal.InfiniteNeg (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinite y)) -> (Hyperreal.InfiniteNeg (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_add_not_infinite Hyperreal.infiniteNeg_add_not_infiniteₓ'. -/
 theorem infiniteNeg_add_not_infinite {x y : ℝ*} :
     InfiniteNeg x → ¬Infinite y → InfiniteNeg (x + y) := fun hx hy =>
   infiniteNeg_add_not_infinitePos hx (not_or.mp hy).1
 #align hyperreal.infinite_neg_add_not_infinite Hyperreal.infiniteNeg_add_not_infinite
 
+#print Hyperreal.infinitePos_of_tendsto_top /-
 theorem infinitePos_of_tendsto_top {f : ℕ → ℝ} (hf : Tendsto f atTop atTop) :
     InfinitePos (ofSeq f) := fun r =>
   have hf' := tendsto_atTop_atTop.mp hf
@@ -640,7 +1114,9 @@ theorem infinitePos_of_tendsto_top {f : ℕ → ℝ} (hf : Tendsto f atTop atTop
         exact fun a har => le_of_lt (hi' a (lt_of_le_of_lt har (lt_add_one _)))
     Germ.coe_lt.2 <| mem_hyperfilter_of_finite_compl <| (Set.finite_le_nat _).Subset hS
 #align hyperreal.infinite_pos_of_tendsto_top Hyperreal.infinitePos_of_tendsto_top
+-/
 
+#print Hyperreal.infiniteNeg_of_tendsto_bot /-
 theorem infiniteNeg_of_tendsto_bot {f : ℕ → ℝ} (hf : Tendsto f atTop atBot) :
     InfiniteNeg (ofSeq f) := fun r =>
   have hf' := tendsto_atTop_atBot.mp hf
@@ -652,18 +1128,38 @@ theorem infiniteNeg_of_tendsto_bot {f : ℕ → ℝ} (hf : Tendsto f atTop atBot
         exact fun a har => le_of_lt (hi' a (lt_of_lt_of_le (sub_one_lt _) har))
     Germ.coe_lt.2 <| mem_hyperfilter_of_finite_compl <| (Set.finite_le_nat _).Subset hS
 #align hyperreal.infinite_neg_of_tendsto_bot Hyperreal.infiniteNeg_of_tendsto_bot
+-/
 
+/- warning: hyperreal.not_infinite_neg -> Hyperreal.not_infinite_neg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) x)))
+but is expected to have type
+  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) x)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.not_infinite_neg Hyperreal.not_infinite_negₓ'. -/
 theorem not_infinite_neg {x : ℝ*} : ¬Infinite x → ¬Infinite (-x) :=
-  not_imp_not.mpr infinite_iff_infinite_neg.mpr
+  not_imp_not.mpr infinite_neg.mpr
 #align hyperreal.not_infinite_neg Hyperreal.not_infinite_neg
 
+/- warning: hyperreal.not_infinite_add -> Hyperreal.not_infinite_add is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (Not (Hyperreal.Infinite (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y)))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (Not (Hyperreal.Infinite (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.not_infinite_add Hyperreal.not_infinite_addₓ'. -/
 theorem not_infinite_add {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : ¬Infinite (x + y) :=
   have hx' := exists_st_of_not_infinite hx
   have hy' := exists_st_of_not_infinite hy
   Exists.cases_on hx' <|
-    Exists.cases_on hy' fun r hr s hs => not_infinite_of_exists_st <| ⟨s + r, isSt_add hs hr⟩
+    Exists.cases_on hy' fun r hr s hs =>
+      not_infinite_of_exists_st <| ⟨s + r, Hyperreal.IsSt.add hs hr⟩
 #align hyperreal.not_infinite_add Hyperreal.not_infinite_add
 
+/- warning: hyperreal.not_infinite_iff_exist_lt_gt -> Hyperreal.not_infinite_iff_exist_lt_gt is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, Iff (Not (Hyperreal.Infinite x)) (Exists.{1} Real (fun (r : Real) => Exists.{1} Real (fun (s : Real) => And (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r) x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) s)))))
+but is expected to have type
+  forall {x : Hyperreal}, Iff (Not (Hyperreal.Infinite x)) (Exists.{1} Real (fun (r : Real) => Exists.{1} Real (fun (s : Real) => And (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal r) x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal s)))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.not_infinite_iff_exist_lt_gt Hyperreal.not_infinite_iff_exist_lt_gtₓ'. -/
 theorem not_infinite_iff_exist_lt_gt {x : ℝ*} : ¬Infinite x ↔ ∃ r s : ℝ, (r : ℝ*) < x ∧ x < s :=
   ⟨fun hni =>
     Exists.dcases_on (not_forall.mp (not_or.mp hni).1) <|
@@ -679,14 +1175,18 @@ theorem not_infinite_iff_exist_lt_gt {x : ℝ*} : ¬Infinite x ↔ ∃ r s : ℝ
         not_or.mpr ⟨not_forall.mpr ⟨s, lt_asymm hs.2⟩, not_forall.mpr ⟨r, lt_asymm hs.1⟩⟩⟩
 #align hyperreal.not_infinite_iff_exist_lt_gt Hyperreal.not_infinite_iff_exist_lt_gt
 
+#print Hyperreal.not_infinite_real /-
 theorem not_infinite_real (r : ℝ) : ¬Infinite r := by
   rw [not_infinite_iff_exist_lt_gt] <;>
     exact ⟨r - 1, r + 1, coe_lt_coe.2 <| sub_one_lt r, coe_lt_coe.2 <| lt_add_one r⟩
 #align hyperreal.not_infinite_real Hyperreal.not_infinite_real
+-/
 
-theorem not_real_of_infinite {x : ℝ*} : Infinite x → ∀ r : ℝ, x ≠ r := fun hi r hr =>
+#print Hyperreal.Infinite.ne_real /-
+theorem Hyperreal.Infinite.ne_real {x : ℝ*} : Infinite x → ∀ r : ℝ, x ≠ r := fun hi r hr =>
   not_infinite_real r <| @Eq.subst _ Infinite _ _ hr hi
-#align hyperreal.not_real_of_infinite Hyperreal.not_real_of_infinite
+#align hyperreal.not_real_of_infinite Hyperreal.Infinite.ne_real
+-/
 
 /-!
 ### Facts about `st` that require some infinite machinery
@@ -699,7 +1199,7 @@ private theorem is_st_mul' {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
   have hys' := isSt_iff_abs_sub_lt_delta.mp hys
   have h :=
     not_infinite_iff_exist_lt_gt.mp <|
-      not_imp_not.mpr infinite_iff_infinite_abs.mpr <| not_infinite_of_exists_st ⟨r, hxr⟩
+      not_imp_not.mpr infinite_abs_iff.mpr <| not_infinite_of_exists_st ⟨r, hxr⟩
   Exists.cases_on h fun u h' =>
     Exists.cases_on h' fun t ⟨hu, ht⟩ =>
       isSt_iff_abs_sub_lt_delta.mpr fun d hd =>
@@ -734,10 +1234,17 @@ private theorem is_st_mul' {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
           
 #align hyperreal.is_st_mul' hyperreal.is_st_mul'
 
-theorem isSt_mul {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt y s) : IsSt (x * y) (r * s) :=
+/- warning: hyperreal.is_st_mul -> Hyperreal.IsSt.mul is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (Hyperreal.IsSt (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r s))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal} {r : Real} {s : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.IsSt y s) -> (Hyperreal.IsSt (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r s))
+Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_mul Hyperreal.IsSt.mulₓ'. -/
+theorem Hyperreal.IsSt.mul {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt y s) :
+    IsSt (x * y) (r * s) :=
   have h :=
     not_infinite_iff_exist_lt_gt.mp <|
-      not_imp_not.mpr infinite_iff_infinite_abs.mpr <| not_infinite_of_exists_st ⟨r, hxr⟩
+      not_imp_not.mpr infinite_abs_iff.mpr <| not_infinite_of_exists_st ⟨r, hxr⟩
   Exists.cases_on h fun u h' =>
     Exists.cases_on h' fun t ⟨hu, ht⟩ => by
       by_cases hs : s = 0
@@ -751,37 +1258,62 @@ theorem isSt_mul {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt y s) : Is
           div_mul_cancel (d : ℝ*) (ne_of_gt (lt_of_le_of_lt (abs_nonneg x) ht)), ← coe_div]
         exact mul_lt_mul'' hys' ht (abs_nonneg _) (abs_nonneg _)
       exact is_st_mul' hxr hys hs
-#align hyperreal.is_st_mul Hyperreal.isSt_mul
-
+#align hyperreal.is_st_mul Hyperreal.IsSt.mul
+
+/- warning: hyperreal.not_infinite_mul -> Hyperreal.not_infinite_mul is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (Not (Hyperreal.Infinite (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y)))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (Not (Hyperreal.Infinite (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.not_infinite_mul Hyperreal.not_infinite_mulₓ'. -/
 --AN INFINITE LEMMA THAT REQUIRES SOME MORE ST MACHINERY
 theorem not_infinite_mul {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : ¬Infinite (x * y) :=
   have hx' := exists_st_of_not_infinite hx
   have hy' := exists_st_of_not_infinite hy
   Exists.cases_on hx' <|
-    Exists.cases_on hy' fun r hr s hs => not_infinite_of_exists_st <| ⟨s * r, isSt_mul hs hr⟩
+    Exists.cases_on hy' fun r hr s hs =>
+      not_infinite_of_exists_st <| ⟨s * r, Hyperreal.IsSt.mul hs hr⟩
 #align hyperreal.not_infinite_mul Hyperreal.not_infinite_mul
 
+/- warning: hyperreal.st_add -> Hyperreal.st_add is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (Eq.{1} Real (Hyperreal.st (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Hyperreal.st x) (Hyperreal.st y)))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (Eq.{1} Real (Hyperreal.st (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Hyperreal.st x) (Hyperreal.st y)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.st_add Hyperreal.st_addₓ'. -/
 ---
 theorem st_add {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : st (x + y) = st x + st y :=
   have hx' := isSt_st' hx
   have hy' := isSt_st' hy
   have hxy := isSt_st' (not_infinite_add hx hy)
-  have hxy' := isSt_add hx' hy'
-  isSt_unique hxy hxy'
+  have hxy' := Hyperreal.IsSt.add hx' hy'
+  Hyperreal.IsSt.unique hxy hxy'
 #align hyperreal.st_add Hyperreal.st_add
 
