Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

2196ab36

(last sync)

refactor(algebra/group/basic): rework lemmas on inv and neg (#17483)

This PR adds the following lemma (and its additive equivalent).

theorem inv_eq_iff_eq_inv : a⁻¹ = b ↔ a = b⁻¹

and removes eq_inv_of_eq_inv, eq_inv_iff_eq_inv and inv_eq_iff_inv_eq (and their additive equivalents).

Diff

@@ -510,7 +510,7 @@ begin
 end
 
 lemma inv_Ioi {a : α} (ha : 0 < a) : (Ioi a)⁻¹ = Ioo 0 a⁻¹ :=
-by rw [inv_eq_iff_inv_eq, inv_Ioo_0_left (inv_pos.2 ha), inv_inv]
+by rw [inv_eq_iff_eq_inv, inv_Ioo_0_left (inv_pos.2 ha), inv_inv]
 
 lemma image_const_mul_Ioi_zero {k : Type*} [linear_ordered_field k]
   {x : k} (hx : 0 < x) :

59694bd0

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

2196ab36

bump to nightly-2024-04-26-08

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

ab3b6a0f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
 -/
-import Data.Set.Intervals.UnorderedInterval
-import Data.Set.Intervals.Monoid
+import Order.Interval.Set.UnorderedInterval
+import Algebra.Order.Interval.Set.Monoid
 import Data.Set.Pointwise.Basic
 import Algebra.Order.Field.Basic
 import Algebra.Order.Group.MinMax

2196ab36

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -633,7 +633,7 @@ equal to that of `a` and `b` -/
 theorem abs_sub_le_of_uIcc_subset_uIcc (h : [c, d] ⊆ [a, b]) : |d - c| ≤ |b - a| :=
   by
   rw [← max_sub_min_eq_abs, ← max_sub_min_eq_abs]
-  rw [uIcc_subset_uIcc_iff_le] at h 
+  rw [uIcc_subset_uIcc_iff_le] at h
   exact sub_le_sub h.2 h.1
 #align set.abs_sub_le_of_uIcc_subset_uIcc Set.abs_sub_le_of_uIcc_subset_uIcc
 -/
@@ -1044,7 +1044,7 @@ theorem image_affine_Icc' {a : α} (h : 0 < a) (b c d : α) :
     (fun x => a * x + b) '' Icc c d = Icc (a * c + b) (a * d + b) :=
   by
   suffices (fun x => x + b) '' ((fun x => a * x) '' Icc c d) = Icc (a * c + b) (a * d + b) by
-    rwa [Set.image_image] at this 
+    rwa [Set.image_image] at this
   rw [image_mul_left_Icc' h, image_add_const_Icc]
 #align set.image_affine_Icc' Set.image_affine_Icc'
 -/

2196ab36

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,11 +3,11 @@ Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
 -/
-import Mathbin.Data.Set.Intervals.UnorderedInterval
-import Mathbin.Data.Set.Intervals.Monoid
-import Mathbin.Data.Set.Pointwise.Basic
-import Mathbin.Algebra.Order.Field.Basic
-import Mathbin.Algebra.Order.Group.MinMax
+import Data.Set.Intervals.UnorderedInterval
+import Data.Set.Intervals.Monoid
+import Data.Set.Pointwise.Basic
+import Algebra.Order.Field.Basic
+import Algebra.Order.Group.MinMax
 
 #align_import data.set.pointwise.interval from "leanprover-community/mathlib"@"2196ab363eb097c008d4497125e0dde23fb36db2"

2196ab36

bump to nightly-2023-08-17-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

60285dcc

Diff

@@ -941,7 +941,7 @@ theorem image_mul_const_uIcc (a b c : α) : (fun x => x * a) '' [b, c] = [b * a,
   else
     calc
       (fun x => x * a) '' [b, c] = (fun x => x * a⁻¹) ⁻¹' [b, c] :=
-        (Units.mk0 a ha).mul_right.image_eq_preimage _
+        (Units.mk0 a ha).hMul_right.image_eq_preimage _
       _ = (fun x => x / a) ⁻¹' [b, c] := by simp only [div_eq_mul_inv]
       _ = [b * a, c * a] := preimage_div_const_uIcc ha _ _
 #align set.image_mul_const_uIcc Set.image_mul_const_uIcc
@@ -964,7 +964,7 @@ theorem image_div_const_uIcc (a b c : α) : (fun x => x / a) '' [b, c] = [b / a,
 #print Set.image_mul_right_Icc' /-
 theorem image_mul_right_Icc' (a b : α) {c : α} (h : 0 < c) :
     (fun x => x * c) '' Icc a b = Icc (a * c) (b * c) :=
-  ((Units.mk0 c h.ne').mul_right.image_eq_preimage _).trans (by simp [h, division_def])
+  ((Units.mk0 c h.ne').hMul_right.image_eq_preimage _).trans (by simp [h, division_def])
 #align set.image_mul_right_Icc' Set.image_mul_right_Icc'
 -/
 
@@ -996,7 +996,7 @@ theorem image_mul_left_Icc {a b c : α} (ha : 0 ≤ a) (hbc : b ≤ c) :
 #print Set.image_mul_right_Ioo /-
 theorem image_mul_right_Ioo (a b : α) {c : α} (h : 0 < c) :
     (fun x => x * c) '' Ioo a b = Ioo (a * c) (b * c) :=
-  ((Units.mk0 c h.ne').mul_right.image_eq_preimage _).trans (by simp [h, division_def])
+  ((Units.mk0 c h.ne').hMul_right.image_eq_preimage _).trans (by simp [h, division_def])
 #align set.image_mul_right_Ioo Set.image_mul_right_Ioo
 -/
 
@@ -1028,7 +1028,7 @@ theorem inv_Ioi {a : α} (ha : 0 < a) : (Ioi a)⁻¹ = Ioo 0 a⁻¹ := by
 #print Set.image_const_mul_Ioi_zero /-
 theorem image_const_mul_Ioi_zero {k : Type _} [LinearOrderedField k] {x : k} (hx : 0 < x) :
     (fun y => x * y) '' Ioi (0 : k) = Ioi 0 := by
-  erw [(Units.mk0 x hx.ne').mul_left.image_eq_preimage, preimage_const_mul_Ioi 0 (inv_pos.mpr hx),
+  erw [(Units.mk0 x hx.ne').hMul_left.image_eq_preimage, preimage_const_mul_Ioi 0 (inv_pos.mpr hx),
     zero_div]
 #align set.image_const_mul_Ioi_zero Set.image_const_mul_Ioi_zero
 -/

2196ab36

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
-
-! This file was ported from Lean 3 source module data.set.pointwise.interval
-! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Set.Intervals.UnorderedInterval
 import Mathbin.Data.Set.Intervals.Monoid
@@ -14,6 +9,8 @@ import Mathbin.Data.Set.Pointwise.Basic
 import Mathbin.Algebra.Order.Field.Basic
 import Mathbin.Algebra.Order.Group.MinMax
 
+#align_import data.set.pointwise.interval from "leanprover-community/mathlib"@"2196ab363eb097c008d4497125e0dde23fb36db2"
+
 /-!
 # (Pre)images of intervals

2196ab36

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -42,377 +42,517 @@ variable [OrderedAddCommGroup α] (a b c : α)
 -/
 
 
+#print Set.preimage_const_add_Ici /-
 @[simp]
 theorem preimage_const_add_Ici : (fun x => a + x) ⁻¹' Ici b = Ici (b - a) :=
   ext fun x => sub_le_iff_le_add'.symm
 #align set.preimage_const_add_Ici Set.preimage_const_add_Ici
+-/
 
+#print Set.preimage_const_add_Ioi /-
 @[simp]
 theorem preimage_const_add_Ioi : (fun x => a + x) ⁻¹' Ioi b = Ioi (b - a) :=
   ext fun x => sub_lt_iff_lt_add'.symm
 #align set.preimage_const_add_Ioi Set.preimage_const_add_Ioi
+-/
 
+#print Set.preimage_const_add_Iic /-
 @[simp]
 theorem preimage_const_add_Iic : (fun x => a + x) ⁻¹' Iic b = Iic (b - a) :=
   ext fun x => le_sub_iff_add_le'.symm
 #align set.preimage_const_add_Iic Set.preimage_const_add_Iic
+-/
 
+#print Set.preimage_const_add_Iio /-
 @[simp]
 theorem preimage_const_add_Iio : (fun x => a + x) ⁻¹' Iio b = Iio (b - a) :=
   ext fun x => lt_sub_iff_add_lt'.symm
 #align set.preimage_const_add_Iio Set.preimage_const_add_Iio
+-/
 
+#print Set.preimage_const_add_Icc /-
 @[simp]
 theorem preimage_const_add_Icc : (fun x => a + x) ⁻¹' Icc b c = Icc (b - a) (c - a) := by
   simp [← Ici_inter_Iic]
 #align set.preimage_const_add_Icc Set.preimage_const_add_Icc
+-/
 
+#print Set.preimage_const_add_Ico /-
 @[simp]
 theorem preimage_const_add_Ico : (fun x => a + x) ⁻¹' Ico b c = Ico (b - a) (c - a) := by
   simp [← Ici_inter_Iio]
 #align set.preimage_const_add_Ico Set.preimage_const_add_Ico
+-/
 
+#print Set.preimage_const_add_Ioc /-
 @[simp]
 theorem preimage_const_add_Ioc : (fun x => a + x) ⁻¹' Ioc b c = Ioc (b - a) (c - a) := by
   simp [← Ioi_inter_Iic]
 #align set.preimage_const_add_Ioc Set.preimage_const_add_Ioc
+-/
 
+#print Set.preimage_const_add_Ioo /-
 @[simp]
 theorem preimage_const_add_Ioo : (fun x => a + x) ⁻¹' Ioo b c = Ioo (b - a) (c - a) := by
   simp [← Ioi_inter_Iio]
 #align set.preimage_const_add_Ioo Set.preimage_const_add_Ioo
+-/
 
 /-!
 ### Preimages under `x ↦ x + a`
 -/
 
 
+#print Set.preimage_add_const_Ici /-
 @[simp]
 theorem preimage_add_const_Ici : (fun x => x + a) ⁻¹' Ici b = Ici (b - a) :=
   ext fun x => sub_le_iff_le_add.symm
 #align set.preimage_add_const_Ici Set.preimage_add_const_Ici
+-/
 
+#print Set.preimage_add_const_Ioi /-
 @[simp]
 theorem preimage_add_const_Ioi : (fun x => x + a) ⁻¹' Ioi b = Ioi (b - a) :=
   ext fun x => sub_lt_iff_lt_add.symm
 #align set.preimage_add_const_Ioi Set.preimage_add_const_Ioi
+-/
 
+#print Set.preimage_add_const_Iic /-
 @[simp]
 theorem preimage_add_const_Iic : (fun x => x + a) ⁻¹' Iic b = Iic (b - a) :=
   ext fun x => le_sub_iff_add_le.symm
 #align set.preimage_add_const_Iic Set.preimage_add_const_Iic
+-/
 
+#print Set.preimage_add_const_Iio /-
 @[simp]
 theorem preimage_add_const_Iio : (fun x => x + a) ⁻¹' Iio b = Iio (b - a) :=
   ext fun x => lt_sub_iff_add_lt.symm
 #align set.preimage_add_const_Iio Set.preimage_add_const_Iio
+-/
 
+#print Set.preimage_add_const_Icc /-
 @[simp]
 theorem preimage_add_const_Icc : (fun x => x + a) ⁻¹' Icc b c = Icc (b - a) (c - a) := by
   simp [← Ici_inter_Iic]
 #align set.preimage_add_const_Icc Set.preimage_add_const_Icc
+-/
 
+#print Set.preimage_add_const_Ico /-
 @[simp]
 theorem preimage_add_const_Ico : (fun x => x + a) ⁻¹' Ico b c = Ico (b - a) (c - a) := by
   simp [← Ici_inter_Iio]
 #align set.preimage_add_const_Ico Set.preimage_add_const_Ico
+-/
 
+#print Set.preimage_add_const_Ioc /-
 @[simp]
 theorem preimage_add_const_Ioc : (fun x => x + a) ⁻¹' Ioc b c = Ioc (b - a) (c - a) := by
   simp [← Ioi_inter_Iic]
 #align set.preimage_add_const_Ioc Set.preimage_add_const_Ioc
+-/
 
+#print Set.preimage_add_const_Ioo /-
 @[simp]
 theorem preimage_add_const_Ioo : (fun x => x + a) ⁻¹' Ioo b c = Ioo (b - a) (c - a) := by
   simp [← Ioi_inter_Iio]
 #align set.preimage_add_const_Ioo Set.preimage_add_const_Ioo
+-/
 
 /-!
 ### Preimages under `x ↦ -x`
 -/
 
 
+#print Set.preimage_neg_Ici /-
 @[simp]
 theorem preimage_neg_Ici : -Ici a = Iic (-a) :=
   ext fun x => le_neg
 #align set.preimage_neg_Ici Set.preimage_neg_Ici
+-/
 
+#print Set.preimage_neg_Iic /-
 @[simp]
 theorem preimage_neg_Iic : -Iic a = Ici (-a) :=
   ext fun x => neg_le
 #align set.preimage_neg_Iic Set.preimage_neg_Iic
+-/
 
+#print Set.preimage_neg_Ioi /-
 @[simp]
 theorem preimage_neg_Ioi : -Ioi a = Iio (-a) :=
   ext fun x => lt_neg
 #align set.preimage_neg_Ioi Set.preimage_neg_Ioi
+-/
 
+#print Set.preimage_neg_Iio /-
 @[simp]
 theorem preimage_neg_Iio : -Iio a = Ioi (-a) :=
   ext fun x => neg_lt
 #align set.preimage_neg_Iio Set.preimage_neg_Iio
+-/
 
+#print Set.preimage_neg_Icc /-
 @[simp]
 theorem preimage_neg_Icc : -Icc a b = Icc (-b) (-a) := by simp [← Ici_inter_Iic, inter_comm]
 #align set.preimage_neg_Icc Set.preimage_neg_Icc
+-/
 
+#print Set.preimage_neg_Ico /-
 @[simp]
 theorem preimage_neg_Ico : -Ico a b = Ioc (-b) (-a) := by
   simp [← Ici_inter_Iio, ← Ioi_inter_Iic, inter_comm]
 #align set.preimage_neg_Ico Set.preimage_neg_Ico
+-/
 
+#print Set.preimage_neg_Ioc /-
 @[simp]
 theorem preimage_neg_Ioc : -Ioc a b = Ico (-b) (-a) := by
   simp [← Ioi_inter_Iic, ← Ici_inter_Iio, inter_comm]
 #align set.preimage_neg_Ioc Set.preimage_neg_Ioc
+-/
 
+#print Set.preimage_neg_Ioo /-
 @[simp]
 theorem preimage_neg_Ioo : -Ioo a b = Ioo (-b) (-a) := by simp [← Ioi_inter_Iio, inter_comm]
 #align set.preimage_neg_Ioo Set.preimage_neg_Ioo
+-/
 
 /-!
 ### Preimages under `x ↦ x - a`
 -/
 
 
+#print Set.preimage_sub_const_Ici /-
 @[simp]
 theorem preimage_sub_const_Ici : (fun x => x - a) ⁻¹' Ici b = Ici (b + a) := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_Ici Set.preimage_sub_const_Ici
+-/
 
+#print Set.preimage_sub_const_Ioi /-
 @[simp]
 theorem preimage_sub_const_Ioi : (fun x => x - a) ⁻¹' Ioi b = Ioi (b + a) := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_Ioi Set.preimage_sub_const_Ioi
+-/
 
+#print Set.preimage_sub_const_Iic /-
 @[simp]
 theorem preimage_sub_const_Iic : (fun x => x - a) ⁻¹' Iic b = Iic (b + a) := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_Iic Set.preimage_sub_const_Iic
+-/
 
+#print Set.preimage_sub_const_Iio /-
 @[simp]
 theorem preimage_sub_const_Iio : (fun x => x - a) ⁻¹' Iio b = Iio (b + a) := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_Iio Set.preimage_sub_const_Iio
+-/
 
+#print Set.preimage_sub_const_Icc /-
 @[simp]
 theorem preimage_sub_const_Icc : (fun x => x - a) ⁻¹' Icc b c = Icc (b + a) (c + a) := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_Icc Set.preimage_sub_const_Icc
+-/
 
+#print Set.preimage_sub_const_Ico /-
 @[simp]
 theorem preimage_sub_const_Ico : (fun x => x - a) ⁻¹' Ico b c = Ico (b + a) (c + a) := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_Ico Set.preimage_sub_const_Ico
+-/
 
+#print Set.preimage_sub_const_Ioc /-
 @[simp]
 theorem preimage_sub_const_Ioc : (fun x => x - a) ⁻¹' Ioc b c = Ioc (b + a) (c + a) := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_Ioc Set.preimage_sub_const_Ioc
+-/
 
+#print Set.preimage_sub_const_Ioo /-
 @[simp]
 theorem preimage_sub_const_Ioo : (fun x => x - a) ⁻¹' Ioo b c = Ioo (b + a) (c + a) := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_Ioo Set.preimage_sub_const_Ioo
+-/
 
 /-!
 ### Preimages under `x ↦ a - x`
 -/
 
 
+#print Set.preimage_const_sub_Ici /-
 @[simp]
 theorem preimage_const_sub_Ici : (fun x => a - x) ⁻¹' Ici b = Iic (a - b) :=
   ext fun x => le_sub_comm
 #align set.preimage_const_sub_Ici Set.preimage_const_sub_Ici
+-/
 
+#print Set.preimage_const_sub_Iic /-
 @[simp]
 theorem preimage_const_sub_Iic : (fun x => a - x) ⁻¹' Iic b = Ici (a - b) :=
   ext fun x => sub_le_comm
 #align set.preimage_const_sub_Iic Set.preimage_const_sub_Iic
+-/
 
+#print Set.preimage_const_sub_Ioi /-
 @[simp]
 theorem preimage_const_sub_Ioi : (fun x => a - x) ⁻¹' Ioi b = Iio (a - b) :=
   ext fun x => lt_sub_comm
 #align set.preimage_const_sub_Ioi Set.preimage_const_sub_Ioi
+-/
 
+#print Set.preimage_const_sub_Iio /-
 @[simp]
 theorem preimage_const_sub_Iio : (fun x => a - x) ⁻¹' Iio b = Ioi (a - b) :=
   ext fun x => sub_lt_comm
 #align set.preimage_const_sub_Iio Set.preimage_const_sub_Iio
+-/
 
+#print Set.preimage_const_sub_Icc /-
 @[simp]
 theorem preimage_const_sub_Icc : (fun x => a - x) ⁻¹' Icc b c = Icc (a - c) (a - b) := by
   simp [← Ici_inter_Iic, inter_comm]
 #align set.preimage_const_sub_Icc Set.preimage_const_sub_Icc
+-/
 
+#print Set.preimage_const_sub_Ico /-
 @[simp]
 theorem preimage_const_sub_Ico : (fun x => a - x) ⁻¹' Ico b c = Ioc (a - c) (a - b) := by
   simp [← Ioi_inter_Iic, ← Ici_inter_Iio, inter_comm]
 #align set.preimage_const_sub_Ico Set.preimage_const_sub_Ico
+-/
 
+#print Set.preimage_const_sub_Ioc /-
 @[simp]
 theorem preimage_const_sub_Ioc : (fun x => a - x) ⁻¹' Ioc b c = Ico (a - c) (a - b) := by
   simp [← Ioi_inter_Iic, ← Ici_inter_Iio, inter_comm]
 #align set.preimage_const_sub_Ioc Set.preimage_const_sub_Ioc
+-/
 
+#print Set.preimage_const_sub_Ioo /-
 @[simp]
 theorem preimage_const_sub_Ioo : (fun x => a - x) ⁻¹' Ioo b c = Ioo (a - c) (a - b) := by
   simp [← Ioi_inter_Iio, inter_comm]
 #align set.preimage_const_sub_Ioo Set.preimage_const_sub_Ioo
+-/
 
 /-!
 ### Images under `x ↦ a + x`
 -/
 
 
+#print Set.image_const_add_Iic /-
 @[simp]
 theorem image_const_add_Iic : (fun x => a + x) '' Iic b = Iic (a + b) := by simp [add_comm]
 #align set.image_const_add_Iic Set.image_const_add_Iic
+-/
 
+#print Set.image_const_add_Iio /-
 @[simp]
 theorem image_const_add_Iio : (fun x => a + x) '' Iio b = Iio (a + b) := by simp [add_comm]
 #align set.image_const_add_Iio Set.image_const_add_Iio
+-/
 
 /-!
 ### Images under `x ↦ x + a`
 -/
 
 
+#print Set.image_add_const_Iic /-
 @[simp]
 theorem image_add_const_Iic : (fun x => x + a) '' Iic b = Iic (b + a) := by simp
 #align set.image_add_const_Iic Set.image_add_const_Iic
+-/
 
+#print Set.image_add_const_Iio /-
 @[simp]
 theorem image_add_const_Iio : (fun x => x + a) '' Iio b = Iio (b + a) := by simp
 #align set.image_add_const_Iio Set.image_add_const_Iio
+-/
 
 /-!
 ### Images under `x ↦ -x`
 -/
 
 
+#print Set.image_neg_Ici /-
 theorem image_neg_Ici : Neg.neg '' Ici a = Iic (-a) := by simp
 #align set.image_neg_Ici Set.image_neg_Ici
+-/
 
+#print Set.image_neg_Iic /-
 theorem image_neg_Iic : Neg.neg '' Iic a = Ici (-a) := by simp
 #align set.image_neg_Iic Set.image_neg_Iic
+-/
 
+#print Set.image_neg_Ioi /-
 theorem image_neg_Ioi : Neg.neg '' Ioi a = Iio (-a) := by simp
 #align set.image_neg_Ioi Set.image_neg_Ioi
+-/
 
+#print Set.image_neg_Iio /-
 theorem image_neg_Iio : Neg.neg '' Iio a = Ioi (-a) := by simp
 #align set.image_neg_Iio Set.image_neg_Iio
+-/
 
+#print Set.image_neg_Icc /-
 theorem image_neg_Icc : Neg.neg '' Icc a b = Icc (-b) (-a) := by simp
 #align set.image_neg_Icc Set.image_neg_Icc
+-/
 
