data.real.cau_seq_completion | Mathlib porting status

(last sync)

chore(data/real/cau_seq_completion): remove use of parameters (#18122)

This helps with porting

Diff

@@ -16,85 +16,87 @@ namespace cau_seq.completion
 open cau_seq
 
 section
-parameters {α : Type*} [linear_ordered_field α]
-parameters {β : Type*} [ring β] {abv : β → α} [is_absolute_value abv]
+variables {α : Type*} [linear_ordered_field α]
+variables {β : Type*} [ring β] (abv : β → α) [is_absolute_value abv]
 
 /-- The Cauchy completion of a ring with absolute value. -/
 def Cauchy := @quotient (cau_seq _ abv) cau_seq.equiv
 
+variables {abv}
+
 /-- The map from Cauchy sequences into the Cauchy completion. -/
-def mk : cau_seq _ abv → Cauchy := quotient.mk
+def mk : cau_seq _ abv → Cauchy abv := quotient.mk
 
-@[simp] theorem mk_eq_mk (f) : @eq Cauchy ⟦f⟧ (mk f) := rfl
+@[simp] theorem mk_eq_mk (f) : @eq (Cauchy abv) ⟦f⟧ (mk f) := rfl
 
-theorem mk_eq {f g} : mk f = mk g ↔ f ≈ g := quotient.eq
+theorem mk_eq {f g : cau_seq _ abv} : mk f = mk g ↔ f ≈ g := quotient.eq
 
 /-- The map from the original ring into the Cauchy completion. -/
-def of_rat (x : β) : Cauchy := mk (const abv x)
+def of_rat (x : β) : Cauchy abv := mk (const abv x)
 
-instance : has_zero Cauchy := ⟨of_rat 0⟩
-instance : has_one Cauchy := ⟨of_rat 1⟩
-instance : inhabited Cauchy := ⟨0⟩
+instance : has_zero (Cauchy abv) := ⟨of_rat 0⟩
+instance : has_one (Cauchy abv) := ⟨of_rat 1⟩
+instance : inhabited (Cauchy abv) := ⟨0⟩
 
-theorem of_rat_zero : of_rat 0 = 0 := rfl
-theorem of_rat_one : of_rat 1 = 1 := rfl
+theorem of_rat_zero : (of_rat 0 : Cauchy abv) = 0 := rfl
+theorem of_rat_one : (of_rat 1 : Cauchy abv) = 1 := rfl
 
-@[simp] theorem mk_eq_zero {f} : mk f = 0 ↔ lim_zero f :=
+@[simp] theorem mk_eq_zero {f : cau_seq _ abv} : mk f = 0 ↔ lim_zero f :=
 by have : mk f = 0 ↔ lim_zero (f - 0) := quotient.eq;
    rwa sub_zero at this
 
-instance : has_add Cauchy :=
+instance : has_add (Cauchy abv) :=
 ⟨quotient.map₂ (+) $ λ f₁ g₁ hf f₂ g₂ hg, add_equiv_add hf hg⟩
 
 @[simp] theorem mk_add (f g : cau_seq β abv) : mk f + mk g = mk (f + g) := rfl
 
-instance : has_neg Cauchy :=
+instance : has_neg (Cauchy abv) :=
 ⟨quotient.map has_neg.neg $ λ f₁ f₂ hf, neg_equiv_neg hf⟩
 
 @[simp] theorem mk_neg (f : cau_seq β abv) : -mk f = mk (-f) := rfl
 
-instance : has_mul Cauchy :=
+instance : has_mul (Cauchy abv) :=
 ⟨quotient.map₂ (*) $ λ f₁ g₁ hf f₂ g₂ hg, mul_equiv_mul hf hg⟩
 
 @[simp] theorem mk_mul (f g : cau_seq β abv) : mk f * mk g = mk (f * g) := rfl
 
-instance : has_sub Cauchy :=
+instance : has_sub (Cauchy abv) :=
 ⟨quotient.map₂ has_sub.sub $ λ f₁ g₁ hf f₂ g₂ hg, sub_equiv_sub hf hg⟩
 
 @[simp] theorem mk_sub (f g : cau_seq β abv) : mk f - mk g = mk (f - g) := rfl
 
-instance {γ : Type*} [has_smul γ β] [is_scalar_tower γ β β] : has_smul γ Cauchy :=
+instance {γ : Type*} [has_smul γ β] [is_scalar_tower γ β β] : has_smul γ (Cauchy abv) :=
 ⟨λ c, quotient.map ((•) c) $ λ f₁ g₁ hf, smul_equiv_smul _ hf⟩
 
 @[simp] theorem mk_smul  {γ : Type*} [has_smul γ β] [is_scalar_tower γ β β] (c : γ)
   (f : cau_seq β abv) :
   c • mk f = mk (c • f) := rfl
 
-instance : has_pow Cauchy ℕ :=
+instance : has_pow (Cauchy abv) ℕ :=
 ⟨λ x n, quotient.map (^ n) (λ f₁ g₁ hf, pow_equiv_pow hf _) x⟩
 
 @[simp] theorem mk_pow (n : ℕ) (f : cau_seq β abv) : mk f ^ n = mk (f ^ n) := rfl
 
-instance : has_nat_cast Cauchy := ⟨λ n, mk n⟩
-instance : has_int_cast Cauchy := ⟨λ n, mk n⟩
+instance : has_nat_cast (Cauchy abv) := ⟨λ n, mk n⟩
+instance : has_int_cast (Cauchy abv) := ⟨λ n, mk n⟩
 
-@[simp] theorem of_rat_nat_cast (n : ℕ) : of_rat n = n := rfl
-@[simp] theorem of_rat_int_cast (z : ℤ) : of_rat z = z := rfl
+@[simp] theorem of_rat_nat_cast (n : ℕ) : (of_rat n : Cauchy abv) = n := rfl
+@[simp] theorem of_rat_int_cast (z : ℤ) : (of_rat z : Cauchy abv) = z := rfl
 
-theorem of_rat_add (x y : β) : of_rat (x + y) = of_rat x + of_rat y :=
+theorem of_rat_add (x y : β) : of_rat (x + y) = (of_rat x + of_rat y : Cauchy abv) :=
 congr_arg mk (const_add _ _)
 
-theorem of_rat_neg (x : β) : of_rat (-x) = -of_rat x :=
+theorem of_rat_neg (x : β) : of_rat (-x) = (-of_rat x : Cauchy abv) :=
 congr_arg mk (const_neg _)
 
-theorem of_rat_mul (x y : β) : of_rat (x * y) = of_rat x * of_rat y :=
+theorem of_rat_mul (x y : β) : of_rat (x * y) = (of_rat x * of_rat y : Cauchy abv) :=
 congr_arg mk (const_mul _ _)
 
-private lemma zero_def : 0 = mk 0 := rfl
+private lemma zero_def : 0 = (mk 0 : Cauchy abv) := rfl
 
-private lemma one_def : 1 = mk 1 := rfl
+private lemma one_def : 1 = (mk 1 : Cauchy abv) := rfl
 
-instance : ring Cauchy :=
+instance : ring (Cauchy abv) :=
 function.surjective.ring mk (surjective_quotient_mk _)
   zero_def.symm one_def.symm (λ _ _, (mk_add _ _).symm) (λ _ _, (mk_mul _ _).symm)
   (λ _, (mk_neg _).symm) (λ _ _, (mk_sub _ _).symm)
@@ -103,24 +105,23 @@ function.surjective.ring mk (surjective_quotient_mk _)
 
 /-- `cau_seq.completion.of_rat` as a `ring_hom`  -/
 @[simps]
-def of_rat_ring_hom : β →+* Cauchy :=
+def of_rat_ring_hom : β →+* Cauchy abv :=
 { to_fun := of_rat,
   map_zero' := of_rat_zero,
   map_one' := of_rat_one,
   map_add' := of_rat_add,
   map_mul' := of_rat_mul, }
 
-theorem of_rat_sub (x y : β) : of_rat (x - y) = of_rat x - of_rat y :=
+theorem of_rat_sub (x y : β) : of_rat (x - y) = (of_rat x - of_rat y : Cauchy abv) :=
 congr_arg mk (const_sub _ _)
 
 end
 
 section
-parameters {α : Type*} [linear_ordered_field α]
-parameters {β : Type*} [comm_ring β] {abv : β → α} [is_absolute_value abv]
-local notation `Cauchy` := @Cauchy _ _ _ _ abv _
+variables {α : Type*} [linear_ordered_field α]
+variables {β : Type*} [comm_ring β] {abv : β → α} [is_absolute_value abv]
 
-instance : comm_ring Cauchy :=
+instance : comm_ring (Cauchy abv) :=
 function.surjective.comm_ring mk (surjective_quotient_mk _)
   zero_def.symm one_def.symm (λ _ _, (mk_add _ _).symm) (λ _ _, (mk_mul _ _).symm)
   (λ _, (mk_neg _).symm) (λ _ _, (mk_sub _ _).symm)
@@ -132,15 +133,14 @@ end
 open_locale classical
 section
 
-parameters {α : Type*} [linear_ordered_field α]
-parameters {β : Type*} [division_ring β] {abv : β → α} [is_absolute_value abv]
-local notation `Cauchy` := @Cauchy _ _ _ _ abv _
+variables {α : Type*} [linear_ordered_field α]
+variables {β : Type*} [division_ring β] {abv : β → α} [is_absolute_value abv]
 
-instance : has_rat_cast Cauchy := ⟨λ q, of_rat q⟩
+instance : has_rat_cast (Cauchy abv) := ⟨λ q, of_rat q⟩
 
-@[simp] theorem of_rat_rat_cast (q : ℚ) : of_rat (↑q : β) = (q : Cauchy) := rfl
+@[simp] theorem of_rat_rat_cast (q : ℚ) : of_rat (↑q : β) = (q : Cauchy abv) := rfl
 
-noncomputable instance : has_inv Cauchy :=
+noncomputable instance : has_inv (Cauchy abv) :=
 ⟨λ x, quotient.lift_on x
   (λ f, mk $ if h : lim_zero f then 0 else inv f h) $
 λ f g fg, begin
@@ -156,7 +156,7 @@ noncomputable instance : has_inv Cauchy :=
         mul_assoc, Ig', mul_one] }
 end⟩
 
-@[simp] theorem inv_zero : (0 : Cauchy)⁻¹ = 0 :=
+@[simp] theorem inv_zero : (0 : Cauchy abv)⁻¹ = 0 :=
 congr_arg mk $ by rw dif_pos; [refl, exact zero_lim_zero]
 
 @[simp] theorem inv_mk {f} (hf) : (@mk α _ β _ abv _ f)⁻¹ = mk (inv f hf) :=
@@ -167,26 +167,26 @@ have lim_zero (1 - 0), from setoid.symm h,
 have lim_zero 1, by simpa,
 one_ne_zero $ const_lim_zero.1 this
 
-lemma zero_ne_one : (0 : Cauchy) ≠ 1 :=
+lemma zero_ne_one : (0 : Cauchy abv) ≠ 1 :=
 λ h, cau_seq_zero_ne_one $ mk_eq.1 h
 
-protected theorem inv_mul_cancel {x : Cauchy} : x ≠ 0 → x⁻¹ * x = 1 :=
+protected theorem inv_mul_cancel {x : Cauchy abv} : x ≠ 0 → x⁻¹ * x = 1 :=
 quotient.induction_on x $ λ f hf, begin
   simp at hf, simp [hf],
   exact quotient.sound (cau_seq.inv_mul_cancel hf)
 end
 
-protected theorem mul_inv_cancel {x : Cauchy} : x ≠ 0 → x * x⁻¹ = 1 :=
+protected theorem mul_inv_cancel {x : Cauchy abv} : x ≠ 0 → x * x⁻¹ = 1 :=
 quotient.induction_on x $ λ f hf, begin
   simp at hf, simp [hf],
   exact quotient.sound (cau_seq.mul_inv_cancel hf)
 end
 
-theorem of_rat_inv (x : β) : of_rat (x⁻¹) = ((of_rat x)⁻¹ : Cauchy) :=
+theorem of_rat_inv (x : β) : of_rat (x⁻¹) = ((of_rat x)⁻¹ : Cauchy abv) :=
 congr_arg mk $ by split_ifs with h; [simp [const_lim_zero.1 h], refl]
 
 /-- The Cauchy completion forms a division ring. -/
-noncomputable instance : division_ring Cauchy :=
+noncomputable instance : division_ring (Cauchy abv) :=
 { inv              := has_inv.inv,
   mul_inv_cancel   := λ x, cau_seq.completion.mul_inv_cancel,
   exists_pair_ne   := ⟨0, 1, zero_ne_one⟩,
@@ -196,7 +196,7 @@ noncomputable instance : division_ring Cauchy :=
     by rw [rat.cast_mk', of_rat_mul, of_rat_int_cast, of_rat_inv, of_rat_nat_cast],
   .. Cauchy.ring }
 
-theorem of_rat_div (x y : β) : of_rat (x / y) = (of_rat x / of_rat y : Cauchy) :=
+theorem of_rat_div (x y : β) : of_rat (x / y) = (of_rat x / of_rat y : Cauchy abv) :=
 by simp only [div_eq_mul_inv, of_rat_inv, of_rat_mul]
 
 /-- Show the first 10 items of a representative of this equivalence class of cauchy sequences.
@@ -204,7 +204,7 @@ by simp only [div_eq_mul_inv, of_rat_inv, of_rat_mul]
 The representative chosen is the one passed in the VM to `quot.mk`, so two cauchy sequences
 converging to the same number may be printed differently.
 -/
-meta instance [has_repr β] : has_repr Cauchy :=
+meta instance [has_repr β] : has_repr (Cauchy abv) :=
 { repr := λ r,
   let N := 10, seq := r.unquot in
     "(sorry /- " ++ (", ".intercalate $ (list.range N).map $ repr ∘ seq) ++ ", ... -/)" }
@@ -212,12 +212,11 @@ meta instance [has_repr β] : has_repr Cauchy :=
 end
 
 section
-parameters {α : Type*} [linear_ordered_field α]
-parameters {β : Type*} [field β] {abv : β → α} [is_absolute_value abv]
-local notation `Cauchy` := @Cauchy _ _ _ _ abv _
+variables {α : Type*} [linear_ordered_field α]
+variables {β : Type*} [field β] {abv : β → α} [is_absolute_value abv]
 
 /-- The Cauchy completion forms a field. -/
-noncomputable instance : field Cauchy :=
+noncomputable instance : field (Cauchy abv) :=
 { .. Cauchy.division_ring,
   .. Cauchy.comm_ring }

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-08-08

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

e7589225

Diff

@@ -326,7 +326,7 @@ noncomputable instance : DivisionRing (Cauchy abv) :=
     exists_pair_ne := ⟨0, 1, zero_ne_one⟩
     inv_zero := inv_zero
     ratCast := fun q => ofRat q
-    ratCast_mk := fun n d hd hnd => by
+    ratCast_def := fun n d hd hnd => by
       rw [Rat.cast_mk', of_rat_mul, of_rat_int_cast, of_rat_inv, of_rat_nat_cast] }
 
 #print CauSeq.Completion.ofRat_div /-

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Robert Y. Lewis
 -/
-import Data.Real.CauSeq
+import Algebra.Order.CauSeq.Basic
 
 #align_import data.real.cau_seq_completion from "leanprover-community/mathlib"@"f2f413b9d4be3a02840d0663dace76e8fe3da053"

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -88,7 +88,7 @@ theorem ofRat_one : (ofRat 1 : Cauchy abv) = 1 :=
 #print CauSeq.Completion.mk_eq_zero /-
 @[simp]
 theorem mk_eq_zero {f : CauSeq _ abv} : mk f = 0 ↔ LimZero f := by
-  have : mk f = 0 ↔ lim_zero (f - 0) := Quotient.eq' <;> rwa [sub_zero] at this 
+  have : mk f = 0 ↔ lim_zero (f - 0) := Quotient.eq' <;> rwa [sub_zero] at this
 #align cau_seq.completion.mk_eq_zero CauSeq.Completion.mk_eq_zero
 -/
 