+/- warning: hyperreal.st_neg -> Hyperreal.st_neg is a dubious translation:
+lean 3 declaration is
+  forall (x : Hyperreal), Eq.{1} Real (Hyperreal.st (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) x)) (Neg.neg.{0} Real Real.hasNeg (Hyperreal.st x))
+but is expected to have type
+  forall (x : Hyperreal), Eq.{1} Real (Hyperreal.st (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) x)) (Neg.neg.{0} Real Real.instNegReal (Hyperreal.st x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.st_neg Hyperreal.st_negₓ'. -/
 theorem st_neg (x : ℝ*) : st (-x) = -st x :=
   if h : Infinite x then by
     rw [st_infinite h, st_infinite (infinite_iff_infinite_neg.mp h), neg_zero]
-  else isSt_unique (isSt_st' (not_infinite_neg h)) (isSt_neg (isSt_st' h))
+  else Hyperreal.IsSt.unique (isSt_st' (not_infinite_neg h)) (Hyperreal.IsSt.neg (isSt_st' h))
 #align hyperreal.st_neg Hyperreal.st_neg
 
+/- warning: hyperreal.st_mul -> Hyperreal.st_mul is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (Eq.{1} Real (Hyperreal.st (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Hyperreal.st x) (Hyperreal.st y)))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Not (Hyperreal.Infinite y)) -> (Eq.{1} Real (Hyperreal.st (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Hyperreal.st x) (Hyperreal.st y)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.st_mul Hyperreal.st_mulₓ'. -/
 theorem st_mul {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : st (x * y) = st x * st y :=
   have hx' := isSt_st' hx
   have hy' := isSt_st' hy
   have hxy := isSt_st' (not_infinite_mul hx hy)
-  have hxy' := isSt_mul hx' hy'
-  isSt_unique hxy hxy'
+  have hxy' := Hyperreal.IsSt.mul hx' hy'
+  Hyperreal.IsSt.unique hxy hxy'
 #align hyperreal.st_mul Hyperreal.st_mul
 
 /-!
@@ -789,23 +1321,53 @@ theorem st_mul {x y : ℝ*} (hx : ¬Infinite x) (hy : ¬Infinite y) : st (x * y)
 -/
 
 
+/- warning: hyperreal.infinitesimal_def -> Hyperreal.infinitesimal_def is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, Iff (Hyperreal.Infinitesimal x) (forall (r : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (And (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))))
+but is expected to have type
+  forall {x : Hyperreal}, Iff (Hyperreal.Infinitesimal x) (forall (r : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (And (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (Hyperreal.ofReal r)) x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal r))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_def Hyperreal.infinitesimal_defₓ'. -/
 theorem infinitesimal_def {x : ℝ*} : Infinitesimal x ↔ ∀ r : ℝ, 0 < r → -(r : ℝ*) < x ∧ x < r :=
   ⟨fun hi r hr => by convert hi r hr <;> simp, fun hi d hd => by convert hi d hd <;> simp⟩
 #align hyperreal.infinitesimal_def Hyperreal.infinitesimal_def
 
+/- warning: hyperreal.lt_of_pos_of_infinitesimal -> Hyperreal.lt_of_pos_of_infinitesimal is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)))
+but is expected to have type
+  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal r)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.lt_of_pos_of_infinitesimal Hyperreal.lt_of_pos_of_infinitesimalₓ'. -/
 theorem lt_of_pos_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r : ℝ, 0 < r → x < r :=
   fun hi r hr => ((infinitesimal_def.mp hi) r hr).2
 #align hyperreal.lt_of_pos_of_infinitesimal Hyperreal.lt_of_pos_of_infinitesimal
 
+/- warning: hyperreal.lt_neg_of_pos_of_infinitesimal -> Hyperreal.lt_neg_of_pos_of_infinitesimal is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) x))
+but is expected to have type
+  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (Hyperreal.ofReal r)) x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.lt_neg_of_pos_of_infinitesimal Hyperreal.lt_neg_of_pos_of_infinitesimalₓ'. -/
 theorem lt_neg_of_pos_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r : ℝ, 0 < r → -↑r < x :=
   fun hi r hr => ((infinitesimal_def.mp hi) r hr).1
 #align hyperreal.lt_neg_of_pos_of_infinitesimal Hyperreal.lt_neg_of_pos_of_infinitesimal
 
+/- warning: hyperreal.gt_of_neg_of_infinitesimal -> Hyperreal.gt_of_neg_of_infinitesimal is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.hasLt r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r) x))
+but is expected to have type
+  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (forall (r : Real), (LT.lt.{0} Real Real.instLTReal r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Hyperreal.ofReal r) x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.gt_of_neg_of_infinitesimal Hyperreal.gt_of_neg_of_infinitesimalₓ'. -/
 theorem gt_of_neg_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r : ℝ, r < 0 → ↑r < x :=
   fun hi r hr => by
   convert((infinitesimal_def.mp hi) (-r) (neg_pos.mpr hr)).1 <;> exact (neg_neg ↑r).symm
 #align hyperreal.gt_of_neg_of_infinitesimal Hyperreal.gt_of_neg_of_infinitesimal
 
+/- warning: hyperreal.abs_lt_real_iff_infinitesimal -> Hyperreal.abs_lt_real_iff_infinitesimal is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, Iff (Hyperreal.Infinitesimal x) (forall (r : Real), (Ne.{1} Real r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) (SemilatticeSup.toHasSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (LinearOrder.toLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))))
+but is expected to have type
+  forall {x : Hyperreal}, Iff (Hyperreal.Infinitesimal x) (forall (r : Real), (Ne.{1} Real r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x) (Abs.abs.{0} Hyperreal (Neg.toHasAbs.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) (SemilatticeSup.toSup.{0} Hyperreal (Lattice.toSemilatticeSup.{0} Hyperreal (DistribLattice.toLattice.{0} Hyperreal (instDistribLattice.{0} Hyperreal (LinearOrderedRing.toLinearOrder.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) (Hyperreal.ofReal r))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.abs_lt_real_iff_infinitesimal Hyperreal.abs_lt_real_iff_infinitesimalₓ'. -/
 theorem abs_lt_real_iff_infinitesimal {x : ℝ*} : Infinitesimal x ↔ ∀ r : ℝ, r ≠ 0 → |x| < |r| :=
   ⟨fun hi r hr =>
     abs_lt.mpr (by rw [← coe_abs] <;> exact infinitesimal_def.mp hi (|r|) (abs_pos.2 hr)), fun hR =>
@@ -813,59 +1375,129 @@ theorem abs_lt_real_iff_infinitesimal {x : ℝ*} : Infinitesimal x ↔ ∀ r : 
       abs_lt.mp <| (abs_of_pos <| coe_pos.2 hr) ▸ hR r <| ne_of_gt hr⟩
 #align hyperreal.abs_lt_real_iff_infinitesimal Hyperreal.abs_lt_real_iff_infinitesimal
 
+/- warning: hyperreal.infinitesimal_zero -> Hyperreal.infinitesimal_zero is a dubious translation:
+lean 3 declaration is
+  Hyperreal.Infinitesimal (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))
+but is expected to have type
+  Hyperreal.Infinitesimal (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_zero Hyperreal.infinitesimal_zeroₓ'. -/
 theorem infinitesimal_zero : Infinitesimal 0 :=
   isSt_refl_real 0
 #align hyperreal.infinitesimal_zero Hyperreal.infinitesimal_zero
 
-theorem zero_of_infinitesimal_real {r : ℝ} : Infinitesimal r → r = 0 :=
+/- warning: hyperreal.zero_of_infinitesimal_real -> Hyperreal.Infinitesimal.eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {r : Real}, (Hyperreal.Infinitesimal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) -> (Eq.{1} Real r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {r : Real}, (Hyperreal.Infinitesimal (Hyperreal.ofReal r)) -> (Eq.{1} Real r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.zero_of_infinitesimal_real Hyperreal.Infinitesimal.eq_zeroₓ'. -/
+theorem Hyperreal.Infinitesimal.eq_zero {r : ℝ} : Infinitesimal r → r = 0 :=
   eq_of_isSt_real
-#align hyperreal.zero_of_infinitesimal_real Hyperreal.zero_of_infinitesimal_real
-
-theorem zero_iff_infinitesimal_real {r : ℝ} : Infinitesimal r ↔ r = 0 :=
-  ⟨zero_of_infinitesimal_real, fun hr => by rw [hr] <;> exact infinitesimal_zero⟩
-#align hyperreal.zero_iff_infinitesimal_real Hyperreal.zero_iff_infinitesimal_real
-
-theorem infinitesimal_add {x y : ℝ*} (hx : Infinitesimal x) (hy : Infinitesimal y) :
+#align hyperreal.zero_of_infinitesimal_real Hyperreal.Infinitesimal.eq_zero
+
+/- warning: hyperreal.zero_iff_infinitesimal_real -> Hyperreal.infinitesimal_real_iff is a dubious translation:
+lean 3 declaration is
+  forall {r : Real}, Iff (Hyperreal.Infinitesimal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)) (Eq.{1} Real r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {r : Real}, Iff (Hyperreal.Infinitesimal (Hyperreal.ofReal r)) (Eq.{1} Real r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.zero_iff_infinitesimal_real Hyperreal.infinitesimal_real_iffₓ'. -/
+theorem infinitesimal_real_iff {r : ℝ} : Infinitesimal r ↔ r = 0 :=
+  ⟨Hyperreal.Infinitesimal.eq_zero, fun hr => by rw [hr] <;> exact infinitesimal_zero⟩
+#align hyperreal.zero_iff_infinitesimal_real Hyperreal.infinitesimal_real_iff
+
+/- warning: hyperreal.infinitesimal_add -> Hyperreal.Infinitesimal.add is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.Infinitesimal x) -> (Hyperreal.Infinitesimal y) -> (Hyperreal.Infinitesimal (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toHasAdd.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.Infinitesimal x) -> (Hyperreal.Infinitesimal y) -> (Hyperreal.Infinitesimal (HAdd.hAdd.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHAdd.{0} Hyperreal (Distrib.toAdd.{0} Hyperreal (NonUnitalNonAssocSemiring.toDistrib.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_add Hyperreal.Infinitesimal.addₓ'. -/
+theorem Hyperreal.Infinitesimal.add {x y : ℝ*} (hx : Infinitesimal x) (hy : Infinitesimal y) :
     Infinitesimal (x + y) := by simpa only [add_zero] using is_st_add hx hy
-#align hyperreal.infinitesimal_add Hyperreal.infinitesimal_add
-
-theorem infinitesimal_neg {x : ℝ*} (hx : Infinitesimal x) : Infinitesimal (-x) := by
+#align hyperreal.infinitesimal_add Hyperreal.Infinitesimal.add
+
+/- warning: hyperreal.infinitesimal_neg -> Hyperreal.Infinitesimal.neg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (Hyperreal.Infinitesimal (Neg.neg.{0} Hyperreal (SubNegMonoid.toHasNeg.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))) x))
+but is expected to have type
+  forall {x : Hyperreal}, (Hyperreal.Infinitesimal x) -> (Hyperreal.Infinitesimal (Neg.neg.{0} Hyperreal (Ring.toNeg.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))) x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_neg Hyperreal.Infinitesimal.negₓ'. -/
+theorem Hyperreal.Infinitesimal.neg {x : ℝ*} (hx : Infinitesimal x) : Infinitesimal (-x) := by
   simpa only [neg_zero] using is_st_neg hx
-#align hyperreal.infinitesimal_neg Hyperreal.infinitesimal_neg
-
-theorem infinitesimal_neg_iff {x : ℝ*} : Infinitesimal x ↔ Infinitesimal (-x) :=
-  ⟨infinitesimal_neg, fun h => neg_neg x ▸ @infinitesimal_neg (-x) h⟩
-#align hyperreal.infinitesimal_neg_iff Hyperreal.infinitesimal_neg_iff
-
-theorem infinitesimal_mul {x y : ℝ*} (hx : Infinitesimal x) (hy : Infinitesimal y) :
+#align hyperreal.infinitesimal_neg Hyperreal.Infinitesimal.neg
+
+theorem infinitesimal_neg {x : ℝ*} : Infinitesimal x ↔ Infinitesimal (-x) :=
+  ⟨Hyperreal.Infinitesimal.neg, fun h => neg_neg x ▸ @Hyperreal.Infinitesimal.neg (-x) h⟩
+#align hyperreal.infinitesimal_neg_iff Hyperreal.infinitesimal_negₓ
+
+/- warning: hyperreal.infinitesimal_mul -> Hyperreal.Infinitesimal.mul is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.Infinitesimal x) -> (Hyperreal.Infinitesimal y) -> (Hyperreal.Infinitesimal (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.Infinitesimal x) -> (Hyperreal.Infinitesimal y) -> (Hyperreal.Infinitesimal (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_mul Hyperreal.Infinitesimal.mulₓ'. -/
+theorem Hyperreal.Infinitesimal.mul {x y : ℝ*} (hx : Infinitesimal x) (hy : Infinitesimal y) :
     Infinitesimal (x * y) := by simpa only [MulZeroClass.mul_zero] using is_st_mul hx hy
-#align hyperreal.infinitesimal_mul Hyperreal.infinitesimal_mul
-
+#align hyperreal.infinitesimal_mul Hyperreal.Infinitesimal.mul
+
+/- warning: hyperreal.infinitesimal_of_tendsto_zero -> Hyperreal.infinitesimal_of_tendsto_zero is a dubious translation:
+lean 3 declaration is
+  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) -> (Hyperreal.Infinitesimal (Hyperreal.ofSeq f))
+but is expected to have type
+  forall {f : Nat -> Real}, (Filter.Tendsto.{0, 0} Nat Real f (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) -> (Hyperreal.Infinitesimal (Hyperreal.ofSeq f))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_of_tendsto_zero Hyperreal.infinitesimal_of_tendsto_zeroₓ'. -/
 theorem infinitesimal_of_tendsto_zero {f : ℕ → ℝ} :
     Tendsto f atTop (𝓝 0) → Infinitesimal (ofSeq f) := fun hf d hd => by
   rw [sub_eq_add_neg, ← coe_neg, ← coe_add, ← coe_add, zero_add, zero_add] <;>
     exact ⟨neg_lt_of_tendsto_zero_of_pos hf hd, lt_of_tendsto_zero_of_pos hf hd⟩
 #align hyperreal.infinitesimal_of_tendsto_zero Hyperreal.infinitesimal_of_tendsto_zero
 