+#print Set.image_neg_Ico /-
 theorem image_neg_Ico : Neg.neg '' Ico a b = Ioc (-b) (-a) := by simp
 #align set.image_neg_Ico Set.image_neg_Ico
+-/
 
+#print Set.image_neg_Ioc /-
 theorem image_neg_Ioc : Neg.neg '' Ioc a b = Ico (-b) (-a) := by simp
 #align set.image_neg_Ioc Set.image_neg_Ioc
+-/
 
+#print Set.image_neg_Ioo /-
 theorem image_neg_Ioo : Neg.neg '' Ioo a b = Ioo (-b) (-a) := by simp
 #align set.image_neg_Ioo Set.image_neg_Ioo
+-/
 
 /-!
 ### Images under `x ↦ a - x`
 -/
 
 
+#print Set.image_const_sub_Ici /-
 @[simp]
 theorem image_const_sub_Ici : (fun x => a - x) '' Ici b = Iic (a - b) := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x]
 #align set.image_const_sub_Ici Set.image_const_sub_Ici
+-/
 
+#print Set.image_const_sub_Iic /-
 @[simp]
 theorem image_const_sub_Iic : (fun x => a - x) '' Iic b = Ici (a - b) := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x, add_comm]
 #align set.image_const_sub_Iic Set.image_const_sub_Iic
+-/
 
+#print Set.image_const_sub_Ioi /-
 @[simp]
 theorem image_const_sub_Ioi : (fun x => a - x) '' Ioi b = Iio (a - b) := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x]
 #align set.image_const_sub_Ioi Set.image_const_sub_Ioi
+-/
 
+#print Set.image_const_sub_Iio /-
 @[simp]
 theorem image_const_sub_Iio : (fun x => a - x) '' Iio b = Ioi (a - b) := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x, add_comm]
 #align set.image_const_sub_Iio Set.image_const_sub_Iio
+-/
 
+#print Set.image_const_sub_Icc /-
 @[simp]
 theorem image_const_sub_Icc : (fun x => a - x) '' Icc b c = Icc (a - c) (a - b) := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x, add_comm]
 #align set.image_const_sub_Icc Set.image_const_sub_Icc
+-/
 
+#print Set.image_const_sub_Ico /-
 @[simp]
 theorem image_const_sub_Ico : (fun x => a - x) '' Ico b c = Ioc (a - c) (a - b) := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x, add_comm]
 #align set.image_const_sub_Ico Set.image_const_sub_Ico
+-/
 
+#print Set.image_const_sub_Ioc /-
 @[simp]
 theorem image_const_sub_Ioc : (fun x => a - x) '' Ioc b c = Ico (a - c) (a - b) := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x, add_comm]
 #align set.image_const_sub_Ioc Set.image_const_sub_Ioc
+-/
 
+#print Set.image_const_sub_Ioo /-
 @[simp]
 theorem image_const_sub_Ioo : (fun x => a - x) '' Ioo b c = Ioo (a - c) (a - b) := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x, add_comm]
 #align set.image_const_sub_Ioo Set.image_const_sub_Ioo
+-/
 
 /-!
 ### Images under `x ↦ x - a`
 -/
 
 
+#print Set.image_sub_const_Ici /-
 @[simp]
 theorem image_sub_const_Ici : (fun x => x - a) '' Ici b = Ici (b - a) := by simp [sub_eq_neg_add]
 #align set.image_sub_const_Ici Set.image_sub_const_Ici
+-/
 
+#print Set.image_sub_const_Iic /-
 @[simp]
 theorem image_sub_const_Iic : (fun x => x - a) '' Iic b = Iic (b - a) := by simp [sub_eq_neg_add]
 #align set.image_sub_const_Iic Set.image_sub_const_Iic
+-/
 
+#print Set.image_sub_const_Ioi /-
 @[simp]
 theorem image_sub_const_Ioi : (fun x => x - a) '' Ioi b = Ioi (b - a) := by simp [sub_eq_neg_add]
 #align set.image_sub_const_Ioi Set.image_sub_const_Ioi
+-/
 
+#print Set.image_sub_const_Iio /-
 @[simp]
 theorem image_sub_const_Iio : (fun x => x - a) '' Iio b = Iio (b - a) := by simp [sub_eq_neg_add]
 #align set.image_sub_const_Iio Set.image_sub_const_Iio
+-/
 
+#print Set.image_sub_const_Icc /-
 @[simp]
 theorem image_sub_const_Icc : (fun x => x - a) '' Icc b c = Icc (b - a) (c - a) := by
   simp [sub_eq_neg_add]
 #align set.image_sub_const_Icc Set.image_sub_const_Icc
+-/
 
+#print Set.image_sub_const_Ico /-
 @[simp]
 theorem image_sub_const_Ico : (fun x => x - a) '' Ico b c = Ico (b - a) (c - a) := by
   simp [sub_eq_neg_add]
 #align set.image_sub_const_Ico Set.image_sub_const_Ico
+-/
 
+#print Set.image_sub_const_Ioc /-
 @[simp]
 theorem image_sub_const_Ioc : (fun x => x - a) '' Ioc b c = Ioc (b - a) (c - a) := by
   simp [sub_eq_neg_add]
 #align set.image_sub_const_Ioc Set.image_sub_const_Ioc
+-/
 
+#print Set.image_sub_const_Ioo /-
 @[simp]
 theorem image_sub_const_Ioo : (fun x => x - a) '' Ioo b c = Ioo (b - a) (c - a) := by
   simp [sub_eq_neg_add]
 #align set.image_sub_const_Ioo Set.image_sub_const_Ioo
+-/
 
 /-!
 ### Bijections
 -/
 
 
+#print Set.Iic_add_bij /-
 theorem Iic_add_bij : BijOn (· + a) (Iic b) (Iic (b + a)) :=
   image_add_const_Iic a b ▸ ((add_left_injective _).InjOn _).bijOn_image
 #align set.Iic_add_bij Set.Iic_add_bij
+-/
 
+#print Set.Iio_add_bij /-
 theorem Iio_add_bij : BijOn (· + a) (Iio b) (Iio (b + a)) :=
   image_add_const_Iio a b ▸ ((add_left_injective _).InjOn _).bijOn_image
 #align set.Iio_add_bij Set.Iio_add_bij
+-/
 
 end OrderedAddCommGroup
 
@@ -420,56 +560,77 @@ section LinearOrderedAddCommGroup
 
 variable [LinearOrderedAddCommGroup α] (a b c d : α)
 
+#print Set.preimage_const_add_uIcc /-
 @[simp]
 theorem preimage_const_add_uIcc : (fun x => a + x) ⁻¹' [b, c] = [b - a, c - a] := by
   simp only [← Icc_min_max, preimage_const_add_Icc, min_sub_sub_right, max_sub_sub_right]
 #align set.preimage_const_add_uIcc Set.preimage_const_add_uIcc
+-/
 
+#print Set.preimage_add_const_uIcc /-
 @[simp]
 theorem preimage_add_const_uIcc : (fun x => x + a) ⁻¹' [b, c] = [b - a, c - a] := by
   simpa only [add_comm] using preimage_const_add_uIcc a b c
 #align set.preimage_add_const_uIcc Set.preimage_add_const_uIcc
+-/
 
+#print Set.preimage_neg_uIcc /-
 @[simp]
 theorem preimage_neg_uIcc : -[a, b] = [-a, -b] := by
   simp only [← Icc_min_max, preimage_neg_Icc, min_neg_neg, max_neg_neg]
 #align set.preimage_neg_uIcc Set.preimage_neg_uIcc
+-/
 
+#print Set.preimage_sub_const_uIcc /-
 @[simp]
 theorem preimage_sub_const_uIcc : (fun x => x - a) ⁻¹' [b, c] = [b + a, c + a] := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_uIcc Set.preimage_sub_const_uIcc
+-/
 
+#print Set.preimage_const_sub_uIcc /-
 @[simp]
 theorem preimage_const_sub_uIcc : (fun x => a - x) ⁻¹' [b, c] = [a - b, a - c] :=
   by
   simp_rw [← Icc_min_max, preimage_const_sub_Icc]
   simp only [sub_eq_add_neg, min_add_add_left, max_add_add_left, min_neg_neg, max_neg_neg]
 #align set.preimage_const_sub_uIcc Set.preimage_const_sub_uIcc
+-/
 
+#print Set.image_const_add_uIcc /-
 @[simp]
 theorem image_const_add_uIcc : (fun x => a + x) '' [b, c] = [a + b, a + c] := by simp [add_comm]
 #align set.image_const_add_uIcc Set.image_const_add_uIcc
+-/
 
+#print Set.image_add_const_uIcc /-
 @[simp]
 theorem image_add_const_uIcc : (fun x => x + a) '' [b, c] = [b + a, c + a] := by simp
 #align set.image_add_const_uIcc Set.image_add_const_uIcc
+-/
 
+#print Set.image_const_sub_uIcc /-
 @[simp]
 theorem image_const_sub_uIcc : (fun x => a - x) '' [b, c] = [a - b, a - c] := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x]
 #align set.image_const_sub_uIcc Set.image_const_sub_uIcc
+-/
 
+#print Set.image_sub_const_uIcc /-
 @[simp]
 theorem image_sub_const_uIcc : (fun x => x - a) '' [b, c] = [b - a, c - a] := by
   simp [sub_eq_add_neg, add_comm]
 #align set.image_sub_const_uIcc Set.image_sub_const_uIcc
+-/
 
+#print Set.image_neg_uIcc /-
 theorem image_neg_uIcc : Neg.neg '' [a, b] = [-a, -b] := by simp
 #align set.image_neg_uIcc Set.image_neg_uIcc
+-/
 
 variable {a b c d}
 
+#print Set.abs_sub_le_of_uIcc_subset_uIcc /-
 /-- If `[c, d]` is a subinterval of `[a, b]`, then the distance between `c` and `d` is less than or
 equal to that of `a` and `b` -/
 theorem abs_sub_le_of_uIcc_subset_uIcc (h : [c, d] ⊆ [a, b]) : |d - c| ≤ |b - a| :=
@@ -478,18 +639,23 @@ theorem abs_sub_le_of_uIcc_subset_uIcc (h : [c, d] ⊆ [a, b]) : |d - c| ≤ |b
   rw [uIcc_subset_uIcc_iff_le] at h 
   exact sub_le_sub h.2 h.1
 #align set.abs_sub_le_of_uIcc_subset_uIcc Set.abs_sub_le_of_uIcc_subset_uIcc
+-/
 
+#print Set.abs_sub_left_of_mem_uIcc /-
 /-- If `c ∈ [a, b]`, then the distance between `a` and `c` is less than or equal to
 that of `a` and `b`  -/
 theorem abs_sub_left_of_mem_uIcc (h : c ∈ [a, b]) : |c - a| ≤ |b - a| :=
   abs_sub_le_of_uIcc_subset_uIcc <| uIcc_subset_uIcc_left h
 #align set.abs_sub_left_of_mem_uIcc Set.abs_sub_left_of_mem_uIcc
+-/
 
+#print Set.abs_sub_right_of_mem_uIcc /-
 /-- If `x ∈ [a, b]`, then the distance between `c` and `b` is less than or equal to
 that of `a` and `b`  -/
 theorem abs_sub_right_of_mem_uIcc (h : c ∈ [a, b]) : |b - c| ≤ |b - a| :=
   abs_sub_le_of_uIcc_subset_uIcc <| uIcc_subset_uIcc_right h
 #align set.abs_sub_right_of_mem_uIcc Set.abs_sub_right_of_mem_uIcc
+-/
 
 end LinearOrderedAddCommGroup
 
@@ -502,184 +668,249 @@ section LinearOrderedField
 
 variable [LinearOrderedField α] {a : α}
 
+#print Set.preimage_mul_const_Iio /-
 @[simp]
 theorem preimage_mul_const_Iio (a : α) {c : α} (h : 0 < c) :
     (fun x => x * c) ⁻¹' Iio a = Iio (a / c) :=
   ext fun x => (lt_div_iff h).symm
 #align set.preimage_mul_const_Iio Set.preimage_mul_const_Iio
+-/
 
+#print Set.preimage_mul_const_Ioi /-
 @[simp]
 theorem preimage_mul_const_Ioi (a : α) {c : α} (h : 0 < c) :
     (fun x => x * c) ⁻¹' Ioi a = Ioi (a / c) :=
   ext fun x => (div_lt_iff h).symm
 #align set.preimage_mul_const_Ioi Set.preimage_mul_const_Ioi
+-/
 
+#print Set.preimage_mul_const_Iic /-
 @[simp]
 theorem preimage_mul_const_Iic (a : α) {c : α} (h : 0 < c) :
     (fun x => x * c) ⁻¹' Iic a = Iic (a / c) :=
   ext fun x => (le_div_iff h).symm
 #align set.preimage_mul_const_Iic Set.preimage_mul_const_Iic
+-/
 
+#print Set.preimage_mul_const_Ici /-
 @[simp]
 theorem preimage_mul_const_Ici (a : α) {c : α} (h : 0 < c) :
     (fun x => x * c) ⁻¹' Ici a = Ici (a / c) :=
   ext fun x => (div_le_iff h).symm
 #align set.preimage_mul_const_Ici Set.preimage_mul_const_Ici
+-/
 
+#print Set.preimage_mul_const_Ioo /-
 @[simp]
 theorem preimage_mul_const_Ioo (a b : α) {c : α} (h : 0 < c) :
     (fun x => x * c) ⁻¹' Ioo a b = Ioo (a / c) (b / c) := by simp [← Ioi_inter_Iio, h]
 #align set.preimage_mul_const_Ioo Set.preimage_mul_const_Ioo
+-/
 
+#print Set.preimage_mul_const_Ioc /-
 @[simp]
 theorem preimage_mul_const_Ioc (a b : α) {c : α} (h : 0 < c) :
     (fun x => x * c) ⁻¹' Ioc a b = Ioc (a / c) (b / c) := by simp [← Ioi_inter_Iic, h]
 #align set.preimage_mul_const_Ioc Set.preimage_mul_const_Ioc
+-/
 
+#print Set.preimage_mul_const_Ico /-
 @[simp]
 theorem preimage_mul_const_Ico (a b : α) {c : α} (h : 0 < c) :
     (fun x => x * c) ⁻¹' Ico a b = Ico (a / c) (b / c) := by simp [← Ici_inter_Iio, h]
 #align set.preimage_mul_const_Ico Set.preimage_mul_const_Ico
+-/
 
+#print Set.preimage_mul_const_Icc /-
 @[simp]
 theorem preimage_mul_const_Icc (a b : α) {c : α} (h : 0 < c) :
     (fun x => x * c) ⁻¹' Icc a b = Icc (a / c) (b / c) := by simp [← Ici_inter_Iic, h]
 #align set.preimage_mul_const_Icc Set.preimage_mul_const_Icc
+-/
 
+#print Set.preimage_mul_const_Iio_of_neg /-
 @[simp]
 theorem preimage_mul_const_Iio_of_neg (a : α) {c : α} (h : c < 0) :
     (fun x => x * c) ⁻¹' Iio a = Ioi (a / c) :=
   ext fun x => (div_lt_iff_of_neg h).symm
 #align set.preimage_mul_const_Iio_of_neg Set.preimage_mul_const_Iio_of_neg
+-/
 
+#print Set.preimage_mul_const_Ioi_of_neg /-
 @[simp]
 theorem preimage_mul_const_Ioi_of_neg (a : α) {c : α} (h : c < 0) :
     (fun x => x * c) ⁻¹' Ioi a = Iio (a / c) :=
   ext fun x => (lt_div_iff_of_neg h).symm
 #align set.preimage_mul_const_Ioi_of_neg Set.preimage_mul_const_Ioi_of_neg
+-/
 
+#print Set.preimage_mul_const_Iic_of_neg /-
 @[simp]
 theorem preimage_mul_const_Iic_of_neg (a : α) {c : α} (h : c < 0) :
     (fun x => x * c) ⁻¹' Iic a = Ici (a / c) :=
   ext fun x => (div_le_iff_of_neg h).symm
 #align set.preimage_mul_const_Iic_of_neg Set.preimage_mul_const_Iic_of_neg
+-/
 
+#print Set.preimage_mul_const_Ici_of_neg /-
 @[simp]
 theorem preimage_mul_const_Ici_of_neg (a : α) {c : α} (h : c < 0) :
     (fun x => x * c) ⁻¹' Ici a = Iic (a / c) :=
   ext fun x => (le_div_iff_of_neg h).symm
 #align set.preimage_mul_const_Ici_of_neg Set.preimage_mul_const_Ici_of_neg
+-/
 
+#print Set.preimage_mul_const_Ioo_of_neg /-
 @[simp]
 theorem preimage_mul_const_Ioo_of_neg (a b : α) {c : α} (h : c < 0) :
     (fun x => x * c) ⁻¹' Ioo a b = Ioo (b / c) (a / c) := by simp [← Ioi_inter_Iio, h, inter_comm]
 #align set.preimage_mul_const_Ioo_of_neg Set.preimage_mul_const_Ioo_of_neg
+-/
 
+#print Set.preimage_mul_const_Ioc_of_neg /-
 @[simp]
 theorem preimage_mul_const_Ioc_of_neg (a b : α) {c : α} (h : c < 0) :
     (fun x => x * c) ⁻¹' Ioc a b = Ico (b / c) (a / c) := by
   simp [← Ioi_inter_Iic, ← Ici_inter_Iio, h, inter_comm]
 #align set.preimage_mul_const_Ioc_of_neg Set.preimage_mul_const_Ioc_of_neg
+-/
 
+#print Set.preimage_mul_const_Ico_of_neg /-
 @[simp]
 theorem preimage_mul_const_Ico_of_neg (a b : α) {c : α} (h : c < 0) :
     (fun x => x * c) ⁻¹' Ico a b = Ioc (b / c) (a / c) := by
   simp [← Ici_inter_Iio, ← Ioi_inter_Iic, h, inter_comm]
 #align set.preimage_mul_const_Ico_of_neg Set.preimage_mul_const_Ico_of_neg
+-/
 
+#print Set.preimage_mul_const_Icc_of_neg /-
 @[simp]
 theorem preimage_mul_const_Icc_of_neg (a b : α) {c : α} (h : c < 0) :
     (fun x => x * c) ⁻¹' Icc a b = Icc (b / c) (a / c) := by simp [← Ici_inter_Iic, h, inter_comm]
 #align set.preimage_mul_const_Icc_of_neg Set.preimage_mul_const_Icc_of_neg
+-/
 
+#print Set.preimage_const_mul_Iio /-
 @[simp]
 theorem preimage_const_mul_Iio (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹' Iio a = Iio (a / c) :=
   ext fun x => (lt_div_iff' h).symm
 #align set.preimage_const_mul_Iio Set.preimage_const_mul_Iio
+-/
 
+#print Set.preimage_const_mul_Ioi /-
 @[simp]
 theorem preimage_const_mul_Ioi (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹' Ioi a = Ioi (a / c) :=
   ext fun x => (div_lt_iff' h).symm
 #align set.preimage_const_mul_Ioi Set.preimage_const_mul_Ioi
+-/
 
+#print Set.preimage_const_mul_Iic /-
 @[simp]
 theorem preimage_const_mul_Iic (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹' Iic a = Iic (a / c) :=
   ext fun x => (le_div_iff' h).symm
 #align set.preimage_const_mul_Iic Set.preimage_const_mul_Iic
+-/
 
+#print Set.preimage_const_mul_Ici /-
 @[simp]
 theorem preimage_const_mul_Ici (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹' Ici a = Ici (a / c) :=
   ext fun x => (div_le_iff' h).symm
 #align set.preimage_const_mul_Ici Set.preimage_const_mul_Ici
+-/
 
+#print Set.preimage_const_mul_Ioo /-
 @[simp]
 theorem preimage_const_mul_Ioo (a b : α) {c : α} (h : 0 < c) :
     (· * ·) c ⁻¹' Ioo a b = Ioo (a / c) (b / c) := by simp [← Ioi_inter_Iio, h]
 #align set.preimage_const_mul_Ioo Set.preimage_const_mul_Ioo
+-/
 
+#print Set.preimage_const_mul_Ioc /-
 @[simp]
 theorem preimage_const_mul_Ioc (a b : α) {c : α} (h : 0 < c) :
     (· * ·) c ⁻¹' Ioc a b = Ioc (a / c) (b / c) := by simp [← Ioi_inter_Iic, h]
 #align set.preimage_const_mul_Ioc Set.preimage_const_mul_Ioc
+-/
 
+#print Set.preimage_const_mul_Ico /-
 @[simp]
 theorem preimage_const_mul_Ico (a b : α) {c : α} (h : 0 < c) :
     (· * ·) c ⁻¹' Ico a b = Ico (a / c) (b / c) := by simp [← Ici_inter_Iio, h]
 #align set.preimage_const_mul_Ico Set.preimage_const_mul_Ico
+-/
 
+#print Set.preimage_const_mul_Icc /-
 @[simp]
 theorem preimage_const_mul_Icc (a b : α) {c : α} (h : 0 < c) :
     (· * ·) c ⁻¹' Icc a b = Icc (a / c) (b / c) := by simp [← Ici_inter_Iic, h]
 #align set.preimage_const_mul_Icc Set.preimage_const_mul_Icc
+-/
 
+#print Set.preimage_const_mul_Iio_of_neg /-
 @[simp]
 theorem preimage_const_mul_Iio_of_neg (a : α) {c : α} (h : c < 0) :
     (· * ·) c ⁻¹' Iio a = Ioi (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Iio_of_neg a h
 #align set.preimage_const_mul_Iio_of_neg Set.preimage_const_mul_Iio_of_neg
+-/
 
+#print Set.preimage_const_mul_Ioi_of_neg /-
 @[simp]
 theorem preimage_const_mul_Ioi_of_neg (a : α) {c : α} (h : c < 0) :
     (· * ·) c ⁻¹' Ioi a = Iio (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Ioi_of_neg a h
 #align set.preimage_const_mul_Ioi_of_neg Set.preimage_const_mul_Ioi_of_neg
+-/
 