@@ -266,7 +266,7 @@ noncomputable instance : Inv (Cauchy abv) :=
         have If : mk (inv f hf) * mk f = 1 := mk_eq.2 (inv_mul_cancel hf)
         have Ig : mk (inv g hg) * mk g = 1 := mk_eq.2 (inv_mul_cancel hg)
         have Ig' : mk g * mk (inv g hg) = 1 := mk_eq.2 (mul_inv_cancel hg)
-        rw [mk_eq.2 fg, ← Ig] at If 
+        rw [mk_eq.2 fg, ← Ig] at If
         rw [← mul_one (mk (inv f hf)), ← Ig', ← mul_assoc, If, mul_assoc, Ig', mul_one]⟩
 
 #print CauSeq.Completion.inv_zero /-
@@ -299,7 +299,7 @@ theorem zero_ne_one : (0 : Cauchy abv) ≠ 1 := fun h => cau_seq_zero_ne_one <|
 #print CauSeq.Completion.inv_mul_cancel /-
 protected theorem inv_mul_cancel {x : Cauchy abv} : x ≠ 0 → x⁻¹ * x = 1 :=
   Quotient.inductionOn x fun f hf => by
-    simp at hf ; simp [hf]
+    simp at hf; simp [hf]
     exact Quotient.sound (CauSeq.inv_mul_cancel hf)
 #align cau_seq.completion.inv_mul_cancel CauSeq.Completion.inv_mul_cancel
 -/
@@ -307,7 +307,7 @@ protected theorem inv_mul_cancel {x : Cauchy abv} : x ≠ 0 → x⁻¹ * x = 1 :
 #print CauSeq.Completion.mul_inv_cancel /-
 protected theorem mul_inv_cancel {x : Cauchy abv} : x ≠ 0 → x * x⁻¹ = 1 :=
   Quotient.inductionOn x fun f hf => by
-    simp at hf ; simp [hf]
+    simp at hf; simp [hf]
     exact Quotient.sound (CauSeq.mul_inv_cancel hf)
 #align cau_seq.completion.mul_inv_cancel CauSeq.Completion.mul_inv_cancel
 -/
@@ -473,12 +473,12 @@ theorem lim_neg (f : CauSeq β abv) : lim (-f) = -lim f :=
 #print CauSeq.lim_eq_zero_iff /-
 theorem lim_eq_zero_iff (f : CauSeq β abv) : lim f = 0 ↔ LimZero f :=
   ⟨fun h => by
-    have hf := equiv_lim f <;> rw [h] at hf  <;>
+    have hf := equiv_lim f <;> rw [h] at hf <;>
       exact (lim_zero_congr hf).mpr (const_lim_zero.mpr rfl),
     fun h =>
     by
     have h₁ : f = f - const abv 0 := ext fun n => by simp [sub_apply, const_apply]
-    rw [h₁] at h  <;> exact lim_eq_of_equiv_const h⟩
+    rw [h₁] at h <;> exact lim_eq_of_equiv_const h⟩
 #align cau_seq.lim_eq_zero_iff CauSeq.lim_eq_zero_iff
 -/
 
@@ -490,7 +490,7 @@ variable {β : Type _} [Field β] {abv : β → α} [IsAbsoluteValue abv] [IsCom
 
 #print CauSeq.lim_inv /-
 theorem lim_inv {f : CauSeq β abv} (hf : ¬LimZero f) : lim (inv f hf) = (lim f)⁻¹ :=
-  have hl : lim f ≠ 0 := by rwa [← lim_eq_zero_iff] at hf 
+  have hl : lim f ≠ 0 := by rwa [← lim_eq_zero_iff] at hf
   lim_eq_of_equiv_const <|
     show LimZero (inv f hf - const abv (lim f)⁻¹) from
       have h₁ : ∀ (g f : CauSeq β abv) (hf : ¬LimZero f), LimZero (g - f * inv f hf * g) :=

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Robert Y. Lewis
 -/
-import Mathbin.Data.Real.CauSeq
+import Data.Real.CauSeq
 
 #align_import data.real.cau_seq_completion from "leanprover-community/mathlib"@"f2f413b9d4be3a02840d0663dace76e8fe3da053"

bump to nightly-2023-09-14-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/001ffdc42920050657fd45bd2b8bfbec8eaaeb29

4e7aae4f

Diff

@@ -198,7 +198,7 @@ private theorem one_def : 1 = (mk 1 : Cauchy abv) :=
   rfl
 
 instance : Ring (Cauchy abv) :=
-  Function.Surjective.ring mk (surjective_quotient_mk _) zero_def.symm one_def.symm
+  Function.Surjective.ring mk (surjective_quotient_mk' _) zero_def.symm one_def.symm
     (fun _ _ => (mk_add _ _).symm) (fun _ _ => (mk_mul _ _).symm) (fun _ => (mk_neg _).symm)
     (fun _ _ => (mk_sub _ _).symm) (fun _ _ => (mk_smul _ _).symm) (fun _ _ => (mk_smul _ _).symm)
     (fun _ _ => (mk_pow _ _).symm) (fun _ => rfl) fun _ => rfl
@@ -230,7 +230,7 @@ variable {α : Type _} [LinearOrderedField α]
 variable {β : Type _} [CommRing β] {abv : β → α} [IsAbsoluteValue abv]
 
 instance : CommRing (Cauchy abv) :=
-  Function.Surjective.commRing mk (surjective_quotient_mk _) zero_def.symm one_def.symm
+  Function.Surjective.commRing mk (surjective_quotient_mk' _) zero_def.symm one_def.symm
     (fun _ _ => (mk_add _ _).symm) (fun _ _ => (mk_mul _ _).symm) (fun _ => (mk_neg _).symm)
     (fun _ _ => (mk_sub _ _).symm) (fun _ _ => (mk_smul _ _).symm) (fun _ _ => (mk_smul _ _).symm)
     (fun _ _ => (mk_pow _ _).symm) (fun _ => rfl) fun _ => rfl

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Robert Y. Lewis
-
-! This file was ported from Lean 3 source module data.real.cau_seq_completion
-! leanprover-community/mathlib commit f2f413b9d4be3a02840d0663dace76e8fe3da053
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Real.CauSeq
 
+#align_import data.real.cau_seq_completion from "leanprover-community/mathlib"@"f2f413b9d4be3a02840d0663dace76e8fe3da053"
+
 /-!
 # Cauchy completion

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -47,14 +47,18 @@ def mk : CauSeq _ abv → Cauchy abv :=
 #align cau_seq.completion.mk CauSeq.Completion.mk
 -/
 
+#print CauSeq.Completion.mk_eq_mk /-
 @[simp]
 theorem mk_eq_mk (f) : @Eq (Cauchy abv) ⟦f⟧ (mk f) :=
   rfl
 #align cau_seq.completion.mk_eq_mk CauSeq.Completion.mk_eq_mk
+-/
 
+#print CauSeq.Completion.mk_eq /-
 theorem mk_eq {f g : CauSeq _ abv} : mk f = mk g ↔ f ≈ g :=
   Quotient.eq'
 #align cau_seq.completion.mk_eq CauSeq.Completion.mk_eq
+-/
 
 #print CauSeq.Completion.ofRat /-
 /-- The map from the original ring into the Cauchy completion. -/
@@ -72,67 +76,85 @@ instance : One (Cauchy abv) :=
 instance : Inhabited (Cauchy abv) :=
   ⟨0⟩
 
+#print CauSeq.Completion.ofRat_zero /-
 theorem ofRat_zero : (ofRat 0 : Cauchy abv) = 0 :=
   rfl
 #align cau_seq.completion.of_rat_zero CauSeq.Completion.ofRat_zero
+-/
 
+#print CauSeq.Completion.ofRat_one /-
 theorem ofRat_one : (ofRat 1 : Cauchy abv) = 1 :=
   rfl
 #align cau_seq.completion.of_rat_one CauSeq.Completion.ofRat_one
+-/
 
+#print CauSeq.Completion.mk_eq_zero /-
 @[simp]
 theorem mk_eq_zero {f : CauSeq _ abv} : mk f = 0 ↔ LimZero f := by
   have : mk f = 0 ↔ lim_zero (f - 0) := Quotient.eq' <;> rwa [sub_zero] at this 
 #align cau_seq.completion.mk_eq_zero CauSeq.Completion.mk_eq_zero
+-/
 
 instance : Add (Cauchy abv) :=
   ⟨Quotient.map₂ (· + ·) fun f₁ g₁ hf f₂ g₂ hg => add_equiv_add hf hg⟩
 
+#print CauSeq.Completion.mk_add /-
 @[simp]
 theorem mk_add (f g : CauSeq β abv) : mk f + mk g = mk (f + g) :=
   rfl
 #align cau_seq.completion.mk_add CauSeq.Completion.mk_add
+-/
 
 instance : Neg (Cauchy abv) :=
   ⟨Quotient.map Neg.neg fun f₁ f₂ hf => neg_equiv_neg hf⟩
 
+#print CauSeq.Completion.mk_neg /-
 @[simp]
 theorem mk_neg (f : CauSeq β abv) : -mk f = mk (-f) :=
   rfl
 #align cau_seq.completion.mk_neg CauSeq.Completion.mk_neg
+-/
 
 instance : Mul (Cauchy abv) :=
   ⟨Quotient.map₂ (· * ·) fun f₁ g₁ hf f₂ g₂ hg => mul_equiv_mul hf hg⟩
 
+#print CauSeq.Completion.mk_mul /-
 @[simp]
 theorem mk_mul (f g : CauSeq β abv) : mk f * mk g = mk (f * g) :=
   rfl
 #align cau_seq.completion.mk_mul CauSeq.Completion.mk_mul
+-/
 
 instance : Sub (Cauchy abv) :=
   ⟨Quotient.map₂ Sub.sub fun f₁ g₁ hf f₂ g₂ hg => sub_equiv_sub hf hg⟩
 
+#print CauSeq.Completion.mk_sub /-
 @[simp]
 theorem mk_sub (f g : CauSeq β abv) : mk f - mk g = mk (f - g) :=
   rfl
 #align cau_seq.completion.mk_sub CauSeq.Completion.mk_sub
+-/
 
 instance {γ : Type _} [SMul γ β] [IsScalarTower γ β β] : SMul γ (Cauchy abv) :=
   ⟨fun c => Quotient.map ((· • ·) c) fun f₁ g₁ hf => smul_equiv_smul _ hf⟩
 
+#print CauSeq.Completion.mk_smul /-
 @[simp]
 theorem mk_smul {γ : Type _} [SMul γ β] [IsScalarTower γ β β] (c : γ) (f : CauSeq β abv) :
     c • mk f = mk (c • f) :=
   rfl
 #align cau_seq.completion.mk_smul CauSeq.Completion.mk_smul
+-/
 
 instance : Pow (Cauchy abv) ℕ :=
   ⟨fun x n => Quotient.map (· ^ n) (fun f₁ g₁ hf => pow_equiv_pow hf _) x⟩
 
+#print CauSeq.Completion.mk_pow /-
 @[simp]
 theorem mk_pow (n : ℕ) (f : CauSeq β abv) : mk f ^ n = mk (f ^ n) :=
   rfl
 #align cau_seq.completion.mk_pow CauSeq.Completion.mk_pow
+-/
 
 instance : NatCast (Cauchy abv) :=
   ⟨fun n => mk n⟩
@@ -140,27 +162,37 @@ instance : NatCast (Cauchy abv) :=
 instance : IntCast (Cauchy abv) :=
   ⟨fun n => mk n⟩
 
+#print CauSeq.Completion.ofRat_natCast /-
 @[simp]
 theorem ofRat_natCast (n : ℕ) : (ofRat n : Cauchy abv) = n :=
   rfl
 #align cau_seq.completion.of_rat_nat_cast CauSeq.Completion.ofRat_natCast
+-/
 
+#print CauSeq.Completion.ofRat_intCast /-
 @[simp]
 theorem ofRat_intCast (z : ℤ) : (ofRat z : Cauchy abv) = z :=
   rfl
 #align cau_seq.completion.of_rat_int_cast CauSeq.Completion.ofRat_intCast
+-/
 
+#print CauSeq.Completion.ofRat_add /-
 theorem ofRat_add (x y : β) : ofRat (x + y) = (ofRat x + ofRat y : Cauchy abv) :=
   congr_arg mk (const_add _ _)
 #align cau_seq.completion.of_rat_add CauSeq.Completion.ofRat_add
+-/
 
+#print CauSeq.Completion.ofRat_neg /-
 theorem ofRat_neg (x : β) : ofRat (-x) = (-ofRat x : Cauchy abv) :=
   congr_arg mk (const_neg _)
 #align cau_seq.completion.of_rat_neg CauSeq.Completion.ofRat_neg
+-/
 
+#print CauSeq.Completion.ofRat_mul /-
 theorem ofRat_mul (x y : β) : ofRat (x * y) = (ofRat x * ofRat y : Cauchy abv) :=
   congr_arg mk (const_mul _ _)
 #align cau_seq.completion.of_rat_mul CauSeq.Completion.ofRat_mul
+-/
 
 private theorem zero_def : 0 = (mk 0 : Cauchy abv) :=
   rfl
@@ -186,9 +218,11 @@ def ofRatRingHom : β →+* Cauchy abv where
 #align cau_seq.completion.of_rat_ring_hom CauSeq.Completion.ofRatRingHom
 -/
 
+#print CauSeq.Completion.ofRat_sub /-
 theorem ofRat_sub (x y : β) : ofRat (x - y) = (ofRat x - ofRat y : Cauchy abv) :=
   congr_arg mk (const_sub _ _)
 #align cau_seq.completion.of_rat_sub CauSeq.Completion.ofRat_sub
+-/
 
 end
 
@@ -217,10 +251,12 @@ variable {β : Type _} [DivisionRing β] {abv : β → α} [IsAbsoluteValue abv]
 instance : HasRatCast (Cauchy abv) :=
   ⟨fun q => ofRat q⟩
 
+#print CauSeq.Completion.ofRat_ratCast /-
 @[simp]
 theorem ofRat_ratCast (q : ℚ) : ofRat (↑q : β) = (q : Cauchy abv) :=
   rfl
 #align cau_seq.completion.of_rat_rat_cast CauSeq.Completion.ofRat_ratCast
+-/
 
 noncomputable instance : Inv (Cauchy abv) :=
   ⟨fun x =>
@@ -236,40 +272,54 @@ noncomputable instance : Inv (Cauchy abv) :=
         rw [mk_eq.2 fg, ← Ig] at If 
         rw [← mul_one (mk (inv f hf)), ← Ig', ← mul_assoc, If, mul_assoc, Ig', mul_one]⟩
 
+#print CauSeq.Completion.inv_zero /-
 @[simp]
 theorem inv_zero : (0 : Cauchy abv)⁻¹ = 0 :=
   congr_arg mk <| by rw [dif_pos] <;> [rfl; exact zero_lim_zero]
 #align cau_seq.completion.inv_zero CauSeq.Completion.inv_zero
+-/
 
+#print CauSeq.Completion.inv_mk /-
 @[simp]
 theorem inv_mk {f} (hf) : (@mk α _ β _ abv _ f)⁻¹ = mk (inv f hf) :=
   congr_arg mk <| by rw [dif_neg]
 #align cau_seq.completion.inv_mk CauSeq.Completion.inv_mk
+-/
 
+#print CauSeq.Completion.cau_seq_zero_ne_one /-
 theorem cau_seq_zero_ne_one : ¬(0 : CauSeq _ abv) ≈ 1 := fun h =>
   have : LimZero (1 - 0) := Setoid.symm h
   have : LimZero 1 := by simpa
   one_ne_zero <| const_limZero.1 this
 #align cau_seq.completion.cau_seq_zero_ne_one CauSeq.Completion.cau_seq_zero_ne_one
+-/
 
+#print CauSeq.Completion.zero_ne_one /-
 theorem zero_ne_one : (0 : Cauchy abv) ≠ 1 := fun h => cau_seq_zero_ne_one <| mk_eq.1 h
 #align cau_seq.completion.zero_ne_one CauSeq.Completion.zero_ne_one
+-/
 
+#print CauSeq.Completion.inv_mul_cancel /-
 protected theorem inv_mul_cancel {x : Cauchy abv} : x ≠ 0 → x⁻¹ * x = 1 :=
   Quotient.inductionOn x fun f hf => by
     simp at hf ; simp [hf]
     exact Quotient.sound (CauSeq.inv_mul_cancel hf)
 #align cau_seq.completion.inv_mul_cancel CauSeq.Completion.inv_mul_cancel
+-/
 
+#print CauSeq.Completion.mul_inv_cancel /-
 protected theorem mul_inv_cancel {x : Cauchy abv} : x ≠ 0 → x * x⁻¹ = 1 :=
   Quotient.inductionOn x fun f hf => by
     simp at hf ; simp [hf]
     exact Quotient.sound (CauSeq.mul_inv_cancel hf)
 #align cau_seq.completion.mul_inv_cancel CauSeq.Completion.mul_inv_cancel
+-/
 
+#print CauSeq.Completion.ofRat_inv /-
 theorem ofRat_inv (x : β) : ofRat x⁻¹ = ((ofRat x)⁻¹ : Cauchy abv) :=
   congr_arg mk <| by split_ifs with h <;> [simp [const_lim_zero.1 h]; rfl]
 #align cau_seq.completion.of_rat_inv CauSeq.Completion.ofRat_inv
+-/
 
 /-- The Cauchy completion forms a division ring. -/
 noncomputable instance : DivisionRing (Cauchy abv) :=
@@ -282,9 +332,11 @@ noncomputable instance : DivisionRing (Cauchy abv) :=
     ratCast_mk := fun n d hd hnd => by
       rw [Rat.cast_mk', of_rat_mul, of_rat_int_cast, of_rat_inv, of_rat_nat_cast] }
 
+#print CauSeq.Completion.ofRat_div /-
 theorem ofRat_div (x y : β) : ofRat (x / y) = (ofRat x / ofRat y : Cauchy abv) := by
   simp only [div_eq_mul_inv, of_rat_inv, of_rat_mul]
 #align cau_seq.completion.of_rat_div CauSeq.Completion.ofRat_div
+-/
 
 /-- Show the first 10 items of a representative of this equivalence class of cauchy sequences.
 