+#print Hyperreal.infinitesimal_epsilon /-
 theorem infinitesimal_epsilon : Infinitesimal ε :=
   infinitesimal_of_tendsto_zero tendsto_inverse_atTop_nhds_0_nat
 #align hyperreal.infinitesimal_epsilon Hyperreal.infinitesimal_epsilon
+-/
 
+/- warning: hyperreal.not_real_of_infinitesimal_ne_zero -> Hyperreal.not_real_of_infinitesimal_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall (x : Hyperreal), (Hyperreal.Infinitesimal x) -> (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (forall (r : Real), Ne.{1} Hyperreal x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r))
+but is expected to have type
+  forall (x : Hyperreal), (Hyperreal.Infinitesimal x) -> (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (forall (r : Real), Ne.{1} Hyperreal x (Hyperreal.ofReal r))
+Case conversion may be inaccurate. Consider using '#align hyperreal.not_real_of_infinitesimal_ne_zero Hyperreal.not_real_of_infinitesimal_ne_zeroₓ'. -/
 theorem not_real_of_infinitesimal_ne_zero (x : ℝ*) : Infinitesimal x → x ≠ 0 → ∀ r : ℝ, x ≠ r :=
   fun hi hx r hr =>
-  hx <| hr.trans <| coe_eq_zero.2 <| isSt_unique (hr.symm ▸ isSt_refl_real r : IsSt x r) hi
+  hx <|
+    hr.trans <| coe_eq_zero.2 <| Hyperreal.IsSt.unique (hr.symm ▸ isSt_refl_real r : IsSt x r) hi
 #align hyperreal.not_real_of_infinitesimal_ne_zero Hyperreal.not_real_of_infinitesimal_ne_zero
 
-theorem infinitesimal_sub_isSt {x : ℝ*} {r : ℝ} (hxr : IsSt x r) : Infinitesimal (x - r) :=
+/- warning: hyperreal.infinitesimal_sub_is_st -> Hyperreal.IsSt.infinitesimal_sub is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {r : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.Infinitesimal (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (SubNegMonoid.toHasSub.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) r)))
+but is expected to have type
+  forall {x : Hyperreal} {r : Real}, (Hyperreal.IsSt x r) -> (Hyperreal.Infinitesimal (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (Ring.toSub.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal r)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_sub_is_st Hyperreal.IsSt.infinitesimal_subₓ'. -/
+theorem Hyperreal.IsSt.infinitesimal_sub {x : ℝ*} {r : ℝ} (hxr : IsSt x r) :
+    Infinitesimal (x - r) :=
   show IsSt (x - r) 0 by
     rw [sub_eq_add_neg, ← add_neg_self r]
     exact is_st_add hxr (is_st_refl_real (-r))
-#align hyperreal.infinitesimal_sub_is_st Hyperreal.infinitesimal_sub_isSt
-
+#align hyperreal.infinitesimal_sub_is_st Hyperreal.IsSt.infinitesimal_sub
+
+/- warning: hyperreal.infinitesimal_sub_st -> Hyperreal.infinitesimal_sub_st is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Hyperreal.Infinitesimal (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (SubNegMonoid.toHasSub.{0} Hyperreal (AddGroup.toSubNegMonoid.{0} Hyperreal (AddGroupWithOne.toAddGroup.{0} Hyperreal (AddCommGroupWithOne.toAddGroupWithOne.{0} Hyperreal (Ring.toAddCommGroupWithOne.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Hyperreal (HasLiftT.mk.{1, 1} Real Hyperreal (CoeTCₓ.coe.{1, 1} Real Hyperreal Hyperreal.hasCoeT)) (Hyperreal.st x))))
+but is expected to have type
+  forall {x : Hyperreal}, (Not (Hyperreal.Infinite x)) -> (Hyperreal.Infinitesimal (HSub.hSub.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHSub.{0} Hyperreal (Ring.toSub.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (Hyperreal.ofReal (Hyperreal.st x))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_sub_st Hyperreal.infinitesimal_sub_stₓ'. -/
 theorem infinitesimal_sub_st {x : ℝ*} (hx : ¬Infinite x) : Infinitesimal (x - st x) :=
-  infinitesimal_sub_isSt <| isSt_st' hx
+  Hyperreal.IsSt.infinitesimal_sub <| isSt_st' hx
 #align hyperreal.infinitesimal_sub_st Hyperreal.infinitesimal_sub_st
 
+/- warning: hyperreal.infinite_pos_iff_infinitesimal_inv_pos -> Hyperreal.infinitePos_iff_infinitesimal_inv_pos is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (And (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)))
+but is expected to have type
+  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos x) (And (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_iff_infinitesimal_inv_pos Hyperreal.infinitePos_iff_infinitesimal_inv_posₓ'. -/
 theorem infinitePos_iff_infinitesimal_inv_pos {x : ℝ*} :
     InfinitePos x ↔ Infinitesimal x⁻¹ ∧ 0 < x⁻¹ :=
   ⟨fun hip =>
@@ -880,21 +1512,39 @@ theorem infinitePos_iff_infinitesimal_inv_pos {x : ℝ*} :
           ((infinitesimal_def.mp hi) (|r|)⁻¹ (inv_pos.2 (abs_pos.2 h))).2)⟩
 #align hyperreal.infinite_pos_iff_infinitesimal_inv_pos Hyperreal.infinitePos_iff_infinitesimal_inv_pos
 
+/- warning: hyperreal.infinite_neg_iff_infinitesimal_inv_neg -> Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (And (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))))
+but is expected to have type
+  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg x) (And (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_iff_infinitesimal_inv_neg Hyperreal.infiniteNeg_iff_infinitesimal_inv_negₓ'. -/
 theorem infiniteNeg_iff_infinitesimal_inv_neg {x : ℝ*} :
     InfiniteNeg x ↔ Infinitesimal x⁻¹ ∧ x⁻¹ < 0 :=
   ⟨fun hin =>
     by
-    have hin' := infinitePos_iff_infinitesimal_inv_pos.mp (infinitePos_neg_of_infiniteNeg hin)
+    have hin' := infinitePos_iff_infinitesimal_inv_pos.mp (Hyperreal.InfiniteNeg.neg hin)
     rwa [infinitesimal_neg_iff, ← neg_pos, neg_inv], fun hin => by
     rwa [← neg_pos, infinitesimal_neg_iff, neg_inv, ← infinite_pos_iff_infinitesimal_inv_pos, ←
       infinite_neg_iff_infinite_pos_neg] at hin⟩
 #align hyperreal.infinite_neg_iff_infinitesimal_inv_neg Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg
 
+/- warning: hyperreal.infinitesimal_inv_of_infinite -> Hyperreal.infinitesimal_inv_of_infinite is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Hyperreal.Infinite x) -> (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x))
+but is expected to have type
+  forall {x : Hyperreal}, (Hyperreal.Infinite x) -> (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_inv_of_infinite Hyperreal.infinitesimal_inv_of_infiniteₓ'. -/
 theorem infinitesimal_inv_of_infinite {x : ℝ*} : Infinite x → Infinitesimal x⁻¹ := fun hi =>
   Or.cases_on hi (fun hip => (infinitePos_iff_infinitesimal_inv_pos.mp hip).1) fun hin =>
     (infiniteNeg_iff_infinitesimal_inv_neg.mp hin).1
 #align hyperreal.infinitesimal_inv_of_infinite Hyperreal.infinitesimal_inv_of_infinite
 