+#print Set.preimage_const_mul_Iic_of_neg /-
 @[simp]
 theorem preimage_const_mul_Iic_of_neg (a : α) {c : α} (h : c < 0) :
     (· * ·) c ⁻¹' Iic a = Ici (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Iic_of_neg a h
 #align set.preimage_const_mul_Iic_of_neg Set.preimage_const_mul_Iic_of_neg
+-/
 
+#print Set.preimage_const_mul_Ici_of_neg /-
 @[simp]
 theorem preimage_const_mul_Ici_of_neg (a : α) {c : α} (h : c < 0) :
     (· * ·) c ⁻¹' Ici a = Iic (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Ici_of_neg a h
 #align set.preimage_const_mul_Ici_of_neg Set.preimage_const_mul_Ici_of_neg
+-/
 
+#print Set.preimage_const_mul_Ioo_of_neg /-
 @[simp]
 theorem preimage_const_mul_Ioo_of_neg (a b : α) {c : α} (h : c < 0) :
     (· * ·) c ⁻¹' Ioo a b = Ioo (b / c) (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Ioo_of_neg a b h
 #align set.preimage_const_mul_Ioo_of_neg Set.preimage_const_mul_Ioo_of_neg
+-/
 
+#print Set.preimage_const_mul_Ioc_of_neg /-
 @[simp]
 theorem preimage_const_mul_Ioc_of_neg (a b : α) {c : α} (h : c < 0) :
     (· * ·) c ⁻¹' Ioc a b = Ico (b / c) (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Ioc_of_neg a b h
 #align set.preimage_const_mul_Ioc_of_neg Set.preimage_const_mul_Ioc_of_neg
+-/
 
+#print Set.preimage_const_mul_Ico_of_neg /-
 @[simp]
 theorem preimage_const_mul_Ico_of_neg (a b : α) {c : α} (h : c < 0) :
     (· * ·) c ⁻¹' Ico a b = Ioc (b / c) (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Ico_of_neg a b h
 #align set.preimage_const_mul_Ico_of_neg Set.preimage_const_mul_Ico_of_neg
+-/
 
+#print Set.preimage_const_mul_Icc_of_neg /-
 @[simp]
 theorem preimage_const_mul_Icc_of_neg (a b : α) {c : α} (h : c < 0) :
     (· * ·) c ⁻¹' Icc a b = Icc (b / c) (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Icc_of_neg a b h
 #align set.preimage_const_mul_Icc_of_neg Set.preimage_const_mul_Icc_of_neg
+-/
 
+#print Set.preimage_mul_const_uIcc /-
 @[simp]
 theorem preimage_mul_const_uIcc (ha : a ≠ 0) (b c : α) :
     (fun x => x * a) ⁻¹' [b, c] = [b / a, c / a] :=
@@ -688,19 +919,25 @@ theorem preimage_mul_const_uIcc (ha : a ≠ 0) (b c : α) :
       simp [← Icc_min_max, h, h.le, min_div_div_right_of_nonpos, max_div_div_right_of_nonpos])
     fun ha : 0 < a => by simp [← Icc_min_max, ha, ha.le, min_div_div_right, max_div_div_right]
 #align set.preimage_mul_const_uIcc Set.preimage_mul_const_uIcc
+-/
 
+#print Set.preimage_const_mul_uIcc /-
 @[simp]
 theorem preimage_const_mul_uIcc (ha : a ≠ 0) (b c : α) :
     (fun x => a * x) ⁻¹' [b, c] = [b / a, c / a] := by
   simp only [← preimage_mul_const_uIcc ha, mul_comm]
 #align set.preimage_const_mul_uIcc Set.preimage_const_mul_uIcc
+-/
 
+#print Set.preimage_div_const_uIcc /-
 @[simp]
 theorem preimage_div_const_uIcc (ha : a ≠ 0) (b c : α) :
     (fun x => x / a) ⁻¹' [b, c] = [b * a, c * a] := by
   simp only [div_eq_mul_inv, preimage_mul_const_uIcc (inv_ne_zero ha), inv_inv]
 #align set.preimage_div_const_uIcc Set.preimage_div_const_uIcc
+-/
 
+#print Set.image_mul_const_uIcc /-
 @[simp]
 theorem image_mul_const_uIcc (a b c : α) : (fun x => x * a) '' [b, c] = [b * a, c * a] :=
   if ha : a = 0 then by simp [ha]
@@ -711,22 +948,30 @@ theorem image_mul_const_uIcc (a b c : α) : (fun x => x * a) '' [b, c] = [b * a,
       _ = (fun x => x / a) ⁻¹' [b, c] := by simp only [div_eq_mul_inv]
       _ = [b * a, c * a] := preimage_div_const_uIcc ha _ _
 #align set.image_mul_const_uIcc Set.image_mul_const_uIcc
+-/
 
+#print Set.image_const_mul_uIcc /-
 @[simp]
 theorem image_const_mul_uIcc (a b c : α) : (fun x => a * x) '' [b, c] = [a * b, a * c] := by
   simpa only [mul_comm] using image_mul_const_uIcc a b c
 #align set.image_const_mul_uIcc Set.image_const_mul_uIcc
+-/
 
+#print Set.image_div_const_uIcc /-
 @[simp]
 theorem image_div_const_uIcc (a b c : α) : (fun x => x / a) '' [b, c] = [b / a, c / a] := by
   simp only [div_eq_mul_inv, image_mul_const_uIcc]
 #align set.image_div_const_uIcc Set.image_div_const_uIcc
+-/
 
+#print Set.image_mul_right_Icc' /-
 theorem image_mul_right_Icc' (a b : α) {c : α} (h : 0 < c) :
     (fun x => x * c) '' Icc a b = Icc (a * c) (b * c) :=
   ((Units.mk0 c h.ne').mul_right.image_eq_preimage _).trans (by simp [h, division_def])
 #align set.image_mul_right_Icc' Set.image_mul_right_Icc'
+-/
 
+#print Set.image_mul_right_Icc /-
 theorem image_mul_right_Icc {a b c : α} (hab : a ≤ b) (hc : 0 ≤ c) :
     (fun x => x * c) '' Icc a b = Icc (a * c) (b * c) :=
   by
@@ -735,27 +980,37 @@ theorem image_mul_right_Icc {a b c : α} (hab : a ≤ b) (hc : 0 ≤ c) :
     simp [(nonempty_Icc.2 hab).image_const]
   exact image_mul_right_Icc' a b ‹0 < c›
 #align set.image_mul_right_Icc Set.image_mul_right_Icc
+-/
 
+#print Set.image_mul_left_Icc' /-
 theorem image_mul_left_Icc' {a : α} (h : 0 < a) (b c : α) :
     (· * ·) a '' Icc b c = Icc (a * b) (a * c) := by
   convert image_mul_right_Icc' b c h using 1 <;> simp only [mul_comm _ a]
 #align set.image_mul_left_Icc' Set.image_mul_left_Icc'
+-/
 
+#print Set.image_mul_left_Icc /-
 theorem image_mul_left_Icc {a b c : α} (ha : 0 ≤ a) (hbc : b ≤ c) :
     (· * ·) a '' Icc b c = Icc (a * b) (a * c) := by
   convert image_mul_right_Icc hbc ha using 1 <;> simp only [mul_comm _ a]
 #align set.image_mul_left_Icc Set.image_mul_left_Icc
+-/
 
+#print Set.image_mul_right_Ioo /-
 theorem image_mul_right_Ioo (a b : α) {c : α} (h : 0 < c) :
     (fun x => x * c) '' Ioo a b = Ioo (a * c) (b * c) :=
   ((Units.mk0 c h.ne').mul_right.image_eq_preimage _).trans (by simp [h, division_def])
 #align set.image_mul_right_Ioo Set.image_mul_right_Ioo
+-/
 
+#print Set.image_mul_left_Ioo /-
 theorem image_mul_left_Ioo {a : α} (h : 0 < a) (b c : α) :
     (· * ·) a '' Ioo b c = Ioo (a * b) (a * c) := by
   convert image_mul_right_Ioo b c h using 1 <;> simp only [mul_comm _ a]
 #align set.image_mul_left_Ioo Set.image_mul_left_Ioo
+-/
 
+#print Set.inv_Ioo_0_left /-
 /-- The (pre)image under `inv` of `Ioo 0 a` is `Ioi a⁻¹`. -/
 theorem inv_Ioo_0_left {a : α} (ha : 0 < a) : (Ioo 0 a)⁻¹ = Ioi a⁻¹ :=
   by
@@ -765,22 +1020,28 @@ theorem inv_Ioo_0_left {a : α} (ha : 0 < a) : (Ioo 0 a)⁻¹ = Ioi a⁻¹ :=
       ⟨inv_pos.2 <| (inv_pos.2 ha).trans h,
         inv_inv a ▸ (inv_lt_inv ((inv_pos.2 ha).trans h) (inv_pos.2 ha)).2 h⟩⟩
 #align set.inv_Ioo_0_left Set.inv_Ioo_0_left
+-/
 
+#print Set.inv_Ioi /-
 theorem inv_Ioi {a : α} (ha : 0 < a) : (Ioi a)⁻¹ = Ioo 0 a⁻¹ := by
   rw [inv_eq_iff_eq_inv, inv_Ioo_0_left (inv_pos.2 ha), inv_inv]
 #align set.inv_Ioi Set.inv_Ioi
+-/
 
+#print Set.image_const_mul_Ioi_zero /-
 theorem image_const_mul_Ioi_zero {k : Type _} [LinearOrderedField k] {x : k} (hx : 0 < x) :
     (fun y => x * y) '' Ioi (0 : k) = Ioi 0 := by
   erw [(Units.mk0 x hx.ne').mul_left.image_eq_preimage, preimage_const_mul_Ioi 0 (inv_pos.mpr hx),
     zero_div]
 #align set.image_const_mul_Ioi_zero Set.image_const_mul_Ioi_zero
+-/
 
 /-!
 ### Images under `x ↦ a * x + b`
 -/
 
 
+#print Set.image_affine_Icc' /-
 @[simp]
 theorem image_affine_Icc' {a : α} (h : 0 < a) (b c d : α) :
     (fun x => a * x + b) '' Icc c d = Icc (a * c + b) (a * d + b) :=
@@ -789,6 +1050,7 @@ theorem image_affine_Icc' {a : α} (h : 0 < a) (b c d : α) :
     rwa [Set.image_image] at this 
   rw [image_mul_left_Icc' h, image_add_const_Icc]
 #align set.image_affine_Icc' Set.image_affine_Icc'
+-/
 
 end LinearOrderedField

2196ab36

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -710,7 +710,6 @@ theorem image_mul_const_uIcc (a b c : α) : (fun x => x * a) '' [b, c] = [b * a,
         (Units.mk0 a ha).mul_right.image_eq_preimage _
       _ = (fun x => x / a) ⁻¹' [b, c] := by simp only [div_eq_mul_inv]
       _ = [b * a, c * a] := preimage_div_const_uIcc ha _ _
-      
 #align set.image_mul_const_uIcc Set.image_mul_const_uIcc
 
 @[simp]

2196ab36

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -475,7 +475,7 @@ equal to that of `a` and `b` -/
 theorem abs_sub_le_of_uIcc_subset_uIcc (h : [c, d] ⊆ [a, b]) : |d - c| ≤ |b - a| :=
   by
   rw [← max_sub_min_eq_abs, ← max_sub_min_eq_abs]
-  rw [uIcc_subset_uIcc_iff_le] at h
+  rw [uIcc_subset_uIcc_iff_le] at h 
   exact sub_le_sub h.2 h.1
 #align set.abs_sub_le_of_uIcc_subset_uIcc Set.abs_sub_le_of_uIcc_subset_uIcc
 
@@ -787,7 +787,7 @@ theorem image_affine_Icc' {a : α} (h : 0 < a) (b c d : α) :
     (fun x => a * x + b) '' Icc c d = Icc (a * c + b) (a * d + b) :=
   by
   suffices (fun x => x + b) '' ((fun x => a * x) '' Icc c d) = Icc (a * c + b) (a * d + b) by
-    rwa [Set.image_image] at this
+    rwa [Set.image_image] at this 
   rw [image_mul_left_Icc' h, image_add_const_Icc]
 #align set.image_affine_Icc' Set.image_affine_Icc'

2196ab36

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -27,7 +27,7 @@ lemmas about preimages and images of all intervals. We also prove a few lemmas a
 -/
 
 
-open Interval Pointwise
+open scoped Interval Pointwise
 
 variable {α : Type _}

2196ab36

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -42,89 +42,41 @@ variable [OrderedAddCommGroup α] (a b c : α)
 -/
 
 
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-Case conversion may be inaccurate. Consider using '#align set.preimage_const_add_Ici Set.preimage_const_add_Iciₓ'. -/
 @[simp]
 theorem preimage_const_add_Ici : (fun x => a + x) ⁻¹' Ici b = Ici (b - a) :=
   ext fun x => sub_le_iff_le_add'.symm
 #align set.preimage_const_add_Ici Set.preimage_const_add_Ici
 
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-Case conversion may be inaccurate. Consider using '#align set.preimage_const_add_Ioi Set.preimage_const_add_Ioiₓ'. -/
 @[simp]
 theorem preimage_const_add_Ioi : (fun x => a + x) ⁻¹' Ioi b = Ioi (b - a) :=
   ext fun x => sub_lt_iff_lt_add'.symm
 #align set.preimage_const_add_Ioi Set.preimage_const_add_Ioi
 
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-Case conversion may be inaccurate. Consider using '#align set.preimage_const_add_Iic Set.preimage_const_add_Iicₓ'. -/
 @[simp]
 theorem preimage_const_add_Iic : (fun x => a + x) ⁻¹' Iic b = Iic (b - a) :=
   ext fun x => le_sub_iff_add_le'.symm
 #align set.preimage_const_add_Iic Set.preimage_const_add_Iic
 
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 @[simp]
 theorem preimage_const_add_Iio : (fun x => a + x) ⁻¹' Iio b = Iio (b - a) :=
   ext fun x => lt_sub_iff_add_lt'.symm
 #align set.preimage_const_add_Iio Set.preimage_const_add_Iio
 
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 @[simp]
 theorem preimage_const_add_Icc : (fun x => a + x) ⁻¹' Icc b c = Icc (b - a) (c - a) := by
   simp [← Ici_inter_Iic]
 #align set.preimage_const_add_Icc Set.preimage_const_add_Icc
 
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 @[simp]
 theorem preimage_const_add_Ico : (fun x => a + x) ⁻¹' Ico b c = Ico (b - a) (c - a) := by
   simp [← Ici_inter_Iio]
 #align set.preimage_const_add_Ico Set.preimage_const_add_Ico
 
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 @[simp]
 theorem preimage_const_add_Ioc : (fun x => a + x) ⁻¹' Ioc b c = Ioc (b - a) (c - a) := by
   simp [← Ioi_inter_Iic]
 #align set.preimage_const_add_Ioc Set.preimage_const_add_Ioc
 
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 @[simp]
 theorem preimage_const_add_Ioo : (fun x => a + x) ⁻¹' Ioo b c = Ioo (b - a) (c - a) := by
   simp [← Ioi_inter_Iio]
@@ -135,89 +87,41 @@ theorem preimage_const_add_Ioo : (fun x => a + x) ⁻¹' Ioo b c = Ioo (b - a) (
 -/
 
 
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 @[simp]
 theorem preimage_add_const_Ici : (fun x => x + a) ⁻¹' Ici b = Ici (b - a) :=
   ext fun x => sub_le_iff_le_add.symm
 #align set.preimage_add_const_Ici Set.preimage_add_const_Ici
 
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 @[simp]
 theorem preimage_add_const_Ioi : (fun x => x + a) ⁻¹' Ioi b = Ioi (b - a) :=
   ext fun x => sub_lt_iff_lt_add.symm
 #align set.preimage_add_const_Ioi Set.preimage_add_const_Ioi
 
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 @[simp]
 theorem preimage_add_const_Iic : (fun x => x + a) ⁻¹' Iic b = Iic (b - a) :=
   ext fun x => le_sub_iff_add_le.symm
 #align set.preimage_add_const_Iic Set.preimage_add_const_Iic
 
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 @[simp]
 theorem preimage_add_const_Iio : (fun x => x + a) ⁻¹' Iio b = Iio (b - a) :=
   ext fun x => lt_sub_iff_add_lt.symm
 #align set.preimage_add_const_Iio Set.preimage_add_const_Iio
 
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 @[simp]
 theorem preimage_add_const_Icc : (fun x => x + a) ⁻¹' Icc b c = Icc (b - a) (c - a) := by
   simp [← Ici_inter_Iic]
 #align set.preimage_add_const_Icc Set.preimage_add_const_Icc
 
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 @[simp]
 theorem preimage_add_const_Ico : (fun x => x + a) ⁻¹' Ico b c = Ico (b - a) (c - a) := by
   simp [← Ici_inter_Iio]
 #align set.preimage_add_const_Ico Set.preimage_add_const_Ico
 
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 @[simp]
 theorem preimage_add_const_Ioc : (fun x => x + a) ⁻¹' Ioc b c = Ioc (b - a) (c - a) := by
   simp [← Ioi_inter_Iic]
 #align set.preimage_add_const_Ioc Set.preimage_add_const_Ioc
 
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 @[simp]
 theorem preimage_add_const_Ioo : (fun x => x + a) ⁻¹' Ioo b c = Ioo (b - a) (c - a) := by
   simp [← Ioi_inter_Iio]
@@ -228,88 +132,40 @@ theorem preimage_add_const_Ioo : (fun x => x + a) ⁻¹' Ioo b c = Ioo (b - a) (
 -/
 
 
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 @[simp]
 theorem preimage_neg_Ici : -Ici a = Iic (-a) :=
   ext fun x => le_neg
 #align set.preimage_neg_Ici Set.preimage_neg_Ici
 
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 @[simp]
 theorem preimage_neg_Iic : -Iic a = Ici (-a) :=
   ext fun x => neg_le
 #align set.preimage_neg_Iic Set.preimage_neg_Iic
 
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 @[simp]
 theorem preimage_neg_Ioi : -Ioi a = Iio (-a) :=
   ext fun x => lt_neg
 #align set.preimage_neg_Ioi Set.preimage_neg_Ioi
 
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 @[simp]
 theorem preimage_neg_Iio : -Iio a = Ioi (-a) :=
   ext fun x => neg_lt
 #align set.preimage_neg_Iio Set.preimage_neg_Iio
 
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 @[simp]
 theorem preimage_neg_Icc : -Icc a b = Icc (-b) (-a) := by simp [← Ici_inter_Iic, inter_comm]
 #align set.preimage_neg_Icc Set.preimage_neg_Icc
 
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 @[simp]
 theorem preimage_neg_Ico : -Ico a b = Ioc (-b) (-a) := by
   simp [← Ici_inter_Iio, ← Ioi_inter_Iic, inter_comm]
 #align set.preimage_neg_Ico Set.preimage_neg_Ico
 
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 @[simp]
 theorem preimage_neg_Ioc : -Ioc a b = Ico (-b) (-a) := by
   simp [← Ioi_inter_Iic, ← Ici_inter_Iio, inter_comm]
 #align set.preimage_neg_Ioc Set.preimage_neg_Ioc
 
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 @[simp]
 theorem preimage_neg_Ioo : -Ioo a b = Ioo (-b) (-a) := by simp [← Ioi_inter_Iio, inter_comm]
 #align set.preimage_neg_Ioo Set.preimage_neg_Ioo
@@ -319,89 +175,41 @@ theorem preimage_neg_Ioo : -Ioo a b = Ioo (-b) (-a) := by simp [← Ioi_inter_Ii
 -/
 
 
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 @[simp]
 theorem preimage_sub_const_Ici : (fun x => x - a) ⁻¹' Ici b = Ici (b + a) := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_Ici Set.preimage_sub_const_Ici
 
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 @[simp]
 theorem preimage_sub_const_Ioi : (fun x => x - a) ⁻¹' Ioi b = Ioi (b + a) := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_Ioi Set.preimage_sub_const_Ioi
 
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 @[simp]
 theorem preimage_sub_const_Iic : (fun x => x - a) ⁻¹' Iic b = Iic (b + a) := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_Iic Set.preimage_sub_const_Iic
 
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 @[simp]
 theorem preimage_sub_const_Iio : (fun x => x - a) ⁻¹' Iio b = Iio (b + a) := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_Iio Set.preimage_sub_const_Iio
 
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 @[simp]
 theorem preimage_sub_const_Icc : (fun x => x - a) ⁻¹' Icc b c = Icc (b + a) (c + a) := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_Icc Set.preimage_sub_const_Icc
 
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 @[simp]
 theorem preimage_sub_const_Ico : (fun x => x - a) ⁻¹' Ico b c = Ico (b + a) (c + a) := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_Ico Set.preimage_sub_const_Ico
 
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 @[simp]
 theorem preimage_sub_const_Ioc : (fun x => x - a) ⁻¹' Ioc b c = Ioc (b + a) (c + a) := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_Ioc Set.preimage_sub_const_Ioc
 
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 @[simp]
 theorem preimage_sub_const_Ioo : (fun x => x - a) ⁻¹' Ioo b c = Ioo (b + a) (c + a) := by
   simp [sub_eq_add_neg]
@@ -412,89 +220,41 @@ theorem preimage_sub_const_Ioo : (fun x => x - a) ⁻¹' Ioo b c = Ioo (b + a) (
 -/
 
 
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 @[simp]
 theorem preimage_const_sub_Ici : (fun x => a - x) ⁻¹' Ici b = Iic (a - b) :=
   ext fun x => le_sub_comm
 #align set.preimage_const_sub_Ici Set.preimage_const_sub_Ici
 
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 @[simp]
 theorem preimage_const_sub_Iic : (fun x => a - x) ⁻¹' Iic b = Ici (a - b) :=
   ext fun x => sub_le_comm
 #align set.preimage_const_sub_Iic Set.preimage_const_sub_Iic
 
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 @[simp]
 theorem preimage_const_sub_Ioi : (fun x => a - x) ⁻¹' Ioi b = Iio (a - b) :=
   ext fun x => lt_sub_comm
 #align set.preimage_const_sub_Ioi Set.preimage_const_sub_Ioi
 
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 @[simp]
 theorem preimage_const_sub_Iio : (fun x => a - x) ⁻¹' Iio b = Ioi (a - b) :=
   ext fun x => sub_lt_comm
 #align set.preimage_const_sub_Iio Set.preimage_const_sub_Iio
 