@@ -337,9 +389,11 @@ variable {β : Type _} [Ring β] {abv : β → α} [IsAbsoluteValue abv]
 
 variable [IsComplete β abv]
 
+#print CauSeq.complete /-
 theorem complete : ∀ s : CauSeq β abv, ∃ b : β, s ≈ const abv b :=
   IsComplete.isComplete
 #align cau_seq.complete CauSeq.complete
+-/
 
 #print CauSeq.lim /-
 /-- The limit of a Cauchy sequence in a complete ring. Chosen non-computably. -/
@@ -348,21 +402,29 @@ noncomputable def lim (s : CauSeq β abv) : β :=
 #align cau_seq.lim CauSeq.lim
 -/
 
+#print CauSeq.equiv_lim /-
 theorem equiv_lim (s : CauSeq β abv) : s ≈ const abv (lim s) :=
   Classical.choose_spec (complete s)
 #align cau_seq.equiv_lim CauSeq.equiv_lim
+-/
 
+#print CauSeq.eq_lim_of_const_equiv /-
 theorem eq_lim_of_const_equiv {f : CauSeq β abv} {x : β} (h : CauSeq.const abv x ≈ f) : x = lim f :=
   const_equiv.mp <| Setoid.trans h <| equiv_lim f
 #align cau_seq.eq_lim_of_const_equiv CauSeq.eq_lim_of_const_equiv
+-/
 
+#print CauSeq.lim_eq_of_equiv_const /-
 theorem lim_eq_of_equiv_const {f : CauSeq β abv} {x : β} (h : f ≈ CauSeq.const abv x) : lim f = x :=
   (eq_lim_of_const_equiv <| Setoid.symm h).symm
 #align cau_seq.lim_eq_of_equiv_const CauSeq.lim_eq_of_equiv_const
+-/
 
+#print CauSeq.lim_eq_lim_of_equiv /-
 theorem lim_eq_lim_of_equiv {f g : CauSeq β abv} (h : f ≈ g) : lim f = lim g :=
   lim_eq_of_equiv_const <| Setoid.trans h <| equiv_lim g
 #align cau_seq.lim_eq_lim_of_equiv CauSeq.lim_eq_lim_of_equiv
+-/
 
 #print CauSeq.lim_const /-
 @[simp]
@@ -371,13 +433,16 @@ theorem lim_const (x : β) : lim (const abv x) = x :=
 #align cau_seq.lim_const CauSeq.lim_const
 -/
 
+#print CauSeq.lim_add /-
 theorem lim_add (f g : CauSeq β abv) : lim f + lim g = lim (f + g) :=
   eq_lim_of_const_equiv <|
     show LimZero (const abv (lim f + lim g) - (f + g)) by
       rw [const_add, add_sub_add_comm] <;>
         exact add_lim_zero (Setoid.symm (equiv_lim f)) (Setoid.symm (equiv_lim g))
 #align cau_seq.lim_add CauSeq.lim_add
+-/
 
+#print CauSeq.lim_mul_lim /-
 theorem lim_mul_lim (f g : CauSeq β abv) : lim f * lim g = lim (f * g) :=
   eq_lim_of_const_equiv <|
     show LimZero (const abv (lim f * lim g) - f * g)
@@ -391,18 +456,24 @@ theorem lim_mul_lim (f g : CauSeq β abv) : lim f * lim g = lim (f * g) :=
           add_lim_zero (mul_lim_zero_left _ (Setoid.symm (equiv_lim _)))
             (mul_lim_zero_right _ (Setoid.symm (equiv_lim _)))
 #align cau_seq.lim_mul_lim CauSeq.lim_mul_lim
+-/
 
+#print CauSeq.lim_mul /-
 theorem lim_mul (f : CauSeq β abv) (x : β) : lim f * x = lim (f * const abv x) := by
   rw [← lim_mul_lim, lim_const]
 #align cau_seq.lim_mul CauSeq.lim_mul
+-/
 
+#print CauSeq.lim_neg /-
 theorem lim_neg (f : CauSeq β abv) : lim (-f) = -lim f :=
   lim_eq_of_equiv_const
     (show LimZero (-f - const abv (-lim f)) by
       rw [const_neg, sub_neg_eq_add, add_comm, ← sub_eq_add_neg] <;>
         exact Setoid.symm (equiv_lim f))
 #align cau_seq.lim_neg CauSeq.lim_neg
+-/
 
+#print CauSeq.lim_eq_zero_iff /-
 theorem lim_eq_zero_iff (f : CauSeq β abv) : lim f = 0 ↔ LimZero f :=
   ⟨fun h => by
     have hf := equiv_lim f <;> rw [h] at hf  <;>
@@ -412,6 +483,7 @@ theorem lim_eq_zero_iff (f : CauSeq β abv) : lim f = 0 ↔ LimZero f :=
     have h₁ : f = f - const abv 0 := ext fun n => by simp [sub_apply, const_apply]
     rw [h₁] at h  <;> exact lim_eq_of_equiv_const h⟩
 #align cau_seq.lim_eq_zero_iff CauSeq.lim_eq_zero_iff
+-/
 
 end
 
@@ -419,6 +491,7 @@ section
 
 variable {β : Type _} [Field β] {abv : β → α} [IsAbsoluteValue abv] [IsComplete β abv]
 
+#print CauSeq.lim_inv /-
 theorem lim_inv {f : CauSeq β abv} (hf : ¬LimZero f) : lim (inv f hf) = (lim f)⁻¹ :=
   have hl : lim f ≠ 0 := by rwa [← lim_eq_zero_iff] at hf 
   lim_eq_of_equiv_const <|
@@ -443,6 +516,7 @@ theorem lim_inv {f : CauSeq β abv} (hf : ¬LimZero f) : lim (inv f hf) = (lim f
                 (by rw [← mul_assoc] <;> exact h₁ _ _ _)
       (limZero_congr h₂).mpr <| mul_limZero_left _ (Setoid.symm (equiv_lim f))
 #align cau_seq.lim_inv CauSeq.lim_inv
+-/
 
 end
 
@@ -450,21 +524,29 @@ section
 
 variable [IsComplete α abs]
 
+#print CauSeq.lim_le /-
 theorem lim_le {f : CauSeq α abs} {x : α} (h : f ≤ CauSeq.const abs x) : lim f ≤ x :=
   CauSeq.const_le.1 <| CauSeq.le_of_eq_of_le (Setoid.symm (equiv_lim f)) h
 #align cau_seq.lim_le CauSeq.lim_le
+-/
 
+#print CauSeq.le_lim /-
 theorem le_lim {f : CauSeq α abs} {x : α} (h : CauSeq.const abs x ≤ f) : x ≤ lim f :=
   CauSeq.const_le.1 <| CauSeq.le_of_le_of_eq h (equiv_lim f)
 #align cau_seq.le_lim CauSeq.le_lim
+-/
 
+#print CauSeq.lt_lim /-
 theorem lt_lim {f : CauSeq α abs} {x : α} (h : CauSeq.const abs x < f) : x < lim f :=
   CauSeq.const_lt.1 <| CauSeq.lt_of_lt_of_eq h (equiv_lim f)
 #align cau_seq.lt_lim CauSeq.lt_lim
+-/
 
+#print CauSeq.lim_lt /-
 theorem lim_lt {f : CauSeq α abs} {x : α} (h : f < CauSeq.const abs x) : lim f < x :=
   CauSeq.const_lt.1 <| CauSeq.lt_of_eq_of_lt (Setoid.symm (equiv_lim f)) h
 #align cau_seq.lim_lt CauSeq.lim_lt
+-/
 
 end

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -82,7 +82,7 @@ theorem ofRat_one : (ofRat 1 : Cauchy abv) = 1 :=
 
 @[simp]
 theorem mk_eq_zero {f : CauSeq _ abv} : mk f = 0 ↔ LimZero f := by
-  have : mk f = 0 ↔ lim_zero (f - 0) := Quotient.eq' <;> rwa [sub_zero] at this
+  have : mk f = 0 ↔ lim_zero (f - 0) := Quotient.eq' <;> rwa [sub_zero] at this 
 #align cau_seq.completion.mk_eq_zero CauSeq.Completion.mk_eq_zero
 
 instance : Add (Cauchy abv) :=
@@ -233,12 +233,12 @@ noncomputable instance : Inv (Cauchy abv) :=
         have If : mk (inv f hf) * mk f = 1 := mk_eq.2 (inv_mul_cancel hf)
         have Ig : mk (inv g hg) * mk g = 1 := mk_eq.2 (inv_mul_cancel hg)
         have Ig' : mk g * mk (inv g hg) = 1 := mk_eq.2 (mul_inv_cancel hg)
-        rw [mk_eq.2 fg, ← Ig] at If
+        rw [mk_eq.2 fg, ← Ig] at If 
         rw [← mul_one (mk (inv f hf)), ← Ig', ← mul_assoc, If, mul_assoc, Ig', mul_one]⟩
 
 @[simp]
 theorem inv_zero : (0 : Cauchy abv)⁻¹ = 0 :=
-  congr_arg mk <| by rw [dif_pos] <;> [rfl;exact zero_lim_zero]
+  congr_arg mk <| by rw [dif_pos] <;> [rfl; exact zero_lim_zero]
 #align cau_seq.completion.inv_zero CauSeq.Completion.inv_zero
 
 @[simp]
@@ -257,18 +257,18 @@ theorem zero_ne_one : (0 : Cauchy abv) ≠ 1 := fun h => cau_seq_zero_ne_one <|
 
 protected theorem inv_mul_cancel {x : Cauchy abv} : x ≠ 0 → x⁻¹ * x = 1 :=
   Quotient.inductionOn x fun f hf => by
-    simp at hf; simp [hf]
+    simp at hf ; simp [hf]
     exact Quotient.sound (CauSeq.inv_mul_cancel hf)
 #align cau_seq.completion.inv_mul_cancel CauSeq.Completion.inv_mul_cancel
 
 protected theorem mul_inv_cancel {x : Cauchy abv} : x ≠ 0 → x * x⁻¹ = 1 :=
   Quotient.inductionOn x fun f hf => by
-    simp at hf; simp [hf]
+    simp at hf ; simp [hf]
     exact Quotient.sound (CauSeq.mul_inv_cancel hf)
 #align cau_seq.completion.mul_inv_cancel CauSeq.Completion.mul_inv_cancel
 
 theorem ofRat_inv (x : β) : ofRat x⁻¹ = ((ofRat x)⁻¹ : Cauchy abv) :=
-  congr_arg mk <| by split_ifs with h <;> [simp [const_lim_zero.1 h];rfl]
+  congr_arg mk <| by split_ifs with h <;> [simp [const_lim_zero.1 h]; rfl]
 #align cau_seq.completion.of_rat_inv CauSeq.Completion.ofRat_inv
 
 /-- The Cauchy completion forms a division ring. -/
@@ -405,12 +405,12 @@ theorem lim_neg (f : CauSeq β abv) : lim (-f) = -lim f :=
 
 theorem lim_eq_zero_iff (f : CauSeq β abv) : lim f = 0 ↔ LimZero f :=
   ⟨fun h => by
-    have hf := equiv_lim f <;> rw [h] at hf <;>
+    have hf := equiv_lim f <;> rw [h] at hf  <;>
       exact (lim_zero_congr hf).mpr (const_lim_zero.mpr rfl),
     fun h =>
     by
     have h₁ : f = f - const abv 0 := ext fun n => by simp [sub_apply, const_apply]
-    rw [h₁] at h <;> exact lim_eq_of_equiv_const h⟩
+    rw [h₁] at h  <;> exact lim_eq_of_equiv_const h⟩
 #align cau_seq.lim_eq_zero_iff CauSeq.lim_eq_zero_iff
 
 end
@@ -420,7 +420,7 @@ section
 variable {β : Type _} [Field β] {abv : β → α} [IsAbsoluteValue abv] [IsComplete β abv]
 
 theorem lim_inv {f : CauSeq β abv} (hf : ¬LimZero f) : lim (inv f hf) = (lim f)⁻¹ :=
-  have hl : lim f ≠ 0 := by rwa [← lim_eq_zero_iff] at hf
+  have hl : lim f ≠ 0 := by rwa [← lim_eq_zero_iff] at hf 
   lim_eq_of_equiv_const <|
     show LimZero (inv f hf - const abv (lim f)⁻¹) from
       have h₁ : ∀ (g f : CauSeq β abv) (hf : ¬LimZero f), LimZero (g - f * inv f hf * g) :=

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -206,7 +206,7 @@ instance : CommRing (Cauchy abv) :=
 
 end
 
-open Classical
+open scoped Classical
 
 section

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -47,23 +47,11 @@ def mk : CauSeq _ abv → Cauchy abv :=
 #align cau_seq.completion.mk CauSeq.Completion.mk
 -/
 
-/- warning: cau_seq.completion.mk_eq_mk -> CauSeq.Completion.mk_eq_mk is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (f : CauSeq.{u1, u2} α _inst_1 β _inst_2 abv), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (Quotient.mk'.{succ u2} (CauSeq.{u1, u2} α _inst_1 β _inst_2 abv) (CauSeq.equiv.{u1, u2} α β _inst_1 _inst_2 abv _inst_3) f) (CauSeq.Completion.mk.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 f)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] {β : Type.{u1}} [_inst_2 : Ring.{u1} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u2, u1} α (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) β (Ring.toSemiring.{u1} β _inst_2) abv] (f : CauSeq.{u2, u1} α _inst_1 β _inst_2 abv), Eq.{succ u1} (CauSeq.Completion.Cauchy.{u2, u1} α _inst_1 β _inst_2 abv _inst_3) (Quotient.mk.{succ u1} (CauSeq.{u2, u1} α _inst_1 β _inst_2 abv) (CauSeq.equiv.{u2, u1} α β _inst_1 _inst_2 abv _inst_3) f) (CauSeq.Completion.mk.{u2, u1} α _inst_1 β _inst_2 abv _inst_3 f)
-Case conversion may be inaccurate. Consider using '#align cau_seq.completion.mk_eq_mk CauSeq.Completion.mk_eq_mkₓ'. -/
 @[simp]
 theorem mk_eq_mk (f) : @Eq (Cauchy abv) ⟦f⟧ (mk f) :=
   rfl
 #align cau_seq.completion.mk_eq_mk CauSeq.Completion.mk_eq_mk
 
-/- warning: cau_seq.completion.mk_eq -> CauSeq.Completion.mk_eq is a dubious translation:
-lean 3 declaration is
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 theorem mk_eq {f g : CauSeq _ abv} : mk f = mk g ↔ f ≈ g :=
   Quotient.eq'
 #align cau_seq.completion.mk_eq CauSeq.Completion.mk_eq
@@ -84,32 +72,14 @@ instance : One (Cauchy abv) :=
 instance : Inhabited (Cauchy abv) :=
   ⟨0⟩
 