+/- warning: hyperreal.infinite_of_infinitesimal_inv -> Hyperreal.infinite_of_infinitesimal_inv is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) -> (Hyperreal.Infinite x)
+but is expected to have type
+  forall {x : Hyperreal}, (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)) -> (Hyperreal.Infinite x)
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_of_infinitesimal_inv Hyperreal.infinite_of_infinitesimal_invₓ'. -/
 theorem infinite_of_infinitesimal_inv {x : ℝ*} (h0 : x ≠ 0) (hi : Infinitesimal x⁻¹) : Infinite x :=
   by
   cases' lt_or_gt_of_ne h0 with hn hp
@@ -902,20 +1552,44 @@ theorem infinite_of_infinitesimal_inv {x : ℝ*} (h0 : x ≠ 0) (hi : Infinitesi
   · exact Or.inl (infinite_pos_iff_infinitesimal_inv_pos.mpr ⟨hi, inv_pos.mpr hp⟩)
 #align hyperreal.infinite_of_infinitesimal_inv Hyperreal.infinite_of_infinitesimal_inv
 
+/- warning: hyperreal.infinite_iff_infinitesimal_inv -> Hyperreal.infinite_iff_infinitesimal_inv is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Iff (Hyperreal.Infinite x) (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)))
+but is expected to have type
+  forall {x : Hyperreal}, (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Iff (Hyperreal.Infinite x) (Hyperreal.Infinitesimal (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_iff_infinitesimal_inv Hyperreal.infinite_iff_infinitesimal_invₓ'. -/
 theorem infinite_iff_infinitesimal_inv {x : ℝ*} (h0 : x ≠ 0) : Infinite x ↔ Infinitesimal x⁻¹ :=
   ⟨infinitesimal_inv_of_infinite, infinite_of_infinitesimal_inv h0⟩
 #align hyperreal.infinite_iff_infinitesimal_inv Hyperreal.infinite_iff_infinitesimal_inv
 
+/- warning: hyperreal.infinitesimal_pos_iff_infinite_pos_inv -> Hyperreal.infinitesimal_pos_iff_infinitePos_inv is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (And (Hyperreal.Infinitesimal x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x))
+but is expected to have type
+  forall {x : Hyperreal}, Iff (Hyperreal.InfinitePos (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)) (And (Hyperreal.Infinitesimal x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_pos_iff_infinite_pos_inv Hyperreal.infinitesimal_pos_iff_infinitePos_invₓ'. -/
 theorem infinitesimal_pos_iff_infinitePos_inv {x : ℝ*} :
     InfinitePos x⁻¹ ↔ Infinitesimal x ∧ 0 < x := by
   convert infinite_pos_iff_infinitesimal_inv_pos <;> simp only [inv_inv]
 #align hyperreal.infinitesimal_pos_iff_infinite_pos_inv Hyperreal.infinitesimal_pos_iff_infinitePos_inv
 
+/- warning: hyperreal.infinitesimal_neg_iff_infinite_neg_inv -> Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (And (Hyperreal.Infinitesimal x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))))
+but is expected to have type
+  forall {x : Hyperreal}, Iff (Hyperreal.InfiniteNeg (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)) (And (Hyperreal.Infinitesimal x) (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_neg_iff_infinite_neg_inv Hyperreal.infinitesimal_neg_iff_infiniteNeg_invₓ'. -/
 theorem infinitesimal_neg_iff_infiniteNeg_inv {x : ℝ*} :
     InfiniteNeg x⁻¹ ↔ Infinitesimal x ∧ x < 0 := by
   convert infinite_neg_iff_infinitesimal_inv_neg <;> simp only [inv_inv]
 #align hyperreal.infinitesimal_neg_iff_infinite_neg_inv Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv
 
+/- warning: hyperreal.infinitesimal_iff_infinite_inv -> Hyperreal.infinitesimal_iff_infinite_inv is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal}, (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Iff (Hyperreal.Infinitesimal x) (Hyperreal.Infinite (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)))
+but is expected to have type
+  forall {x : Hyperreal}, (Ne.{1} Hyperreal x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Iff (Hyperreal.Infinitesimal x) (Hyperreal.Infinite (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinitesimal_iff_infinite_inv Hyperreal.infinitesimal_iff_infinite_invₓ'. -/
 theorem infinitesimal_iff_infinite_inv {x : ℝ*} (h : x ≠ 0) : Infinitesimal x ↔ Infinite x⁻¹ := by
   convert(infinite_iff_infinitesimal_inv (inv_ne_zero h)).symm <;> simp only [inv_inv]
 #align hyperreal.infinitesimal_iff_infinite_inv Hyperreal.infinitesimal_iff_infinite_inv
@@ -925,22 +1599,37 @@ theorem infinitesimal_iff_infinite_inv {x : ℝ*} (h : x ≠ 0) : Infinitesimal
 -/
 
 
+#print Hyperreal.isSt_of_tendsto /-
 theorem isSt_of_tendsto {f : ℕ → ℝ} {r : ℝ} (hf : Tendsto f atTop (𝓝 r)) : IsSt (ofSeq f) r :=
   by
   have hg : Tendsto (fun n => f n - r) atTop (𝓝 0) := sub_self r ▸ hf.sub tendsto_const_nhds
   rw [← zero_add r, ← sub_add_cancel f fun n => r] <;>
     exact is_st_add (infinitesimal_of_tendsto_zero hg) (is_st_refl_real r)
 #align hyperreal.is_st_of_tendsto Hyperreal.isSt_of_tendsto
+-/
 
-theorem isSt_inv {x : ℝ*} {r : ℝ} (hi : ¬Infinitesimal x) : IsSt x r → IsSt x⁻¹ r⁻¹ := fun hxr =>
+/- warning: hyperreal.is_st_inv -> Hyperreal.IsSt.inv is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {r : Real}, (Not (Hyperreal.Infinitesimal x)) -> (Hyperreal.IsSt x r) -> (Hyperreal.IsSt (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x) (Inv.inv.{0} Real Real.hasInv r))
+but is expected to have type
+  forall {x : Hyperreal} {r : Real}, (Not (Hyperreal.Infinitesimal x)) -> (Hyperreal.IsSt x r) -> (Hyperreal.IsSt (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x) (Inv.inv.{0} Real Real.instInvReal r))
+Case conversion may be inaccurate. Consider using '#align hyperreal.is_st_inv Hyperreal.IsSt.invₓ'. -/
+theorem Hyperreal.IsSt.inv {x : ℝ*} {r : ℝ} (hi : ¬Infinitesimal x) : IsSt x r → IsSt x⁻¹ r⁻¹ :=
+  fun hxr =>
   have h : x ≠ 0 := fun h => hi (h.symm ▸ infinitesimal_zero)
   have H := exists_st_of_not_infinite <| not_imp_not.mpr (infinitesimal_iff_infinite_inv h).mpr hi
   Exists.cases_on H fun s hs =>
-    have H' : IsSt 1 (r * s) := mul_inv_cancel h ▸ isSt_mul hxr hs
+    have H' : IsSt 1 (r * s) := mul_inv_cancel h ▸ Hyperreal.IsSt.mul hxr hs
     have H'' : s = r⁻¹ := one_div r ▸ eq_one_div_of_mul_eq_one_right (eq_of_isSt_real H').symm
     H'' ▸ hs
-#align hyperreal.is_st_inv Hyperreal.isSt_inv
-
+#align hyperreal.is_st_inv Hyperreal.IsSt.inv
+
+/- warning: hyperreal.st_inv -> Hyperreal.st_inv is a dubious translation:
+lean 3 declaration is
+  forall (x : Hyperreal), Eq.{1} Real (Hyperreal.st (Inv.inv.{0} Hyperreal (DivInvMonoid.toHasInv.{0} Hyperreal (DivisionRing.toDivInvMonoid.{0} Hyperreal (Field.toDivisionRing.{0} Hyperreal (LinearOrderedField.toField.{0} Hyperreal Hyperreal.linearOrderedField)))) x)) (Inv.inv.{0} Real Real.hasInv (Hyperreal.st x))
+but is expected to have type
+  forall (x : Hyperreal), Eq.{1} Real (Hyperreal.st (Inv.inv.{0} Hyperreal (LinearOrderedField.toInv.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal) x)) (Inv.inv.{0} Real Real.instInvReal (Hyperreal.st x))
+Case conversion may be inaccurate. Consider using '#align hyperreal.st_inv Hyperreal.st_invₓ'. -/
 theorem st_inv (x : ℝ*) : st x⁻¹ = (st x)⁻¹ :=
   by
   by_cases h0 : x = 0
@@ -957,14 +1646,24 @@ theorem st_inv (x : ℝ*) : st x⁻¹ = (st x)⁻¹ :=
 -/
 
 
+#print Hyperreal.infinitePos_omega /-
 theorem infinitePos_omega : InfinitePos ω :=
   infinitePos_iff_infinitesimal_inv_pos.mpr ⟨infinitesimal_epsilon, epsilon_pos⟩
 #align hyperreal.infinite_pos_omega Hyperreal.infinitePos_omega
+-/
 
+#print Hyperreal.infinite_omega /-
 theorem infinite_omega : Infinite ω :=
   (infinite_iff_infinitesimal_inv omega_ne_zero).mpr infinitesimal_epsilon
 #align hyperreal.infinite_omega Hyperreal.infinite_omega
+-/
 
+/- warning: hyperreal.infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos -> Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_posₓ'. -/
 theorem infinitePos_mul_of_infinitePos_not_infinitesimal_pos {x y : ℝ*} :
     InfinitePos x → ¬Infinitesimal y → 0 < y → InfinitePos (x * y) := fun hx hy₁ hy₂ r =>
   have hy₁' := not_forall.mp (by rw [infinitesimal_def] at hy₁ <;> exact hy₁)
@@ -975,68 +1674,140 @@ theorem infinitePos_mul_of_infinitePos_not_infinitesimal_pos {x y : ℝ*} :
       exact mul_lt_mul (hx (r / r₁)) hyr.2 (coe_lt_coe.2 hyr.1) (le_of_lt (hx 0))
 #align hyperreal.infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos
 
+/- warning: hyperreal.infinite_pos_mul_of_not_infinitesimal_pos_infinite_pos -> Hyperreal.infinitePos_mul_of_not_infinitesimal_pos_infinitePos is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_mul_of_not_infinitesimal_pos_infinite_pos Hyperreal.infinitePos_mul_of_not_infinitesimal_pos_infinitePosₓ'. -/
 theorem infinitePos_mul_of_not_infinitesimal_pos_infinitePos {x y : ℝ*} :
     ¬Infinitesimal x → 0 < x → InfinitePos y → InfinitePos (x * y) := fun hx hp hy => by
   rw [mul_comm] <;> exact infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos hy hx hp
 #align hyperreal.infinite_pos_mul_of_not_infinitesimal_pos_infinite_pos Hyperreal.infinitePos_mul_of_not_infinitesimal_pos_infinitePos
 