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 @[simp]
 theorem preimage_const_sub_Icc : (fun x => a - x) ⁻¹' Icc b c = Icc (a - c) (a - b) := by
   simp [← Ici_inter_Iic, inter_comm]
 #align set.preimage_const_sub_Icc Set.preimage_const_sub_Icc
 
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 @[simp]
 theorem preimage_const_sub_Ico : (fun x => a - x) ⁻¹' Ico b c = Ioc (a - c) (a - b) := by
   simp [← Ioi_inter_Iic, ← Ici_inter_Iio, inter_comm]
 #align set.preimage_const_sub_Ico Set.preimage_const_sub_Ico
 
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 @[simp]
 theorem preimage_const_sub_Ioc : (fun x => a - x) ⁻¹' Ioc b c = Ico (a - c) (a - b) := by
   simp [← Ioi_inter_Iic, ← Ici_inter_Iio, inter_comm]
 #align set.preimage_const_sub_Ioc Set.preimage_const_sub_Ioc
 
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 @[simp]
 theorem preimage_const_sub_Ioo : (fun x => a - x) ⁻¹' Ioo b c = Ioo (a - c) (a - b) := by
   simp [← Ioi_inter_Iio, inter_comm]
@@ -505,22 +265,10 @@ theorem preimage_const_sub_Ioo : (fun x => a - x) ⁻¹' Ioo b c = Ioo (a - c) (
 -/
 
 
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 @[simp]
 theorem image_const_add_Iic : (fun x => a + x) '' Iic b = Iic (a + b) := by simp [add_comm]
 #align set.image_const_add_Iic Set.image_const_add_Iic
 
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 @[simp]
 theorem image_const_add_Iio : (fun x => a + x) '' Iio b = Iio (a + b) := by simp [add_comm]
 #align set.image_const_add_Iio Set.image_const_add_Iio
@@ -530,22 +278,10 @@ theorem image_const_add_Iio : (fun x => a + x) '' Iio b = Iio (a + b) := by simp
 -/
 
 
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 @[simp]
 theorem image_add_const_Iic : (fun x => x + a) '' Iic b = Iic (b + a) := by simp
 #align set.image_add_const_Iic Set.image_add_const_Iic
 
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 @[simp]
 theorem image_add_const_Iio : (fun x => x + a) '' Iio b = Iio (b + a) := by simp
 #align set.image_add_const_Iio Set.image_add_const_Iio
@@ -555,75 +291,27 @@ theorem image_add_const_Iio : (fun x => x + a) '' Iio b = Iio (b + a) := by simp
 -/
 
 
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 theorem image_neg_Ici : Neg.neg '' Ici a = Iic (-a) := by simp
 #align set.image_neg_Ici Set.image_neg_Ici
 
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 theorem image_neg_Iic : Neg.neg '' Iic a = Ici (-a) := by simp
 #align set.image_neg_Iic Set.image_neg_Iic
 
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 theorem image_neg_Ioi : Neg.neg '' Ioi a = Iio (-a) := by simp
 #align set.image_neg_Ioi Set.image_neg_Ioi
 
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 theorem image_neg_Iio : Neg.neg '' Iio a = Ioi (-a) := by simp
 #align set.image_neg_Iio Set.image_neg_Iio
 
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 theorem image_neg_Icc : Neg.neg '' Icc a b = Icc (-b) (-a) := by simp
 #align set.image_neg_Icc Set.image_neg_Icc
 
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 theorem image_neg_Ico : Neg.neg '' Ico a b = Ioc (-b) (-a) := by simp
 #align set.image_neg_Ico Set.image_neg_Ico
 
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 theorem image_neg_Ioc : Neg.neg '' Ioc a b = Ico (-b) (-a) := by simp
 #align set.image_neg_Ioc Set.image_neg_Ioc
 
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 theorem image_neg_Ioo : Neg.neg '' Ioo a b = Ioo (-b) (-a) := by simp
 #align set.image_neg_Ioo Set.image_neg_Ioo
 
@@ -632,89 +320,41 @@ theorem image_neg_Ioo : Neg.neg '' Ioo a b = Ioo (-b) (-a) := by simp
 -/
 
 
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 @[simp]
 theorem image_const_sub_Ici : (fun x => a - x) '' Ici b = Iic (a - b) := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x]
 #align set.image_const_sub_Ici Set.image_const_sub_Ici
 
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 @[simp]
 theorem image_const_sub_Iic : (fun x => a - x) '' Iic b = Ici (a - b) := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x, add_comm]
 #align set.image_const_sub_Iic Set.image_const_sub_Iic
 
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 @[simp]
 theorem image_const_sub_Ioi : (fun x => a - x) '' Ioi b = Iio (a - b) := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x]
 #align set.image_const_sub_Ioi Set.image_const_sub_Ioi
 
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 @[simp]
 theorem image_const_sub_Iio : (fun x => a - x) '' Iio b = Ioi (a - b) := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x, add_comm]
 #align set.image_const_sub_Iio Set.image_const_sub_Iio
 
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 @[simp]
 theorem image_const_sub_Icc : (fun x => a - x) '' Icc b c = Icc (a - c) (a - b) := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x, add_comm]
 #align set.image_const_sub_Icc Set.image_const_sub_Icc
 
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 @[simp]
 theorem image_const_sub_Ico : (fun x => a - x) '' Ico b c = Ioc (a - c) (a - b) := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x, add_comm]
 #align set.image_const_sub_Ico Set.image_const_sub_Ico
 
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 @[simp]
 theorem image_const_sub_Ioc : (fun x => a - x) '' Ioc b c = Ico (a - c) (a - b) := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x, add_comm]
 #align set.image_const_sub_Ioc Set.image_const_sub_Ioc
 
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 @[simp]
 theorem image_const_sub_Ioo : (fun x => a - x) '' Ioo b c = Ioo (a - c) (a - b) := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x, add_comm]
@@ -725,85 +365,37 @@ theorem image_const_sub_Ioo : (fun x => a - x) '' Ioo b c = Ioo (a - c) (a - b)
 -/
 
 
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 @[simp]
 theorem image_sub_const_Ici : (fun x => x - a) '' Ici b = Ici (b - a) := by simp [sub_eq_neg_add]
 #align set.image_sub_const_Ici Set.image_sub_const_Ici
 
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 @[simp]
 theorem image_sub_const_Iic : (fun x => x - a) '' Iic b = Iic (b - a) := by simp [sub_eq_neg_add]
 #align set.image_sub_const_Iic Set.image_sub_const_Iic
 
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 @[simp]
 theorem image_sub_const_Ioi : (fun x => x - a) '' Ioi b = Ioi (b - a) := by simp [sub_eq_neg_add]
 #align set.image_sub_const_Ioi Set.image_sub_const_Ioi
 
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 @[simp]
 theorem image_sub_const_Iio : (fun x => x - a) '' Iio b = Iio (b - a) := by simp [sub_eq_neg_add]
 #align set.image_sub_const_Iio Set.image_sub_const_Iio
 
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 @[simp]
 theorem image_sub_const_Icc : (fun x => x - a) '' Icc b c = Icc (b - a) (c - a) := by
   simp [sub_eq_neg_add]
 #align set.image_sub_const_Icc Set.image_sub_const_Icc
 
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 @[simp]
 theorem image_sub_const_Ico : (fun x => x - a) '' Ico b c = Ico (b - a) (c - a) := by
   simp [sub_eq_neg_add]
 #align set.image_sub_const_Ico Set.image_sub_const_Ico
 
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 @[simp]
 theorem image_sub_const_Ioc : (fun x => x - a) '' Ioc b c = Ioc (b - a) (c - a) := by
   simp [sub_eq_neg_add]
 #align set.image_sub_const_Ioc Set.image_sub_const_Ioc
 
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 @[simp]
 theorem image_sub_const_Ioo : (fun x => x - a) '' Ioo b c = Ioo (b - a) (c - a) := by
   simp [sub_eq_neg_add]
@@ -814,22 +406,10 @@ theorem image_sub_const_Ioo : (fun x => x - a) '' Ioo b c = Ioo (b - a) (c - a)
 -/
 
 
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 theorem Iic_add_bij : BijOn (· + a) (Iic b) (Iic (b + a)) :=
   image_add_const_Iic a b ▸ ((add_left_injective _).InjOn _).bijOn_image
 #align set.Iic_add_bij Set.Iic_add_bij
 
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 theorem Iio_add_bij : BijOn (· + a) (Iio b) (Iio (b + a)) :=
   image_add_const_Iio a b ▸ ((add_left_injective _).InjOn _).bijOn_image
 #align set.Iio_add_bij Set.Iio_add_bij
@@ -840,56 +420,26 @@ section LinearOrderedAddCommGroup
 
 variable [LinearOrderedAddCommGroup α] (a b c d : α)
 
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 @[simp]
 theorem preimage_const_add_uIcc : (fun x => a + x) ⁻¹' [b, c] = [b - a, c - a] := by
   simp only [← Icc_min_max, preimage_const_add_Icc, min_sub_sub_right, max_sub_sub_right]
 #align set.preimage_const_add_uIcc Set.preimage_const_add_uIcc
 
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 @[simp]
 theorem preimage_add_const_uIcc : (fun x => x + a) ⁻¹' [b, c] = [b - a, c - a] := by
   simpa only [add_comm] using preimage_const_add_uIcc a b c
 #align set.preimage_add_const_uIcc Set.preimage_add_const_uIcc
 
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 @[simp]
 theorem preimage_neg_uIcc : -[a, b] = [-a, -b] := by
   simp only [← Icc_min_max, preimage_neg_Icc, min_neg_neg, max_neg_neg]
 #align set.preimage_neg_uIcc Set.preimage_neg_uIcc
 
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 @[simp]
 theorem preimage_sub_const_uIcc : (fun x => x - a) ⁻¹' [b, c] = [b + a, c + a] := by
   simp [sub_eq_add_neg]
 #align set.preimage_sub_const_uIcc Set.preimage_sub_const_uIcc
 
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 @[simp]
 theorem preimage_const_sub_uIcc : (fun x => a - x) ⁻¹' [b, c] = [a - b, a - c] :=
   by
@@ -897,65 +447,29 @@ theorem preimage_const_sub_uIcc : (fun x => a - x) ⁻¹' [b, c] = [a - b, a - c
   simp only [sub_eq_add_neg, min_add_add_left, max_add_add_left, min_neg_neg, max_neg_neg]
 #align set.preimage_const_sub_uIcc Set.preimage_const_sub_uIcc
 
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 @[simp]
 theorem image_const_add_uIcc : (fun x => a + x) '' [b, c] = [a + b, a + c] := by simp [add_comm]
 #align set.image_const_add_uIcc Set.image_const_add_uIcc
 
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 @[simp]
 theorem image_add_const_uIcc : (fun x => x + a) '' [b, c] = [b + a, c + a] := by simp
 #align set.image_add_const_uIcc Set.image_add_const_uIcc
 
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 @[simp]
 theorem image_const_sub_uIcc : (fun x => a - x) '' [b, c] = [a - b, a - c] := by
   simp [sub_eq_add_neg, image_comp (fun x => a + x) fun x => -x]
 #align set.image_const_sub_uIcc Set.image_const_sub_uIcc
 
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 @[simp]
 theorem image_sub_const_uIcc : (fun x => x - a) '' [b, c] = [b - a, c - a] := by
   simp [sub_eq_add_neg, add_comm]
 #align set.image_sub_const_uIcc Set.image_sub_const_uIcc
 
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 theorem image_neg_uIcc : Neg.neg '' [a, b] = [-a, -b] := by simp
 #align set.image_neg_uIcc Set.image_neg_uIcc
 
 variable {a b c d}
 
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 /-- If `[c, d]` is a subinterval of `[a, b]`, then the distance between `c` and `d` is less than or
 equal to that of `a` and `b` -/
 theorem abs_sub_le_of_uIcc_subset_uIcc (h : [c, d] ⊆ [a, b]) : |d - c| ≤ |b - a| :=
@@ -965,24 +479,12 @@ theorem abs_sub_le_of_uIcc_subset_uIcc (h : [c, d] ⊆ [a, b]) : |d - c| ≤ |b
   exact sub_le_sub h.2 h.1
 #align set.abs_sub_le_of_uIcc_subset_uIcc Set.abs_sub_le_of_uIcc_subset_uIcc
 
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 /-- If `c ∈ [a, b]`, then the distance between `a` and `c` is less than or equal to
 that of `a` and `b`  -/
 theorem abs_sub_left_of_mem_uIcc (h : c ∈ [a, b]) : |c - a| ≤ |b - a| :=
   abs_sub_le_of_uIcc_subset_uIcc <| uIcc_subset_uIcc_left h
 #align set.abs_sub_left_of_mem_uIcc Set.abs_sub_left_of_mem_uIcc
 
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 /-- If `x ∈ [a, b]`, then the distance between `c` and `b` is less than or equal to
 that of `a` and `b`  -/
 theorem abs_sub_right_of_mem_uIcc (h : c ∈ [a, b]) : |b - c| ≤ |b - a| :=
@@ -1000,382 +502,184 @@ section LinearOrderedField
 
 variable [LinearOrderedField α] {a : α}
 
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 @[simp]
 theorem preimage_mul_const_Iio (a : α) {c : α} (h : 0 < c) :
     (fun x => x * c) ⁻¹' Iio a = Iio (a / c) :=
   ext fun x => (lt_div_iff h).symm
 #align set.preimage_mul_const_Iio Set.preimage_mul_const_Iio
 
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-Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Ioi Set.preimage_mul_const_Ioiₓ'. -/
 @[simp]
 theorem preimage_mul_const_Ioi (a : α) {c : α} (h : 0 < c) :
     (fun x => x * c) ⁻¹' Ioi a = Ioi (a / c) :=
   ext fun x => (div_lt_iff h).symm
 #align set.preimage_mul_const_Ioi Set.preimage_mul_const_Ioi
 
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 @[simp]
 theorem preimage_mul_const_Iic (a : α) {c : α} (h : 0 < c) :
     (fun x => x * c) ⁻¹' Iic a = Iic (a / c) :=
   ext fun x => (le_div_iff h).symm
 #align set.preimage_mul_const_Iic Set.preimage_mul_const_Iic
 
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 @[simp]
 theorem preimage_mul_const_Ici (a : α) {c : α} (h : 0 < c) :
     (fun x => x * c) ⁻¹' Ici a = Ici (a / c) :=
   ext fun x => (div_le_iff h).symm
 #align set.preimage_mul_const_Ici Set.preimage_mul_const_Ici
 
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 @[simp]
 theorem preimage_mul_const_Ioo (a b : α) {c : α} (h : 0 < c) :
     (fun x => x * c) ⁻¹' Ioo a b = Ioo (a / c) (b / c) := by simp [← Ioi_inter_Iio, h]
 #align set.preimage_mul_const_Ioo Set.preimage_mul_const_Ioo
 
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 @[simp]
 theorem preimage_mul_const_Ioc (a b : α) {c : α} (h : 0 < c) :
     (fun x => x * c) ⁻¹' Ioc a b = Ioc (a / c) (b / c) := by simp [← Ioi_inter_Iic, h]
 #align set.preimage_mul_const_Ioc Set.preimage_mul_const_Ioc
 
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 @[simp]
 theorem preimage_mul_const_Ico (a b : α) {c : α} (h : 0 < c) :
     (fun x => x * c) ⁻¹' Ico a b = Ico (a / c) (b / c) := by simp [← Ici_inter_Iio, h]
 #align set.preimage_mul_const_Ico Set.preimage_mul_const_Ico
 
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 @[simp]
 theorem preimage_mul_const_Icc (a b : α) {c : α} (h : 0 < c) :
     (fun x => x * c) ⁻¹' Icc a b = Icc (a / c) (b / c) := by simp [← Ici_inter_Iic, h]
 #align set.preimage_mul_const_Icc Set.preimage_mul_const_Icc
 
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 @[simp]
 theorem preimage_mul_const_Iio_of_neg (a : α) {c : α} (h : c < 0) :
     (fun x => x * c) ⁻¹' Iio a = Ioi (a / c) :=
   ext fun x => (div_lt_iff_of_neg h).symm
 #align set.preimage_mul_const_Iio_of_neg Set.preimage_mul_const_Iio_of_neg
 
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 @[simp]
 theorem preimage_mul_const_Ioi_of_neg (a : α) {c : α} (h : c < 0) :
     (fun x => x * c) ⁻¹' Ioi a = Iio (a / c) :=
   ext fun x => (lt_div_iff_of_neg h).symm
 #align set.preimage_mul_const_Ioi_of_neg Set.preimage_mul_const_Ioi_of_neg
 
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 @[simp]
 theorem preimage_mul_const_Iic_of_neg (a : α) {c : α} (h : c < 0) :
     (fun x => x * c) ⁻¹' Iic a = Ici (a / c) :=
   ext fun x => (div_le_iff_of_neg h).symm
 #align set.preimage_mul_const_Iic_of_neg Set.preimage_mul_const_Iic_of_neg
 
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 @[simp]
 theorem preimage_mul_const_Ici_of_neg (a : α) {c : α} (h : c < 0) :
     (fun x => x * c) ⁻¹' Ici a = Iic (a / c) :=
   ext fun x => (le_div_iff_of_neg h).symm
 #align set.preimage_mul_const_Ici_of_neg Set.preimage_mul_const_Ici_of_neg
 
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 @[simp]
 theorem preimage_mul_const_Ioo_of_neg (a b : α) {c : α} (h : c < 0) :
     (fun x => x * c) ⁻¹' Ioo a b = Ioo (b / c) (a / c) := by simp [← Ioi_inter_Iio, h, inter_comm]
 #align set.preimage_mul_const_Ioo_of_neg Set.preimage_mul_const_Ioo_of_neg
 
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 @[simp]
 theorem preimage_mul_const_Ioc_of_neg (a b : α) {c : α} (h : c < 0) :
     (fun x => x * c) ⁻¹' Ioc a b = Ico (b / c) (a / c) := by
   simp [← Ioi_inter_Iic, ← Ici_inter_Iio, h, inter_comm]
 #align set.preimage_mul_const_Ioc_of_neg Set.preimage_mul_const_Ioc_of_neg
 
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 @[simp]
 theorem preimage_mul_const_Ico_of_neg (a b : α) {c : α} (h : c < 0) :
     (fun x => x * c) ⁻¹' Ico a b = Ioc (b / c) (a / c) := by
   simp [← Ici_inter_Iio, ← Ioi_inter_Iic, h, inter_comm]
 #align set.preimage_mul_const_Ico_of_neg Set.preimage_mul_const_Ico_of_neg
 
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 @[simp]
 theorem preimage_mul_const_Icc_of_neg (a b : α) {c : α} (h : c < 0) :
     (fun x => x * c) ⁻¹' Icc a b = Icc (b / c) (a / c) := by simp [← Ici_inter_Iic, h, inter_comm]
 #align set.preimage_mul_const_Icc_of_neg Set.preimage_mul_const_Icc_of_neg
 
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 @[simp]
 theorem preimage_const_mul_Iio (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹' Iio a = Iio (a / c) :=
   ext fun x => (lt_div_iff' h).symm
 #align set.preimage_const_mul_Iio Set.preimage_const_mul_Iio
 
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 @[simp]
 theorem preimage_const_mul_Ioi (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹' Ioi a = Ioi (a / c) :=
   ext fun x => (div_lt_iff' h).symm
 #align set.preimage_const_mul_Ioi Set.preimage_const_mul_Ioi
 
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 @[simp]
 theorem preimage_const_mul_Iic (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹' Iic a = Iic (a / c) :=
   ext fun x => (le_div_iff' h).symm
 #align set.preimage_const_mul_Iic Set.preimage_const_mul_Iic
 
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 @[simp]
 theorem preimage_const_mul_Ici (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹' Ici a = Ici (a / c) :=
   ext fun x => (div_le_iff' h).symm
 #align set.preimage_const_mul_Ici Set.preimage_const_mul_Ici
 
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 @[simp]
 theorem preimage_const_mul_Ioo (a b : α) {c : α} (h : 0 < c) :
     (· * ·) c ⁻¹' Ioo a b = Ioo (a / c) (b / c) := by simp [← Ioi_inter_Iio, h]
 #align set.preimage_const_mul_Ioo Set.preimage_const_mul_Ioo
 
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 @[simp]
 theorem preimage_const_mul_Ioc (a b : α) {c : α} (h : 0 < c) :
     (· * ·) c ⁻¹' Ioc a b = Ioc (a / c) (b / c) := by simp [← Ioi_inter_Iic, h]
 #align set.preimage_const_mul_Ioc Set.preimage_const_mul_Ioc
 
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 @[simp]
 theorem preimage_const_mul_Ico (a b : α) {c : α} (h : 0 < c) :
     (· * ·) c ⁻¹' Ico a b = Ico (a / c) (b / c) := by simp [← Ici_inter_Iio, h]
 #align set.preimage_const_mul_Ico Set.preimage_const_mul_Ico
 
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 @[simp]
 theorem preimage_const_mul_Icc (a b : α) {c : α} (h : 0 < c) :
     (· * ·) c ⁻¹' Icc a b = Icc (a / c) (b / c) := by simp [← Ici_inter_Iic, h]
 #align set.preimage_const_mul_Icc Set.preimage_const_mul_Icc
 
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 @[simp]
 theorem preimage_const_mul_Iio_of_neg (a : α) {c : α} (h : c < 0) :
     (· * ·) c ⁻¹' Iio a = Ioi (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Iio_of_neg a h
 #align set.preimage_const_mul_Iio_of_neg Set.preimage_const_mul_Iio_of_neg
 
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 @[simp]
 theorem preimage_const_mul_Ioi_of_neg (a : α) {c : α} (h : c < 0) :
     (· * ·) c ⁻¹' Ioi a = Iio (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Ioi_of_neg a h
 #align set.preimage_const_mul_Ioi_of_neg Set.preimage_const_mul_Ioi_of_neg
 
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 @[simp]
 theorem preimage_const_mul_Iic_of_neg (a : α) {c : α} (h : c < 0) :
     (· * ·) c ⁻¹' Iic a = Ici (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Iic_of_neg a h
 #align set.preimage_const_mul_Iic_of_neg Set.preimage_const_mul_Iic_of_neg
 