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 theorem ofRat_zero : (ofRat 0 : Cauchy abv) = 0 :=
   rfl
 #align cau_seq.completion.of_rat_zero CauSeq.Completion.ofRat_zero
 
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 theorem ofRat_one : (ofRat 1 : Cauchy abv) = 1 :=
   rfl
 #align cau_seq.completion.of_rat_one CauSeq.Completion.ofRat_one
 
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 @[simp]
 theorem mk_eq_zero {f : CauSeq _ abv} : mk f = 0 ↔ LimZero f := by
   have : mk f = 0 ↔ lim_zero (f - 0) := Quotient.eq' <;> rwa [sub_zero] at this
@@ -118,12 +88,6 @@ theorem mk_eq_zero {f : CauSeq _ abv} : mk f = 0 ↔ LimZero f := by
 instance : Add (Cauchy abv) :=
   ⟨Quotient.map₂ (· + ·) fun f₁ g₁ hf f₂ g₂ hg => add_equiv_add hf hg⟩
 
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 @[simp]
 theorem mk_add (f g : CauSeq β abv) : mk f + mk g = mk (f + g) :=
   rfl
@@ -132,12 +96,6 @@ theorem mk_add (f g : CauSeq β abv) : mk f + mk g = mk (f + g) :=
 instance : Neg (Cauchy abv) :=
   ⟨Quotient.map Neg.neg fun f₁ f₂ hf => neg_equiv_neg hf⟩
 
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 @[simp]
 theorem mk_neg (f : CauSeq β abv) : -mk f = mk (-f) :=
   rfl
@@ -146,12 +104,6 @@ theorem mk_neg (f : CauSeq β abv) : -mk f = mk (-f) :=
 instance : Mul (Cauchy abv) :=
   ⟨Quotient.map₂ (· * ·) fun f₁ g₁ hf f₂ g₂ hg => mul_equiv_mul hf hg⟩
 
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 @[simp]
 theorem mk_mul (f g : CauSeq β abv) : mk f * mk g = mk (f * g) :=
   rfl
@@ -160,12 +112,6 @@ theorem mk_mul (f g : CauSeq β abv) : mk f * mk g = mk (f * g) :=
 instance : Sub (Cauchy abv) :=
   ⟨Quotient.map₂ Sub.sub fun f₁ g₁ hf f₂ g₂ hg => sub_equiv_sub hf hg⟩
 
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 @[simp]
 theorem mk_sub (f g : CauSeq β abv) : mk f - mk g = mk (f - g) :=
   rfl
@@ -174,12 +120,6 @@ theorem mk_sub (f g : CauSeq β abv) : mk f - mk g = mk (f - g) :=
 instance {γ : Type _} [SMul γ β] [IsScalarTower γ β β] : SMul γ (Cauchy abv) :=
   ⟨fun c => Quotient.map ((· • ·) c) fun f₁ g₁ hf => smul_equiv_smul _ hf⟩
 
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 @[simp]
 theorem mk_smul {γ : Type _} [SMul γ β] [IsScalarTower γ β β] (c : γ) (f : CauSeq β abv) :
     c • mk f = mk (c • f) :=
@@ -189,12 +129,6 @@ theorem mk_smul {γ : Type _} [SMul γ β] [IsScalarTower γ β β] (c : γ) (f
 instance : Pow (Cauchy abv) ℕ :=
   ⟨fun x n => Quotient.map (· ^ n) (fun f₁ g₁ hf => pow_equiv_pow hf _) x⟩
 
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 @[simp]
 theorem mk_pow (n : ℕ) (f : CauSeq β abv) : mk f ^ n = mk (f ^ n) :=
   rfl
@@ -206,54 +140,24 @@ instance : NatCast (Cauchy abv) :=
 instance : IntCast (Cauchy abv) :=
   ⟨fun n => mk n⟩
 
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 @[simp]
 theorem ofRat_natCast (n : ℕ) : (ofRat n : Cauchy abv) = n :=
   rfl
 #align cau_seq.completion.of_rat_nat_cast CauSeq.Completion.ofRat_natCast
 
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 @[simp]
 theorem ofRat_intCast (z : ℤ) : (ofRat z : Cauchy abv) = z :=
   rfl
 #align cau_seq.completion.of_rat_int_cast CauSeq.Completion.ofRat_intCast
 
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 theorem ofRat_add (x y : β) : ofRat (x + y) = (ofRat x + ofRat y : Cauchy abv) :=
   congr_arg mk (const_add _ _)
 #align cau_seq.completion.of_rat_add CauSeq.Completion.ofRat_add
 
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 theorem ofRat_neg (x : β) : ofRat (-x) = (-ofRat x : Cauchy abv) :=
   congr_arg mk (const_neg _)
 #align cau_seq.completion.of_rat_neg CauSeq.Completion.ofRat_neg
 
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 theorem ofRat_mul (x y : β) : ofRat (x * y) = (ofRat x * ofRat y : Cauchy abv) :=
   congr_arg mk (const_mul _ _)
 #align cau_seq.completion.of_rat_mul CauSeq.Completion.ofRat_mul
@@ -282,12 +186,6 @@ def ofRatRingHom : β →+* Cauchy abv where
 #align cau_seq.completion.of_rat_ring_hom CauSeq.Completion.ofRatRingHom
 -/
 
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 theorem ofRat_sub (x y : β) : ofRat (x - y) = (ofRat x - ofRat y : Cauchy abv) :=
   congr_arg mk (const_sub _ _)
 #align cau_seq.completion.of_rat_sub CauSeq.Completion.ofRat_sub
@@ -319,12 +217,6 @@ variable {β : Type _} [DivisionRing β] {abv : β → α} [IsAbsoluteValue abv]
 instance : HasRatCast (Cauchy abv) :=
   ⟨fun q => ofRat q⟩
 
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 @[simp]
 theorem ofRat_ratCast (q : ℚ) : ofRat (↑q : β) = (q : Cauchy abv) :=
   rfl
@@ -344,79 +236,37 @@ noncomputable instance : Inv (Cauchy abv) :=
         rw [mk_eq.2 fg, ← Ig] at If
         rw [← mul_one (mk (inv f hf)), ← Ig', ← mul_assoc, If, mul_assoc, Ig', mul_one]⟩
 
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 @[simp]
 theorem inv_zero : (0 : Cauchy abv)⁻¹ = 0 :=
   congr_arg mk <| by rw [dif_pos] <;> [rfl;exact zero_lim_zero]
 #align cau_seq.completion.inv_zero CauSeq.Completion.inv_zero
 
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 @[simp]
 theorem inv_mk {f} (hf) : (@mk α _ β _ abv _ f)⁻¹ = mk (inv f hf) :=
   congr_arg mk <| by rw [dif_neg]
 #align cau_seq.completion.inv_mk CauSeq.Completion.inv_mk
 
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 theorem cau_seq_zero_ne_one : ¬(0 : CauSeq _ abv) ≈ 1 := fun h =>
   have : LimZero (1 - 0) := Setoid.symm h
   have : LimZero 1 := by simpa
   one_ne_zero <| const_limZero.1 this
 #align cau_seq.completion.cau_seq_zero_ne_one CauSeq.Completion.cau_seq_zero_ne_one
 
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 theorem zero_ne_one : (0 : Cauchy abv) ≠ 1 := fun h => cau_seq_zero_ne_one <| mk_eq.1 h
 #align cau_seq.completion.zero_ne_one CauSeq.Completion.zero_ne_one
 
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 protected theorem inv_mul_cancel {x : Cauchy abv} : x ≠ 0 → x⁻¹ * x = 1 :=
   Quotient.inductionOn x fun f hf => by
     simp at hf; simp [hf]
     exact Quotient.sound (CauSeq.inv_mul_cancel hf)
 #align cau_seq.completion.inv_mul_cancel CauSeq.Completion.inv_mul_cancel
 
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 protected theorem mul_inv_cancel {x : Cauchy abv} : x ≠ 0 → x * x⁻¹ = 1 :=
   Quotient.inductionOn x fun f hf => by
     simp at hf; simp [hf]
     exact Quotient.sound (CauSeq.mul_inv_cancel hf)
 #align cau_seq.completion.mul_inv_cancel CauSeq.Completion.mul_inv_cancel
 
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 theorem ofRat_inv (x : β) : ofRat x⁻¹ = ((ofRat x)⁻¹ : Cauchy abv) :=
   congr_arg mk <| by split_ifs with h <;> [simp [const_lim_zero.1 h];rfl]
 #align cau_seq.completion.of_rat_inv CauSeq.Completion.ofRat_inv
@@ -432,12 +282,6 @@ noncomputable instance : DivisionRing (Cauchy abv) :=
     ratCast_mk := fun n d hd hnd => by
       rw [Rat.cast_mk', of_rat_mul, of_rat_int_cast, of_rat_inv, of_rat_nat_cast] }
 
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 theorem ofRat_div (x y : β) : ofRat (x / y) = (ofRat x / ofRat y : Cauchy abv) := by
   simp only [div_eq_mul_inv, of_rat_inv, of_rat_mul]
 #align cau_seq.completion.of_rat_div CauSeq.Completion.ofRat_div
@@ -493,12 +337,6 @@ variable {β : Type _} [Ring β] {abv : β → α} [IsAbsoluteValue abv]
 
 variable [IsComplete β abv]
 
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 theorem complete : ∀ s : CauSeq β abv, ∃ b : β, s ≈ const abv b :=
   IsComplete.isComplete
 #align cau_seq.complete CauSeq.complete
@@ -510,42 +348,18 @@ noncomputable def lim (s : CauSeq β abv) : β :=
 #align cau_seq.lim CauSeq.lim
 -/
 
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 theorem equiv_lim (s : CauSeq β abv) : s ≈ const abv (lim s) :=
   Classical.choose_spec (complete s)
 #align cau_seq.equiv_lim CauSeq.equiv_lim
 
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 theorem eq_lim_of_const_equiv {f : CauSeq β abv} {x : β} (h : CauSeq.const abv x ≈ f) : x = lim f :=
   const_equiv.mp <| Setoid.trans h <| equiv_lim f
 #align cau_seq.eq_lim_of_const_equiv CauSeq.eq_lim_of_const_equiv
 
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 theorem lim_eq_of_equiv_const {f : CauSeq β abv} {x : β} (h : f ≈ CauSeq.const abv x) : lim f = x :=
   (eq_lim_of_const_equiv <| Setoid.symm h).symm
 #align cau_seq.lim_eq_of_equiv_const CauSeq.lim_eq_of_equiv_const
 
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 theorem lim_eq_lim_of_equiv {f g : CauSeq β abv} (h : f ≈ g) : lim f = lim g :=
   lim_eq_of_equiv_const <| Setoid.trans h <| equiv_lim g
 #align cau_seq.lim_eq_lim_of_equiv CauSeq.lim_eq_lim_of_equiv
@@ -557,12 +371,6 @@ theorem lim_const (x : β) : lim (const abv x) = x :=
 #align cau_seq.lim_const CauSeq.lim_const
 -/
 
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 theorem lim_add (f g : CauSeq β abv) : lim f + lim g = lim (f + g) :=
   eq_lim_of_const_equiv <|
     show LimZero (const abv (lim f + lim g) - (f + g)) by
@@ -570,12 +378,6 @@ theorem lim_add (f g : CauSeq β abv) : lim f + lim g = lim (f + g) :=
         exact add_lim_zero (Setoid.symm (equiv_lim f)) (Setoid.symm (equiv_lim g))
 #align cau_seq.lim_add CauSeq.lim_add
 
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-Case conversion may be inaccurate. Consider using '#align cau_seq.lim_mul_lim CauSeq.lim_mul_limₓ'. -/
 theorem lim_mul_lim (f g : CauSeq β abv) : lim f * lim g = lim (f * g) :=
   eq_lim_of_const_equiv <|
     show LimZero (const abv (lim f * lim g) - f * g)
@@ -590,22 +392,10 @@ theorem lim_mul_lim (f g : CauSeq β abv) : lim f * lim g = lim (f * g) :=
             (mul_lim_zero_right _ (Setoid.symm (equiv_lim _)))
 #align cau_seq.lim_mul_lim CauSeq.lim_mul_lim
 
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 theorem lim_mul (f : CauSeq β abv) (x : β) : lim f * x = lim (f * const abv x) := by
   rw [← lim_mul_lim, lim_const]
 #align cau_seq.lim_mul CauSeq.lim_mul
 
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 theorem lim_neg (f : CauSeq β abv) : lim (-f) = -lim f :=
   lim_eq_of_equiv_const
     (show LimZero (-f - const abv (-lim f)) by
@@ -613,12 +403,6 @@ theorem lim_neg (f : CauSeq β abv) : lim (-f) = -lim f :=
         exact Setoid.symm (equiv_lim f))
 #align cau_seq.lim_neg CauSeq.lim_neg
 
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 theorem lim_eq_zero_iff (f : CauSeq β abv) : lim f = 0 ↔ LimZero f :=
   ⟨fun h => by
     have hf := equiv_lim f <;> rw [h] at hf <;>
@@ -635,12 +419,6 @@ section
 
 variable {β : Type _} [Field β] {abv : β → α} [IsAbsoluteValue abv] [IsComplete β abv]
 
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 theorem lim_inv {f : CauSeq β abv} (hf : ¬LimZero f) : lim (inv f hf) = (lim f)⁻¹ :=
   have hl : lim f ≠ 0 := by rwa [← lim_eq_zero_iff] at hf
   lim_eq_of_equiv_const <|
@@ -672,42 +450,18 @@ section
 
 variable [IsComplete α abs]
 
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-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLe.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLECauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
-Case conversion may be inaccurate. Consider using '#align cau_seq.lim_le CauSeq.lim_leₓ'. -/
 theorem lim_le {f : CauSeq α abs} {x : α} (h : f ≤ CauSeq.const abs x) : lim f ≤ x :=
   CauSeq.const_le.1 <| CauSeq.le_of_eq_of_le (Setoid.symm (equiv_lim f)) h
 #align cau_seq.lim_le CauSeq.lim_le
 
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-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLECauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
-Case conversion may be inaccurate. Consider using '#align cau_seq.le_lim CauSeq.le_limₓ'. -/
 theorem le_lim {f : CauSeq α abs} {x : α} (h : CauSeq.const abs x ≤ f) : x ≤ lim f :=
   CauSeq.const_le.1 <| CauSeq.le_of_le_of_eq h (equiv_lim f)
 #align cau_seq.le_lim CauSeq.le_lim
 
-/- warning: cau_seq.lt_lim -> CauSeq.lt_lim is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLt.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLTCauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
-Case conversion may be inaccurate. Consider using '#align cau_seq.lt_lim CauSeq.lt_limₓ'. -/
 theorem lt_lim {f : CauSeq α abs} {x : α} (h : CauSeq.const abs x < f) : x < lim f :=
   CauSeq.const_lt.1 <| CauSeq.lt_of_lt_of_eq h (equiv_lim f)
 #align cau_seq.lt_lim CauSeq.lt_lim
 
-/- warning: cau_seq.lim_lt -> CauSeq.lim_lt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLt.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLTCauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
-Case conversion may be inaccurate. Consider using '#align cau_seq.lim_lt CauSeq.lim_ltₓ'. -/
 theorem lim_lt {f : CauSeq α abs} {x : α} (h : f < CauSeq.const abs x) : lim f < x :=
   CauSeq.const_lt.1 <| CauSeq.lt_of_eq_of_lt (Setoid.symm (equiv_lim f)) h
 #align cau_seq.lim_lt CauSeq.lim_lt

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -337,8 +337,7 @@ noncomputable instance : Inv (Cauchy abv) :=
       have := lim_zero_congr fg
       by_cases hf : lim_zero f
       · simp [hf, this.1 hf, Setoid.refl]
-      · have hg := mt this.2 hf
-        simp [hf, hg]
+      · have hg := mt this.2 hf; simp [hf, hg]
         have If : mk (inv f hf) * mk f = 1 := mk_eq.2 (inv_mul_cancel hf)
         have Ig : mk (inv g hg) * mk g = 1 := mk_eq.2 (inv_mul_cancel hg)
         have Ig' : mk g * mk (inv g hg) = 1 := mk_eq.2 (mul_inv_cancel hg)