+/- warning: hyperreal.infinite_pos_mul_of_infinite_neg_not_infinitesimal_neg -> Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) y (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) y (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_mul_of_infinite_neg_not_infinitesimal_neg Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_negₓ'. -/
 theorem infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg {x y : ℝ*} :
     InfiniteNeg x → ¬Infinitesimal y → y < 0 → InfinitePos (x * y) := by
   rw [infinite_neg_iff_infinite_pos_neg, ← neg_pos, ← neg_mul_neg, infinitesimal_neg_iff] <;>
     exact infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos
 #align hyperreal.infinite_pos_mul_of_infinite_neg_not_infinitesimal_neg Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg
 
+/- warning: hyperreal.infinite_pos_mul_of_not_infinitesimal_neg_infinite_neg -> Hyperreal.infinitePos_mul_of_not_infinitesimal_neg_infiniteNeg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_mul_of_not_infinitesimal_neg_infinite_neg Hyperreal.infinitePos_mul_of_not_infinitesimal_neg_infiniteNegₓ'. -/
 theorem infinitePos_mul_of_not_infinitesimal_neg_infiniteNeg {x y : ℝ*} :
     ¬Infinitesimal x → x < 0 → InfiniteNeg y → InfinitePos (x * y) := fun hx hp hy => by
   rw [mul_comm] <;> exact infinite_pos_mul_of_infinite_neg_not_infinitesimal_neg hy hx hp
 #align hyperreal.infinite_pos_mul_of_not_infinitesimal_neg_infinite_neg Hyperreal.infinitePos_mul_of_not_infinitesimal_neg_infiniteNeg
 
+/- warning: hyperreal.infinite_neg_mul_of_infinite_pos_not_infinitesimal_neg -> Hyperreal.infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) y (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) y (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_mul_of_infinite_pos_not_infinitesimal_neg Hyperreal.infiniteNeg_mul_of_infinitePos_not_infinitesimal_negₓ'. -/
 theorem infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg {x y : ℝ*} :
     InfinitePos x → ¬Infinitesimal y → y < 0 → InfiniteNeg (x * y) := by
   rw [infinite_neg_iff_infinite_pos_neg, ← neg_pos, neg_mul_eq_mul_neg, infinitesimal_neg_iff] <;>
     exact infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos
 #align hyperreal.infinite_neg_mul_of_infinite_pos_not_infinitesimal_neg Hyperreal.infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg
 
+/- warning: hyperreal.infinite_neg_mul_of_not_infinitesimal_neg_infinite_pos -> Hyperreal.infiniteNeg_mul_of_not_infinitesimal_neg_infinitePos is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))))))))) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) x (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_mul_of_not_infinitesimal_neg_infinite_pos Hyperreal.infiniteNeg_mul_of_not_infinitesimal_neg_infinitePosₓ'. -/
 theorem infiniteNeg_mul_of_not_infinitesimal_neg_infinitePos {x y : ℝ*} :
     ¬Infinitesimal x → x < 0 → InfinitePos y → InfiniteNeg (x * y) := fun hx hp hy => by
   rw [mul_comm] <;> exact infinite_neg_mul_of_infinite_pos_not_infinitesimal_neg hy hx hp
 #align hyperreal.infinite_neg_mul_of_not_infinitesimal_neg_infinite_pos Hyperreal.infiniteNeg_mul_of_not_infinitesimal_neg_infinitePos
 
+/- warning: hyperreal.infinite_neg_mul_of_infinite_neg_not_infinitesimal_pos -> Hyperreal.infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Not (Hyperreal.Infinitesimal y)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_mul_of_infinite_neg_not_infinitesimal_pos Hyperreal.infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_posₓ'. -/
 theorem infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos {x y : ℝ*} :
     InfiniteNeg x → ¬Infinitesimal y → 0 < y → InfiniteNeg (x * y) := by
   rw [infinite_neg_iff_infinite_pos_neg, infinite_neg_iff_infinite_pos_neg, neg_mul_eq_neg_mul] <;>
     exact infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos
 #align hyperreal.infinite_neg_mul_of_infinite_neg_not_infinitesimal_pos Hyperreal.infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos
 
+/- warning: hyperreal.infinite_neg_mul_of_not_infinitesimal_pos_infinite_neg -> Hyperreal.infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNeg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (OrderedAddCommGroup.toPartialOrder.{0} Hyperreal (StrictOrderedRing.toOrderedAddCommGroup.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) (OfNat.ofNat.{0} Hyperreal 0 (OfNat.mk.{0} Hyperreal 0 (Zero.zero.{0} Hyperreal (MulZeroClass.toHasZero.{0} Hyperreal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Hyperreal (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField)))))))))))) x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (LT.lt.{0} Hyperreal (Preorder.toLT.{0} Hyperreal (PartialOrder.toPreorder.{0} Hyperreal (StrictOrderedRing.toPartialOrder.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))) (OfNat.ofNat.{0} Hyperreal 0 (Zero.toOfNat0.{0} Hyperreal (CommMonoidWithZero.toZero.{0} Hyperreal (CommGroupWithZero.toCommMonoidWithZero.{0} Hyperreal (Semifield.toCommGroupWithZero.{0} Hyperreal (LinearOrderedSemifield.toSemifield.{0} Hyperreal (LinearOrderedField.toLinearOrderedSemifield.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal))))))) x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_mul_of_not_infinitesimal_pos_infinite_neg Hyperreal.infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNegₓ'. -/
 theorem infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNeg {x y : ℝ*} :
     ¬Infinitesimal x → 0 < x → InfiniteNeg y → InfiniteNeg (x * y) := fun hx hp hy => by
   rw [mul_comm] <;> exact infinite_neg_mul_of_infinite_neg_not_infinitesimal_pos hy hx hp
 #align hyperreal.infinite_neg_mul_of_not_infinitesimal_pos_infinite_neg Hyperreal.infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNeg
 
+/- warning: hyperreal.infinite_pos_mul_infinite_pos -> Hyperreal.infinitePos_mul_infinitePos is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_mul_infinite_pos Hyperreal.infinitePos_mul_infinitePosₓ'. -/
 theorem infinitePos_mul_infinitePos {x y : ℝ*} :
     InfinitePos x → InfinitePos y → InfinitePos (x * y) := fun hx hy =>
-  infinitePos_mul_of_infinitePos_not_infinitesimal_pos hx (not_infinitesimal_of_infinitePos hy)
-    (hy 0)
+  infinitePos_mul_of_infinitePos_not_infinitesimal_pos hx
+    (Hyperreal.InfinitePos.not_infinitesimal hy) (hy 0)
 #align hyperreal.infinite_pos_mul_infinite_pos Hyperreal.infinitePos_mul_infinitePos
 
+/- warning: hyperreal.infinite_neg_mul_infinite_neg -> Hyperreal.infiniteNeg_mul_infiniteNeg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfinitePos (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_mul_infinite_neg Hyperreal.infiniteNeg_mul_infiniteNegₓ'. -/
 theorem infiniteNeg_mul_infiniteNeg {x y : ℝ*} :
     InfiniteNeg x → InfiniteNeg y → InfinitePos (x * y) := fun hx hy =>
-  infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg hx (not_infinitesimal_of_infiniteNeg hy)
-    (hy 0)
+  infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg hx
+    (Hyperreal.InfiniteNeg.not_infinitesimal hy) (hy 0)
 #align hyperreal.infinite_neg_mul_infinite_neg Hyperreal.infiniteNeg_mul_infiniteNeg
 
+/- warning: hyperreal.infinite_pos_mul_infinite_neg -> Hyperreal.infinitePos_mul_infiniteNeg is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfinitePos x) -> (Hyperreal.InfiniteNeg y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_pos_mul_infinite_neg Hyperreal.infinitePos_mul_infiniteNegₓ'. -/
 theorem infinitePos_mul_infiniteNeg {x y : ℝ*} :
     InfinitePos x → InfiniteNeg y → InfiniteNeg (x * y) := fun hx hy =>
-  infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg hx (not_infinitesimal_of_infiniteNeg hy)
-    (hy 0)
+  infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg hx
+    (Hyperreal.InfiniteNeg.not_infinitesimal hy) (hy 0)
 #align hyperreal.infinite_pos_mul_infinite_neg Hyperreal.infinitePos_mul_infiniteNeg
 
+/- warning: hyperreal.infinite_neg_mul_infinite_pos -> Hyperreal.infiniteNeg_mul_infinitePos is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.InfiniteNeg x) -> (Hyperreal.InfinitePos y) -> (Hyperreal.InfiniteNeg (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_neg_mul_infinite_pos Hyperreal.infiniteNeg_mul_infinitePosₓ'. -/
 theorem infiniteNeg_mul_infinitePos {x y : ℝ*} :
     InfiniteNeg x → InfinitePos y → InfiniteNeg (x * y) := fun hx hy =>
-  infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos hx (not_infinitesimal_of_infinitePos hy)
-    (hy 0)
+  infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos hx
+    (Hyperreal.InfinitePos.not_infinitesimal hy) (hy 0)
 #align hyperreal.infinite_neg_mul_infinite_pos Hyperreal.infiniteNeg_mul_infinitePos
 
+/- warning: hyperreal.infinite_mul_of_infinite_not_infinitesimal -> Hyperreal.infinite_mul_of_infinite_not_infinitesimal is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.Infinite x) -> (Not (Hyperreal.Infinitesimal y)) -> (Hyperreal.Infinite (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.Infinite x) -> (Not (Hyperreal.Infinitesimal y)) -> (Hyperreal.Infinite (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_mul_of_infinite_not_infinitesimal Hyperreal.infinite_mul_of_infinite_not_infinitesimalₓ'. -/
 theorem infinite_mul_of_infinite_not_infinitesimal {x y : ℝ*} :
     Infinite x → ¬Infinitesimal y → Infinite (x * y) := fun hx hy =>
   have h0 : y < 0 ∨ 0 < y := lt_or_gt_of_ne fun H0 => hy (Eq.substr H0 (isSt_refl_real 0))
@@ -1049,13 +1820,25 @@ theorem infinite_mul_of_infinite_not_infinitesimal {x y : ℝ*} :
       fun H0 Hx => Or.inr (infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos Hx hy H0))
 #align hyperreal.infinite_mul_of_infinite_not_infinitesimal Hyperreal.infinite_mul_of_infinite_not_infinitesimal
 