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 @[simp]
 theorem preimage_const_mul_Ici_of_neg (a : α) {c : α} (h : c < 0) :
     (· * ·) c ⁻¹' Ici a = Iic (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Ici_of_neg a h
 #align set.preimage_const_mul_Ici_of_neg Set.preimage_const_mul_Ici_of_neg
 
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 @[simp]
 theorem preimage_const_mul_Ioo_of_neg (a b : α) {c : α} (h : c < 0) :
     (· * ·) c ⁻¹' Ioo a b = Ioo (b / c) (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Ioo_of_neg a b h
 #align set.preimage_const_mul_Ioo_of_neg Set.preimage_const_mul_Ioo_of_neg
 
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 @[simp]
 theorem preimage_const_mul_Ioc_of_neg (a b : α) {c : α} (h : c < 0) :
     (· * ·) c ⁻¹' Ioc a b = Ico (b / c) (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Ioc_of_neg a b h
 #align set.preimage_const_mul_Ioc_of_neg Set.preimage_const_mul_Ioc_of_neg
 
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 @[simp]
 theorem preimage_const_mul_Ico_of_neg (a b : α) {c : α} (h : c < 0) :
     (· * ·) c ⁻¹' Ico a b = Ioc (b / c) (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Ico_of_neg a b h
 #align set.preimage_const_mul_Ico_of_neg Set.preimage_const_mul_Ico_of_neg
 
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 @[simp]
 theorem preimage_const_mul_Icc_of_neg (a b : α) {c : α} (h : c < 0) :
     (· * ·) c ⁻¹' Icc a b = Icc (b / c) (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Icc_of_neg a b h
 #align set.preimage_const_mul_Icc_of_neg Set.preimage_const_mul_Icc_of_neg
 
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 @[simp]
 theorem preimage_mul_const_uIcc (ha : a ≠ 0) (b c : α) :
     (fun x => x * a) ⁻¹' [b, c] = [b / a, c / a] :=
@@ -1385,36 +689,18 @@ theorem preimage_mul_const_uIcc (ha : a ≠ 0) (b c : α) :
     fun ha : 0 < a => by simp [← Icc_min_max, ha, ha.le, min_div_div_right, max_div_div_right]
 #align set.preimage_mul_const_uIcc Set.preimage_mul_const_uIcc
 
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 @[simp]
 theorem preimage_const_mul_uIcc (ha : a ≠ 0) (b c : α) :
     (fun x => a * x) ⁻¹' [b, c] = [b / a, c / a] := by
   simp only [← preimage_mul_const_uIcc ha, mul_comm]
 #align set.preimage_const_mul_uIcc Set.preimage_const_mul_uIcc
 
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 @[simp]
 theorem preimage_div_const_uIcc (ha : a ≠ 0) (b c : α) :
     (fun x => x / a) ⁻¹' [b, c] = [b * a, c * a] := by
   simp only [div_eq_mul_inv, preimage_mul_const_uIcc (inv_ne_zero ha), inv_inv]
 #align set.preimage_div_const_uIcc Set.preimage_div_const_uIcc
 
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 @[simp]
 theorem image_mul_const_uIcc (a b c : α) : (fun x => x * a) '' [b, c] = [b * a, c * a] :=
   if ha : a = 0 then by simp [ha]
@@ -1427,45 +713,21 @@ theorem image_mul_const_uIcc (a b c : α) : (fun x => x * a) '' [b, c] = [b * a,
       
 #align set.image_mul_const_uIcc Set.image_mul_const_uIcc
 
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 @[simp]
 theorem image_const_mul_uIcc (a b c : α) : (fun x => a * x) '' [b, c] = [a * b, a * c] := by
   simpa only [mul_comm] using image_mul_const_uIcc a b c
 #align set.image_const_mul_uIcc Set.image_const_mul_uIcc
 
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 @[simp]
 theorem image_div_const_uIcc (a b c : α) : (fun x => x / a) '' [b, c] = [b / a, c / a] := by
   simp only [div_eq_mul_inv, image_mul_const_uIcc]
 #align set.image_div_const_uIcc Set.image_div_const_uIcc
 
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 theorem image_mul_right_Icc' (a b : α) {c : α} (h : 0 < c) :
     (fun x => x * c) '' Icc a b = Icc (a * c) (b * c) :=
   ((Units.mk0 c h.ne').mul_right.image_eq_preimage _).trans (by simp [h, division_def])
 #align set.image_mul_right_Icc' Set.image_mul_right_Icc'
 
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-Case conversion may be inaccurate. Consider using '#align set.image_mul_right_Icc Set.image_mul_right_Iccₓ'. -/
 theorem image_mul_right_Icc {a b c : α} (hab : a ≤ b) (hc : 0 ≤ c) :
     (fun x => x * c) '' Icc a b = Icc (a * c) (b * c) :=
   by
@@ -1475,56 +737,26 @@ theorem image_mul_right_Icc {a b c : α} (hab : a ≤ b) (hc : 0 ≤ c) :
   exact image_mul_right_Icc' a b ‹0 < c›
 #align set.image_mul_right_Icc Set.image_mul_right_Icc
 
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-Case conversion may be inaccurate. Consider using '#align set.image_mul_left_Icc' Set.image_mul_left_Icc'ₓ'. -/
 theorem image_mul_left_Icc' {a : α} (h : 0 < a) (b c : α) :
     (· * ·) a '' Icc b c = Icc (a * b) (a * c) := by
   convert image_mul_right_Icc' b c h using 1 <;> simp only [mul_comm _ a]
 #align set.image_mul_left_Icc' Set.image_mul_left_Icc'
 
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-Case conversion may be inaccurate. Consider using '#align set.image_mul_left_Icc Set.image_mul_left_Iccₓ'. -/
 theorem image_mul_left_Icc {a b c : α} (ha : 0 ≤ a) (hbc : b ≤ c) :
     (· * ·) a '' Icc b c = Icc (a * b) (a * c) := by
   convert image_mul_right_Icc hbc ha using 1 <;> simp only [mul_comm _ a]
 #align set.image_mul_left_Icc Set.image_mul_left_Icc
 
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 theorem image_mul_right_Ioo (a b : α) {c : α} (h : 0 < c) :
     (fun x => x * c) '' Ioo a b = Ioo (a * c) (b * c) :=
   ((Units.mk0 c h.ne').mul_right.image_eq_preimage _).trans (by simp [h, division_def])
 #align set.image_mul_right_Ioo Set.image_mul_right_Ioo
 
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 theorem image_mul_left_Ioo {a : α} (h : 0 < a) (b c : α) :
     (· * ·) a '' Ioo b c = Ioo (a * b) (a * c) := by
   convert image_mul_right_Ioo b c h using 1 <;> simp only [mul_comm _ a]
 #align set.image_mul_left_Ioo Set.image_mul_left_Ioo
 
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 /-- The (pre)image under `inv` of `Ioo 0 a` is `Ioi a⁻¹`. -/
 theorem inv_Ioo_0_left {a : α} (ha : 0 < a) : (Ioo 0 a)⁻¹ = Ioi a⁻¹ :=
   by
@@ -1535,22 +767,10 @@ theorem inv_Ioo_0_left {a : α} (ha : 0 < a) : (Ioo 0 a)⁻¹ = Ioi a⁻¹ :=
         inv_inv a ▸ (inv_lt_inv ((inv_pos.2 ha).trans h) (inv_pos.2 ha)).2 h⟩⟩
 #align set.inv_Ioo_0_left Set.inv_Ioo_0_left
 
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 theorem inv_Ioi {a : α} (ha : 0 < a) : (Ioi a)⁻¹ = Ioo 0 a⁻¹ := by
   rw [inv_eq_iff_eq_inv, inv_Ioo_0_left (inv_pos.2 ha), inv_inv]
 #align set.inv_Ioi Set.inv_Ioi
 
-/- warning: set.image_const_mul_Ioi_zero -> Set.image_const_mul_Ioi_zero is a dubious translation:
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-  forall {k : Type.{u1}} [_inst_2 : LinearOrderedField.{u1} k] {x : k}, (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_2))))))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_2))))))))))) x) -> (Eq.{succ u1} (Set.{u1} k) (Set.image.{u1, u1} k k (fun (y : k) => HMul.hMul.{u1, u1, u1} k k k (instHMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_2)))))) x y) (Set.Ioi.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_2)))))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_2))))))))))))) (Set.Ioi.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_2)))))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_2)))))))))))))
-but is expected to have type
-  forall {k : Type.{u1}} [_inst_2 : LinearOrderedField.{u1} k] {x : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (StrictOrderedRing.toPartialOrder.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_2)))))) (OfNat.ofNat.{u1} k 0 (Zero.toOfNat0.{u1} k (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (LinearOrderedSemifield.toSemifield.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_2))))))) x) -> (Eq.{succ u1} (Set.{u1} k) (Set.image.{u1, u1} k k (fun (y : k) => HMul.hMul.{u1, u1, u1} k k k (instHMul.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_2))))))) x y) (Set.Ioi.{u1} k (PartialOrder.toPreorder.{u1} k (StrictOrderedRing.toPartialOrder.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_2))))) (OfNat.ofNat.{u1} k 0 (Zero.toOfNat0.{u1} k (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (LinearOrderedSemifield.toSemifield.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_2))))))))) (Set.Ioi.{u1} k (PartialOrder.toPreorder.{u1} k (StrictOrderedRing.toPartialOrder.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_2))))) (OfNat.ofNat.{u1} k 0 (Zero.toOfNat0.{u1} k (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (LinearOrderedSemifield.toSemifield.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_2)))))))))
-Case conversion may be inaccurate. Consider using '#align set.image_const_mul_Ioi_zero Set.image_const_mul_Ioi_zeroₓ'. -/
 theorem image_const_mul_Ioi_zero {k : Type _} [LinearOrderedField k] {x : k} (hx : 0 < x) :
     (fun y => x * y) '' Ioi (0 : k) = Ioi 0 := by
   erw [(Units.mk0 x hx.ne').mul_left.image_eq_preimage, preimage_const_mul_Ioi 0 (inv_pos.mpr hx),
@@ -1562,12 +782,6 @@ theorem image_const_mul_Ioi_zero {k : Type _} [LinearOrderedField k] {x : k} (hx
 -/
 
 
-/- warning: set.image_affine_Icc' -> Set.image_affine_Icc' is a dubious translation:
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-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (b : α) (c : α) (d : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (fun (x : α) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a x) b) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) c d)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c) b) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a d) b)))
-Case conversion may be inaccurate. Consider using '#align set.image_affine_Icc' Set.image_affine_Icc'ₓ'. -/
 @[simp]
 theorem image_affine_Icc' {a : α} (h : 0 < a) (b c d : α) :
     (fun x => a * x + b) '' Icc c d = Icc (a * c + b) (a * d + b) :=

2196ab36

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -952,7 +952,7 @@ variable {a b c d}
 
 /- warning: set.abs_sub_le_of_uIcc_subset_uIcc -> Set.abs_sub_le_of_uIcc_subset_uIcc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.uIcc.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)) c d) (Set.uIcc.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) d c)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.uIcc.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)) c d) (Set.uIcc.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) d c)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.uIcc.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))) c d) (Set.uIcc.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) d c)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
 Case conversion may be inaccurate. Consider using '#align set.abs_sub_le_of_uIcc_subset_uIcc Set.abs_sub_le_of_uIcc_subset_uIccₓ'. -/
@@ -967,7 +967,7 @@ theorem abs_sub_le_of_uIcc_subset_uIcc (h : [c, d] ⊆ [a, b]) : |d - c| ≤ |b
 
 /- warning: set.abs_sub_left_of_mem_uIcc -> Set.abs_sub_left_of_mem_uIcc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c (Set.uIcc.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) c a)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c (Set.uIcc.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) c a)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c (Set.uIcc.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) c a)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
 Case conversion may be inaccurate. Consider using '#align set.abs_sub_left_of_mem_uIcc Set.abs_sub_left_of_mem_uIccₓ'. -/
@@ -979,7 +979,7 @@ theorem abs_sub_left_of_mem_uIcc (h : c ∈ [a, b]) : |c - a| ≤ |b - a| :=
 
 /- warning: set.abs_sub_right_of_mem_uIcc -> Set.abs_sub_right_of_mem_uIcc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c (Set.uIcc.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b c)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c (Set.uIcc.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b c)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c (Set.uIcc.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b c)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
 Case conversion may be inaccurate. Consider using '#align set.abs_sub_right_of_mem_uIcc Set.abs_sub_right_of_mem_uIccₓ'. -/
@@ -1002,7 +1002,7 @@ variable [LinearOrderedField α] {a : α}
 
 /- warning: set.preimage_mul_const_Iio -> Set.preimage_mul_const_Iio is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Iio.{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)))))) a)) (Set.Iio.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Iio.{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)))))) a)) (Set.Iio.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Iio Set.preimage_mul_const_Iioₓ'. -/
@@ -1014,7 +1014,7 @@ theorem preimage_mul_const_Iio (a : α) {c : α} (h : 0 < c) :
 
 /- warning: set.preimage_mul_const_Ioi -> Set.preimage_mul_const_Ioi is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ioi.{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)))))) a)) (Set.Ioi.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ioi.{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)))))) a)) (Set.Ioi.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Ioi Set.preimage_mul_const_Ioiₓ'. -/
@@ -1026,7 +1026,7 @@ theorem preimage_mul_const_Ioi (a : α) {c : α} (h : 0 < c) :
 
 /- warning: set.preimage_mul_const_Iic -> Set.preimage_mul_const_Iic is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Iic.{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)))))) a)) (Set.Iic.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Iic.{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)))))) a)) (Set.Iic.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Iic Set.preimage_mul_const_Iicₓ'. -/
@@ -1038,7 +1038,7 @@ theorem preimage_mul_const_Iic (a : α) {c : α} (h : 0 < c) :
 
 /- warning: set.preimage_mul_const_Ici -> Set.preimage_mul_const_Ici is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ici.{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)))))) a)) (Set.Ici.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ici.{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)))))) a)) (Set.Ici.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Ici Set.preimage_mul_const_Iciₓ'. -/
@@ -1050,7 +1050,7 @@ theorem preimage_mul_const_Ici (a : α) {c : α} (h : 0 < c) :
 
 /- warning: set.preimage_mul_const_Ioo -> Set.preimage_mul_const_Ioo is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ioo.{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)))))) a b)) (Set.Ioo.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ioo.{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)))))) a b)) (Set.Ioo.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Ioo Set.preimage_mul_const_Iooₓ'. -/
@@ -1061,7 +1061,7 @@ theorem preimage_mul_const_Ioo (a b : α) {c : α} (h : 0 < c) :
 
 /- warning: set.preimage_mul_const_Ioc -> Set.preimage_mul_const_Ioc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ioc.{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)))))) a b)) (Set.Ioc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ioc.{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)))))) a b)) (Set.Ioc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Ioc Set.preimage_mul_const_Iocₓ'. -/
@@ -1072,7 +1072,7 @@ theorem preimage_mul_const_Ioc (a b : α) {c : α} (h : 0 < c) :
 
 /- warning: set.preimage_mul_const_Ico -> Set.preimage_mul_const_Ico is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ico.{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)))))) a b)) (Set.Ico.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ico.{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)))))) a b)) (Set.Ico.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Ico Set.preimage_mul_const_Icoₓ'. -/
@@ -1083,7 +1083,7 @@ theorem preimage_mul_const_Ico (a b : α) {c : α} (h : 0 < c) :
 
 /- warning: set.preimage_mul_const_Icc -> Set.preimage_mul_const_Icc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Icc.{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)))))) a b)) (Set.Icc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Icc.{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)))))) a b)) (Set.Icc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Icc Set.preimage_mul_const_Iccₓ'. -/
@@ -1094,7 +1094,7 @@ theorem preimage_mul_const_Icc (a b : α) {c : α} (h : 0 < c) :
 
 /- warning: set.preimage_mul_const_Iio_of_neg -> Set.preimage_mul_const_Iio_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Iio.{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)))))) a)) (Set.Ioi.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Iio.{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)))))) a)) (Set.Ioi.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Iio_of_neg Set.preimage_mul_const_Iio_of_negₓ'. -/
@@ -1106,7 +1106,7 @@ theorem preimage_mul_const_Iio_of_neg (a : α) {c : α} (h : c < 0) :
 
 /- warning: set.preimage_mul_const_Ioi_of_neg -> Set.preimage_mul_const_Ioi_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ioi.{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)))))) a)) (Set.Iio.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ioi.{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)))))) a)) (Set.Iio.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Ioi_of_neg Set.preimage_mul_const_Ioi_of_negₓ'. -/
@@ -1118,7 +1118,7 @@ theorem preimage_mul_const_Ioi_of_neg (a : α) {c : α} (h : c < 0) :
 
 /- warning: set.preimage_mul_const_Iic_of_neg -> Set.preimage_mul_const_Iic_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Iic.{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)))))) a)) (Set.Ici.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Iic.{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)))))) a)) (Set.Ici.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Iic_of_neg Set.preimage_mul_const_Iic_of_negₓ'. -/
@@ -1130,7 +1130,7 @@ theorem preimage_mul_const_Iic_of_neg (a : α) {c : α} (h : c < 0) :
 
 /- warning: set.preimage_mul_const_Ici_of_neg -> Set.preimage_mul_const_Ici_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ici.{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)))))) a)) (Set.Iic.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ici.{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)))))) a)) (Set.Iic.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Ici_of_neg Set.preimage_mul_const_Ici_of_negₓ'. -/
@@ -1142,7 +1142,7 @@ theorem preimage_mul_const_Ici_of_neg (a : α) {c : α} (h : c < 0) :
 
 /- warning: set.preimage_mul_const_Ioo_of_neg -> Set.preimage_mul_const_Ioo_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ioo.{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)))))) a b)) (Set.Ioo.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ioo.{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)))))) a b)) (Set.Ioo.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Ioo_of_neg Set.preimage_mul_const_Ioo_of_negₓ'. -/
@@ -1153,7 +1153,7 @@ theorem preimage_mul_const_Ioo_of_neg (a b : α) {c : α} (h : c < 0) :
 
 /- warning: set.preimage_mul_const_Ioc_of_neg -> Set.preimage_mul_const_Ioc_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ioc.{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)))))) a b)) (Set.Ico.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ioc.{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)))))) a b)) (Set.Ico.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Ioc_of_neg Set.preimage_mul_const_Ioc_of_negₓ'. -/
@@ -1165,7 +1165,7 @@ theorem preimage_mul_const_Ioc_of_neg (a b : α) {c : α} (h : c < 0) :
 
 /- warning: set.preimage_mul_const_Ico_of_neg -> Set.preimage_mul_const_Ico_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ico.{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)))))) a b)) (Set.Ioc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ico.{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)))))) a b)) (Set.Ioc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Ico_of_neg Set.preimage_mul_const_Ico_of_negₓ'. -/
@@ -1177,7 +1177,7 @@ theorem preimage_mul_const_Ico_of_neg (a b : α) {c : α} (h : c < 0) :
 
 /- warning: set.preimage_mul_const_Icc_of_neg -> Set.preimage_mul_const_Icc_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Icc.{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)))))) a b)) (Set.Icc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Icc.{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)))))) a b)) (Set.Icc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_mul_const_Icc_of_neg Set.preimage_mul_const_Icc_of_negₓ'. -/
@@ -1188,7 +1188,7 @@ theorem preimage_mul_const_Icc_of_neg (a b : α) {c : α} (h : c < 0) :
 
 /- warning: set.preimage_const_mul_Iio -> Set.preimage_const_mul_Iio is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Iio.{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)))))) a)) (Set.Iio.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Iio.{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)))))) a)) (Set.Iio.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4695 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4697 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4695 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4697) c) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Iio Set.preimage_const_mul_Iioₓ'. -/
@@ -1199,7 +1199,7 @@ theorem preimage_const_mul_Iio (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹
 
 /- warning: set.preimage_const_mul_Ioi -> Set.preimage_const_mul_Ioi is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioi.{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)))))) a)) (Set.Ioi.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioi.{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)))))) a)) (Set.Ioi.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4750 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4752 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4750 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4752) c) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ioi Set.preimage_const_mul_Ioiₓ'. -/
@@ -1210,7 +1210,7 @@ theorem preimage_const_mul_Ioi (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹
 
 /- warning: set.preimage_const_mul_Iic -> Set.preimage_const_mul_Iic is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Iic.{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)))))) a)) (Set.Iic.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Iic.{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)))))) a)) (Set.Iic.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4805 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4807 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4805 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4807) c) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Iic Set.preimage_const_mul_Iicₓ'. -/
@@ -1221,7 +1221,7 @@ theorem preimage_const_mul_Iic (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹
 
 /- warning: set.preimage_const_mul_Ici -> Set.preimage_const_mul_Ici is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ici.{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)))))) a)) (Set.Ici.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ici.{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)))))) a)) (Set.Ici.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4860 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4862 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4860 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4862) c) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ici Set.preimage_const_mul_Iciₓ'. -/
@@ -1232,7 +1232,7 @@ theorem preimage_const_mul_Ici (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹
 
 /- warning: set.preimage_const_mul_Ioo -> Set.preimage_const_mul_Ioo is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioo.{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)))))) a b)) (Set.Ioo.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioo.{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)))))) a b)) (Set.Ioo.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4916 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4918 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4916 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4918) c) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ioo Set.preimage_const_mul_Iooₓ'. -/
@@ -1243,7 +1243,7 @@ theorem preimage_const_mul_Ioo (a b : α) {c : α} (h : 0 < c) :
 
 /- warning: set.preimage_const_mul_Ioc -> Set.preimage_const_mul_Ioc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioc.{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)))))) a b)) (Set.Ioc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioc.{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)))))) a b)) (Set.Ioc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4975 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4977 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4975 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4977) c) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ioc Set.preimage_const_mul_Iocₓ'. -/
@@ -1254,7 +1254,7 @@ theorem preimage_const_mul_Ioc (a b : α) {c : α} (h : 0 < c) :
 