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -260,11 +260,9 @@ theorem ofRat_mul (x y : β) : ofRat (x * y) = (ofRat x * ofRat y : Cauchy abv)
 
 private theorem zero_def : 0 = (mk 0 : Cauchy abv) :=
   rfl
-#align cau_seq.completion.zero_def cau_seq.completion.zero_def
 
 private theorem one_def : 1 = (mk 1 : Cauchy abv) :=
   rfl
-#align cau_seq.completion.one_def cau_seq.completion.one_def
 
 instance : Ring (Cauchy abv) :=
   Function.Surjective.ring mk (surjective_quotient_mk _) zero_def.symm one_def.symm

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -355,7 +355,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align cau_seq.completion.inv_zero CauSeq.Completion.inv_zeroₓ'. -/
 @[simp]
 theorem inv_zero : (0 : Cauchy abv)⁻¹ = 0 :=
-  congr_arg mk <| by rw [dif_pos] <;> [rfl, exact zero_lim_zero]
+  congr_arg mk <| by rw [dif_pos] <;> [rfl;exact zero_lim_zero]
 #align cau_seq.completion.inv_zero CauSeq.Completion.inv_zero
 
 /- warning: cau_seq.completion.inv_mk -> CauSeq.Completion.inv_mk is a dubious translation:
@@ -421,7 +421,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : DivisionRing.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) β (DivisionSemiring.toSemiring.{u2} β (DivisionRing.toDivisionSemiring.{u2} β _inst_2)) abv] (x : β), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β (DivisionRing.toRing.{u2} β _inst_2) abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β (DivisionRing.toRing.{u2} β _inst_2) abv _inst_3 (Inv.inv.{u2} β (DivisionRing.toInv.{u2} β _inst_2) x)) (Inv.inv.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β (DivisionRing.toRing.{u2} β _inst_2) abv _inst_3) (CauSeq.Completion.instInvCauchyToRing.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β (DivisionRing.toRing.{u2} β _inst_2) abv _inst_3 x))
 Case conversion may be inaccurate. Consider using '#align cau_seq.completion.of_rat_inv CauSeq.Completion.ofRat_invₓ'. -/
 theorem ofRat_inv (x : β) : ofRat x⁻¹ = ((ofRat x)⁻¹ : Cauchy abv) :=
-  congr_arg mk <| by split_ifs with h <;> [simp [const_lim_zero.1 h], rfl]
+  congr_arg mk <| by split_ifs with h <;> [simp [const_lim_zero.1 h];rfl]
 #align cau_seq.completion.of_rat_inv CauSeq.Completion.ofRat_inv
 
 /-- The Cauchy completion forms a division ring. -/

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -677,7 +677,7 @@ variable [IsComplete α abs]
 
 /- warning: cau_seq.lim_le -> CauSeq.lim_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLe.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLe.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLECauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
 Case conversion may be inaccurate. Consider using '#align cau_seq.lim_le CauSeq.lim_leₓ'. -/
@@ -687,7 +687,7 @@ theorem lim_le {f : CauSeq α abs} {x : α} (h : f ≤ CauSeq.const abs x) : lim
 
 /- warning: cau_seq.le_lim -> CauSeq.le_lim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLe.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLe.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLECauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align cau_seq.le_lim CauSeq.le_limₓ'. -/
@@ -697,7 +697,7 @@ theorem le_lim {f : CauSeq α abs} {x : α} (h : CauSeq.const abs x ≤ f) : x 
 
 /- warning: cau_seq.lt_lim -> CauSeq.lt_lim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLt.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLt.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLTCauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align cau_seq.lt_lim CauSeq.lt_limₓ'. -/
@@ -707,7 +707,7 @@ theorem lt_lim {f : CauSeq α abs} {x : α} (h : CauSeq.const abs x < f) : x < l
 
 /- warning: cau_seq.lim_lt -> CauSeq.lim_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLt.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLt.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLTCauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
 Case conversion may be inaccurate. Consider using '#align cau_seq.lim_lt CauSeq.lim_ltₓ'. -/

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -98,7 +98,7 @@ theorem ofRat_zero : (ofRat 0 : Cauchy abv) = 0 :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv], Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (OfNat.ofNat.{u2} β 1 (OfNat.mk.{u2} β 1 (One.one.{u2} β (AddMonoidWithOne.toOne.{u2} β (AddGroupWithOne.toAddMonoidWithOne.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β _inst_2)))))))) (OfNat.ofNat.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) 1 (OfNat.mk.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) 1 (One.one.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.hasOne.{u1, u2} α _inst_1 β _inst_2 abv _inst_3))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv], Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (OfNat.ofNat.{u2} β 1 (One.toOfNat1.{u2} β (NonAssocRing.toOne.{u2} β (Ring.toNonAssocRing.{u2} β _inst_2))))) (OfNat.ofNat.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) 1 (One.toOfNat1.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.instOneCauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv], Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (OfNat.ofNat.{u2} β 1 (One.toOfNat1.{u2} β (Semiring.toOne.{u2} β (Ring.toSemiring.{u2} β _inst_2))))) (OfNat.ofNat.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) 1 (One.toOfNat1.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.instOneCauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3)))
 Case conversion may be inaccurate. Consider using '#align cau_seq.completion.of_rat_one CauSeq.Completion.ofRat_oneₓ'. -/
 theorem ofRat_one : (ofRat 1 : Cauchy abv) = 1 :=
   rfl
@@ -210,7 +210,7 @@ instance : IntCast (Cauchy abv) :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (n : Nat), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat β (HasLiftT.mk.{1, succ u2} Nat β (CoeTCₓ.coe.{1, succ u2} Nat β (Nat.castCoe.{u2} β (AddMonoidWithOne.toNatCast.{u2} β (AddGroupWithOne.toAddMonoidWithOne.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β _inst_2))))))) n)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (HasLiftT.mk.{1, succ u2} Nat (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CoeTCₓ.coe.{1, succ u2} Nat (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (Nat.castCoe.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.hasNatCast.{u1, u2} α _inst_1 β _inst_2 abv _inst_3)))) n)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (n : Nat), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (Nat.cast.{u2} β (NonAssocRing.toNatCast.{u2} β (Ring.toNonAssocRing.{u2} β _inst_2)) n)) (Nat.cast.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.instNatCastCauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) n)
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (n : Nat), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (Nat.cast.{u2} β (Semiring.toNatCast.{u2} β (Ring.toSemiring.{u2} β _inst_2)) n)) (Nat.cast.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.instNatCastCauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) n)
 Case conversion may be inaccurate. Consider using '#align cau_seq.completion.of_rat_nat_cast CauSeq.Completion.ofRat_natCastₓ'. -/
 @[simp]
 theorem ofRat_natCast (n : ℕ) : (ofRat n : Cauchy abv) = n :=

bump to nightly-2023-03-27-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

0e4ebd8c

Diff

@@ -96,7 +96,7 @@ theorem ofRat_zero : (ofRat 0 : Cauchy abv) = 0 :=
 
 /- warning: cau_seq.completion.of_rat_one -> CauSeq.Completion.ofRat_one is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv], Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (OfNat.ofNat.{u2} β 1 (OfNat.mk.{u2} β 1 (One.one.{u2} β (AddMonoidWithOne.toOne.{u2} β (AddGroupWithOne.toAddMonoidWithOne.{u2} β (NonAssocRing.toAddGroupWithOne.{u2} β (Ring.toNonAssocRing.{u2} β _inst_2)))))))) (OfNat.ofNat.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) 1 (OfNat.mk.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) 1 (One.one.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.hasOne.{u1, u2} α _inst_1 β _inst_2 abv _inst_3))))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv], Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (OfNat.ofNat.{u2} β 1 (OfNat.mk.{u2} β 1 (One.one.{u2} β (AddMonoidWithOne.toOne.{u2} β (AddGroupWithOne.toAddMonoidWithOne.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β _inst_2)))))))) (OfNat.ofNat.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) 1 (OfNat.mk.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) 1 (One.one.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.hasOne.{u1, u2} α _inst_1 β _inst_2 abv _inst_3))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv], Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (OfNat.ofNat.{u2} β 1 (One.toOfNat1.{u2} β (NonAssocRing.toOne.{u2} β (Ring.toNonAssocRing.{u2} β _inst_2))))) (OfNat.ofNat.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) 1 (One.toOfNat1.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.instOneCauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3)))
 Case conversion may be inaccurate. Consider using '#align cau_seq.completion.of_rat_one CauSeq.Completion.ofRat_oneₓ'. -/
@@ -208,7 +208,7 @@ instance : IntCast (Cauchy abv) :=
 
 /- warning: cau_seq.completion.of_rat_nat_cast -> CauSeq.Completion.ofRat_natCast is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (n : Nat), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat β (HasLiftT.mk.{1, succ u2} Nat β (CoeTCₓ.coe.{1, succ u2} Nat β (Nat.castCoe.{u2} β (AddMonoidWithOne.toNatCast.{u2} β (AddGroupWithOne.toAddMonoidWithOne.{u2} β (NonAssocRing.toAddGroupWithOne.{u2} β (Ring.toNonAssocRing.{u2} β _inst_2))))))) n)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (HasLiftT.mk.{1, succ u2} Nat (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CoeTCₓ.coe.{1, succ u2} Nat (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (Nat.castCoe.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.hasNatCast.{u1, u2} α _inst_1 β _inst_2 abv _inst_3)))) n)
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (n : Nat), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat β (HasLiftT.mk.{1, succ u2} Nat β (CoeTCₓ.coe.{1, succ u2} Nat β (Nat.castCoe.{u2} β (AddMonoidWithOne.toNatCast.{u2} β (AddGroupWithOne.toAddMonoidWithOne.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β _inst_2))))))) n)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (HasLiftT.mk.{1, succ u2} Nat (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CoeTCₓ.coe.{1, succ u2} Nat (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (Nat.castCoe.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.hasNatCast.{u1, u2} α _inst_1 β _inst_2 abv _inst_3)))) n)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (n : Nat), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (Nat.cast.{u2} β (NonAssocRing.toNatCast.{u2} β (Ring.toNonAssocRing.{u2} β _inst_2)) n)) (Nat.cast.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.instNatCastCauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) n)
 Case conversion may be inaccurate. Consider using '#align cau_seq.completion.of_rat_nat_cast CauSeq.Completion.ofRat_natCastₓ'. -/
@@ -219,7 +219,7 @@ theorem ofRat_natCast (n : ℕ) : (ofRat n : Cauchy abv) = n :=
 
 /- warning: cau_seq.completion.of_rat_int_cast -> CauSeq.Completion.ofRat_intCast is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (z : Int), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Int β (HasLiftT.mk.{1, succ u2} Int β (CoeTCₓ.coe.{1, succ u2} Int β (Int.castCoe.{u2} β (AddGroupWithOne.toHasIntCast.{u2} β (NonAssocRing.toAddGroupWithOne.{u2} β (Ring.toNonAssocRing.{u2} β _inst_2)))))) z)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Int (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (HasLiftT.mk.{1, succ u2} Int (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CoeTCₓ.coe.{1, succ u2} Int (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (Int.castCoe.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.hasIntCast.{u1, u2} α _inst_1 β _inst_2 abv _inst_3)))) z)
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (z : Int), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Int β (HasLiftT.mk.{1, succ u2} Int β (CoeTCₓ.coe.{1, succ u2} Int β (Int.castCoe.{u2} β (AddGroupWithOne.toHasIntCast.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β _inst_2)))))) z)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Int (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (HasLiftT.mk.{1, succ u2} Int (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CoeTCₓ.coe.{1, succ u2} Int (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (Int.castCoe.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.hasIntCast.{u1, u2} α _inst_1 β _inst_2 abv _inst_3)))) z)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (z : Int), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (Int.cast.{u2} β (Ring.toIntCast.{u2} β _inst_2) z)) (Int.cast.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.instIntCastCauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) z)
 Case conversion may be inaccurate. Consider using '#align cau_seq.completion.of_rat_int_cast CauSeq.Completion.ofRat_intCastₓ'. -/
@@ -240,7 +240,7 @@ theorem ofRat_add (x y : β) : ofRat (x + y) = (ofRat x + ofRat y : Cauchy abv)
 
 /- warning: cau_seq.completion.of_rat_neg -> CauSeq.Completion.ofRat_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (x : β), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (Neg.neg.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (NonAssocRing.toAddGroupWithOne.{u2} β (Ring.toNonAssocRing.{u2} β _inst_2))))) x)) (Neg.neg.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.hasNeg.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 x))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (x : β), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (Neg.neg.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β _inst_2))))) x)) (Neg.neg.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.hasNeg.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 x))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (x : β), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (Neg.neg.{u2} β (Ring.toNeg.{u2} β _inst_2) x)) (Neg.neg.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.instNegCauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 x))
 Case conversion may be inaccurate. Consider using '#align cau_seq.completion.of_rat_neg CauSeq.Completion.ofRat_negₓ'. -/
@@ -286,7 +286,7 @@ def ofRatRingHom : β →+* Cauchy abv where
 
 /- warning: cau_seq.completion.of_rat_sub -> CauSeq.Completion.ofRat_sub is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (x : β) (y : β), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (HSub.hSub.{u2, u2, u2} β β β (instHSub.{u2} β (SubNegMonoid.toHasSub.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (NonAssocRing.toAddGroupWithOne.{u2} β (Ring.toNonAssocRing.{u2} β _inst_2)))))) x y)) (HSub.hSub.{u2, u2, u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (instHSub.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.hasSub.{u1, u2} α _inst_1 β _inst_2 abv _inst_3)) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 x) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 y))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (x : β) (y : β), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (HSub.hSub.{u2, u2, u2} β β β (instHSub.{u2} β (SubNegMonoid.toHasSub.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β _inst_2)))))) x y)) (HSub.hSub.{u2, u2, u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (instHSub.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.hasSub.{u1, u2} α _inst_1 β _inst_2 abv _inst_3)) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 x) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 y))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (x : β) (y : β), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (HSub.hSub.{u2, u2, u2} β β β (instHSub.{u2} β (Ring.toSub.{u2} β _inst_2)) x y)) (HSub.hSub.{u2, u2, u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (instHSub.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.instSubCauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3)) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 x) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 y))
 Case conversion may be inaccurate. Consider using '#align cau_seq.completion.of_rat_sub CauSeq.Completion.ofRat_subₓ'. -/
@@ -605,7 +605,7 @@ theorem lim_mul (f : CauSeq β abv) (x : β) : lim f * x = lim (f * const abv x)
 
 /- warning: cau_seq.lim_neg -> CauSeq.lim_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] [_inst_4 : CauSeq.IsComplete.{u1, u2} α _inst_1 β _inst_2 abv _inst_3] (f : CauSeq.{u1, u2} α _inst_1 β _inst_2 abv), Eq.{succ u2} β (CauSeq.lim.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 _inst_4 (Neg.neg.{u2} (CauSeq.{u1, u2} α _inst_1 β _inst_2 abv) (CauSeq.hasNeg.{u1, u2} α β _inst_1 _inst_2 abv _inst_3) f)) (Neg.neg.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (NonAssocRing.toAddGroupWithOne.{u2} β (Ring.toNonAssocRing.{u2} β _inst_2))))) (CauSeq.lim.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 _inst_4 f))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] [_inst_4 : CauSeq.IsComplete.{u1, u2} α _inst_1 β _inst_2 abv _inst_3] (f : CauSeq.{u1, u2} α _inst_1 β _inst_2 abv), Eq.{succ u2} β (CauSeq.lim.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 _inst_4 (Neg.neg.{u2} (CauSeq.{u1, u2} α _inst_1 β _inst_2 abv) (CauSeq.hasNeg.{u1, u2} α β _inst_1 _inst_2 abv _inst_3) f)) (Neg.neg.{u2} β (SubNegMonoid.toHasNeg.{u2} β (AddGroup.toSubNegMonoid.{u2} β (AddGroupWithOne.toAddGroup.{u2} β (AddCommGroupWithOne.toAddGroupWithOne.{u2} β (Ring.toAddCommGroupWithOne.{u2} β _inst_2))))) (CauSeq.lim.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 _inst_4 f))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : LinearOrderedField.{u2} α] {β : Type.{u1}} [_inst_2 : Ring.{u1} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u2, u1} α (OrderedCommSemiring.toOrderedSemiring.{u2} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} α (LinearOrderedField.toLinearOrderedSemifield.{u2} α _inst_1))))) β (Ring.toSemiring.{u1} β _inst_2) abv] [_inst_4 : CauSeq.IsComplete.{u2, u1} α _inst_1 β _inst_2 abv _inst_3] (f : CauSeq.{u2, u1} α _inst_1 β _inst_2 abv), Eq.{succ u1} β (CauSeq.lim.{u2, u1} α _inst_1 β _inst_2 abv _inst_3 _inst_4 (Neg.neg.{u1} (CauSeq.{u2, u1} α _inst_1 β _inst_2 abv) (CauSeq.instNegCauSeq.{u2, u1} α β _inst_1 _inst_2 abv _inst_3) f)) (Neg.neg.{u1} β (Ring.toNeg.{u1} β _inst_2) (CauSeq.lim.{u2, u1} α _inst_1 β _inst_2 abv _inst_3 _inst_4 f))
 Case conversion may be inaccurate. Consider using '#align cau_seq.lim_neg CauSeq.lim_negₓ'. -/
@@ -677,7 +677,7 @@ variable [IsComplete α abs]
 