+/- warning: hyperreal.infinite_mul_of_not_infinitesimal_infinite -> Hyperreal.infinite_mul_of_not_infinitesimal_infinite is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (Hyperreal.Infinite y) -> (Hyperreal.Infinite (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Not (Hyperreal.Infinitesimal x)) -> (Hyperreal.Infinite y) -> (Hyperreal.Infinite (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite_mul_of_not_infinitesimal_infinite Hyperreal.infinite_mul_of_not_infinitesimal_infiniteₓ'. -/
 theorem infinite_mul_of_not_infinitesimal_infinite {x y : ℝ*} :
     ¬Infinitesimal x → Infinite y → Infinite (x * y) := fun hx hy => by
   rw [mul_comm] <;> exact infinite_mul_of_infinite_not_infinitesimal hy hx
 #align hyperreal.infinite_mul_of_not_infinitesimal_infinite Hyperreal.infinite_mul_of_not_infinitesimal_infinite
 
+/- warning: hyperreal.infinite.mul -> Hyperreal.Infinite.mul is a dubious translation:
+lean 3 declaration is
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.Infinite x) -> (Hyperreal.Infinite y) -> (Hyperreal.Infinite (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (Distrib.toHasMul.{0} Hyperreal (Ring.toDistrib.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.linearOrderedField))))))) x y))
+but is expected to have type
+  forall {x : Hyperreal} {y : Hyperreal}, (Hyperreal.Infinite x) -> (Hyperreal.Infinite y) -> (Hyperreal.Infinite (HMul.hMul.{0, 0, 0} Hyperreal Hyperreal Hyperreal (instHMul.{0} Hyperreal (NonUnitalNonAssocRing.toMul.{0} Hyperreal (NonAssocRing.toNonUnitalNonAssocRing.{0} Hyperreal (Ring.toNonAssocRing.{0} Hyperreal (StrictOrderedRing.toRing.{0} Hyperreal (LinearOrderedRing.toStrictOrderedRing.{0} Hyperreal (LinearOrderedCommRing.toLinearOrderedRing.{0} Hyperreal (LinearOrderedField.toLinearOrderedCommRing.{0} Hyperreal Hyperreal.instLinearOrderedFieldHyperreal)))))))) x y))
+Case conversion may be inaccurate. Consider using '#align hyperreal.infinite.mul Hyperreal.Infinite.mulₓ'. -/
 theorem Infinite.mul {x y : ℝ*} : Infinite x → Infinite y → Infinite (x * y) := fun hx hy =>
-  infinite_mul_of_infinite_not_infinitesimal hx (not_infinitesimal_of_infinite hy)
+  infinite_mul_of_infinite_not_infinitesimal hx (Hyperreal.Infinite.not_infinitesimal hy)
 #align hyperreal.infinite.mul Hyperreal.Infinite.mul
 
 end Hyperreal

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

@@ -803,7 +803,7 @@ theorem lt_neg_of_pos_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r :
 
 theorem gt_of_neg_of_infinitesimal {x : ℝ*} : Infinitesimal x → ∀ r : ℝ, r < 0 → ↑r < x :=
   fun hi r hr => by
-  convert ((infinitesimal_def.mp hi) (-r) (neg_pos.mpr hr)).1 <;> exact (neg_neg ↑r).symm
+  convert((infinitesimal_def.mp hi) (-r) (neg_pos.mpr hr)).1 <;> exact (neg_neg ↑r).symm
 #align hyperreal.gt_of_neg_of_infinitesimal Hyperreal.gt_of_neg_of_infinitesimal
 
 theorem abs_lt_real_iff_infinitesimal {x : ℝ*} : Infinitesimal x ↔ ∀ r : ℝ, r ≠ 0 → |x| < |r| :=
@@ -917,7 +917,7 @@ theorem infinitesimal_neg_iff_infiniteNeg_inv {x : ℝ*} :
 #align hyperreal.infinitesimal_neg_iff_infinite_neg_inv Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv
 
 theorem infinitesimal_iff_infinite_inv {x : ℝ*} (h : x ≠ 0) : Infinitesimal x ↔ Infinite x⁻¹ := by
-  convert (infinite_iff_infinitesimal_inv (inv_ne_zero h)).symm <;> simp only [inv_inv]
+  convert(infinite_iff_infinitesimal_inv (inv_ne_zero h)).symm <;> simp only [inv_inv]
 #align hyperreal.infinitesimal_iff_infinite_inv Hyperreal.infinitesimal_iff_infinite_inv
 
 /-!

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -747,7 +747,7 @@ theorem isSt_mul {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt y s) : Is
           is_st_iff_abs_sub_lt_delta.mp hys (d / t)
             (div_pos hd (coe_pos.1 (lt_of_le_of_lt (abs_nonneg x) ht)))
         rw [hs, coe_zero, sub_zero] at hys'
-        rw [hs, mul_zero, coe_zero, sub_zero, abs_mul, mul_comm, ←
+        rw [hs, MulZeroClass.mul_zero, coe_zero, sub_zero, abs_mul, mul_comm, ←
           div_mul_cancel (d : ℝ*) (ne_of_gt (lt_of_le_of_lt (abs_nonneg x) ht)), ← coe_div]
         exact mul_lt_mul'' hys' ht (abs_nonneg _) (abs_nonneg _)
       exact is_st_mul' hxr hys hs
@@ -838,7 +838,7 @@ theorem infinitesimal_neg_iff {x : ℝ*} : Infinitesimal x ↔ Infinitesimal (-x
 #align hyperreal.infinitesimal_neg_iff Hyperreal.infinitesimal_neg_iff
 
 theorem infinitesimal_mul {x y : ℝ*} (hx : Infinitesimal x) (hy : Infinitesimal y) :
-    Infinitesimal (x * y) := by simpa only [mul_zero] using is_st_mul hx hy
+    Infinitesimal (x * y) := by simpa only [MulZeroClass.mul_zero] using is_st_mul hx hy
 #align hyperreal.infinitesimal_mul Hyperreal.infinitesimal_mul
 
 theorem infinitesimal_of_tendsto_zero {f : ℕ → ℝ} :

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

@@ -706,10 +706,10 @@ private theorem is_st_mul' {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
         calc
           |x * y - r * s| = |x * (y - s) + (x - r) * s| := by
             rw [mul_sub, sub_mul, add_sub, sub_add_cancel]
-          _ ≤ |x * (y - s)| + |(x - r) * s| := abs_add _ _
+          _ ≤ |x * (y - s)| + |(x - r) * s| := (abs_add _ _)
           _ ≤ |x| * |y - s| + |x - r| * |s| := by simp only [abs_mul]
           _ ≤ |x| * (d / t / 2 : ℝ) + (d / |s| / 2 : ℝ) * |s| :=
-            add_le_add
+            (add_le_add
               (mul_le_mul_of_nonneg_left
                   (le_of_lt <|
                     hys' _ <|
@@ -717,7 +717,7 @@ private theorem is_st_mul' {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
                 abs_nonneg _)
               (mul_le_mul_of_nonneg_right
                   (le_of_lt <| hxr' _ <| half_pos <| div_pos hd <| abs_pos.2 hs) <|
-                abs_nonneg _)
+                abs_nonneg _))
           _ = (d / 2 * (|x| / t) + d / 2 : ℝ*) :=
             by
             push_cast [-Filter.Germ.const_div]
@@ -726,10 +726,10 @@ private theorem is_st_mul' {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt
             have : (2 : ℝ*) ≠ 0 := two_ne_zero
             field_simp [*, add_mul, mul_add, mul_assoc, mul_comm, mul_left_comm]
           _ < (d / 2 * 1 + d / 2 : ℝ*) :=
-            add_lt_add_right
+            (add_lt_add_right
               (mul_lt_mul_of_pos_left ((div_lt_one <| lt_of_le_of_lt (abs_nonneg x) ht).mpr ht) <|
                 half_pos <| coe_pos.2 hd)
-              _
+              _)
           _ = (d : ℝ*) := by rw [mul_one, add_halves]
           
 #align hyperreal.is_st_mul' hyperreal.is_st_mul'

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

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

| Statement | New name | Old name | |

@@ -819,7 +819,7 @@ theorem infinitePos_mul_of_infinitePos_not_infinitesimal_pos {x y : ℝ*} :
   let ⟨r₁, hy₁''⟩ := hy₁'
   have hyr : 0 < r₁ ∧ ↑r₁ ≤ y := by
     rwa [not_imp, ← abs_lt, not_lt, abs_of_pos hy₂] at hy₁''
-  rw [← div_mul_cancel r (ne_of_gt hyr.1), coe_mul]
+  rw [← div_mul_cancel₀ r (ne_of_gt hyr.1), coe_mul]
   exact mul_lt_mul (hx (r / r₁)) hyr.2 (coe_lt_coe.2 hyr.1) (le_of_lt (hx 0))
 #align hyperreal.infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos
 

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

• "new lemma"
• "added lemma"

@@ -150,7 +150,7 @@ theorem coe_min (x y : ℝ) : ((min x y : ℝ) : ℝ*) = min ↑x ↑y :=
 def ofSeq (f : ℕ → ℝ) : ℝ* := (↑f : Germ (hyperfilter ℕ : Filter ℕ) ℝ)
 #align hyperreal.of_seq Hyperreal.ofSeq
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 theorem ofSeq_surjective : Function.Surjective ofSeq := Quot.exists_rep
 
 theorem ofSeq_lt_ofSeq {f g : ℕ → ℝ} : ofSeq f < ofSeq g ↔ ∀ᶠ n in hyperfilter ℕ, f n < g n :=

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

@@ -526,7 +526,8 @@ theorem infinitePos_abs_iff_infinite_abs {x : ℝ*} : InfinitePos |x| ↔ Infini
   cases le_total 0 x <;> simp [*, abs_of_nonneg, abs_of_nonpos, infinite_neg]
 #align hyperreal.infinite_iff_infinite_abs Hyperreal.infinite_abs_iffₓ
 
--- Porting note: swapped LHS with RHS; todo: make it a `simp` lemma
+-- Porting note: swapped LHS with RHS;
+-- Porting note (#11215): TODO: make it a `simp` lemma
 @[simp] theorem infinitePos_abs_iff_infinite {x : ℝ*} : InfinitePos |x| ↔ Infinite x :=
   infinitePos_abs_iff_infinite_abs.trans infinite_abs_iff
 #align hyperreal.infinite_iff_infinite_pos_abs Hyperreal.infinitePos_abs_iff_infiniteₓ
@@ -904,7 +905,7 @@ theorem Infinite.mul {x y : ℝ*} : Infinite x → Infinite y → Infinite (x *
 end Hyperreal
 
 /-
-Porting note: todo: restore `positivity` plugin
+Porting note (#11215): TODO: restore `positivity` plugin
 
 namespace Tactic
 

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.