 /- warning: set.preimage_const_mul_Ico -> Set.preimage_const_mul_Ico is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ico.{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)))))) a b)) (Set.Ico.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ico.{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)))))) a b)) (Set.Ico.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5034 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5036 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5034 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5036) c) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ico Set.preimage_const_mul_Icoₓ'. -/
@@ -1265,7 +1265,7 @@ theorem preimage_const_mul_Ico (a b : α) {c : α} (h : 0 < c) :
 
 /- warning: set.preimage_const_mul_Icc -> Set.preimage_const_mul_Icc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Icc.{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)))))) a b)) (Set.Icc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Icc.{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)))))) a b)) (Set.Icc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5093 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5095 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5093 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5095) c) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Icc Set.preimage_const_mul_Iccₓ'. -/
@@ -1276,7 +1276,7 @@ theorem preimage_const_mul_Icc (a b : α) {c : α} (h : 0 < c) :
 
 /- warning: set.preimage_const_mul_Iio_of_neg -> Set.preimage_const_mul_Iio_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Iio.{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)))))) a)) (Set.Ioi.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Iio.{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)))))) a)) (Set.Ioi.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5151 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5153 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5151 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5153) c) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Iio_of_neg Set.preimage_const_mul_Iio_of_negₓ'. -/
@@ -1288,7 +1288,7 @@ theorem preimage_const_mul_Iio_of_neg (a : α) {c : α} (h : c < 0) :
 
 /- warning: set.preimage_const_mul_Ioi_of_neg -> Set.preimage_const_mul_Ioi_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioi.{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)))))) a)) (Set.Iio.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioi.{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)))))) a)) (Set.Iio.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5207 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5209 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5207 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5209) c) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ioi_of_neg Set.preimage_const_mul_Ioi_of_negₓ'. -/
@@ -1300,7 +1300,7 @@ theorem preimage_const_mul_Ioi_of_neg (a : α) {c : α} (h : c < 0) :
 
 /- warning: set.preimage_const_mul_Iic_of_neg -> Set.preimage_const_mul_Iic_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Iic.{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)))))) a)) (Set.Ici.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Iic.{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)))))) a)) (Set.Ici.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5263 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5265 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5263 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5265) c) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Iic_of_neg Set.preimage_const_mul_Iic_of_negₓ'. -/
@@ -1312,7 +1312,7 @@ theorem preimage_const_mul_Iic_of_neg (a : α) {c : α} (h : c < 0) :
 
 /- warning: set.preimage_const_mul_Ici_of_neg -> Set.preimage_const_mul_Ici_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ici.{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)))))) a)) (Set.Iic.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ici.{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)))))) a)) (Set.Iic.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5319 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5321 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5319 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5321) c) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ici_of_neg Set.preimage_const_mul_Ici_of_negₓ'. -/
@@ -1324,7 +1324,7 @@ theorem preimage_const_mul_Ici_of_neg (a : α) {c : α} (h : c < 0) :
 
 /- warning: set.preimage_const_mul_Ioo_of_neg -> Set.preimage_const_mul_Ioo_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioo.{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)))))) a b)) (Set.Ioo.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioo.{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)))))) a b)) (Set.Ioo.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5376 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5378 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5376 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5378) c) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ioo_of_neg Set.preimage_const_mul_Ioo_of_negₓ'. -/
@@ -1336,7 +1336,7 @@ theorem preimage_const_mul_Ioo_of_neg (a b : α) {c : α} (h : c < 0) :
 
 /- warning: set.preimage_const_mul_Ioc_of_neg -> Set.preimage_const_mul_Ioc_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioc.{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)))))) a b)) (Set.Ico.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioc.{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)))))) a b)) (Set.Ico.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5442 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5444 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5442 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5444) c) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ioc_of_neg Set.preimage_const_mul_Ioc_of_negₓ'. -/
@@ -1348,7 +1348,7 @@ theorem preimage_const_mul_Ioc_of_neg (a b : α) {c : α} (h : c < 0) :
 
 /- warning: set.preimage_const_mul_Ico_of_neg -> Set.preimage_const_mul_Ico_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ico.{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)))))) a b)) (Set.Ioc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ico.{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)))))) a b)) (Set.Ioc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5508 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5510 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5508 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5510) c) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ico_of_neg Set.preimage_const_mul_Ico_of_negₓ'. -/
@@ -1360,7 +1360,7 @@ theorem preimage_const_mul_Ico_of_neg (a b : α) {c : α} (h : c < 0) :
 
 /- warning: set.preimage_const_mul_Icc_of_neg -> Set.preimage_const_mul_Icc_of_neg is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Icc.{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)))))) a b)) (Set.Icc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Icc.{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)))))) a b)) (Set.Icc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5574 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5576 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5574 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5576) c) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Icc_of_neg Set.preimage_const_mul_Icc_of_negₓ'. -/
@@ -1451,7 +1451,7 @@ theorem image_div_const_uIcc (a b c : α) : (fun x => x / a) '' [b, c] = [b / a,
 
 /- warning: set.image_mul_right_Icc' -> Set.image_mul_right_Icc' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Icc.{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)))))) a b)) (Set.Icc.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) b c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Icc.{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)))))) a b)) (Set.Icc.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) b c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) b c)))
 Case conversion may be inaccurate. Consider using '#align set.image_mul_right_Icc' Set.image_mul_right_Icc'ₓ'. -/
@@ -1462,7 +1462,7 @@ theorem image_mul_right_Icc' (a b : α) {c : α} (h : 0 < c) :
 
 /- warning: set.image_mul_right_Icc -> Set.image_mul_right_Icc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α} {b : α} {c : α}, (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))))))) a b) -> (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Icc.{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)))))) a b)) (Set.Icc.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) b c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α} {b : α} {c : α}, (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))))))) a b) -> (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Icc.{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)))))) a b)) (Set.Icc.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) b c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α} {b : α} {c : α}, (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)))))) a b) -> (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) b c)))
 Case conversion may be inaccurate. Consider using '#align set.image_mul_right_Icc Set.image_mul_right_Iccₓ'. -/
@@ -1477,7 +1477,7 @@ theorem image_mul_right_Icc {a b c : α} (hab : a ≤ b) (hc : 0 ≤ c) :
 
 /- warning: set.image_mul_left_Icc' -> Set.image_mul_left_Icc' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (b : α) (c : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a) (Set.Icc.{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)))))) b c)) (Set.Icc.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (b : α) (c : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a) (Set.Icc.{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)))))) b c)) (Set.Icc.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (b : α) (c : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6254 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6256 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6254 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6256) a) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) b c)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c)))
 Case conversion may be inaccurate. Consider using '#align set.image_mul_left_Icc' Set.image_mul_left_Icc'ₓ'. -/
@@ -1488,7 +1488,7 @@ theorem image_mul_left_Icc' {a : α} (h : 0 < a) (b c : α) :
 
 /- warning: set.image_mul_left_Icc -> Set.image_mul_left_Icc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α} {b : α} {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (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))))))) b c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a) (Set.Icc.{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)))))) b c)) (Set.Icc.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α} {b : α} {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (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))))))) b c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a) (Set.Icc.{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)))))) b c)) (Set.Icc.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α} {b : α} {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (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)))))) b c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6356 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6358 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6356 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6358) a) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) b c)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c)))
 Case conversion may be inaccurate. Consider using '#align set.image_mul_left_Icc Set.image_mul_left_Iccₓ'. -/
@@ -1499,7 +1499,7 @@ theorem image_mul_left_Icc {a b c : α} (ha : 0 ≤ a) (hbc : b ≤ c) :
 
 /- warning: set.image_mul_right_Ioo -> Set.image_mul_right_Ioo is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ioo.{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)))))) a b)) (Set.Ioo.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) b c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) x c) (Set.Ioo.{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)))))) a b)) (Set.Ioo.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) b c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (fun (x : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x c) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) b c)))
 Case conversion may be inaccurate. Consider using '#align set.image_mul_right_Ioo Set.image_mul_right_Iooₓ'. -/
@@ -1510,7 +1510,7 @@ theorem image_mul_right_Ioo (a b : α) {c : α} (h : 0 < c) :
 
 /- warning: set.image_mul_left_Ioo -> Set.image_mul_left_Ioo is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (b : α) (c : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a) (Set.Ioo.{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)))))) b c)) (Set.Ioo.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (b : α) (c : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a) (Set.Ioo.{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)))))) b c)) (Set.Ioo.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (b : α) (c : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6516 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6518 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6516 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6518) a) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) b c)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c)))
 Case conversion may be inaccurate. Consider using '#align set.image_mul_left_Ioo Set.image_mul_left_Iooₓ'. -/
@@ -1521,7 +1521,7 @@ theorem image_mul_left_Ioo {a : α} (h : 0 < a) (b c : α) :
 
 /- warning: set.inv_Ioo_0_left -> Set.inv_Ioo_0_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (Eq.{succ u1} (Set.{u1} α) (Inv.inv.{u1} (Set.{u1} α) (Set.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (Set.Ioo.{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)))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a)) (Set.Ioi.{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)))))) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) a)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (Eq.{succ u1} (Set.{u1} α) (Inv.inv.{u1} (Set.{u1} α) (Set.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (Set.Ioo.{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)))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a)) (Set.Ioi.{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)))))) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (Eq.{succ u1} (Set.{u1} α) (Inv.inv.{u1} (Set.{u1} α) (Set.inv.{u1} α (LinearOrderedField.toInv.{u1} α _inst_1)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (Inv.inv.{u1} α (LinearOrderedField.toInv.{u1} α _inst_1) a)))
 Case conversion may be inaccurate. Consider using '#align set.inv_Ioo_0_left Set.inv_Ioo_0_leftₓ'. -/
@@ -1537,7 +1537,7 @@ theorem inv_Ioo_0_left {a : α} (ha : 0 < a) : (Ioo 0 a)⁻¹ = Ioi a⁻¹ :=
 
 /- warning: set.inv_Ioi -> Set.inv_Ioi is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (Eq.{succ u1} (Set.{u1} α) (Inv.inv.{u1} (Set.{u1} α) (Set.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (Set.Ioi.{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)))))) a)) (Set.Ioo.{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)))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) a)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (Eq.{succ u1} (Set.{u1} α) (Inv.inv.{u1} (Set.{u1} α) (Set.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) (Set.Ioi.{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)))))) a)) (Set.Ioo.{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)))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))) a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (Eq.{succ u1} (Set.{u1} α) (Inv.inv.{u1} (Set.{u1} α) (Set.inv.{u1} α (LinearOrderedField.toInv.{u1} α _inst_1)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) (Inv.inv.{u1} α (LinearOrderedField.toInv.{u1} α _inst_1) a)))
 Case conversion may be inaccurate. Consider using '#align set.inv_Ioi Set.inv_Ioiₓ'. -/
@@ -1547,7 +1547,7 @@ theorem inv_Ioi {a : α} (ha : 0 < a) : (Ioi a)⁻¹ = Ioo 0 a⁻¹ := by
 
 /- warning: set.image_const_mul_Ioi_zero -> Set.image_const_mul_Ioi_zero is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} [_inst_2 : LinearOrderedField.{u1} k] {x : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_2))))))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_2))))))))))) x) -> (Eq.{succ u1} (Set.{u1} k) (Set.image.{u1, u1} k k (fun (y : k) => HMul.hMul.{u1, u1, u1} k k k (instHMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_2)))))) x y) (Set.Ioi.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_2)))))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_2))))))))))))) (Set.Ioi.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_2)))))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_2)))))))))))))
+  forall {k : Type.{u1}} [_inst_2 : LinearOrderedField.{u1} k] {x : k}, (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_2))))))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_2))))))))))) x) -> (Eq.{succ u1} (Set.{u1} k) (Set.image.{u1, u1} k k (fun (y : k) => HMul.hMul.{u1, u1, u1} k k k (instHMul.{u1} k (Distrib.toHasMul.{u1} k (Ring.toDistrib.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_2)))))) x y) (Set.Ioi.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_2)))))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_2))))))))))))) (Set.Ioi.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (StrictOrderedRing.toOrderedAddCommGroup.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_2)))))) (OfNat.ofNat.{u1} k 0 (OfNat.mk.{u1} k 0 (Zero.zero.{u1} k (MulZeroClass.toHasZero.{u1} k (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} k (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_2)))))))))))))
 but is expected to have type
   forall {k : Type.{u1}} [_inst_2 : LinearOrderedField.{u1} k] {x : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (StrictOrderedRing.toPartialOrder.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_2)))))) (OfNat.ofNat.{u1} k 0 (Zero.toOfNat0.{u1} k (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (LinearOrderedSemifield.toSemifield.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_2))))))) x) -> (Eq.{succ u1} (Set.{u1} k) (Set.image.{u1, u1} k k (fun (y : k) => HMul.hMul.{u1, u1, u1} k k k (instHMul.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_2))))))) x y) (Set.Ioi.{u1} k (PartialOrder.toPreorder.{u1} k (StrictOrderedRing.toPartialOrder.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_2))))) (OfNat.ofNat.{u1} k 0 (Zero.toOfNat0.{u1} k (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (LinearOrderedSemifield.toSemifield.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_2))))))))) (Set.Ioi.{u1} k (PartialOrder.toPreorder.{u1} k (StrictOrderedRing.toPartialOrder.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_2))))) (OfNat.ofNat.{u1} k 0 (Zero.toOfNat0.{u1} k (CommMonoidWithZero.toZero.{u1} k (CommGroupWithZero.toCommMonoidWithZero.{u1} k (Semifield.toCommGroupWithZero.{u1} k (LinearOrderedSemifield.toSemifield.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_2)))))))))
 Case conversion may be inaccurate. Consider using '#align set.image_const_mul_Ioi_zero Set.image_const_mul_Ioi_zeroₓ'. -/
@@ -1564,7 +1564,7 @@ theorem image_const_mul_Ioi_zero {k : Type _} [LinearOrderedField k] {x : k} (hx
 
 /- warning: set.image_affine_Icc' -> Set.image_affine_Icc' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (b : α) (c : α) (d : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (fun (x : α) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a x) b) (Set.Icc.{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)))))) c d)) (Set.Icc.{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)))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c) b) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a d) b)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (b : α) (c : α) (d : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (fun (x : α) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a x) b) (Set.Icc.{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)))))) c d)) (Set.Icc.{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)))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c) b) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a d) b)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (b : α) (c : α) (d : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (fun (x : α) => HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a x) b) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) c d)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c) b) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a d) b)))
 Case conversion may be inaccurate. Consider using '#align set.image_affine_Icc' Set.image_affine_Icc'ₓ'. -/

2196ab36

bump to nightly-2023-05-03-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

aa7b8e08

Diff

@@ -1190,7 +1190,7 @@ theorem preimage_mul_const_Icc_of_neg (a b : α) {c : α} (h : c < 0) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Iio.{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)))))) a)) (Set.Iio.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4697 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4699 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4697 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4699) c) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4695 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4697 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4695 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4697) c) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Iio Set.preimage_const_mul_Iioₓ'. -/
 @[simp]
 theorem preimage_const_mul_Iio (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹' Iio a = Iio (a / c) :=
@@ -1201,7 +1201,7 @@ theorem preimage_const_mul_Iio (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioi.{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)))))) a)) (Set.Ioi.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4752 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4754 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4752 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4754) c) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4750 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4752 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4750 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4752) c) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ioi Set.preimage_const_mul_Ioiₓ'. -/
 @[simp]
 theorem preimage_const_mul_Ioi (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹' Ioi a = Ioi (a / c) :=
@@ -1212,7 +1212,7 @@ theorem preimage_const_mul_Ioi (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Iic.{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)))))) a)) (Set.Iic.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4807 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4809 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4807 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4809) c) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4805 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4807 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4805 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4807) c) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Iic Set.preimage_const_mul_Iicₓ'. -/
 @[simp]
 theorem preimage_const_mul_Iic (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹' Iic a = Iic (a / c) :=
@@ -1223,7 +1223,7 @@ theorem preimage_const_mul_Iic (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ici.{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)))))) a)) (Set.Ici.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4862 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4864 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4862 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4864) c) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4860 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4862 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4860 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4862) c) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ici Set.preimage_const_mul_Iciₓ'. -/
 @[simp]
 theorem preimage_const_mul_Ici (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹' Ici a = Ici (a / c) :=
@@ -1234,7 +1234,7 @@ theorem preimage_const_mul_Ici (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioo.{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)))))) a b)) (Set.Ioo.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4918 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4920 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4918 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4920) c) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4916 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4918 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4916 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4918) c) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ioo Set.preimage_const_mul_Iooₓ'. -/
 @[simp]
 theorem preimage_const_mul_Ioo (a b : α) {c : α} (h : 0 < c) :
@@ -1245,7 +1245,7 @@ theorem preimage_const_mul_Ioo (a b : α) {c : α} (h : 0 < c) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioc.{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)))))) a b)) (Set.Ioc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4977 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4979 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4977 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4979) c) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4975 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4977 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4975 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.4977) c) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ioc Set.preimage_const_mul_Iocₓ'. -/
 @[simp]
 theorem preimage_const_mul_Ioc (a b : α) {c : α} (h : 0 < c) :
@@ -1256,7 +1256,7 @@ theorem preimage_const_mul_Ioc (a b : α) {c : α} (h : 0 < c) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ico.{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)))))) a b)) (Set.Ico.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5036 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5038 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5036 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5038) c) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5034 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5036 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5034 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5036) c) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ico Set.preimage_const_mul_Icoₓ'. -/
 @[simp]
 theorem preimage_const_mul_Ico (a b : α) {c : α} (h : 0 < c) :
@@ -1267,7 +1267,7 @@ theorem preimage_const_mul_Ico (a b : α) {c : α} (h : 0 < c) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Icc.{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)))))) a b)) (Set.Icc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5095 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5097 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5095 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5097) c) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) c) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5093 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5095 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5093 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5095) c) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Icc Set.preimage_const_mul_Iccₓ'. -/
 @[simp]
 theorem preimage_const_mul_Icc (a b : α) {c : α} (h : 0 < c) :
@@ -1278,7 +1278,7 @@ theorem preimage_const_mul_Icc (a b : α) {c : α} (h : 0 < c) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Iio.{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)))))) a)) (Set.Ioi.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5153 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5155 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5153 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5155) c) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5151 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5153 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5151 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5153) c) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Iio_of_neg Set.preimage_const_mul_Iio_of_negₓ'. -/
 @[simp]
 theorem preimage_const_mul_Iio_of_neg (a : α) {c : α} (h : c < 0) :
@@ -1290,7 +1290,7 @@ theorem preimage_const_mul_Iio_of_neg (a : α) {c : α} (h : c < 0) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioi.{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)))))) a)) (Set.Iio.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5209 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5211 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5209 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5211) c) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5207 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5209 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5207 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5209) c) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ioi_of_neg Set.preimage_const_mul_Ioi_of_negₓ'. -/
 @[simp]
 theorem preimage_const_mul_Ioi_of_neg (a : α) {c : α} (h : c < 0) :
@@ -1302,7 +1302,7 @@ theorem preimage_const_mul_Ioi_of_neg (a : α) {c : α} (h : c < 0) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Iic.{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)))))) a)) (Set.Ici.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5265 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5267 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5265 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5267) c) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5263 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5265 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5263 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5265) c) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Iic_of_neg Set.preimage_const_mul_Iic_of_negₓ'. -/
 @[simp]
 theorem preimage_const_mul_Iic_of_neg (a : α) {c : α} (h : c < 0) :
@@ -1314,7 +1314,7 @@ theorem preimage_const_mul_Iic_of_neg (a : α) {c : α} (h : c < 0) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ici.{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)))))) a)) (Set.Iic.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5321 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5323 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5321 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5323) c) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5319 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5321 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5319 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5321) c) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ici_of_neg Set.preimage_const_mul_Ici_of_negₓ'. -/
 @[simp]
 theorem preimage_const_mul_Ici_of_neg (a : α) {c : α} (h : c < 0) :
@@ -1326,7 +1326,7 @@ theorem preimage_const_mul_Ici_of_neg (a : α) {c : α} (h : c < 0) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioo.{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)))))) a b)) (Set.Ioo.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5378 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5380 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5378 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5380) c) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5376 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5378 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5376 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5378) c) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ioo_of_neg Set.preimage_const_mul_Ioo_of_negₓ'. -/
 @[simp]
 theorem preimage_const_mul_Ioo_of_neg (a b : α) {c : α} (h : c < 0) :
@@ -1338,7 +1338,7 @@ theorem preimage_const_mul_Ioo_of_neg (a b : α) {c : α} (h : c < 0) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ioc.{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)))))) a b)) (Set.Ico.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5444 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5446 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5444 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5446) c) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5442 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5444 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5442 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5444) c) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ioc_of_neg Set.preimage_const_mul_Ioc_of_negₓ'. -/
 @[simp]
 theorem preimage_const_mul_Ioc_of_neg (a b : α) {c : α} (h : c < 0) :
@@ -1350,7 +1350,7 @@ theorem preimage_const_mul_Ioc_of_neg (a b : α) {c : α} (h : c < 0) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Ico.{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)))))) a b)) (Set.Ioc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5510 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5512 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5510 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5512) c) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5508 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5510 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5508 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5510) c) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Ico_of_neg Set.preimage_const_mul_Ico_of_negₓ'. -/
 @[simp]
 theorem preimage_const_mul_Ico_of_neg (a b : α) {c : α} (h : c < 0) :
@@ -1362,7 +1362,7 @@ theorem preimage_const_mul_Ico_of_neg (a b : α) {c : α} (h : c < 0) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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))))))) c (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) c) (Set.Icc.{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)))))) a b)) (Set.Icc.{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)))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (DivInvMonoid.toHasDiv.{u1} α (DivisionRing.toDivInvMonoid.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5576 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5578 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5576 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5578) c) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] (a : α) (b : α) {c : α}, (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)))))) c (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1)))))))) -> (Eq.{succ u1} (Set.{u1} α) (Set.preimage.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5574 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5576 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5574 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.5576) c) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a b)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) b c) (HDiv.hDiv.{u1, u1, u1} α α α (instHDiv.{u1} α (LinearOrderedField.toDiv.{u1} α _inst_1)) a c)))
 Case conversion may be inaccurate. Consider using '#align set.preimage_const_mul_Icc_of_neg Set.preimage_const_mul_Icc_of_negₓ'. -/
 @[simp]
 theorem preimage_const_mul_Icc_of_neg (a b : α) {c : α} (h : c < 0) :
@@ -1479,7 +1479,7 @@ theorem image_mul_right_Icc {a b c : α} (hab : a ≤ b) (hc : 0 ≤ c) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (b : α) (c : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a) (Set.Icc.{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)))))) b c)) (Set.Icc.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (b : α) (c : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6256 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6258 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6256 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6258) a) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) b c)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (b : α) (c : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6254 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6256 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6254 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6256) a) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) b c)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c)))
 Case conversion may be inaccurate. Consider using '#align set.image_mul_left_Icc' Set.image_mul_left_Icc'ₓ'. -/
 theorem image_mul_left_Icc' {a : α} (h : 0 < a) (b c : α) :
     (· * ·) a '' Icc b c = Icc (a * b) (a * c) := by
@@ -1490,7 +1490,7 @@ theorem image_mul_left_Icc' {a : α} (h : 0 < a) (b c : α) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α} {b : α} {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (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))))))) b c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a) (Set.Icc.{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)))))) b c)) (Set.Icc.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α} {b : α} {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (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)))))) b c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6358 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6360 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6358 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6360) a) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) b c)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α} {b : α} {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (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)))))) b c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6356 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6358 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6356 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6358) a) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) b c)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c)))
 Case conversion may be inaccurate. Consider using '#align set.image_mul_left_Icc Set.image_mul_left_Iccₓ'. -/
 theorem image_mul_left_Icc {a b c : α} (ha : 0 ≤ a) (hbc : b ≤ c) :
     (· * ·) a '' Icc b c = Icc (a * b) (a * c) := by
@@ -1512,7 +1512,7 @@ theorem image_mul_right_Ioo (a b : α) {c : α} (h : 0 < c) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (b : α) (c : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a) (Set.Ioo.{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)))))) b c)) (Set.Ioo.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (b : α) (c : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6518 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6520 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6518 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6520) a) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) b c)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (b : α) (c : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6516 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6518 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6516 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6518) a) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) b c)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c)))
 Case conversion may be inaccurate. Consider using '#align set.image_mul_left_Ioo Set.image_mul_left_Iooₓ'. -/
 theorem image_mul_left_Ioo {a : α} (h : 0 < a) (b c : α) :
     (· * ·) a '' Ioo b c = Ioo (a * b) (a * c) := by