 /- warning: cau_seq.lim_le -> CauSeq.lim_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLe.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLe.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLECauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
 Case conversion may be inaccurate. Consider using '#align cau_seq.lim_le CauSeq.lim_leₓ'. -/
@@ -687,7 +687,7 @@ theorem lim_le {f : CauSeq α abs} {x : α} (h : f ≤ CauSeq.const abs x) : lim
 
 /- warning: cau_seq.le_lim -> CauSeq.le_lim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLe.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLe.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLECauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align cau_seq.le_lim CauSeq.le_limₓ'. -/
@@ -697,7 +697,7 @@ theorem le_lim {f : CauSeq α abs} {x : α} (h : CauSeq.const abs x ≤ f) : x 
 
 /- warning: cau_seq.lt_lim -> CauSeq.lt_lim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLt.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLt.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLTCauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align cau_seq.lt_lim CauSeq.lt_limₓ'. -/
@@ -707,7 +707,7 @@ theorem lt_lim {f : CauSeq α abs} {x : α} (h : CauSeq.const abs x < f) : x < l
 
 /- warning: cau_seq.lim_lt -> CauSeq.lim_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLt.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLt.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLTCauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
 Case conversion may be inaccurate. Consider using '#align cau_seq.lim_lt CauSeq.lim_ltₓ'. -/

bump to nightly-2023-03-24-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/b19481deb571022990f1baa9cbf9172e6757a479

6eace303

Diff

@@ -94,11 +94,15 @@ theorem ofRat_zero : (ofRat 0 : Cauchy abv) = 0 :=
   rfl
 #align cau_seq.completion.of_rat_zero CauSeq.Completion.ofRat_zero
 
-#print CauSeq.Completion.ofRat_one /-
+/- warning: cau_seq.completion.of_rat_one -> CauSeq.Completion.ofRat_one is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv], Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (OfNat.ofNat.{u2} β 1 (OfNat.mk.{u2} β 1 (One.one.{u2} β (AddMonoidWithOne.toOne.{u2} β (AddGroupWithOne.toAddMonoidWithOne.{u2} β (NonAssocRing.toAddGroupWithOne.{u2} β (Ring.toNonAssocRing.{u2} β _inst_2)))))))) (OfNat.ofNat.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) 1 (OfNat.mk.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) 1 (One.one.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.hasOne.{u1, u2} α _inst_1 β _inst_2 abv _inst_3))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv], Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (OfNat.ofNat.{u2} β 1 (One.toOfNat1.{u2} β (NonAssocRing.toOne.{u2} β (Ring.toNonAssocRing.{u2} β _inst_2))))) (OfNat.ofNat.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) 1 (One.toOfNat1.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.instOneCauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3)))
+Case conversion may be inaccurate. Consider using '#align cau_seq.completion.of_rat_one CauSeq.Completion.ofRat_oneₓ'. -/
 theorem ofRat_one : (ofRat 1 : Cauchy abv) = 1 :=
   rfl
 #align cau_seq.completion.of_rat_one CauSeq.Completion.ofRat_one
--/
 
 /- warning: cau_seq.completion.mk_eq_zero -> CauSeq.Completion.mk_eq_zero is a dubious translation:
 lean 3 declaration is
@@ -202,12 +206,16 @@ instance : NatCast (Cauchy abv) :=
 instance : IntCast (Cauchy abv) :=
   ⟨fun n => mk n⟩
 
-#print CauSeq.Completion.ofRat_natCast /-
+/- warning: cau_seq.completion.of_rat_nat_cast -> CauSeq.Completion.ofRat_natCast is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (n : Nat), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat β (HasLiftT.mk.{1, succ u2} Nat β (CoeTCₓ.coe.{1, succ u2} Nat β (Nat.castCoe.{u2} β (AddMonoidWithOne.toNatCast.{u2} β (AddGroupWithOne.toAddMonoidWithOne.{u2} β (NonAssocRing.toAddGroupWithOne.{u2} β (Ring.toNonAssocRing.{u2} β _inst_2))))))) n)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (HasLiftT.mk.{1, succ u2} Nat (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CoeTCₓ.coe.{1, succ u2} Nat (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (Nat.castCoe.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.Cauchy.hasNatCast.{u1, u2} α _inst_1 β _inst_2 abv _inst_3)))) n)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : Ring.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β _inst_2) abv] (n : Nat), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β _inst_2 abv _inst_3 (Nat.cast.{u2} β (NonAssocRing.toNatCast.{u2} β (Ring.toNonAssocRing.{u2} β _inst_2)) n)) (Nat.cast.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) (CauSeq.Completion.instNatCastCauchy.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) n)
+Case conversion may be inaccurate. Consider using '#align cau_seq.completion.of_rat_nat_cast CauSeq.Completion.ofRat_natCastₓ'. -/
 @[simp]
 theorem ofRat_natCast (n : ℕ) : (ofRat n : Cauchy abv) = n :=
   rfl
 #align cau_seq.completion.of_rat_nat_cast CauSeq.Completion.ofRat_natCast
--/
 
 /- warning: cau_seq.completion.of_rat_int_cast -> CauSeq.Completion.ofRat_intCast is a dubious translation:
 lean 3 declaration is

bump to nightly-2023-03-11-22

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

a8ee822f

Diff

@@ -310,14 +310,14 @@ variable {α : Type _} [LinearOrderedField α]
 
 variable {β : Type _} [DivisionRing β] {abv : β → α} [IsAbsoluteValue abv]
 
-instance : RatCast (Cauchy abv) :=
+instance : HasRatCast (Cauchy abv) :=
   ⟨fun q => ofRat q⟩
 
 /- warning: cau_seq.completion.of_rat_rat_cast -> CauSeq.Completion.ofRat_ratCast is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : DivisionRing.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (StrictOrderedSemiring.toOrderedSemiring.{u1} α (StrictOrderedRing.toStrictOrderedSemiring.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) β (Ring.toSemiring.{u2} β (DivisionRing.toRing.{u2} β _inst_2)) abv] (q : Rat), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β (DivisionRing.toRing.{u2} β _inst_2) abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β (DivisionRing.toRing.{u2} β _inst_2) abv _inst_3 ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Rat β (HasLiftT.mk.{1, succ u2} Rat β (CoeTCₓ.coe.{1, succ u2} Rat β (Rat.castCoe.{u2} β (DivisionRing.toHasRatCast.{u2} β _inst_2)))) q)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Rat (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β (DivisionRing.toRing.{u2} β _inst_2) abv _inst_3) (HasLiftT.mk.{1, succ u2} Rat (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β (DivisionRing.toRing.{u2} β _inst_2) abv _inst_3) (CoeTCₓ.coe.{1, succ u2} Rat (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β (DivisionRing.toRing.{u2} β _inst_2) abv _inst_3) (Rat.castCoe.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β (DivisionRing.toRing.{u2} β _inst_2) abv _inst_3) (CauSeq.Completion.Cauchy.hasRatCast.{u1, u2} α _inst_1 β _inst_2 abv _inst_3)))) q)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : DivisionRing.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) β (DivisionSemiring.toSemiring.{u2} β (DivisionRing.toDivisionSemiring.{u2} β _inst_2)) abv] (q : Rat), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β (DivisionRing.toRing.{u2} β _inst_2) abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β (DivisionRing.toRing.{u2} β _inst_2) abv _inst_3 (RatCast.ratCast.{u2} β (DivisionRing.toRatCast.{u2} β _inst_2) q)) (RatCast.ratCast.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β (DivisionRing.toRing.{u2} β _inst_2) abv _inst_3) (CauSeq.Completion.instRatCastCauchyToRing.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) q)
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {β : Type.{u2}} [_inst_2 : DivisionRing.{u2} β] {abv : β -> α} [_inst_3 : IsAbsoluteValue.{u1, u2} α (OrderedCommSemiring.toOrderedSemiring.{u1} α (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} α (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} α (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))) β (DivisionSemiring.toSemiring.{u2} β (DivisionRing.toDivisionSemiring.{u2} β _inst_2)) abv] (q : Rat), Eq.{succ u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β (DivisionRing.toRing.{u2} β _inst_2) abv _inst_3) (CauSeq.Completion.ofRat.{u1, u2} α _inst_1 β (DivisionRing.toRing.{u2} β _inst_2) abv _inst_3 (Rat.cast.{u2} β (DivisionRing.toRatCast.{u2} β _inst_2) q)) (Rat.cast.{u2} (CauSeq.Completion.Cauchy.{u1, u2} α _inst_1 β (DivisionRing.toRing.{u2} β _inst_2) abv _inst_3) (CauSeq.Completion.instRatCastCauchyToRing.{u1, u2} α _inst_1 β _inst_2 abv _inst_3) q)
 Case conversion may be inaccurate. Consider using '#align cau_seq.completion.of_rat_rat_cast CauSeq.Completion.ofRat_ratCastₓ'. -/
 @[simp]
 theorem ofRat_ratCast (q : ℚ) : ofRat (↑q : β) = (q : Cauchy abv) :=

bump to nightly-2023-02-28-04

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

2097f8af

Diff

@@ -671,7 +671,7 @@ variable [IsComplete α abs]
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLe.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLECauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToHasSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLECauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
 Case conversion may be inaccurate. Consider using '#align cau_seq.lim_le CauSeq.lim_leₓ'. -/
 theorem lim_le {f : CauSeq α abs} {x : α} (h : f ≤ CauSeq.const abs x) : lim f ≤ x :=
   CauSeq.const_le.1 <| CauSeq.le_of_eq_of_le (Setoid.symm (equiv_lim f)) h
@@ -681,7 +681,7 @@ theorem lim_le {f : CauSeq α abs} {x : α} (h : f ≤ CauSeq.const abs x) : lim
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLe.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLECauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToHasSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LE.le.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLECauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align cau_seq.le_lim CauSeq.le_limₓ'. -/
 theorem le_lim {f : CauSeq α abs} {x : α} (h : CauSeq.const abs x ≤ f) : x ≤ lim f :=
   CauSeq.const_le.1 <| CauSeq.le_of_le_of_eq h (equiv_lim f)
@@ -691,7 +691,7 @@ theorem le_lim {f : CauSeq α abs} {x : α} (h : CauSeq.const abs x ≤ f) : x 
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLt.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLTCauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToHasSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLTCauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x) f) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) x (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f))
 Case conversion may be inaccurate. Consider using '#align cau_seq.lt_lim CauSeq.lt_limₓ'. -/
 theorem lt_lim {f : CauSeq α abs} {x : α} (h : CauSeq.const abs x < f) : x < lim f :=
   CauSeq.const_lt.1 <| CauSeq.lt_of_lt_of_eq h (equiv_lim f)
@@ -701,7 +701,7 @@ theorem lt_lim {f : CauSeq α abs} {x : α} (h : CauSeq.const abs x < f) : x < l
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (CauSeq.hasLt.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (StrictOrderedRing.toOrderedAddCommGroup.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddGroupWithOne.toAddGroup.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLTCauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToHasSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] [_inst_2 : CauSeq.IsComplete.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))] {f : CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))} {x : α}, (LT.lt.{u1} (CauSeq.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))))))) (CauSeq.instLTCauSeqToRingToDivisionRingToFieldAbsToHasAbsToNegToSupToSemilatticeSupToLatticeInstDistribLatticeToLinearOrderToLinearOrderedRingToLinearOrderedCommRing.{u1} α _inst_1) f (CauSeq.const.{u1, u1} α α _inst_1 (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (StrictOrderedRing.toRing.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) x)) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1)))))) (CauSeq.lim.{u1, u1} α _inst_1 α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (Ring.toNeg.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedRing.toLinearOrder.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))))))) (IsAbsoluteValue.abs_isAbsoluteValue.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))) _inst_2 f) x)
 Case conversion may be inaccurate. Consider using '#align cau_seq.lim_lt CauSeq.lim_ltₓ'. -/
 theorem lim_lt {f : CauSeq α abs} {x : α} (h : f < CauSeq.const abs x) : lim f < x :=
   CauSeq.const_lt.1 <| CauSeq.lt_of_eq_of_lt (Setoid.symm (equiv_lim f)) h

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

feat: NNRat.cast (#11203)

Define the canonical coercion from the nonnegative rationals to any division semiring.

From LeanAPAP

1a5d1288

Diff

@@ -203,8 +203,10 @@ section
 variable {α : Type*} [LinearOrderedField α]
 variable {β : Type*} [DivisionRing β] {abv : β → α} [IsAbsoluteValue abv]
 
+instance instNNRatCast : NNRatCast (Cauchy abv) where nnratCast q := ofRat q
 instance instRatCast : RatCast (Cauchy abv) where ratCast q := ofRat q
 
+@[simp, norm_cast] lemma ofRat_nnratCast (q : ℚ≥0) : ofRat (q : β) = (q : Cauchy abv) := rfl
 @[simp, norm_cast] lemma ofRat_ratCast (q : ℚ) : ofRat (q : β) = (q : Cauchy abv) := rfl
 #align cau_seq.completion.of_rat_rat_cast CauSeq.Completion.ofRat_ratCast
 
@@ -272,8 +274,11 @@ noncomputable instance Cauchy.divisionRing : DivisionRing (Cauchy abv) where
   exists_pair_ne := ⟨0, 1, zero_ne_one⟩
   inv_zero := inv_zero
   mul_inv_cancel x := CauSeq.Completion.mul_inv_cancel
+  nnqsmul := (· • ·)
   qsmul := (· • ·)
+  nnratCast_def q := by simp_rw [← ofRat_nnratCast, NNRat.cast_def, ofRat_div, ofRat_natCast]
   ratCast_def q := by rw [← ofRat_ratCast, Rat.cast_def, ofRat_div, ofRat_natCast, ofRat_intCast]
+  nnqsmul_def q x := Quotient.inductionOn x fun f ↦ congr_arg mk <| ext fun i ↦ NNRat.smul_def _ _
   qsmul_def q x := Quotient.inductionOn x fun f ↦ congr_arg mk <| ext fun i ↦ Rat.smul_def _ _
 
 /-- Show the first 10 items of a representative of this equivalence class of cauchy sequences.

chore: Final cleanup before NNRat.cast (#12360)

This is the parts of the diff of #11203 which don't mention NNRat.cast.

Use more where notation.
Write qsmul := _ instead of qsmul := qsmulRec _ to make the instances more robust to definition changes.
Delete qsmulRec.
Move qsmul before ratCast_def in instance declarations.
Name more instances.
Rename rat_smul to qsmul.

cb179b1b

Diff

@@ -203,12 +203,9 @@ section
 variable {α : Type*} [LinearOrderedField α]
 variable {β : Type*} [DivisionRing β] {abv : β → α} [IsAbsoluteValue abv]
 
-instance : RatCast (Cauchy abv) :=
-  ⟨fun q => ofRat q⟩
+instance instRatCast : RatCast (Cauchy abv) where ratCast q := ofRat q
 
-@[simp, coe]
-theorem ofRat_ratCast (q : ℚ) : ofRat (↑q : β) = (q : (Cauchy abv)) :=
-  rfl
+@[simp, norm_cast] lemma ofRat_ratCast (q : ℚ) : ofRat (q : β) = (q : Cauchy abv) := rfl
 #align cau_seq.completion.of_rat_rat_cast CauSeq.Completion.ofRat_ratCast
 
 noncomputable instance : Inv (Cauchy abv) :=
@@ -275,8 +272,8 @@ noncomputable instance Cauchy.divisionRing : DivisionRing (Cauchy abv) where
   exists_pair_ne := ⟨0, 1, zero_ne_one⟩
   inv_zero := inv_zero
   mul_inv_cancel x := CauSeq.Completion.mul_inv_cancel
-  ratCast_def q := by rw [← ofRat_ratCast, Rat.cast_def, ofRat_div, ofRat_natCast, ofRat_intCast]
   qsmul := (· • ·)
+  ratCast_def q := by rw [← ofRat_ratCast, Rat.cast_def, ofRat_div, ofRat_natCast, ofRat_intCast]
   qsmul_def q x := Quotient.inductionOn x fun f ↦ congr_arg mk <| ext fun i ↦ Rat.smul_def _ _
 
 /-- Show the first 10 items of a representative of this equivalence class of cauchy sequences.

refactor: Avoid Rat internals in the definition of Field (#11639)

Soon, there will be NNRat analogs of the Rat fields in the definition of Field. NNRat is less nicely a structure than Rat, hence there is a need to reduce the dependency of Field on the internals of Rat.