@@ -13,7 +13,8 @@ import Mathlib.Analysis.SpecificLimits.Basic
 -/
 
 
-open Filter Germ Topology Classical
+open scoped Classical
+open Filter Germ Topology
 
 /-- Hyperreal numbers on the ultrafilter extending the cofinite filter -/
 def Hyperreal : Type :=

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -149,7 +149,7 @@ theorem coe_min (x y : ℝ) : ((min x y : ℝ) : ℝ*) = min ↑x ↑y :=
 def ofSeq (f : ℕ → ℝ) : ℝ* := (↑f : Germ (hyperfilter ℕ : Filter ℕ) ℝ)
 #align hyperreal.of_seq Hyperreal.ofSeq
 
--- porting note: new lemma
+-- Porting note: new lemma
 theorem ofSeq_surjective : Function.Surjective ofSeq := Quot.exists_rep
 
 theorem ofSeq_lt_ofSeq {f g : ℕ → ℝ} : ofSeq f < ofSeq g ↔ ∀ᶠ n in hyperfilter ℕ, f n < g n :=
@@ -264,7 +264,7 @@ theorem isSt_of_tendsto {f : ℕ → ℝ} {r : ℝ} (hf : Tendsto f atTop (𝓝
   isSt_ofSeq_iff_tendsto.2 <| hf.mono_left Nat.hyperfilter_le_atTop
 #align hyperreal.is_st_of_tendsto Hyperreal.isSt_of_tendsto
 
--- porting note: moved up, renamed
+-- Porting note: moved up, renamed
 protected theorem IsSt.lt {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt y s) (hrs : r < s) :
     x < y := by
   rcases ofSeq_surjective x with ⟨f, rfl⟩
@@ -463,17 +463,17 @@ theorem InfiniteNeg.neg {x : ℝ*} : InfiniteNeg x → InfinitePos (-x) := fun h
   lt_neg.mp (hp (-r))
 #align hyperreal.infinite_pos_neg_of_infinite_neg Hyperreal.InfiniteNeg.neg
 
--- porting note: swapped LHS with RHS; added @[simp]
+-- Porting note: swapped LHS with RHS; added @[simp]
 @[simp] theorem infiniteNeg_neg {x : ℝ*} : InfiniteNeg (-x) ↔ InfinitePos x :=
   ⟨fun hin => neg_neg x ▸ hin.neg, InfinitePos.neg⟩
 #align hyperreal.infinite_pos_iff_infinite_neg_neg Hyperreal.infiniteNeg_negₓ
 
--- porting note: swapped LHS with RHS; added @[simp]
+-- Porting note: swapped LHS with RHS; added @[simp]
 @[simp] theorem infinitePos_neg {x : ℝ*} : InfinitePos (-x) ↔ InfiniteNeg x :=
   ⟨fun hin => neg_neg x ▸ hin.neg, InfiniteNeg.neg⟩
 #align hyperreal.infinite_neg_iff_infinite_pos_neg Hyperreal.infinitePos_negₓ
 
--- porting note: swapped LHS with RHS; added @[simp]
+-- Porting note: swapped LHS with RHS; added @[simp]
 @[simp] theorem infinite_neg {x : ℝ*} : Infinite (-x) ↔ Infinite x :=
   or_comm.trans <| infiniteNeg_neg.or infinitePos_neg
 #align hyperreal.infinite_iff_infinite_neg Hyperreal.infinite_negₓ
@@ -520,12 +520,12 @@ theorem infinitePos_abs_iff_infinite_abs {x : ℝ*} : InfinitePos |x| ↔ Infini
   infinitePos_iff_infinite_of_nonneg (abs_nonneg _)
 #align hyperreal.infinite_pos_abs_iff_infinite_abs Hyperreal.infinitePos_abs_iff_infinite_abs
 
--- porting note: swapped LHS with RHS; added @[simp]
+-- Porting note: swapped LHS with RHS; added @[simp]
 @[simp] theorem infinite_abs_iff {x : ℝ*} : Infinite |x| ↔ Infinite x := by
   cases le_total 0 x <;> simp [*, abs_of_nonneg, abs_of_nonpos, infinite_neg]
 #align hyperreal.infinite_iff_infinite_abs Hyperreal.infinite_abs_iffₓ
 
--- porting note: swapped LHS with RHS; todo: make it a `simp` lemma
+-- Porting note: swapped LHS with RHS; todo: make it a `simp` lemma
 @[simp] theorem infinitePos_abs_iff_infinite {x : ℝ*} : InfinitePos |x| ↔ Infinite x :=
   infinitePos_abs_iff_infinite_abs.trans infinite_abs_iff
 #align hyperreal.infinite_iff_infinite_pos_abs Hyperreal.infinitePos_abs_iff_infiniteₓ
@@ -688,7 +688,7 @@ theorem infinitesimal_zero : Infinitesimal 0 := isSt_refl_real 0
 theorem Infinitesimal.eq_zero {r : ℝ} : Infinitesimal r → r = 0 := eq_of_isSt_real
 #align hyperreal.zero_of_infinitesimal_real Hyperreal.Infinitesimal.eq_zero
 
--- porting note: swapped LHS with RHS; added `@[simp]`
+-- Porting note: swapped LHS with RHS; added `@[simp]`
 @[simp] theorem infinitesimal_real_iff {r : ℝ} : Infinitesimal r ↔ r = 0 :=
   isSt_real_iff_eq
 #align hyperreal.zero_iff_infinitesimal_real Hyperreal.infinitesimal_real_iff
@@ -701,7 +701,7 @@ nonrec theorem Infinitesimal.neg {x : ℝ*} (hx : Infinitesimal x) : Infinitesim
   simpa only [neg_zero] using hx.neg
 #align hyperreal.infinitesimal_neg Hyperreal.Infinitesimal.neg
 
--- porting note: swapped LHS and RHS, added `@[simp]`
+-- Porting note: swapped LHS and RHS, added `@[simp]`
 @[simp] theorem infinitesimal_neg {x : ℝ*} : Infinitesimal (-x) ↔ Infinitesimal x :=
   ⟨fun h => neg_neg x ▸ h.neg, Infinitesimal.neg⟩
 #align hyperreal.infinitesimal_neg_iff Hyperreal.infinitesimal_negₓ

See here on Zulip.

This PR changes a bunch of names containing nhds_0 or/and lt_1 to nhds_zero or/and lt_one.

@@ -215,7 +215,7 @@ theorem gt_of_tendsto_zero_of_neg {f : ℕ → ℝ} (hf : Tendsto f atTop (𝓝
 #align hyperreal.gt_of_tendsto_zero_of_neg Hyperreal.gt_of_tendsto_zero_of_neg
 
 theorem epsilon_lt_pos (x : ℝ) : 0 < x → ε < x :=
-  lt_of_tendsto_zero_of_pos tendsto_inverse_atTop_nhds_0_nat
+  lt_of_tendsto_zero_of_pos tendsto_inverse_atTop_nhds_zero_nat
 #align hyperreal.epsilon_lt_pos Hyperreal.epsilon_lt_pos
 
 /-- Standard part predicate -/
@@ -716,7 +716,7 @@ theorem infinitesimal_of_tendsto_zero {f : ℕ → ℝ} (h : Tendsto f atTop (
 #align hyperreal.infinitesimal_of_tendsto_zero Hyperreal.infinitesimal_of_tendsto_zero
 
 theorem infinitesimal_epsilon : Infinitesimal ε :=
-  infinitesimal_of_tendsto_zero tendsto_inverse_atTop_nhds_0_nat
+  infinitesimal_of_tendsto_zero tendsto_inverse_atTop_nhds_zero_nat
 #align hyperreal.infinitesimal_epsilon Hyperreal.infinitesimal_epsilon
 
 theorem not_real_of_infinitesimal_ne_zero (x : ℝ*) : Infinitesimal x → x ≠ 0 → ∀ r : ℝ, x ≠ r :=

Subset of #9319

@@ -294,7 +294,7 @@ theorem not_infinite_of_exists_st {x : ℝ*} : (∃ r : ℝ, IsSt x r) → ¬Inf
 #align hyperreal.not_infinite_of_exists_st Hyperreal.not_infinite_of_exists_st
 
 theorem Infinite.st_eq {x : ℝ*} (hi : Infinite x) : st x = 0 :=
-  dif_neg <| fun ⟨_r, hr⟩ ↦ hr.not_infinite hi
+  dif_neg fun ⟨_r, hr⟩ ↦ hr.not_infinite hi
 #align hyperreal.st_infinite Hyperreal.Infinite.st_eq
 
 theorem isSt_sSup {x : ℝ*} (hni : ¬Infinite x) : IsSt x (sSup { y : ℝ | (y : ℝ*) < x }) :=
@@ -413,7 +413,7 @@ theorem IsSt.sub {x y : ℝ*} {r s : ℝ} (hxr : IsSt x r) (hys : IsSt y s) : Is
 #align hyperreal.is_st_sub Hyperreal.IsSt.sub
 
 theorem IsSt.le {x y : ℝ*} {r s : ℝ} (hrx : IsSt x r) (hsy : IsSt y s) (hxy : x ≤ y) : r ≤ s :=
-  not_lt.1 <| fun h ↦ hxy.not_lt <| hsy.lt hrx h
+  not_lt.1 fun h ↦ hxy.not_lt <| hsy.lt hrx h
 #align hyperreal.is_st_le_of_le Hyperreal.IsSt.le
 
 theorem st_le_of_le {x y : ℝ*} (hix : ¬Infinite x) (hiy : ¬Infinite y) : x ≤ y → st x ≤ st y :=

Co-authored-by: timotree3 <timorcb@gmail.com>

Co-authored-by: timotree3 <timorcb@gmail.com>

@@ -89,8 +89,11 @@ theorem coe_add (x y : ℝ) : ↑(x + y) = (x + y : ℝ*) :=
 #noalign hyperreal.coe_bit0
 #noalign hyperreal.coe_bit1
 
+-- See note [no_index around OfNat.ofNat]
 @[simp, norm_cast]
-theorem coe_ofNat (n : ℕ) [n.AtLeastTwo] : ((OfNat.ofNat n : ℝ) : ℝ*) = OfNat.ofNat n := rfl
+theorem coe_ofNat (n : ℕ) [n.AtLeastTwo] :
+    ((no_index (OfNat.ofNat n : ℝ)) : ℝ*) = OfNat.ofNat n :=
+  rfl
 
 @[simp, norm_cast]
 theorem coe_mul (x y : ℝ) : ↑(x * y) = (x * y : ℝ*) :=

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Abhimanyu Pallavi Sudhir. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Abhimanyu Pallavi Sudhir
-
-! This file was ported from Lean 3 source module data.real.hyperreal
-! 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.Order.Filter.FilterProduct
 import Mathlib.Analysis.SpecificLimits.Basic
 
+#align_import data.real.hyperreal from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Construction of the hyperreal numbers as an ultraproduct of real sequences.
 -/