2196ab36

bump to nightly-2023-03-17-00

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

c85864d4

Diff

@@ -1490,7 +1490,7 @@ theorem image_mul_left_Icc' {a : α} (h : 0 < a) (b c : α) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α} {b : α} {c : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (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))))))) b c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a) (Set.Icc.{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)))))) b c)) (Set.Icc.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α} {b : α} {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (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)))))) b c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6344 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6346 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6344 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6346) a) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) b c)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α} {b : α} {c : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (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)))))) b c) -> (Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6358 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6360 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6358 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6360) a) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) b c)) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c)))
 Case conversion may be inaccurate. Consider using '#align set.image_mul_left_Icc Set.image_mul_left_Iccₓ'. -/
 theorem image_mul_left_Icc {a b c : α} (ha : 0 ≤ a) (hbc : b ≤ c) :
     (· * ·) a '' Icc b c = Icc (a * b) (a * c) := by
@@ -1512,7 +1512,7 @@ theorem image_mul_right_Ioo (a b : α) {c : α} (h : 0 < c) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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))))))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (MulZeroClass.toHasZero.{u1} α (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))))))) a) -> (forall (b : α) (c : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a) (Set.Ioo.{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)))))) b c)) (Set.Ioo.{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)))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (Distrib.toHasMul.{u1} α (Ring.toDistrib.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1)))))) a c)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (b : α) (c : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6490 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6492 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6490 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6492) a) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) b c)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (forall (b : α) (c : α), Eq.{succ u1} (Set.{u1} α) (Set.image.{u1, u1} α α ((fun (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6518 : α) (x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6520 : α) => HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6518 x._@.Mathlib.Data.Set.Pointwise.Interval._hyg.6520) a) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) b c)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a b) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (NonUnitalNonAssocRing.toMul.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (DivisionRing.toRing.{u1} α (Field.toDivisionRing.{u1} α (LinearOrderedField.toField.{u1} α _inst_1))))))) a c)))
 Case conversion may be inaccurate. Consider using '#align set.image_mul_left_Ioo Set.image_mul_left_Iooₓ'. -/
 theorem image_mul_left_Ioo {a : α} (h : 0 < a) (b c : α) :
     (· * ·) a '' Ioo b c = Ioo (a * b) (a * c) := by

2196ab36

bump to nightly-2023-03-14-02

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

d4b38a42

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
 
 ! This file was ported from Lean 3 source module data.set.pointwise.interval
-! leanprover-community/mathlib commit f16e7a22e11fc09c71f25446ac1db23a24e8a0bd
+! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1542,7 +1542,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} α] {a : α}, (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)))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) a) -> (Eq.{succ u1} (Set.{u1} α) (Inv.inv.{u1} (Set.{u1} α) (Set.inv.{u1} α (LinearOrderedField.toInv.{u1} α _inst_1)) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) a)) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (StrictOrderedRing.toPartialOrder.{u1} α (LinearOrderedRing.toStrictOrderedRing.{u1} α (LinearOrderedCommRing.toLinearOrderedRing.{u1} α (LinearOrderedField.toLinearOrderedCommRing.{u1} α _inst_1))))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (CommMonoidWithZero.toZero.{u1} α (CommGroupWithZero.toCommMonoidWithZero.{u1} α (Semifield.toCommGroupWithZero.{u1} α (LinearOrderedSemifield.toSemifield.{u1} α (LinearOrderedField.toLinearOrderedSemifield.{u1} α _inst_1))))))) (Inv.inv.{u1} α (LinearOrderedField.toInv.{u1} α _inst_1) a)))
 Case conversion may be inaccurate. Consider using '#align set.inv_Ioi Set.inv_Ioiₓ'. -/
 theorem inv_Ioi {a : α} (ha : 0 < a) : (Ioi a)⁻¹ = Ioo 0 a⁻¹ := by
-  rw [inv_eq_iff_inv_eq, inv_Ioo_0_left (inv_pos.2 ha), inv_inv]
+  rw [inv_eq_iff_eq_inv, inv_Ioo_0_left (inv_pos.2 ha), inv_inv]
 #align set.inv_Ioi Set.inv_Ioi
 
 /- warning: set.image_const_mul_Ioi_zero -> Set.image_const_mul_Ioi_zero is a dubious translation:

f16e7a22

bump to nightly-2023-02-28-04

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

2097f8af

Diff

@@ -954,7 +954,7 @@ variable {a b c d}
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Set.uIcc.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)) c d) (Set.uIcc.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) d c)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.uIcc.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))) c d) (Set.uIcc.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) d c)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Set.uIcc.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))) c d) (Set.uIcc.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) d c)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
 Case conversion may be inaccurate. Consider using '#align set.abs_sub_le_of_uIcc_subset_uIcc Set.abs_sub_le_of_uIcc_subset_uIccₓ'. -/
 /-- If `[c, d]` is a subinterval of `[a, b]`, then the distance between `c` and `d` is less than or
 equal to that of `a` and `b` -/
@@ -969,7 +969,7 @@ theorem abs_sub_le_of_uIcc_subset_uIcc (h : [c, d] ⊆ [a, b]) : |d - c| ≤ |b
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c (Set.uIcc.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) c a)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c (Set.uIcc.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) c a)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c (Set.uIcc.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) c a)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
 Case conversion may be inaccurate. Consider using '#align set.abs_sub_left_of_mem_uIcc Set.abs_sub_left_of_mem_uIccₓ'. -/
 /-- If `c ∈ [a, b]`, then the distance between `a` and `c` is less than or equal to
 that of `a` and `b`  -/
@@ -981,7 +981,7 @@ theorem abs_sub_left_of_mem_uIcc (h : c ∈ [a, b]) : |c - a| ≤ |b - a| :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c (Set.uIcc.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b c)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (SubNegMonoid.toHasNeg.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (LinearOrder.toLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c (Set.uIcc.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b c)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) c (Set.uIcc.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b c)) (Abs.abs.{u1} α (Neg.toHasAbs.{u1} α (NegZeroClass.toNeg.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))) (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α (LinearOrderedAddCommGroup.toLinearOrder.{u1} α _inst_1)))))) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))) b a)))
 Case conversion may be inaccurate. Consider using '#align set.abs_sub_right_of_mem_uIcc Set.abs_sub_right_of_mem_uIccₓ'. -/
 /-- If `x ∈ [a, b]`, then the distance between `c` and `b` is less than or equal to
 that of `a` and `b`  -/

f16e7a22

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

2196ab36

chore: Move intervals (#11765)

Move Set.Ixx, Finset.Ixx, Multiset.Ixx together under two different folders:

Order.Interval for their definition and basic properties
Algebra.Order.Interval for their algebraic properties

Move the definitions of Multiset.Ixx to what is now Order.Interval.Multiset. I believe we could just delete this file in a later PR as nothing uses it (and I already had doubts when defining Multiset.Ixx three years ago).

Move the algebraic results out of what is now Order.Interval.Finset.Basic to a new file Algebra.Order.Interval.Finset.Basic.

c7fa7063

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
 -/
-import Mathlib.Data.Set.Intervals.UnorderedInterval
-import Mathlib.Data.Set.Intervals.Monoid
+import Mathlib.Order.Interval.Set.UnorderedInterval
+import Mathlib.Algebra.Order.Interval.Set.Monoid
 import Mathlib.Data.Set.Pointwise.Basic
 import Mathlib.Algebra.Order.Field.Basic
 import Mathlib.Algebra.Order.Group.MinMax

2196ab36

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

@@ -346,11 +346,11 @@ theorem preimage_const_sub_Ioo : (fun x => a - x) ⁻¹' Ioo b c = Ioo (a - c) (
 -/
 
 
--- @[simp] -- Porting note: simp can prove this modulo `add_comm`
+-- @[simp] -- Porting note (#10618): simp can prove this modulo `add_comm`
 theorem image_const_add_Iic : (fun x => a + x) '' Iic b = Iic (a + b) := by simp [add_comm]
 #align set.image_const_add_Iic Set.image_const_add_Iic
 
--- @[simp] -- Porting note: simp can prove this modulo `add_comm`
+-- @[simp] -- Porting note (#10618): simp can prove this modulo `add_comm`
 theorem image_const_add_Iio : (fun x => a + x) '' Iio b = Iio (a + b) := by simp [add_comm]
 #align set.image_const_add_Iio Set.image_const_add_Iio
 
@@ -359,11 +359,11 @@ theorem image_const_add_Iio : (fun x => a + x) '' Iio b = Iio (a + b) := by simp
 -/
 
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem image_add_const_Iic : (fun x => x + a) '' Iic b = Iic (b + a) := by simp
 #align set.image_add_const_Iic Set.image_add_const_Iic
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem image_add_const_Iio : (fun x => x + a) '' Iio b = Iio (b + a) := by simp
 #align set.image_add_const_Iio Set.image_add_const_Iio
 
@@ -536,11 +536,11 @@ theorem preimage_const_sub_uIcc : (fun x => a - x) ⁻¹' [[b, c]] = [[a - b, a
   simp only [sub_eq_add_neg, min_add_add_left, max_add_add_left, min_neg_neg, max_neg_neg]
 #align set.preimage_const_sub_uIcc Set.preimage_const_sub_uIcc
 
--- @[simp] -- Porting note: simp can prove this module `add_comm`
+-- @[simp] -- Porting note (#10618): simp can prove this module `add_comm`
 theorem image_const_add_uIcc : (fun x => a + x) '' [[b, c]] = [[a + b, a + c]] := by simp [add_comm]
 #align set.image_const_add_uIcc Set.image_const_add_uIcc
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem image_add_const_uIcc : (fun x => x + a) '' [[b, c]] = [[b + a, c + a]] := by simp
 #align set.image_add_const_uIcc Set.image_add_const_uIcc

2196ab36

refactor(*): change definition of Set.image2 etc (#9275)

Redefine Set.image2 to use ∃ a ∈ s, ∃ b ∈ t, f a b = c instead of ∃ a b, a ∈ s ∧ b ∈ t ∧ f a b = c.
Redefine Set.seq as Set.image2. The new definition is equal to the old one but rw [Set.seq] gives a different result.
Redefine Filter.map₂ to use ∃ u ∈ f, ∃ v ∈ g, image2 m u v ⊆ s instead of ∃ u v, u ∈ f ∧ v ∈ g ∧ ...
Update lemmas like Set.mem_image2, Finset.mem_image₂, Set.mem_mul, Finset.mem_div etc

The two reasons to make the change are:

∃ a ∈ s, ∃ b ∈ t, _ is a simp-normal form, and
it looks a bit nicer.

8f17470f

Diff

@@ -44,17 +44,17 @@ variable [CovariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (Fun
 
 @[to_additive Icc_add_Icc_subset]
 theorem Icc_mul_Icc_subset' (a b c d : α) : Icc a b * Icc c d ⊆ Icc (a * c) (b * d) := by
-  rintro x ⟨y, z, ⟨hya, hyb⟩, ⟨hzc, hzd⟩, rfl⟩
+  rintro x ⟨y, ⟨hya, hyb⟩, z, ⟨hzc, hzd⟩, rfl⟩
   exact ⟨mul_le_mul' hya hzc, mul_le_mul' hyb hzd⟩
 
 @[to_additive Iic_add_Iic_subset]
 theorem Iic_mul_Iic_subset' (a b : α) : Iic a * Iic b ⊆ Iic (a * b) := by
-  rintro x ⟨y, z, hya, hzb, rfl⟩
+  rintro x ⟨y, hya, z, hzb, rfl⟩
   exact mul_le_mul' hya hzb
 
 @[to_additive Ici_add_Ici_subset]
 theorem Ici_mul_Ici_subset' (a b : α) : Ici a * Ici b ⊆ Ici (a * b) := by
-  rintro x ⟨y, z, hya, hzb, rfl⟩
+  rintro x ⟨y, hya, z, hzb, rfl⟩
   exact mul_le_mul' hya hzb
 
 end ContravariantLE
@@ -67,49 +67,49 @@ variable [CovariantClass α α (· * ·) (· < ·)] [CovariantClass α α (Funct
 @[to_additive Icc_add_Ico_subset]
 theorem Icc_mul_Ico_subset' (a b c d : α) : Icc a b * Ico c d ⊆ Ico (a * c) (b * d) := by
   haveI := covariantClass_le_of_lt
-  rintro x ⟨y, z, ⟨hya, hyb⟩, ⟨hzc, hzd⟩, rfl⟩
+  rintro x ⟨y, ⟨hya, hyb⟩, z, ⟨hzc, hzd⟩, rfl⟩
   exact ⟨mul_le_mul' hya hzc, mul_lt_mul_of_le_of_lt hyb hzd⟩
 
 @[to_additive Ico_add_Icc_subset]
 theorem Ico_mul_Icc_subset' (a b c d : α) : Ico a b * Icc c d ⊆ Ico (a * c) (b * d) := by
   haveI := covariantClass_le_of_lt
-  rintro x ⟨y, z, ⟨hya, hyb⟩, ⟨hzc, hzd⟩, rfl⟩
+  rintro x ⟨y, ⟨hya, hyb⟩, z, ⟨hzc, hzd⟩, rfl⟩
   exact ⟨mul_le_mul' hya hzc, mul_lt_mul_of_lt_of_le hyb hzd⟩
 
 @[to_additive Ioc_add_Ico_subset]
 theorem Ioc_mul_Ico_subset' (a b c d : α) : Ioc a b * Ico c d ⊆ Ioo (a * c) (b * d) := by
   haveI := covariantClass_le_of_lt
-  rintro x ⟨y, z, ⟨hya, hyb⟩, ⟨hzc, hzd⟩, rfl⟩
+  rintro x ⟨y, ⟨hya, hyb⟩, z, ⟨hzc, hzd⟩, rfl⟩
   exact ⟨mul_lt_mul_of_lt_of_le hya hzc, mul_lt_mul_of_le_of_lt hyb hzd⟩
 
 @[to_additive Ico_add_Ioc_subset]
 theorem Ico_mul_Ioc_subset' (a b c d : α) : Ico a b * Ioc c d ⊆ Ioo (a * c) (b * d) := by
   haveI := covariantClass_le_of_lt
-  rintro x ⟨y, z, ⟨hya, hyb⟩, ⟨hzc, hzd⟩, rfl⟩
+  rintro x ⟨y, ⟨hya, hyb⟩, z, ⟨hzc, hzd⟩, rfl⟩
   exact ⟨mul_lt_mul_of_le_of_lt hya hzc, mul_lt_mul_of_lt_of_le hyb hzd⟩
 
 @[to_additive Iic_add_Iio_subset]
 theorem Iic_mul_Iio_subset' (a b : α) : Iic a * Iio b ⊆ Iio (a * b) := by
   haveI := covariantClass_le_of_lt
-  rintro x ⟨y, z, hya, hzb, rfl⟩
+  rintro x ⟨y, hya, z, hzb, rfl⟩
   exact mul_lt_mul_of_le_of_lt hya hzb
 
 @[to_additive Iio_add_Iic_subset]
 theorem Iio_mul_Iic_subset' (a b : α) : Iio a * Iic b ⊆ Iio (a * b) := by
   haveI := covariantClass_le_of_lt
-  rintro x ⟨y, z, hya, hzb, rfl⟩
+  rintro x ⟨y, hya, z, hzb, rfl⟩
   exact mul_lt_mul_of_lt_of_le hya hzb
 
 @[to_additive Ioi_add_Ici_subset]
 theorem Ioi_mul_Ici_subset' (a b : α) : Ioi a * Ici b ⊆ Ioi (a * b) := by
   haveI := covariantClass_le_of_lt
-  rintro x ⟨y, z, hya, hzb, rfl⟩
+  rintro x ⟨y, hya, z, hzb, rfl⟩
   exact mul_lt_mul_of_lt_of_le hya hzb
 
 @[to_additive Ici_add_Ioi_subset]
 theorem Ici_mul_Ioi_subset' (a b : α) : Ici a * Ioi b ⊆ Ioi (a * b) := by
   haveI := covariantClass_le_of_lt
-  rintro x ⟨y, z, hya, hzb, rfl⟩
+  rintro x ⟨y, hya, z, hzb, rfl⟩
   exact mul_lt_mul_of_le_of_lt hya hzb
 
 end ContravariantLT

2196ab36

feat(Data/Set/Pointwise/Interval): inclusions of pointwise +/* (#8368)

As remarked in the docstring, to avoid an explosion of lemmas, the subset operations only cover the cases with the largest possible intervals on the LHS: to conclude that Ioo a b * Ioo c d ⊆ Ioo (a * c) (c * d), you can use monotonicity of * and Finset.Ico_mul_Ioc_subset.

3a722fda

Diff

@@ -27,6 +27,93 @@ variable {α : Type*}
 
 namespace Set
 
+/-! ### Binary pointwise operations
+
+Note that the subset operations below only cover the cases with the largest possible intervals on
+the LHS: to conclude that `Ioo a b * Ioo c d ⊆ Ioo (a * c) (c * d)`, you can use monotonicity of `*`
+and `Set.Ico_mul_Ioc_subset`.
+
+TODO: repeat these lemmas for the generality of `mul_le_mul` (which assumes nonnegativity), which
+the unprimed names have been reserved for
+-/
+
+section ContravariantLE
+
+variable [Mul α] [Preorder α]
+variable [CovariantClass α α (· * ·) (· ≤ ·)] [CovariantClass α α (Function.swap HMul.hMul) LE.le]
+
+@[to_additive Icc_add_Icc_subset]
+theorem Icc_mul_Icc_subset' (a b c d : α) : Icc a b * Icc c d ⊆ Icc (a * c) (b * d) := by
+  rintro x ⟨y, z, ⟨hya, hyb⟩, ⟨hzc, hzd⟩, rfl⟩
+  exact ⟨mul_le_mul' hya hzc, mul_le_mul' hyb hzd⟩
+
+@[to_additive Iic_add_Iic_subset]
+theorem Iic_mul_Iic_subset' (a b : α) : Iic a * Iic b ⊆ Iic (a * b) := by
+  rintro x ⟨y, z, hya, hzb, rfl⟩
+  exact mul_le_mul' hya hzb
+
+@[to_additive Ici_add_Ici_subset]
+theorem Ici_mul_Ici_subset' (a b : α) : Ici a * Ici b ⊆ Ici (a * b) := by
+  rintro x ⟨y, z, hya, hzb, rfl⟩
+  exact mul_le_mul' hya hzb
+
+end ContravariantLE
+
+section ContravariantLT
+
+variable [Mul α] [PartialOrder α]
+variable [CovariantClass α α (· * ·) (· < ·)] [CovariantClass α α (Function.swap HMul.hMul) LT.lt]
+
+@[to_additive Icc_add_Ico_subset]
+theorem Icc_mul_Ico_subset' (a b c d : α) : Icc a b * Ico c d ⊆ Ico (a * c) (b * d) := by
+  haveI := covariantClass_le_of_lt
+  rintro x ⟨y, z, ⟨hya, hyb⟩, ⟨hzc, hzd⟩, rfl⟩
+  exact ⟨mul_le_mul' hya hzc, mul_lt_mul_of_le_of_lt hyb hzd⟩
+
+@[to_additive Ico_add_Icc_subset]
+theorem Ico_mul_Icc_subset' (a b c d : α) : Ico a b * Icc c d ⊆ Ico (a * c) (b * d) := by
+  haveI := covariantClass_le_of_lt
+  rintro x ⟨y, z, ⟨hya, hyb⟩, ⟨hzc, hzd⟩, rfl⟩
+  exact ⟨mul_le_mul' hya hzc, mul_lt_mul_of_lt_of_le hyb hzd⟩
+
+@[to_additive Ioc_add_Ico_subset]
+theorem Ioc_mul_Ico_subset' (a b c d : α) : Ioc a b * Ico c d ⊆ Ioo (a * c) (b * d) := by
+  haveI := covariantClass_le_of_lt
+  rintro x ⟨y, z, ⟨hya, hyb⟩, ⟨hzc, hzd⟩, rfl⟩
+  exact ⟨mul_lt_mul_of_lt_of_le hya hzc, mul_lt_mul_of_le_of_lt hyb hzd⟩
+
+@[to_additive Ico_add_Ioc_subset]
+theorem Ico_mul_Ioc_subset' (a b c d : α) : Ico a b * Ioc c d ⊆ Ioo (a * c) (b * d) := by
+  haveI := covariantClass_le_of_lt
+  rintro x ⟨y, z, ⟨hya, hyb⟩, ⟨hzc, hzd⟩, rfl⟩
+  exact ⟨mul_lt_mul_of_le_of_lt hya hzc, mul_lt_mul_of_lt_of_le hyb hzd⟩
+
+@[to_additive Iic_add_Iio_subset]
+theorem Iic_mul_Iio_subset' (a b : α) : Iic a * Iio b ⊆ Iio (a * b) := by
+  haveI := covariantClass_le_of_lt
+  rintro x ⟨y, z, hya, hzb, rfl⟩
+  exact mul_lt_mul_of_le_of_lt hya hzb
+
+@[to_additive Iio_add_Iic_subset]
+theorem Iio_mul_Iic_subset' (a b : α) : Iio a * Iic b ⊆ Iio (a * b) := by
+  haveI := covariantClass_le_of_lt
+  rintro x ⟨y, z, hya, hzb, rfl⟩
+  exact mul_lt_mul_of_lt_of_le hya hzb
+
+@[to_additive Ioi_add_Ici_subset]
+theorem Ioi_mul_Ici_subset' (a b : α) : Ioi a * Ici b ⊆ Ioi (a * b) := by
+  haveI := covariantClass_le_of_lt
+  rintro x ⟨y, z, hya, hzb, rfl⟩
+  exact mul_lt_mul_of_lt_of_le hya hzb
+
+@[to_additive Ici_add_Ioi_subset]
+theorem Ici_mul_Ioi_subset' (a b : α) : Ici a * Ioi b ⊆ Ioi (a * b) := by
+  haveI := covariantClass_le_of_lt
+  rintro x ⟨y, z, hya, hzb, rfl⟩
+  exact mul_lt_mul_of_le_of_lt hya hzb
+
+end ContravariantLT
+
 section OrderedAddCommGroup
 
 variable [OrderedAddCommGroup α] (a b c : α)