This PR achieves this by restating Field.ratCast_mk' in terms of Rat.num, Rat.den. This requires fixing a few downstream instances.

Reduce the diff of #11203.

Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

9160ea19

Diff

@@ -264,21 +264,20 @@ theorem ofRat_inv (x : β) : ofRat x⁻¹ = ((ofRat x)⁻¹ : (Cauchy abv)) :=
     [simp only [const_limZero.1 h, GroupWithZero.inv_zero, const_zero]; rfl]
 #align cau_seq.completion.of_rat_inv CauSeq.Completion.ofRat_inv
 
-/- porting note: needed to rewrite the proof of ratCast_mk due to simp issues -/
+noncomputable instance instDivInvMonoid : DivInvMonoid (Cauchy abv) where
+
+lemma ofRat_div (x y : β) : ofRat (x / y) = (ofRat x / ofRat y : Cauchy abv) := by
+  simp only [div_eq_mul_inv, ofRat_inv, ofRat_mul]
+#align cau_seq.completion.of_rat_div CauSeq.Completion.ofRat_div
+
 /-- The Cauchy completion forms a division ring. -/
 noncomputable instance Cauchy.divisionRing : DivisionRing (Cauchy abv) where
   exists_pair_ne := ⟨0, 1, zero_ne_one⟩
   inv_zero := inv_zero
   mul_inv_cancel x := CauSeq.Completion.mul_inv_cancel
-  ratCast q := ofRat q
-  ratCast_mk n d hd hnd := by rw [← ofRat_ratCast, Rat.cast_mk', ofRat_mul, ofRat_inv]; rfl
+  ratCast_def q := by rw [← ofRat_ratCast, Rat.cast_def, ofRat_div, ofRat_natCast, ofRat_intCast]
   qsmul := (· • ·)
-  qsmul_eq_mul' q x := Quotient.inductionOn x fun f =>
-    congr_arg mk <| ext fun i => DivisionRing.qsmul_eq_mul' _ _
-
-theorem ofRat_div (x y : β) : ofRat (x / y) = (ofRat x / ofRat y : Cauchy abv) := by
-  simp only [div_eq_mul_inv, ofRat_inv, ofRat_mul]
-#align cau_seq.completion.of_rat_div CauSeq.Completion.ofRat_div
+  qsmul_def q x := Quotient.inductionOn x fun f ↦ congr_arg mk <| ext fun i ↦ Rat.smul_def _ _
 
 /-- Show the first 10 items of a representative of this equivalence class of cauchy sequences.

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

75c86f04

Diff

@@ -22,7 +22,6 @@ open CauSeq
 section
 
 variable {α : Type*} [LinearOrderedField α]
-
 variable {β : Type*} [Ring β] (abv : β → α) [IsAbsoluteValue abv]
 
 -- TODO: rename this to `CauSeq.Completion` instead of `CauSeq.Completion.Cauchy`.
@@ -187,7 +186,6 @@ end
 section
 
 variable {α : Type*} [LinearOrderedField α]
-
 variable {β : Type*} [CommRing β] {abv : β → α} [IsAbsoluteValue abv]
 
 instance Cauchy.commRing : CommRing (Cauchy abv) :=
@@ -203,7 +201,6 @@ open scoped Classical
 section
 
 variable {α : Type*} [LinearOrderedField α]
-
 variable {β : Type*} [DivisionRing β] {abv : β → α} [IsAbsoluteValue abv]
 
 instance : RatCast (Cauchy abv) :=
@@ -299,7 +296,6 @@ end
 section
 
 variable {α : Type*} [LinearOrderedField α]
-
 variable {β : Type*} [Field β] {abv : β → α} [IsAbsoluteValue abv]
 
 /-- The Cauchy completion forms a field. -/
@@ -331,7 +327,6 @@ end
 section
 
 variable {β : Type*} [Ring β] {abv : β → α} [IsAbsoluteValue abv]
-
 variable [IsComplete β abv]
 
 theorem complete : ∀ s : CauSeq β abv, ∃ b : β, s ≈ const abv b :=

fix(Algebra/Order/CauSeq/Completion): fix qsmul instance diamond (#11263)

4b02ae4a

Diff

@@ -267,8 +267,7 @@ theorem ofRat_inv (x : β) : ofRat x⁻¹ = ((ofRat x)⁻¹ : (Cauchy abv)) :=
     [simp only [const_limZero.1 h, GroupWithZero.inv_zero, const_zero]; rfl]
 #align cau_seq.completion.of_rat_inv CauSeq.Completion.ofRat_inv
 
-/- porting note: This takes a long time to compile.
-   Also needed to rewrite the proof of ratCast_mk due to simp issues -/
+/- porting note: needed to rewrite the proof of ratCast_mk due to simp issues -/
 /-- The Cauchy completion forms a division ring. -/
 noncomputable instance Cauchy.divisionRing : DivisionRing (Cauchy abv) where
   exists_pair_ne := ⟨0, 1, zero_ne_one⟩
@@ -276,7 +275,9 @@ noncomputable instance Cauchy.divisionRing : DivisionRing (Cauchy abv) where
   mul_inv_cancel x := CauSeq.Completion.mul_inv_cancel
   ratCast q := ofRat q
   ratCast_mk n d hd hnd := by rw [← ofRat_ratCast, Rat.cast_mk', ofRat_mul, ofRat_inv]; rfl
-  qsmul := qsmulRec _ -- TODO: fix instance diamond
+  qsmul := (· • ·)
+  qsmul_eq_mul' q x := Quotient.inductionOn x fun f =>
+    congr_arg mk <| ext fun i => DivisionRing.qsmul_eq_mul' _ _
 
 theorem ofRat_div (x y : β) : ofRat (x / y) = (ofRat x / ofRat y : Cauchy abv) := by
   simp only [div_eq_mul_inv, ofRat_inv, ofRat_mul]

refactor: do not allow qsmul to default automatically (#11262)

Follows on from #6262. Again, this does not attempt to fix any diamonds; it only identifies where they may be.

71b0e26f

Diff

@@ -276,6 +276,7 @@ noncomputable instance Cauchy.divisionRing : DivisionRing (Cauchy abv) where
   mul_inv_cancel x := CauSeq.Completion.mul_inv_cancel
   ratCast q := ofRat q
   ratCast_mk n d hd hnd := by rw [← ofRat_ratCast, Rat.cast_mk', ofRat_mul, ofRat_inv]; rfl
+  qsmul := qsmulRec _ -- TODO: fix instance diamond
 
 theorem ofRat_div (x y : β) : ofRat (x / y) = (ofRat x / ofRat y : Cauchy abv) := by
   simp only [div_eq_mul_inv, ofRat_inv, ofRat_mul]

chore: squeeze some non-terminal simps (#11247)

This PR accompanies #11246, squeezing some non-terminal simps highlighted by the linter until I decided to stop!

1ad8c3fe

Diff

@@ -263,7 +263,8 @@ protected theorem mul_inv_cancel {x : (Cauchy abv)} : x ≠ 0 → x * x⁻¹ = 1
 #align cau_seq.completion.mul_inv_cancel CauSeq.Completion.mul_inv_cancel
 
 theorem ofRat_inv (x : β) : ofRat x⁻¹ = ((ofRat x)⁻¹ : (Cauchy abv)) :=
-  congr_arg mk <| by split_ifs with h <;> [simp [const_limZero.1 h]; rfl]
+  congr_arg mk <| by split_ifs with h <;>
+    [simp only [const_limZero.1 h, GroupWithZero.inv_zero, const_zero]; rfl]
 #align cau_seq.completion.of_rat_inv CauSeq.Completion.ofRat_inv
 
 /- porting note: This takes a long time to compile.

chore: scope open Classical (#11199)

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.

c747be0a

Diff

@@ -198,7 +198,7 @@ instance Cauchy.commRing : CommRing (Cauchy abv) :=
 
 end
 
-open Classical
+open scoped Classical
 
 section

chore: classify simp can do this porting notes (#10619)

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

de765f60

Diff

@@ -228,7 +228,7 @@ noncomputable instance : Inv (Cauchy abv) :=
         rw [mk_eq.2 fg, ← Ig] at If
         rw [← mul_one (mk (inv f hf)), ← Ig', ← mul_assoc, If, mul_assoc, Ig', mul_one]⟩
 
--- porting note: simp can prove this
+-- porting note (#10618): simp can prove this
 -- @[simp]
 theorem inv_zero : (0 : (Cauchy abv))⁻¹ = 0 :=
   congr_arg mk <| by rw [dif_pos] <;> [rfl; exact zero_limZero]

chore(CauSeq): Cleanup (#10530)

Rename Data.Real.CauSeq to Algebra.Order.CauSeq.Basic
Rename Data.Real.CauSeqCompletion to Algebra.Order.CauSeq.Completion
Move the general lemmas about CauSeq from Data.Complex.Exponential to a new file Algebra.Order.CauSeq.BigOperators
Move the lemmas mentioning Module from Algebra.BigOperators.Intervals to a new file Algebra.BigOperators.Module
Move a few more lemmas to earlier files
Deprecate abv_sum_le_sum_abv as it's a duplicate of IsAbsoluteValue.abv_sum

dc082806

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Robert Y. Lewis
 -/
-import Mathlib.Data.Real.CauSeq
+import Mathlib.Algebra.Order.CauSeq.Basic
 
 #align_import data.real.cau_seq_completion from "leanprover-community/mathlib"@"cf4c49c445991489058260d75dae0ff2b1abca28"

chore: Replace (· op ·) a by (a op ·) (#8843)

I used the regex $\(· (.) ·$ (.)\), replacing with ($2 $1 ·).

d14658b4

Diff

@@ -109,7 +109,7 @@ theorem mk_sub (f g : CauSeq β abv) : mk f - mk g = mk (f - g) :=
 #align cau_seq.completion.mk_sub CauSeq.Completion.mk_sub
 
 instance {γ : Type*} [SMul γ β] [IsScalarTower γ β β] : SMul γ (Cauchy abv) :=
-  ⟨fun c => (Quotient.map ((· • ·) c)) fun _ _ hf => smul_equiv_smul _ hf⟩
+  ⟨fun c => (Quotient.map (c • ·)) fun _ _ hf => smul_equiv_smul _ hf⟩
 
 @[simp]
 theorem mk_smul {γ : Type*} [SMul γ β] [IsScalarTower γ β β] (c : γ) (f : CauSeq β abv) :

chore: remove nonterminal simp (#7580)

Removes nonterminal simps on lines looking like simp [...]

6fc8e6ec

Diff

@@ -221,7 +221,7 @@ noncomputable instance : Inv (Cauchy abv) :=
       by_cases hf : LimZero f
       · simp [hf, this.1 hf, Setoid.refl]
       · have hg := mt this.2 hf
-        simp [hf, hg]
+        simp only [hf, dite_false, hg]
         have If : mk (inv f hf) * mk f = 1 := mk_eq.2 (inv_mul_cancel hf)
         have Ig : mk (inv g hg) * mk g = 1 := mk_eq.2 (inv_mul_cancel hg)
         have Ig' : mk g * mk (inv g hg) = 1 := mk_eq.2 (mul_inv_cancel hg)
@@ -251,14 +251,14 @@ theorem zero_ne_one : (0 : (Cauchy abv)) ≠ 1 := fun h => cau_seq_zero_ne_one <
 protected theorem inv_mul_cancel {x : (Cauchy abv)} : x ≠ 0 → x⁻¹ * x = 1 :=
   Quotient.inductionOn x fun f hf => by
     simp only [mk_eq_mk, ne_eq, mk_eq_zero] at hf
-    simp [hf]
+    simp only [mk_eq_mk, hf, not_false_eq_true, inv_mk, mk_mul]
     exact Quotient.sound (CauSeq.inv_mul_cancel hf)
 #align cau_seq.completion.inv_mul_cancel CauSeq.Completion.inv_mul_cancel
 
 protected theorem mul_inv_cancel {x : (Cauchy abv)} : x ≠ 0 → x * x⁻¹ = 1 :=
   Quotient.inductionOn x fun f hf => by
     simp only [mk_eq_mk, ne_eq, mk_eq_zero] at hf
-    simp [hf]
+    simp only [mk_eq_mk, hf, not_false_eq_true, inv_mk, mk_mul]
     exact Quotient.sound (CauSeq.mul_inv_cancel hf)
 #align cau_seq.completion.mul_inv_cancel CauSeq.Completion.mul_inv_cancel

chore: fix port of surjective_quotient_mk (#7096)

The mathlib3 lemma is about quotient.mk, which takes an instance argument and is translated into mathlib4 as Quotient.mk'.

e36d25ef

Diff

@@ -162,7 +162,7 @@ private theorem one_def : 1 = @mk _ _ _ _ abv _ 1 :=
   rfl
 
 instance Cauchy.ring : Ring (Cauchy abv) :=
-  Function.Surjective.ring mk (surjective_quotient_mk _) zero_def.symm one_def.symm
+  Function.Surjective.ring mk (surjective_quotient_mk' _) zero_def.symm one_def.symm
     (fun _ _ => (mk_add _ _).symm) (fun _ _ => (mk_mul _ _).symm) (fun _ => (mk_neg _).symm)
     (fun _ _ => (mk_sub _ _).symm) (fun _ _ => (mk_smul _ _).symm) (fun _ _ => (mk_smul _ _).symm)
     (fun _ _ => (mk_pow _ _).symm) (fun _ => rfl) fun _ => rfl
@@ -191,7 +191,7 @@ variable {α : Type*} [LinearOrderedField α]
 variable {β : Type*} [CommRing β] {abv : β → α} [IsAbsoluteValue abv]
 
 instance Cauchy.commRing : CommRing (Cauchy abv) :=
-  Function.Surjective.commRing mk (surjective_quotient_mk _) zero_def.symm one_def.symm
+  Function.Surjective.commRing mk (surjective_quotient_mk' _) zero_def.symm one_def.symm
     (fun _ _ => (mk_add _ _).symm) (fun _ _ => (mk_mul _ _).symm) (fun _ => (mk_neg _).symm)
     (fun _ _ => (mk_sub _ _).symm) (fun _ _ => (mk_smul _ _).symm) (fun _ _ => (mk_smul _ _).symm)
     (fun _ _ => (mk_pow _ _).symm) (fun _ => rfl) fun _ => rfl

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -21,9 +21,9 @@ open CauSeq
 
 section
 
-variable {α : Type _} [LinearOrderedField α]
+variable {α : Type*} [LinearOrderedField α]
 
-variable {β : Type _} [Ring β] (abv : β → α) [IsAbsoluteValue abv]
+variable {β : Type*} [Ring β] (abv : β → α) [IsAbsoluteValue abv]
 
 -- TODO: rename this to `CauSeq.Completion` instead of `CauSeq.Completion.Cauchy`.
 /-- The Cauchy completion of a ring with absolute value. -/
@@ -108,11 +108,11 @@ theorem mk_sub (f g : CauSeq β abv) : mk f - mk g = mk (f - g) :=
   rfl
 #align cau_seq.completion.mk_sub CauSeq.Completion.mk_sub
 
-instance {γ : Type _} [SMul γ β] [IsScalarTower γ β β] : SMul γ (Cauchy abv) :=
+instance {γ : Type*} [SMul γ β] [IsScalarTower γ β β] : SMul γ (Cauchy abv) :=
   ⟨fun c => (Quotient.map ((· • ·) c)) fun _ _ hf => smul_equiv_smul _ hf⟩
 