@@ -516,22 +516,22 @@ theorem infiniteNeg_iff_infinite_of_neg {x : ℝ*} (hn : x < 0) : InfiniteNeg x
   .symm <| or_iff_right fun h ↦ h.pos.not_lt hn
 #align hyperreal.infinite_neg_iff_infinite_of_neg Hyperreal.infiniteNeg_iff_infinite_of_neg
 
-theorem infinitePos_abs_iff_infinite_abs {x : ℝ*} : InfinitePos (|x|) ↔ Infinite (|x|) :=
+theorem infinitePos_abs_iff_infinite_abs {x : ℝ*} : InfinitePos |x| ↔ Infinite |x| :=
   infinitePos_iff_infinite_of_nonneg (abs_nonneg _)
 #align hyperreal.infinite_pos_abs_iff_infinite_abs Hyperreal.infinitePos_abs_iff_infinite_abs
 
 -- porting note: swapped LHS with RHS; added @[simp]
-@[simp] theorem infinite_abs_iff {x : ℝ*} : Infinite (|x|) ↔ Infinite x := by
+@[simp] theorem infinite_abs_iff {x : ℝ*} : Infinite |x| ↔ Infinite x := by
   cases le_total 0 x <;> simp [*, abs_of_nonneg, abs_of_nonpos, infinite_neg]
 #align hyperreal.infinite_iff_infinite_abs Hyperreal.infinite_abs_iffₓ
 
 -- porting note: swapped LHS with RHS; todo: make it a `simp` lemma
-@[simp] theorem infinitePos_abs_iff_infinite {x : ℝ*} : InfinitePos (|x|) ↔ Infinite x :=
+@[simp] theorem infinitePos_abs_iff_infinite {x : ℝ*} : InfinitePos |x| ↔ Infinite x :=
   infinitePos_abs_iff_infinite_abs.trans infinite_abs_iff
 #align hyperreal.infinite_iff_infinite_pos_abs Hyperreal.infinitePos_abs_iff_infiniteₓ
 
 theorem infinite_iff_abs_lt_abs {x : ℝ*} : Infinite x ↔ ∀ r : ℝ, (|r| : ℝ*) < |x| :=
-  infinitePos_abs_iff_infinite.symm.trans ⟨fun hI r => coe_abs r ▸ hI (|r|), fun hR r =>
+  infinitePos_abs_iff_infinite.symm.trans ⟨fun hI r => coe_abs r ▸ hI |r|, fun hR r =>
     (le_abs_self _).trans_lt (hR r)⟩
 #align hyperreal.infinite_iff_abs_lt_abs Hyperreal.infinite_iff_abs_lt_abs
 
@@ -678,7 +678,7 @@ theorem gt_of_neg_of_infinitesimal {x : ℝ*} (hi : Infinitesimal x) (r : ℝ) (
 #align hyperreal.gt_of_neg_of_infinitesimal Hyperreal.gt_of_neg_of_infinitesimal
 
 theorem abs_lt_real_iff_infinitesimal {x : ℝ*} : Infinitesimal x ↔ ∀ r : ℝ, r ≠ 0 → |x| < |↑r| :=
-  ⟨fun hi r hr ↦ abs_lt.mpr (coe_abs r ▸ infinitesimal_def.mp hi (|r|) (abs_pos.2 hr)), fun hR ↦
+  ⟨fun hi r hr ↦ abs_lt.mpr (coe_abs r ▸ infinitesimal_def.mp hi |r| (abs_pos.2 hr)), fun hR ↦
     infinitesimal_def.mpr fun r hr => abs_lt.mp <| (abs_of_pos <| coe_pos.2 hr) ▸ hR r <| hr.ne'⟩
 #align hyperreal.abs_lt_real_iff_infinitesimal Hyperreal.abs_lt_real_iff_infinitesimal
 
@@ -743,7 +743,7 @@ theorem infinitePos_iff_infinitesimal_inv_pos {x : ℝ*} :
     @_root_.by_cases (r = 0) (↑r < x) (fun h => Eq.substr h (inv_pos.mp hp)) fun h =>
       lt_of_le_of_lt (coe_le_coe.2 (le_abs_self r))
         ((inv_lt_inv (inv_pos.mp hp) (coe_lt_coe.2 (abs_pos.2 h))).mp
-          ((infinitesimal_def.mp hi) (|r|)⁻¹ (inv_pos.2 (abs_pos.2 h))).2)⟩
+          ((infinitesimal_def.mp hi) |r|⁻¹ (inv_pos.2 (abs_pos.2 h))).2)⟩
 #align hyperreal.infinite_pos_iff_infinitesimal_inv_pos Hyperreal.infinitePos_iff_infinitesimal_inv_pos
 
 theorem infiniteNeg_iff_infinitesimal_inv_neg {x : ℝ*} :

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>

@@ -297,9 +297,9 @@ theorem Infinite.st_eq {x : ℝ*} (hi : Infinite x) : st x = 0 :=
   dif_neg <| fun ⟨_r, hr⟩ ↦ hr.not_infinite hi
 #align hyperreal.st_infinite Hyperreal.Infinite.st_eq
 
-theorem isSt_supₛ {x : ℝ*} (hni : ¬Infinite x) : IsSt x (supₛ { y : ℝ | (y : ℝ*) < x }) :=
+theorem isSt_sSup {x : ℝ*} (hni : ¬Infinite x) : IsSt x (sSup { y : ℝ | (y : ℝ*) < x }) :=
   let S : Set ℝ := { y : ℝ | (y : ℝ*) < x }
-  let R : ℝ := supₛ S
+  let R : ℝ := sSup S
   let ⟨r₁, hr₁⟩ := not_forall.mp (not_or.mp hni).2
   let ⟨r₂, hr₂⟩ := not_forall.mp (not_or.mp hni).1
   have HR₁ : S.Nonempty :=
@@ -310,29 +310,29 @@ theorem isSt_supₛ {x : ℝ*} (hni : ¬Infinite x) : IsSt x (supₛ { y : ℝ |
   ⟨lt_of_not_le fun c =>
       have hc : ∀ y ∈ S, y ≤ R - δ := fun _y hy =>
         coe_le_coe.1 <| le_of_lt <| lt_of_lt_of_le hy c
-      not_lt_of_le (csupₛ_le HR₁ hc) <| sub_lt_self R hδ,
+      not_lt_of_le (csSup_le HR₁ hc) <| sub_lt_self R hδ,
     lt_of_not_le fun c =>
       have hc : ↑(R + δ / 2) < x :=
         lt_of_lt_of_le (add_lt_add_left (coe_lt_coe.2 (half_lt_self hδ)) R) c
-      not_lt_of_le (le_csupₛ HR₂ hc) <| (lt_add_iff_pos_right _).mpr <| half_pos hδ⟩
-#align hyperreal.is_st_Sup Hyperreal.isSt_supₛ
+      not_lt_of_le (le_csSup HR₂ hc) <| (lt_add_iff_pos_right _).mpr <| half_pos hδ⟩
+#align hyperreal.is_st_Sup Hyperreal.isSt_sSup
 
 theorem exists_st_of_not_infinite {x : ℝ*} (hni : ¬Infinite x) : ∃ r : ℝ, IsSt x r :=
-  ⟨supₛ { y : ℝ | (y : ℝ*) < x }, isSt_supₛ hni⟩
+  ⟨sSup { y : ℝ | (y : ℝ*) < x }, isSt_sSup hni⟩
 #align hyperreal.exists_st_of_not_infinite Hyperreal.exists_st_of_not_infinite
 
-theorem st_eq_supₛ {x : ℝ*} : st x = supₛ { y : ℝ | (y : ℝ*) < x } := by
+theorem st_eq_sSup {x : ℝ*} : st x = sSup { y : ℝ | (y : ℝ*) < x } := by
   rcases _root_.em (Infinite x) with (hx|hx)
   · rw [hx.st_eq]
     cases hx with
     | inl hx =>
-      convert Real.supₛ_univ.symm
+      convert Real.sSup_univ.symm
       exact Set.eq_univ_of_forall hx
     | inr hx =>
-      convert Real.supₛ_empty.symm
+      convert Real.sSup_empty.symm
       exact Set.eq_empty_of_forall_not_mem fun y hy ↦ hy.out.not_lt (hx _)
-  · exact (isSt_supₛ hx).st_eq
-#align hyperreal.st_eq_Sup Hyperreal.st_eq_supₛ
+  · exact (isSt_sSup hx).st_eq
+#align hyperreal.st_eq_Sup Hyperreal.st_eq_sSup
 
 theorem exists_st_iff_not_infinite {x : ℝ*} : (∃ r : ℝ, IsSt x r) ↔ ¬Infinite x :=
   ⟨not_infinite_of_exists_st, exists_st_of_not_infinite⟩
@@ -351,7 +351,7 @@ theorem isSt_st_of_exists_st {x : ℝ*} (hx : ∃ r : ℝ, IsSt x r) : IsSt x (s
 #align hyperreal.is_st_st_of_exists_st Hyperreal.isSt_st_of_exists_st
 
 theorem isSt_st' {x : ℝ*} (hx : ¬Infinite x) : IsSt x (st x) :=
-  (isSt_supₛ hx).isSt_st
+  (isSt_sSup hx).isSt_st
 #align hyperreal.is_st_st' Hyperreal.isSt_st'
 
 theorem isSt_st {x : ℝ*} (hx : st x ≠ 0) : IsSt x (st x) :=

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

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

@@ -812,14 +812,13 @@ theorem infinite_omega : Infinite ω :=
 #align hyperreal.infinite_omega Hyperreal.infinite_omega
 
 theorem infinitePos_mul_of_infinitePos_not_infinitesimal_pos {x y : ℝ*} :
-    InfinitePos x → ¬Infinitesimal y → 0 < y → InfinitePos (x * y) := fun hx hy₁ hy₂ r =>
+    InfinitePos x → ¬Infinitesimal y → 0 < y → InfinitePos (x * y) := fun hx hy₁ hy₂ r => by
   have hy₁' := not_forall.mp (mt infinitesimal_def.2 hy₁)
   let ⟨r₁, hy₁''⟩ := hy₁'
   have hyr : 0 < r₁ ∧ ↑r₁ ≤ y := by
     rwa [not_imp, ← abs_lt, not_lt, abs_of_pos hy₂] at hy₁''
-  by
-    rw [← div_mul_cancel r (ne_of_gt hyr.1), coe_mul]
-    exact mul_lt_mul (hx (r / r₁)) hyr.2 (coe_lt_coe.2 hyr.1) (le_of_lt (hx 0))
+  rw [← div_mul_cancel r (ne_of_gt hyr.1), coe_mul]
+  exact mul_lt_mul (hx (r / r₁)) hyr.2 (coe_lt_coe.2 hyr.1) (le_of_lt (hx 0))
 #align hyperreal.infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos
 
 theorem infinitePos_mul_of_not_infinitesimal_pos_infinitePos {x y : ℝ*} :