2196ab36

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

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

d14658b4

Diff

@@ -595,96 +595,96 @@ theorem preimage_mul_const_Icc_of_neg (a b : α) {c : α} (h : c < 0) :
 #align set.preimage_mul_const_Icc_of_neg Set.preimage_mul_const_Icc_of_neg
 
 @[simp]
-theorem preimage_const_mul_Iio (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹' Iio a = Iio (a / c) :=
+theorem preimage_const_mul_Iio (a : α) {c : α} (h : 0 < c) : (c * ·) ⁻¹' Iio a = Iio (a / c) :=
   ext fun _x => (lt_div_iff' h).symm
 #align set.preimage_const_mul_Iio Set.preimage_const_mul_Iio
 
 @[simp]
-theorem preimage_const_mul_Ioi (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹' Ioi a = Ioi (a / c) :=
+theorem preimage_const_mul_Ioi (a : α) {c : α} (h : 0 < c) : (c * ·) ⁻¹' Ioi a = Ioi (a / c) :=
   ext fun _x => (div_lt_iff' h).symm
 #align set.preimage_const_mul_Ioi Set.preimage_const_mul_Ioi
 
 @[simp]
-theorem preimage_const_mul_Iic (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹' Iic a = Iic (a / c) :=
+theorem preimage_const_mul_Iic (a : α) {c : α} (h : 0 < c) : (c * ·) ⁻¹' Iic a = Iic (a / c) :=
   ext fun _x => (le_div_iff' h).symm
 #align set.preimage_const_mul_Iic Set.preimage_const_mul_Iic
 
 @[simp]
-theorem preimage_const_mul_Ici (a : α) {c : α} (h : 0 < c) : (· * ·) c ⁻¹' Ici a = Ici (a / c) :=
+theorem preimage_const_mul_Ici (a : α) {c : α} (h : 0 < c) : (c * ·) ⁻¹' Ici a = Ici (a / c) :=
   ext fun _x => (div_le_iff' h).symm
 #align set.preimage_const_mul_Ici Set.preimage_const_mul_Ici
 
 @[simp]
 theorem preimage_const_mul_Ioo (a b : α) {c : α} (h : 0 < c) :
-    (· * ·) c ⁻¹' Ioo a b = Ioo (a / c) (b / c) := by simp [← Ioi_inter_Iio, h]
+    (c * ·) ⁻¹' Ioo a b = Ioo (a / c) (b / c) := by simp [← Ioi_inter_Iio, h]
 #align set.preimage_const_mul_Ioo Set.preimage_const_mul_Ioo
 
 @[simp]
 theorem preimage_const_mul_Ioc (a b : α) {c : α} (h : 0 < c) :
-    (· * ·) c ⁻¹' Ioc a b = Ioc (a / c) (b / c) := by simp [← Ioi_inter_Iic, h]
+    (c * ·) ⁻¹' Ioc a b = Ioc (a / c) (b / c) := by simp [← Ioi_inter_Iic, h]
 #align set.preimage_const_mul_Ioc Set.preimage_const_mul_Ioc
 
 @[simp]
 theorem preimage_const_mul_Ico (a b : α) {c : α} (h : 0 < c) :
-    (· * ·) c ⁻¹' Ico a b = Ico (a / c) (b / c) := by simp [← Ici_inter_Iio, h]
+    (c * ·) ⁻¹' Ico a b = Ico (a / c) (b / c) := by simp [← Ici_inter_Iio, h]
 #align set.preimage_const_mul_Ico Set.preimage_const_mul_Ico
 
 @[simp]
 theorem preimage_const_mul_Icc (a b : α) {c : α} (h : 0 < c) :
-    (· * ·) c ⁻¹' Icc a b = Icc (a / c) (b / c) := by simp [← Ici_inter_Iic, h]
+    (c * ·) ⁻¹' Icc a b = Icc (a / c) (b / c) := by simp [← Ici_inter_Iic, h]
 #align set.preimage_const_mul_Icc Set.preimage_const_mul_Icc
 
 @[simp]
 theorem preimage_const_mul_Iio_of_neg (a : α) {c : α} (h : c < 0) :
-    (· * ·) c ⁻¹' Iio a = Ioi (a / c) := by
+    (c * ·) ⁻¹' Iio a = Ioi (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Iio_of_neg a h
 #align set.preimage_const_mul_Iio_of_neg Set.preimage_const_mul_Iio_of_neg
 
 @[simp]
 theorem preimage_const_mul_Ioi_of_neg (a : α) {c : α} (h : c < 0) :
-    (· * ·) c ⁻¹' Ioi a = Iio (a / c) := by
+    (c * ·) ⁻¹' Ioi a = Iio (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Ioi_of_neg a h
 #align set.preimage_const_mul_Ioi_of_neg Set.preimage_const_mul_Ioi_of_neg
 
 @[simp]
 theorem preimage_const_mul_Iic_of_neg (a : α) {c : α} (h : c < 0) :
-    (· * ·) c ⁻¹' Iic a = Ici (a / c) := by
+    (c * ·) ⁻¹' Iic a = Ici (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Iic_of_neg a h
 #align set.preimage_const_mul_Iic_of_neg Set.preimage_const_mul_Iic_of_neg
 
 @[simp]
 theorem preimage_const_mul_Ici_of_neg (a : α) {c : α} (h : c < 0) :
-    (· * ·) c ⁻¹' Ici a = Iic (a / c) := by
+    (c * ·) ⁻¹' Ici a = Iic (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Ici_of_neg a h
 #align set.preimage_const_mul_Ici_of_neg Set.preimage_const_mul_Ici_of_neg
 
 @[simp]
 theorem preimage_const_mul_Ioo_of_neg (a b : α) {c : α} (h : c < 0) :
-    (· * ·) c ⁻¹' Ioo a b = Ioo (b / c) (a / c) := by
+    (c * ·) ⁻¹' Ioo a b = Ioo (b / c) (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Ioo_of_neg a b h
 #align set.preimage_const_mul_Ioo_of_neg Set.preimage_const_mul_Ioo_of_neg
 
 @[simp]
 theorem preimage_const_mul_Ioc_of_neg (a b : α) {c : α} (h : c < 0) :
-    (· * ·) c ⁻¹' Ioc a b = Ico (b / c) (a / c) := by
+    (c * ·) ⁻¹' Ioc a b = Ico (b / c) (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Ioc_of_neg a b h
 #align set.preimage_const_mul_Ioc_of_neg Set.preimage_const_mul_Ioc_of_neg
 
 @[simp]
 theorem preimage_const_mul_Ico_of_neg (a b : α) {c : α} (h : c < 0) :
-    (· * ·) c ⁻¹' Ico a b = Ioc (b / c) (a / c) := by
+    (c * ·) ⁻¹' Ico a b = Ioc (b / c) (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Ico_of_neg a b h
 #align set.preimage_const_mul_Ico_of_neg Set.preimage_const_mul_Ico_of_neg
 
 @[simp]
 theorem preimage_const_mul_Icc_of_neg (a b : α) {c : α} (h : c < 0) :
-    (· * ·) c ⁻¹' Icc a b = Icc (b / c) (a / c) := by
+    (c * ·) ⁻¹' Icc a b = Icc (b / c) (a / c) := by
   simpa only [mul_comm] using preimage_mul_const_Icc_of_neg a b h
 #align set.preimage_const_mul_Icc_of_neg Set.preimage_const_mul_Icc_of_neg
 
 @[simp]
 theorem preimage_mul_const_uIcc (ha : a ≠ 0) (b c : α) :
-    (fun x => x * a) ⁻¹' [[b, c]] = [[b / a, c / a]] :=
+    (· * a) ⁻¹' [[b, c]] = [[b / a, c / a]] :=
   (lt_or_gt_of_ne ha).elim
     (fun h => by
       simp [← Icc_min_max, h, h.le, min_div_div_right_of_nonpos, max_div_div_right_of_nonpos])
@@ -693,7 +693,7 @@ theorem preimage_mul_const_uIcc (ha : a ≠ 0) (b c : α) :
 
 @[simp]
 theorem preimage_const_mul_uIcc (ha : a ≠ 0) (b c : α) :
-    (fun x => a * x) ⁻¹' [[b, c]] = [[b / a, c / a]] := by
+    (a * ·) ⁻¹' [[b, c]] = [[b / a, c / a]] := by
   simp only [← preimage_mul_const_uIcc ha, mul_comm]
 #align set.preimage_const_mul_uIcc Set.preimage_const_mul_uIcc
 
@@ -704,17 +704,17 @@ theorem preimage_div_const_uIcc (ha : a ≠ 0) (b c : α) :
 #align set.preimage_div_const_uIcc Set.preimage_div_const_uIcc
 
 @[simp]
-theorem image_mul_const_uIcc (a b c : α) : (fun x => x * a) '' [[b, c]] = [[b * a, c * a]] :=
+theorem image_mul_const_uIcc (a b c : α) : (· * a) '' [[b, c]] = [[b * a, c * a]] :=
   if ha : a = 0 then by simp [ha]
   else calc
-    (fun x => x * a) '' [[b, c]] = (fun x => x * a⁻¹) ⁻¹' [[b, c]] :=
+    (fun x => x * a) '' [[b, c]] = (· * a⁻¹) ⁻¹' [[b, c]] :=
       (Units.mk0 a ha).mulRight.image_eq_preimage _
     _ = (fun x => x / a) ⁻¹' [[b, c]] := by simp only [div_eq_mul_inv]
     _ = [[b * a, c * a]] := preimage_div_const_uIcc ha _ _
 #align set.image_mul_const_uIcc Set.image_mul_const_uIcc
 
 @[simp]
-theorem image_const_mul_uIcc (a b c : α) : (fun x => a * x) '' [[b, c]] = [[a * b, a * c]] := by
+theorem image_const_mul_uIcc (a b c : α) : (a * ·) '' [[b, c]] = [[a * b, a * c]] := by
   simpa only [mul_comm] using image_mul_const_uIcc a b c
 #align set.image_const_mul_uIcc Set.image_const_mul_uIcc
 
@@ -737,12 +737,12 @@ theorem image_mul_right_Icc {a b c : α} (hab : a ≤ b) (hc : 0 ≤ c) :
 #align set.image_mul_right_Icc Set.image_mul_right_Icc
 
 theorem image_mul_left_Icc' {a : α} (h : 0 < a) (b c : α) :
-    (· * ·) a '' Icc b c = Icc (a * b) (a * c) := by
+    (a * ·) '' Icc b c = Icc (a * b) (a * c) := by
   convert image_mul_right_Icc' b c h using 1 <;> simp only [mul_comm _ a]
 #align set.image_mul_left_Icc' Set.image_mul_left_Icc'
 
 theorem image_mul_left_Icc {a b c : α} (ha : 0 ≤ a) (hbc : b ≤ c) :
-    (· * ·) a '' Icc b c = Icc (a * b) (a * c) := by
+    (a * ·) '' Icc b c = Icc (a * b) (a * c) := by
   convert image_mul_right_Icc hbc ha using 1 <;> simp only [mul_comm _ a]
 #align set.image_mul_left_Icc Set.image_mul_left_Icc
 
@@ -752,7 +752,7 @@ theorem image_mul_right_Ioo (a b : α) {c : α} (h : 0 < c) :
 #align set.image_mul_right_Ioo Set.image_mul_right_Ioo
 
 theorem image_mul_left_Ioo {a : α} (h : 0 < a) (b c : α) :
-    (· * ·) a '' Ioo b c = Ioo (a * b) (a * c) := by
+    (a * ·) '' Ioo b c = Ioo (a * b) (a * c) := by
   convert image_mul_right_Ioo b c h using 1 <;> simp only [mul_comm _ a]
 #align set.image_mul_left_Ioo Set.image_mul_left_Ioo
 
@@ -782,8 +782,8 @@ theorem image_const_mul_Ioi_zero {k : Type*} [LinearOrderedField k] {x : k} (hx
 
 @[simp]
 theorem image_affine_Icc' {a : α} (h : 0 < a) (b c d : α) :
-    (fun x => a * x + b) '' Icc c d = Icc (a * c + b) (a * d + b) := by
-  suffices (fun x => x + b) '' ((fun x => a * x) '' Icc c d) = Icc (a * c + b) (a * d + b) by
+    (a * · + b) '' Icc c d = Icc (a * c + b) (a * d + b) := by
+  suffices (· + b) '' ((a * ·) '' Icc c d) = Icc (a * c + b) (a * d + b) by
     rwa [Set.image_image] at this
   rw [image_mul_left_Icc' h, image_add_const_Icc]
 #align set.image_affine_Icc' Set.image_affine_Icc'

2196ab36

chore: bump to v4.3.0-rc2 (#8366)

PR contents

This is the supremum of

#8284
#8056
#8023
#8332
#8226 (already approved)
#7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

switching to using explicit lemmas that have the intended level of application
(config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

40b64f79

Diff

@@ -316,49 +316,49 @@ theorem image_neg_Ioo : Neg.neg '' Ioo a b = Ioo (-b) (-a) := by simp
 
 @[simp]
 theorem image_const_sub_Ici : (fun x => a - x) '' Ici b = Iic (a - b) := by
-  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp] at this
+  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp_def] at this
   simp [sub_eq_add_neg, this, add_comm]
 #align set.image_const_sub_Ici Set.image_const_sub_Ici
 
 @[simp]
 theorem image_const_sub_Iic : (fun x => a - x) '' Iic b = Ici (a - b) := by
-  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp] at this
+  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp_def] at this
   simp [sub_eq_add_neg, this, add_comm]
 #align set.image_const_sub_Iic Set.image_const_sub_Iic
 
 @[simp]
 theorem image_const_sub_Ioi : (fun x => a - x) '' Ioi b = Iio (a - b) := by
-  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp] at this
+  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp_def] at this
   simp [sub_eq_add_neg, this, add_comm]
 #align set.image_const_sub_Ioi Set.image_const_sub_Ioi
 
 @[simp]
 theorem image_const_sub_Iio : (fun x => a - x) '' Iio b = Ioi (a - b) := by
-  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp] at this
+  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp_def] at this
   simp [sub_eq_add_neg, this, add_comm]
 #align set.image_const_sub_Iio Set.image_const_sub_Iio
 
 @[simp]
 theorem image_const_sub_Icc : (fun x => a - x) '' Icc b c = Icc (a - c) (a - b) := by
-  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp] at this
+  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp_def] at this
   simp [sub_eq_add_neg, this, add_comm]
 #align set.image_const_sub_Icc Set.image_const_sub_Icc
 
 @[simp]
 theorem image_const_sub_Ico : (fun x => a - x) '' Ico b c = Ioc (a - c) (a - b) := by
-  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp] at this
+  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp_def] at this
   simp [sub_eq_add_neg, this, add_comm]
 #align set.image_const_sub_Ico Set.image_const_sub_Ico
 
 @[simp]
 theorem image_const_sub_Ioc : (fun x => a - x) '' Ioc b c = Ico (a - c) (a - b) := by
-  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp] at this
+  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp_def] at this
   simp [sub_eq_add_neg, this, add_comm]
 #align set.image_const_sub_Ioc Set.image_const_sub_Ioc
 
 @[simp]
 theorem image_const_sub_Ioo : (fun x => a - x) '' Ioo b c = Ioo (a - c) (a - b) := by
-  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp] at this
+  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp_def] at this
   simp [sub_eq_add_neg, this, add_comm]
 #align set.image_const_sub_Ioo Set.image_const_sub_Ioo
 
@@ -459,7 +459,7 @@ theorem image_add_const_uIcc : (fun x => x + a) '' [[b, c]] = [[b + a, c + a]] :
 
 @[simp]
 theorem image_const_sub_uIcc : (fun x => a - x) '' [[b, c]] = [[a - b, a - c]] := by
-  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp] at this
+  have := image_comp (fun x => a + x) fun x => -x; dsimp [Function.comp_def] at this
   simp [sub_eq_add_neg, this, add_comm]
 #align set.image_const_sub_uIcc Set.image_const_sub_uIcc

2196ab36

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

@@ -23,7 +23,7 @@ lemmas about preimages and images of all intervals. We also prove a few lemmas a
 
 open Interval Pointwise
 
-variable {α : Type _}
+variable {α : Type*}
 
 namespace Set
 
@@ -769,7 +769,7 @@ theorem inv_Ioi {a : α} (ha : 0 < a) : (Ioi a)⁻¹ = Ioo 0 a⁻¹ := by
   rw [inv_eq_iff_eq_inv, inv_Ioo_0_left (inv_pos.2 ha), inv_inv]
 #align set.inv_Ioi Set.inv_Ioi
 
-theorem image_const_mul_Ioi_zero {k : Type _} [LinearOrderedField k] {x : k} (hx : 0 < x) :
+theorem image_const_mul_Ioi_zero {k : Type*} [LinearOrderedField k] {x : k} (hx : 0 < x) :
     (fun y => x * y) '' Ioi (0 : k) = Ioi 0 := by
   erw [(Units.mk0 x hx.ne').mulLeft.image_eq_preimage, preimage_const_mul_Ioi 0 (inv_pos.mpr hx),
     zero_div]

2196ab36

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
-
-! This file was ported from Lean 3 source module data.set.pointwise.interval
-! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Set.Intervals.UnorderedInterval
 import Mathlib.Data.Set.Intervals.Monoid
@@ -14,6 +9,8 @@ import Mathlib.Data.Set.Pointwise.Basic
 import Mathlib.Algebra.Order.Field.Basic
 import Mathlib.Algebra.Order.Group.MinMax
 
+#align_import data.set.pointwise.interval from "leanprover-community/mathlib"@"2196ab363eb097c008d4497125e0dde23fb36db2"
+
 /-!
 # (Pre)images of intervals

2196ab36

chore: fix #align lines (#3640)

This PR fixes two things:

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

2b42dc7c

Diff

@@ -714,7 +714,6 @@ theorem image_mul_const_uIcc (a b c : α) : (fun x => x * a) '' [[b, c]] = [[b *
       (Units.mk0 a ha).mulRight.image_eq_preimage _
     _ = (fun x => x / a) ⁻¹' [[b, c]] := by simp only [div_eq_mul_inv]
     _ = [[b * a, c * a]] := preimage_div_const_uIcc ha _ _
-
 #align set.image_mul_const_uIcc Set.image_mul_const_uIcc
 
 @[simp]

2196ab36

chore: forward-port leanprover-community/mathlib#17483 (#2884)

This forward ports the changes introduced by leanprover-community/mathlib#17483

No change is needed to Mathlib.Data.EReal as the proofs have been golfed in a different way.

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

42673620

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot
 
 ! This file was ported from Lean 3 source module data.set.pointwise.interval
-! leanprover-community/mathlib commit 59694bd07f0a39c5beccba34bd9f413a160782bf
+! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -770,7 +770,7 @@ theorem inv_Ioo_0_left {a : α} (ha : 0 < a) : (Ioo 0 a)⁻¹ = Ioi a⁻¹ := by
 #align set.inv_Ioo_0_left Set.inv_Ioo_0_left
 
 theorem inv_Ioi {a : α} (ha : 0 < a) : (Ioi a)⁻¹ = Ioo 0 a⁻¹ := by
-  rw [inv_eq_iff_inv_eq, inv_Ioo_0_left (inv_pos.2 ha), inv_inv]
+  rw [inv_eq_iff_eq_inv, inv_Ioo_0_left (inv_pos.2 ha), inv_inv]
 #align set.inv_Ioi Set.inv_Ioi
 
 theorem image_const_mul_Ioi_zero {k : Type _} [LinearOrderedField k] {x : k} (hx : 0 < x) :

59694bd0

feat: port Data.Set.Pointwise.Interval (#1481)

feat: port Mathlib.Data.Set.Pointwise.Interval
Initial file copy from mathport
Mathbin -> Mathlib; add import to Mathlib.lean

7a4790bb

`data.set.pointwise.interval` ⟷ `Mathlib.Data.Set.Pointwise.Interval`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 2 + 139

data.set.pointwise.interval ⟷ Mathlib.Data.Set.Pointwise.Interval

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 2 + 139

`data.set.pointwise.interval` ⟷ `Mathlib.Data.Set.Pointwise.Interval`