 @[simp]
-theorem mk_smul {γ : Type _} [SMul γ β] [IsScalarTower γ β β] (c : γ) (f : CauSeq β abv) :
+theorem mk_smul {γ : Type*} [SMul γ β] [IsScalarTower γ β β] (c : γ) (f : CauSeq β abv) :
     c • mk f = mk (c • f) :=
   rfl
 #align cau_seq.completion.mk_smul CauSeq.Completion.mk_smul
@@ -186,9 +186,9 @@ end
 
 section
 
-variable {α : Type _} [LinearOrderedField α]
+variable {α : Type*} [LinearOrderedField α]
 
-variable {β : Type _} [CommRing β] {abv : β → α} [IsAbsoluteValue abv]
+variable {β : Type*} [CommRing β] {abv : β → α} [IsAbsoluteValue abv]
 
 instance Cauchy.commRing : CommRing (Cauchy abv) :=
   Function.Surjective.commRing mk (surjective_quotient_mk _) zero_def.symm one_def.symm
@@ -202,9 +202,9 @@ open Classical
 
 section
 
-variable {α : Type _} [LinearOrderedField α]
+variable {α : Type*} [LinearOrderedField α]
 
-variable {β : Type _} [DivisionRing β] {abv : β → α} [IsAbsoluteValue abv]
+variable {β : Type*} [DivisionRing β] {abv : β → α} [IsAbsoluteValue abv]
 
 instance : RatCast (Cauchy abv) :=
   ⟨fun q => ofRat q⟩
@@ -295,9 +295,9 @@ end
 
 section
 
-variable {α : Type _} [LinearOrderedField α]
+variable {α : Type*} [LinearOrderedField α]
 
-variable {β : Type _} [Field β] {abv : β → α} [IsAbsoluteValue abv]
+variable {β : Type*} [Field β] {abv : β → α} [IsAbsoluteValue abv]
 
 /-- The Cauchy completion forms a field. -/
 noncomputable instance Cauchy.field : Field (Cauchy abv) :=
@@ -307,13 +307,13 @@ end
 
 end CauSeq.Completion
 
-variable {α : Type _} [LinearOrderedField α]
+variable {α : Type*} [LinearOrderedField α]
 
 namespace CauSeq
 
 section
 
-variable (β : Type _) [Ring β] (abv : β → α) [IsAbsoluteValue abv]
+variable (β : Type*) [Ring β] (abv : β → α) [IsAbsoluteValue abv]
 
 /-- A class stating that a ring with an absolute value is complete, i.e. every Cauchy
 sequence has a limit. -/
@@ -327,7 +327,7 @@ end
 
 section
 
-variable {β : Type _} [Ring β] {abv : β → α} [IsAbsoluteValue abv]
+variable {β : Type*} [Ring β] {abv : β → α} [IsAbsoluteValue abv]
 
 variable [IsComplete β abv]
 
@@ -409,7 +409,7 @@ end
 
 section
 
-variable {β : Type _} [Field β] {abv : β → α} [IsAbsoluteValue abv] [IsComplete β abv]
+variable {β : Type*} [Field β] {abv : β → α} [IsAbsoluteValue abv] [IsComplete β abv]
 
 theorem lim_inv {f : CauSeq β abv} (hf : ¬LimZero f) : lim (inv f hf) = (lim f)⁻¹ :=
   have hl : lim f ≠ 0 := by rwa [← lim_eq_zero_iff] at hf

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Robert Y. Lewis
-
-! This file was ported from Lean 3 source module data.real.cau_seq_completion
-! leanprover-community/mathlib commit cf4c49c445991489058260d75dae0ff2b1abca28
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Real.CauSeq
 
+#align_import data.real.cau_seq_completion from "leanprover-community/mathlib"@"cf4c49c445991489058260d75dae0ff2b1abca28"
+
 /-!
 # Cauchy completion

chore: fix many typos (#4967)

These are all doc fixes

6f9e51c3

Diff

@@ -28,7 +28,7 @@ variable {α : Type _} [LinearOrderedField α]
 
 variable {β : Type _} [Ring β] (abv : β → α) [IsAbsoluteValue abv]
 
--- TODO: rename this to `CauSeq.Completion` instead of `CauSeq.Completion.Caucy`.
+-- TODO: rename this to `CauSeq.Completion` instead of `CauSeq.Completion.Cauchy`.
 /-- The Cauchy completion of a ring with absolute value. -/
 def Cauchy :=
   @Quotient (CauSeq _ abv) CauSeq.equiv

chore: fix upper/lowercase in comments (#4360)

Run a non-interactive version of fix-comments.py on all files.
Go through the diff and manually add/discard/edit chunks.

27d257fc

Diff

@@ -285,7 +285,7 @@ theorem ofRat_div (x y : β) : ofRat (x / y) = (ofRat x / ofRat y : Cauchy abv)
 
 /-- Show the first 10 items of a representative of this equivalence class of cauchy sequences.
 
-The representative chosen is the one passed in the VM to `quot.mk`, so two cauchy sequences
+The representative chosen is the one passed in the VM to `Quot.mk`, so two cauchy sequences
 converging to the same number may be printed differently.
 -/
 unsafe instance [Repr β] : Repr (Cauchy abv) where

chore: update std 05-22 (#4248)

The main breaking change is that tac <;> [t1, t2] is now written tac <;> [t1; t2], to avoid clashing with tactics like cases and use that take comma-separated lists.

ac36b28e

Diff

@@ -234,7 +234,7 @@ noncomputable instance : Inv (Cauchy abv) :=
 -- porting note: simp can prove this
 -- @[simp]
 theorem inv_zero : (0 : (Cauchy abv))⁻¹ = 0 :=
-  congr_arg mk <| by rw [dif_pos] <;> [rfl, exact zero_limZero]
+  congr_arg mk <| by rw [dif_pos] <;> [rfl; exact zero_limZero]
 #align cau_seq.completion.inv_zero CauSeq.Completion.inv_zero
 
 @[simp]
@@ -266,7 +266,7 @@ protected theorem mul_inv_cancel {x : (Cauchy abv)} : x ≠ 0 → x * x⁻¹ = 1
 #align cau_seq.completion.mul_inv_cancel CauSeq.Completion.mul_inv_cancel
 
 theorem ofRat_inv (x : β) : ofRat x⁻¹ = ((ofRat x)⁻¹ : (Cauchy abv)) :=
-  congr_arg mk <| by split_ifs with h <;> [simp [const_limZero.1 h], rfl]
+  congr_arg mk <| by split_ifs with h <;> [simp [const_limZero.1 h]; rfl]
 #align cau_seq.completion.of_rat_inv CauSeq.Completion.ofRat_inv
 
 /- porting note: This takes a long time to compile.

chore: bye-bye, solo bys! (#3825)

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".

14167e48

Diff

@@ -219,8 +219,7 @@ theorem ofRat_ratCast (q : ℚ) : ofRat (↑q : β) = (q : (Cauchy abv)) :=
 
 noncomputable instance : Inv (Cauchy abv) :=
   ⟨fun x =>
-    (Quotient.liftOn x fun f => mk <| if h : LimZero f then 0 else inv f h) fun f g fg =>
-      by
+    (Quotient.liftOn x fun f => mk <| if h : LimZero f then 0 else inv f h) fun f g fg => by
       have := limZero_congr fg
       by_cases hf : LimZero f
       · simp [hf, this.1 hf, Setoid.refl]

sync: update sha from backports (#3079)

These files have been primarily modified by backports and need little modification:

topology.basic: #1826 - modified with a porting note, which can now be removed
data.real.cau_seq_completion: #1469 - not a backport, but forgot to update the SHA
order.filter.n_ary.basic: #1967 - this PR forgot to update the SHA
ring_theory.valuation.basic: The change is a small golf that is now included in this PR

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

2d6e2be1

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Robert Y. Lewis
 
 ! This file was ported from Lean 3 source module data.real.cau_seq_completion
-! leanprover-community/mathlib commit 40acfb6aa7516ffe6f91136691df012a64683390
+! leanprover-community/mathlib commit cf4c49c445991489058260d75dae0ff2b1abca28
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

chore: add missing #align statements (#1902)

This PR is the result of a slight variant on the following "algorithm"

take all mathlib 3 names, remove _ and make all uppercase letters into lowercase
take all mathlib 4 names, remove _ and make all uppercase letters into lowercase
look for matches, and create pairs (original_lean3_name, OriginalLean4Name)
for pairs that do not have an align statement:
- use Lean 4 to lookup the file + position of the Lean 4 name
- add an #align statement just before the next empty line
manually fix some tiny mistakes (e.g., empty lines in proofs might cause the #align statement to have been inserted too early)

b72bb858

Diff

@@ -179,6 +179,7 @@ def ofRatRingHom : β →+* (Cauchy abv) where
   map_add' := ofRat_add
   map_mul' := ofRat_mul
 #align cau_seq.completion.of_rat_ring_hom CauSeq.Completion.ofRatRingHom
+#align cau_seq.completion.of_rat_ring_hom_apply CauSeq.Completion.ofRatRingHom_apply
 
 theorem ofRat_sub (x y : β) : ofRat (x - y) = (ofRat x - ofRat y : Cauchy abv) :=
   congr_arg mk (const_sub _ _)

feat: add uppercase lean 3 linter (#1796)

depends on: #1794

Implements a linter for lean 3 declarations containing capital letters (as suggested on Zulip).

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

702d8f3d

Diff

@@ -32,6 +32,7 @@ variable {β : Type _} [Ring β] (abv : β → α) [IsAbsoluteValue abv]
 /-- The Cauchy completion of a ring with absolute value. -/
 def Cauchy :=
   @Quotient (CauSeq _ abv) CauSeq.equiv
+set_option linter.uppercaseLean3 false in
 #align cau_seq.completion.Cauchy CauSeq.Completion.Cauchy
 
 variable {abv}

chore: tidy various files (#1595)

6fe10b88

Diff

@@ -74,7 +74,8 @@ theorem ofRat_one : (ofRat 1 : Cauchy abv) = 1 :=
 
 @[simp]
 theorem mk_eq_zero {f : CauSeq _ abv} : mk f = 0 ↔ LimZero f := by
-  have : mk f = 0 ↔ LimZero (f - 0) := Quotient.eq; rwa [sub_zero] at this
+  have : mk f = 0 ↔ LimZero (f - 0) := Quotient.eq
+  rwa [sub_zero] at this
 #align cau_seq.completion.mk_eq_zero CauSeq.Completion.mk_eq_zero
 
 instance : Add (Cauchy abv) :=
@@ -251,13 +252,15 @@ theorem zero_ne_one : (0 : (Cauchy abv)) ≠ 1 := fun h => cau_seq_zero_ne_one <
 
 protected theorem inv_mul_cancel {x : (Cauchy abv)} : x ≠ 0 → x⁻¹ * x = 1 :=
   Quotient.inductionOn x fun f hf => by
-    simp at hf; simp [hf]
+    simp only [mk_eq_mk, ne_eq, mk_eq_zero] at hf
+    simp [hf]
     exact Quotient.sound (CauSeq.inv_mul_cancel hf)
 #align cau_seq.completion.inv_mul_cancel CauSeq.Completion.inv_mul_cancel
 
 protected theorem mul_inv_cancel {x : (Cauchy abv)} : x ≠ 0 → x * x⁻¹ = 1 :=
   Quotient.inductionOn x fun f hf => by
-    simp at hf; simp [hf]
+    simp only [mk_eq_mk, ne_eq, mk_eq_zero] at hf
+    simp [hf]
     exact Quotient.sound (CauSeq.mul_inv_cancel hf)
 #align cau_seq.completion.mul_inv_cancel CauSeq.Completion.mul_inv_cancel
 
@@ -376,10 +379,10 @@ theorem lim_mul_lim (f g : CauSeq β abv) : lim f * lim g = lim (f * g) :=
               apply Subtype.ext
               rw [coe_add]
               simp [sub_mul, mul_sub]
-      rw [h];
-        exact
-          add_limZero (mul_limZero_left _ (Setoid.symm (equiv_lim _)))
-            (mul_limZero_right _ (Setoid.symm (equiv_lim _)))
+      rw [h]
+      exact
+        add_limZero (mul_limZero_left _ (Setoid.symm (equiv_lim _)))
+          (mul_limZero_right _ (Setoid.symm (equiv_lim _)))
 #align cau_seq.lim_mul_lim CauSeq.lim_mul_lim
 
 theorem lim_mul (f : CauSeq β abv) (x : β) : lim f * x = lim (f * const abv x) := by
@@ -389,8 +392,8 @@ theorem lim_mul (f : CauSeq β abv) (x : β) : lim f * x = lim (f * const abv x)
 theorem lim_neg (f : CauSeq β abv) : lim (-f) = -lim f :=
   lim_eq_of_equiv_const
     (show LimZero (-f - const abv (-lim f)) by
-      rw [const_neg, sub_neg_eq_add, add_comm, ← sub_eq_add_neg];
-        exact Setoid.symm (equiv_lim f))
+      rw [const_neg, sub_neg_eq_add, add_comm, ← sub_eq_add_neg]
+      exact Setoid.symm (equiv_lim f))
 #align cau_seq.lim_neg CauSeq.lim_neg
 
 theorem lim_eq_zero_iff (f : CauSeq β abv) : lim f = 0 ↔ LimZero f :=
@@ -426,15 +429,13 @@ theorem lim_inv {f : CauSeq β abv} (hf : ¬LimZero f) : lim (inv f hf) = (lim f
         LimZero
           (inv f hf - const abv (lim f)⁻¹ -
             (const abv (lim f) - f) * (inv f hf * const abv (lim f)⁻¹)) := by
-              rw [sub_mul, ← sub_add, sub_sub, sub_add_eq_sub_sub, sub_right_comm, sub_add];
-              exact
-                show
-                  LimZero
-                    (inv f hf - const abv (lim f) * (inv f hf * const abv (lim f)⁻¹) -
-                      (const abv (lim f)⁻¹ - f * (inv f hf * const abv (lim f)⁻¹)))
-                  from
-                  sub_limZero (by rw [← mul_assoc, mul_right_comm, const_inv hl]; exact h₁ _ _ _)
-                    (by rw [← mul_assoc]; exact h₁ _ _ _)
+              rw [sub_mul, ← sub_add, sub_sub, sub_add_eq_sub_sub, sub_right_comm, sub_add]
+              show LimZero
+                (inv f hf - const abv (lim f) * (inv f hf * const abv (lim f)⁻¹) -
+                  (const abv (lim f)⁻¹ - f * (inv f hf * const abv (lim f)⁻¹)))
+              exact sub_limZero
+                (by rw [← mul_assoc, mul_right_comm, const_inv hl]; exact h₁ _ _ _)
+                (by rw [← mul_assoc]; exact h₁ _ _ _)
       (limZero_congr h₂).mpr <| mul_limZero_left _ (Setoid.symm (equiv_lim f))
 #align cau_seq.lim_inv CauSeq.lim_inv

fix: unremove Repr (Cauchy abv) (#1524)

This unremoves a working instance from mathlib3

Partially reverts e839638e

d04acbd5

Diff

@@ -279,17 +279,16 @@ theorem ofRat_div (x y : β) : ofRat (x / y) = (ofRat x / ofRat y : Cauchy abv)
   simp only [div_eq_mul_inv, ofRat_inv, ofRat_mul]
 #align cau_seq.completion.of_rat_div CauSeq.Completion.ofRat_div
 
--- Porting note: removed
--- /-- Show the first 10 items of a representative of this equivalence class of cauchy sequences.
-
--- The representative chosen is the one passed in the VM to `quot.mk`, so two cauchy sequences
--- converging to the same number may be printed differently.
--- -/
--- unsafe instance [Repr β] : Repr (Cauchy abv) where
---   reprPrec r _ :=
---     let N := 10
---     let seq := r.unquot
---     "(sorry /- " ++ Std.Format.joinSep ((List.range N).map <| repr ∘ seq) ", " ++ ", ... -/)"
+/-- Show the first 10 items of a representative of this equivalence class of cauchy sequences.
+
+The representative chosen is the one passed in the VM to `quot.mk`, so two cauchy sequences
+converging to the same number may be printed differently.
+-/
+unsafe instance [Repr β] : Repr (Cauchy abv) where
+  reprPrec r _ :=
+    let N := 10
+    let seq := r.unquot
+    "(sorry /- " ++ Std.Format.joinSep ((List.range N).map <| repr ∘ seq) ", " ++ ", ... -/)"
 
 end

feat: port Data.Real.CauSeqCompletion (#1469)

Unreverts #1440

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

d4e2fbc7